Proceedings of FEL 2006, BESSY, Berlin, Germany

MOAAU01

COHERENCE OF E-BEAM RADIATION SOURCES AND FELS –A THEORETICAL OVERVIEWAvi Gover, Egor Dyunin, Tel-Aviv University, Ramat Aviv, Israel.

GENERAL FORMULATION FORRADIATION EMISSION FROMMICROSCOPIC CHARGES~
E(r, ω ) =(3)qThis publication is mostly tutorial. It presents a generaltime-frequency modal-expansion linear formulation forradiation excitation from charges. This, however, can be
employed to analyze front-line FEL research problems.
Starting from description of synchrotron undulator
radiation, the model is extended to describe the coherence
characteristics of stimulated emission devices (FEL
amplifiers and oscillators), and then further extended to
the SASE regime. It is then employed to point out
directions for development of coherent X-UV FEL
sources.
The starting point of our formulation is the general
Maxwell Equations driven by particulate point chargesources (the source dimension is smaller than theemission wavelength):

∂H
∂M
− μ0
∂t
∂t
∂E
∂P
∇×H = ε+J+∂t∂t

∑ Cq (z, ω )E~ q (r )This certainly can be done in a waveguide, but also infree-space, where one can use a discrete set of modes like
Hermit-Gaussian modes, commonly used in laser physics,
or continuous modes – like plane waves. In this latter casethe summation of q degenerates into integration overtransverse wave numbers.
After modal expansion it is possible to simplify
Maxwell’s set of 3-D differential equations into a simple
infinite set of first order ordinary differential equations forthe complex amplitudes Cq(z, ω) [2,3]. These can besolved for each mode at steady state, if the initialcondition Cqin(ω) (the complex amplitudes at the entrance
to the interaction region) is given (see Fig.1). The formal
solution for the increment of the complex amplitudes in
the case of free electron microscopic charges is:∇ × E = −μ(1)

NCqout (ω ) − Cqin (ω ) = ∑ ΔCqj =j =1(

where in general the point sources may be free electrons,
atomic electric dipoles or atomic magnetic dipoles andspins [1]:

N

(

)

(

)

J = ∑ − ev j δ r − r j (t )j =1NP = ∑ p j δ r − r j (t )
j =1

N

(

)

For any charges in the interaction volume the output
amplitudes Cqout can be calculated. Thus the entire output
radiation field can be calculated then by substituting{Cqout} back into the expansion series (3), or using it
otherwise to calculate optical parameters.

(2))

M = ∑ μ j δ r − r j (t )
j =1

(4)

⎫⎪
~
1 N ⎧⎪ ∞= − ∑ ⎨− e ∫ v j (t ) ⋅ E q* r j (t ) eiωt dt ⎬4 j =1⎪⎩ − ∞⎪⎭In this article we focus on free electrons.
Maxwell Equations can be exceedingly simplified in thefrequency domain. In the frequency domain it is possible
in many structures to expand the radiation field in terms~of a complete set of eigenmodes { E q }:pj

{C (ω )}
in
q

-

e

{C (ω )}
out
q

μj
(

~
E(r , ω ) = ∑ Cq (z, ω )E q (r )q

Fig.1: Excitation of radiation modes by particulate charges(Frequency Domain).

FEL Prize and New Lasing

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MOAAU01

Proceedings of FEL 2006, BESSY, Berlin, Germany

This suggests the following picture for modal
excitation: the field amplitude increment of each mode iscomposed of the sum of contributions from the individual
electrons, which correspond to the “wavepackets” emitted
by the individual electrons. To calculate the increment to
the radiation mode amplitude, one must solve a contour
integral along the trajectory of each electron and sum up
the wavepacket contributions.
In principle, the trajectories can be expanded in seriesin terms of the field amplitudes Cq. To zero order, thetrajectories of the electrons are not modified by theradiation field and we know them explicitly. In this casethe contour integrals can be performed straightforwardly.
If all the electrons have the same trajectories (a narrowbeam), then their wavepacket amplitudes are identical,
except for a “start oscillation” or “entrance time” phasefactor [3]:Pq = C qout (ω )

N

N

j =1

iωtoj

∑e

iωtoj

j =1; j ≠iNst+ ∑ ΔC qj

dWq

or

dω

=

2

π

C qout (ω )2

(6)Several physical situations can be distinguished,corresponding to the manner the amplitudes in (5)combine in the complex Cq(ω) plane to produce the total
radiation field. These are shown graphically in Fig.2 [3].
Let us now neglect the stimulated emission terms, andassume no input field Cqin(ω) = 0. When one absolutevalue square the second term in (5) and then average overthe electron phases j, one can distinguish two cases,
corresponding to two different emission processes:(1) The electron entrance times are random (Fig.2a). In
this case only the non-mixed terms in the square of the
sum
do
not
average
down
to
zero
(

(0 ) (ω ) e
C qout (ω ) = C qin (ω ) + ΔC qe
∑

2

(5)

⋅ e iωtoi= 0 ), consequently the spectraljenergy is proportional to the number of particles N. This
process is referred to as spontaneous emission or shotnoise emission, and radiation spectral energy (6) is
proportional to:

j =1

The contribution of the electrons to the total fielddepends to zero order in the fields on the phase relation
between the wavepackets. These contributions (second
term in (5)) give rise to the spontaneous or superradiantemission of the electron beam [3]. At higher order of
expansion in terms of the fields, the modification of theelectron trajectories by the fields, gives rise to stimulated
emission or stimulated absorption, represented by the lastterm of (5).
Once one calculated the mode amplitudes (5) it ispossible to substitute them in (3) to find the total field.
Alternatively, one can use them to calculate opticalparameters as radiation mode power or spectral energy(both are quadratic forms of Cq):

N i ωt
oj

2

=N

∑e

j =1

(7)

j

(2) The electron entrance times are correlated (Fig.2b):
either they enter in a bunch of duration shorter than theradiation period, or periodically at the radiation
frequency. In these cases the wavepackets emitted by theindividual electrons interfere in phase with each other,and the spectral power is proportional to N2:

Cout
q
Cout
q

ΔC
q3

Cout
q
ΔC

ΔC
1q

(a)

ΔC

q2

q3

ΔCst
q3
ΔCst
q1

ΔC
q2
Cin
q

ΔC
q1
(b)

(c)

Fig.2: Superposition of mode wavepacket amplitudes of electrons Cqj in the complex plane: a) spontaneous emission,b) superradiant emission, c) stimulated emission.
2

FEL Prize and New LasingProceedings of FEL 2006, BESSY, Berlin, Germany
N i ωt
oj

2

= N2

∑e

j =1

(8)

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emitted into transverse mode q by a single electron
traversing through an undulator is calculated from (4):j

We term this emission process “superradiance”,
following Dicke [4], who analyzed this case for an
ensemble of molecules having electric or magnetic
dipoles, employing a full quantum formulation (notethough that the superradiance effect is classical even in
Dicke’s problem [1]). Superradiant emission is also
termed coherent emission, as in CSR [5].
(3) When the mode field amplitudes at entrance do notequal to zero (Cqin ≠ 0) (Fig.2c), the electron trajectories
may be modified by the presence of the radiation field,
and the integral (4) will result in, beyond the zero order
expansion approximation, a field-dependent radiation
term (third term in (5)). This is the stimulated Emission
term. In first order expansion in the fields (linear regime),
neglecting inter-mode scattering, and this term is
proportional to the mode field amplitude:

N

j =1

and therefore produces radiation wavepackets in phasewith the incoming wave of amplitude Cqin, and the total
radiation is coherent.

UNDULATOR RADIATION OF A SINGLE
ELECTRON
The formalism and classification described in theprevious section can be applied to any kind of radiation
mechanism: undulator, synchrotron, Smith-Purcell etc.
[3, 6]. We now concentrate on the case of radiativeemission in an undulator. Expressing the radiation field
both in frequency domain and time domain, helps tounderstand the coherence characteristics of undulator
radiation and FEL devices. We therefore will employ on
occasions inverse Fourier transform on the radiation
expressions which are generally derived in thisformulation in the frequency domain.
The frequency domain amplitude of a wavepacket

sinc 2(θL/2)

ω0
1
0.5

-10

-5

0

5

10

15

θL/2
Fig.3 The spectral emission curve of undulator radiationof single electron emission.
FEL Prize and New Lasing

(

{w

j

}

)

(9)

z z

The result is:out(ω ) = eCqjv w ⋅ E∗q (r⊥ 0 )8v z

L sinc(θ (ω )L 2) e iθ (ω )L 2 eiωt 0 j(10)⎛ωwhere θ (ω )L ≡ ⎜⎜

⎝ vz

⎞

− k z (ω ) − k w ⎟⎟ L = (ω − ω 0 )t sl is the
2π

⎠

L
L
is the slippage
detuning parameter); t sl ==−Δω v z v g∑ ΔC qjst ∝ C q

0
-15

⎫⎪
1 ⎧⎪ ∞~
C qout (ω ) = − ⎨− e ∫ v j (t ) ⋅ E q * r j (t ) e iωt dt ⎬4 ⎪⎩ − ∞
⎪⎭
−
ik
z
(
t
)
v (t ) = Re ~v e w j+ v eˆ

time, and ω0, the synchronism frequency, is defined fromθ(ω0) = 0. Substituted in (6), this is a resonant emission
linewidth function, centered on the synchronism
frequency, and having a frequency bandwidth equal to theinverse of the slippage time (Fig.3):
Note that the amplitudes (10) of the wavepackets Cqjout
of different electrons differ only by a phase factor (as in(5))!
One can describe the wavepacket field in the time
domain by performing an inverse Fourier transform overthe complex amplitude function (10):{}E(r, t ) = F −1 Cq (z , ω )E q (r⊥ )e ik z (ω )z =2⎡t − z v

i =1

⎢
⎣

= ∑ Ai E q (r⊥ )cos(k z (ωi )z − ωi t ) rect ⎢⎤z + t sli / 2 ⎥

t sli

⎥
⎦

(11)
In the time domain, the wavepacket is composed of two
simple truncated sinusoidal waveforms (Fig.4). The highfrequency radiation wavepacket of slippage time duration
tsl1 arrives first after a retardation time L/vgl; then theelectron arrives after time L/vz and at the end the low
frequency wavepacket, corresponding to backward
emission in the electron rest-frame, arrives with aradiation (back-slippage) time L/vg2 [7]. Here vg1, vg2 are
the group velocities of the waves propagation in a
waveguide enclosure [7]. In free space vg1 = c, vg2 = -cand the low frequency wavepacket is actually emitted
backward also in the lab frame. In any case this low
frequency wavepacket is not important for the present
discussion and will be neglected in the subsequentdiscussion.
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Proceedings of FEL 2006, BESSY, Berlin, Germany

EMISSION OF A PERIODIC TRAIN OF
ELECTRON BUNCHES
t

tsl2

tsl1
t 0 j + L vz

t 0 j + L vg 1

t 0 j + L v g2

Fig.4: Time domain waveform of a single electron
emission wavepacket.
Tp = Np 2π/ ωb
I(Lw,t)
Lw/Vz

2π/ωb

t

a)

E(Lw,t)t
Lw/Vg

tsl = Nw 2π/ωr

2π/ωr

Examine now superradianat radiative emission from a
train of electron bunches, for example a macro pulse of an
RF accelerator (Fig.5a).
The periodic bunches radiate independently of eachother. The resultant radiation waveform (Fig.5b) is atemporal periodic sequence of the single bunch
wavepackets of Fig.4 (only the high frequency
wavepackets are considered). The duration of the electron
beam macropulse is Tp = Np*2π/ωb: the number ofelectron bunches Np times the bunching period. The
duration of the wavepacket is tsl = Nw*2π/ωr: the numberof wiggles Nw times the optical radiation period. The
Fourier transform of the wave is dominated by these twotime constants. Fig.5c displays the spectral power of thiswaveform (frequency domain) for the common casewhere tsl << 2π/ωb. In this case there is no overlap
between the wavepackets, and consequently there areseveral harmonics under the emission curve.
In the frequency domain, the macropulse spectral
emission curve is the product of the single electron
emission curve (the absolute value square of (10) – Fig.3)
and the macropulse “form factor” [3]:b)dWq/dωM M (ω )Δω = 2π/tsl(⎡ sin N P πω= ⎢⎣ N P sin πω(/ ω b )⎤⎥
/ ω b )⎦

2

(12)

2π/Tp

(n-2)ωb nωb (n+2)ωb(n-1)ωb (n+1)ωbc)

Fig.5: Superradiant (coherent) radiative emission froma macropulse train of e-beam bunches:a) current waveform; b) time domain picture of the
train of phase coherent radiation wavepackets;c) spectral power of the radiation field waveform (b).

UNDULATOR RADIATIVE EMISSION OF
A BUNCH OF ELECTRONS
If we consider now emission from a bunch of N
electrons, its resultant radiative emission field will becomposed of a superposition of wavepackets like the one
in Fig.4 [3]. In the frequency domain the emission
amplitude from all electrons (10) is the same except for aphase factor. Therefore the spectral emission curve is thesame function as of a single electron (Fig.3). It ismultiplied by N in the case of spontaneous emission(when t0j is random - see Eq.7) or by N2 in the case of
superradiant emission (when |t0j-t0| < 2π/ω - see Eq.8).
4The emission is wide band (2π/tsl), but if one can filterout one harmonic, or if ωb > Δωsl , it will have a narrow
linewidth corresponding to the macropulse duration(under the condition of stability of the bunchingfrequency during the entire macropulse duration). Thisobservation will be important also for the later discussion
on the case of FEL oscillator and SASE.
A nice verification of this concept was demonstrated by
the MIT research group [8] who measured superradiant
Smith-Purcell coherent emission using an RF Linac beam.
Carefully filtering out the radiation emission at the 14th
harmonic of the microbunch repetition rate within themacropulse by heterodyne detection techniques, theymeasured the exceedingly narrow linewidth of the total
waveform of the macropoulse radiation. It was indeed
2π/Tp, corresponding to the duration Tp of the e-beammacropulse.
If the electron bunch has a finite duration tb, then theexpression for radiation spectral energy includes also a"bunch–form factor"

M B (ω )2

1 π ωbi ωt=∫ I (t )e dt
Q −π ω2(13)b

FEL Prize and New LasingProceedings of FEL 2006, BESSY, Berlin, Germany(which is equal to unity as long as tb << 2π/ω).
This, in practice, limits the harmonic number nH, that canhave appreciable amplitude out of the infinite numbers ofharmonics that the macropulse form factor (12) admits, ton H << 2π ωt b

(14)

If the waveform of the electron-beam current does notcontain high harmonics (e.g. it is sinusoidally modulated)then there will be no harmonics under the spectral energy
curve in Fig.5b except the fundamental (nH=1), and its
amplitude will be appreciable only within the bandwidthofthesingleelectronemission
spectrum(ω−ωb) < Δω = 2π/tsl. The narrow linewidth (δω ~ 2π/Tp)
radiation of the prebunched FEL follows the detuning
curve of Fig.3 as demonstrated experimentally in [22].
Single harmonic radiative emission can take place also
at high harmonic nH of the bunching frequency ωb. This
will happen (under the condition (14)) if the spacing
between the harmonics exceeds the emission bandwidth:
ω b > Δωsl = 2π t slor

MOAAU01bunching. Contrary to superradiance the bunching is not
set ab-initio, before entrance into the interaction region,but it is created by the input radiation signal, at the signal
frequency, in the first part of the wiggler.
As well known, in a CW (or long pulse) FEL amplifier
the single mode (1-D) incremental power gain is given in
the linear (small signal) small gain regime by (see Fig.6)[6, 16]:

ΔP
P

=Q

(

d
sinc 2 θ (ω ) 2
dθ

)

(16)

The frequency ω of the electron bunching and theconsequent radiation is determined by the input radiation
signal. Thus the bandwidth of emitted radiation isdetermined by the bandwidth of the input signal, and if it
is monochromatic then the output radiation is temporally
coherent (except for admixture of noise (spontaneous
undulator radiation) power emitted in the wiggler. Notehowever that the gain curve (16) (Fig.6, which is thederivative of the spontaneous emission spectral curve
Fig.3) is quite wide still – about one half the width of the
spontaneous emission curve Δωst = π/tsl.

(15)n H < 2π ω0 t sl ≅ N w

Ein(t)
0

In this case, the wavepackets train of Fig.5b merges into
an harmonic wave of the macropulse duration Tp.

2E0

t

a)

Tp
TRF = 2π/ωb

I(Lw,t)FEL AMPLIFIER

Tb

Our main interest is in stimulated emission. Many of
the spectral features of superradiant emission discussed
above apply quite closely also to stimulated emission in
an amplifier configuration. The derivation of theincrements ΔCqst in the wavepacket amplitudes (third termin Eq.5) in the amplifier case is more involved, since it
requires the calculation of the modification of the electron
trajectories by the input radiation field. When this is done,
it is found that also in this case the electron beam isbunched. The classical stimulated emission from anelectron beam, always involves electron beam density0
Eout(Lw,t)

tsl

0

t

b)

t

c)

2E0

Fig.7: RF-Linac FEL Amplifier in the time domain.
a) multi-frquency coherent input signalb) Electron beam macropulse current waveformc) Amplified signal.

Gain

out

dWq

Δω = π/tsl/d ωΔω = π/tsl

1

1
ωb

2π/Tp

0

ωmax ω0ω

Fig.6: The FEL Linear regime small-gain curve.

FEL Prize and New Lasing

ωmax

ω0
ω
Fig.8: Spectral power of the amplifier output radiation
waveform of Fig.7c.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

If the electron beam is not continuous, of course, its
temporal wave-form will modify the spectrum of theamplifier radiation output. Let us consider an FEL
amplifier fed by a train of electron beam pulses(microbunches) from a continuously operating RFLINAC (see Fig.7b). The electron macropulse duration,
micropulse duration and repetition period are typically
Tp = 10 μs, Tb ~ ps, TRF ~ ns respectively. The radiation
signal period (say is the visible spectral region) 2π/ω0 ~ fs
and the slippage time Nw2π/ω0 ~ 10 – 100 fs, are bothmuch shorter than the pulse duration Tb.
Fig.7 depicts this case in the time domain. For didactic
reasons we assume that the input radiation (Fig.7a) is acoherent multi-frequency wide spectrum signal, wider
than the gain bandwidth of the FEL (Δωst ~ π/tsl). The
output signal (Fig.7c) is time gated by the waveform of
the electron beam (Fig.7b) and also frequency filtered by
the gain bandwidth of the FEL during the pulse duration.
The same case is displayed in the frquency domain in
Fig.8. Only radiation frequencies within the gain
bandwidth π/tsl of the gain curve Fig.6 are amplified.
Among the amplified frqeuncies only the ones which areharmonics of the bunching frequency ωb, within a
Tp
TRF = 2π/ωb

I(Lw,t)Tb
0
Eout(Lw,t)

tsl

t

0

t

Fig.9: The time domain waveform of the radiation
wavepackets emitted at saturation by an RF-Linac FEL
oscillator during the electron beam macropulse.
dW qout/dωΔω = π/tsl

Gth = 1/Rrt
1

1/Tp
ωb
0
ωmax

ωr

ω a)

dWqout/dω
Gth = 1/Rrt
1
1/Tp
0

ωr

ω
b)
Fig.10: The spectral power and modes structure ofsaturated FEL oscillator – a)multiple modes, coherently
mode-locked in an RF-Linac FEL, b) Single mode
operation in a quasi-CW or long pulse (electrostatic
accelerator) FEL.
ωmax

6frqeuncy deviation Δω ~ 2π/Tp will contribute coherently
to a Fourier transformation of the waveform in Fig.7c(carried out over the entire macropulse). Consequently the
amplified signal spectrum will contain harmonics of ωb oflinewidth 2π/Tp.

RF – LINAC FEL OSCILLATOR
In laser physics it is customary to present an oscillator
as an amplifier with feedback. In each round-trip aradiation wave-packet synchronous with an overlappinge-beam bunch gets amplified and is reflected back bymirrors into the entrance to the interaction region. It is
assumed that the bunching frequency is commensuratewith the round-trip frequency of the resonator: a new ebeam bunch arrives together with the radiation pulse, andthe amplification process continues up to steady state
saturation.
How does the saturation of an RF Linac FEL look in thetime domain? Fig.9 displays the steady state waveform of
the oscillator radiation in the time domain. It displays
radiation pulses emitted synchronousely with the RFbunches, somewhat modified by the slippage effect (as in
the amplifier case – compare to Fig.7c).
In the frequency domain (Fig.10a), the single path gain
curve is the same as in the amplifier (Fig.8), and the RF
frequency of the e-beam bunches is synchronized (bycavity length detuning) with the round-trip frequency of
the radiation pulses – namely the longitudinal modes of
the resonator. In addition, in the oscillator there is a gain
threshold condition: Pout/Pin > 1/Rrt. In the oscillationbuild-up process all modes (harmonics) are initially
excited. But at saturation only modes with gain higher
than the threshold are filtered in, and have a chance tosurvive the oscillation build-up process (Fig.10a).
The steady state output is as in the superradiantemission case (Fig.5) a finite coherent sum of longitudinalmodes that lie within the gain bandwidth π/tsl of the FEL.
This finite sum of harmonic frequencies looks in the time
domain as a periodic train of radiation pulses synchronous
and with good overlap with the macropulses of e-beambunches train that provides the gain. This is an exact
analogue of an actively locked conventional "mode locked
laser". Also in this case, if the RF frequency is stable overthe macropulse, the coherence of the harmonics is very
high (if they are filtered out), and is determined by the
duration of the macropulse Δω ~ 2π/Tp. Namely, theconsecutive radiation wavepackets are coherent with eachother throughout the macropulse (assuming a single
bunch per round-trip).
It is worth noting that high coherence between theradiation
wavepackets emitted
by consecutive
microbunches was measured in a long-wavelength FEL
oscillator [19]. This was measured both for the
spontaneous and stimulated emission of the FEL. It isremarkable that this coherence was observed when there
are several microbunches in the resonator at the sametime (RF bunching period shorter than the cavity roundtrip time). This is explained there as the result of high

FEL Prize and New LasingProceedings of FEL 2006, BESSY, Berlin, Germany

stability of the e-beam RF frequency and themicrobunches envelop shapes. It is argued that in theparameters regime of the FELIX FEL [19], themicrobunch formfactor (16) is appreciable of the emission
frequency, and the superradiant (coherent) undulaotr
radiation related to the stable shape of the micropulse
current waveform dominates the random shot noiseradiation, and consequently determines the phase of all
wavepackets. This happened both under conditions ofsaturated stimulated emission (oscillator lasing) andabsence of stimulated emission (no overlap of therecirculating wavepackets).

MOAAU01

CW (ELECTROSTATIC ACCELERATOR)FEL OSCILLATOR
What would happen in a CW or a long pulse FEL
oscillator (like an electrostatic accelerator FEL)? In thiscase, there are longitudinal modes due to the round-trip
periodicity, but there is no active mode locking. In
principle, many longitudinal modes can co-exist within
the gain bandwidth, and there is no external que that canphase-lock them.
The oscillation build-up stage involves in this case amode competition process, which arises when theoscillator approaches saturation and arrives to the nonlinear regime. In the FEL, as in other "homogenously
broadened lasers", this process ends with single mode
operation (see Fig.10b). The single mode laser radiation
linewidth is very narrow corresponding to the pulse
duration. It is given by the Fourier transform limitΔωline ~ 2π/Tp, and it tends to zero as Tp(CWoperation). An experimental confirmation for the mode
competition process and the Fourier transform limited
linewidth of the single-surviving mode in an Electrostatic
Accelerator FEL was provided in the Israeli FEL [ 9] (seeFig.11). In [9] a relative linewidth Δωline/ ω0 = 10-6 wasmeasured at frequency f0 = 100 GHz corresponding to apulse duration Tp ~ 10 μs.
What determines the linewidth in the limit Tp?
This fundamental problem was addressed already in theearly days of conventional masers [11] and lasers [12]. In
principle the oscillator line breadth is determined by aprocess of admixture of incoherent radiation with thecoherent stored radiation field in the cavity. This processleads to random phase drift of the radiation mode
amplitude Cq at the saturation stage (the amplitude islocked by the saturation process). In a maser the intrinsic
linewidth results in from incoherent black body radiation
emission into the cavity [11]. In a conventional laser, thelimiting factor is the quantum spontaneous emission [12].
In the FEL the limiting factor is the spontaneous
undulator radiation emission (or the electron beam shotnoise) [9, 13]. The three intrinsic linewidth expressions
are listed in Table 1.

→∞a)Δω/ω0 = 10-5b)
Fig.11: Spectrogram of the radiation output from anelectrostatic accelerator FEL oscillator [9].
a) Multimode spectrum evolving into single mode
operation during the oscillation build-up periods.
b) Fourier transform limited spectrum of the surviving
single mode.

Table 1: Intrinsic Linewidth Conditions(Δν sp )2= 2πkT

Maser

Δν maserLaser

Δν laser = 2πhνFEL

Δν FEL =Gordon, Zeiger,
Townes [11 ]

Pgen

(Δν )
1

(Δν )22

I0 e

HIGH GAIN FEL AMPLIFIER
Our analysis of the FEL in the linear regime is based on
the Pierce TWT model for TWT [14, 6]. It is found thatthe amplitude of the radiation mode Cq(L) in an FEL
amplifier of interaction length L, depends on the input
field amplitude Cq(0) (regular FEL), but also on theamplitudes of the e-beam velocity and current (density)
pre-modulation [15, 16]:

2

2

Pgen

1

→∞

Schawlow,
Townes [12 ]C q (L, ω ) = H E (ω ) C q (ω,0) + H v (ω ) v(ω,0) + H I (ω ) I (ω ,0)(17)

Gover, Amir,
Elias [13 ]where the transfer functions are:
FEL Prize and New Lasing

7

MOAAU01

Proceedings of FEL 2006, BESSY, Berlin, Germany( j − iθ )2 + θ pr 2 ⎞⎟ ei(k +δk )L (18.1)

3

⎛ δk

j =1

⎜
⎝

H E (ω ) = ∑ Res⎜zq

Δ

⎛ ik z L / v0 z

j =1

⎝

(

(

)

1 ⎞ i k zq + δk j L⋅ Pb 2 ⎟ eΔ

3⎛ δk − iθ

j =1

Δ

⎝

⎞
⎟
2 ⎟
⎜v
Γ
L
⎝ 0z
⎠

j

Pb =

(

μ0
ε0

32

⎛ a ⎞
⋅ ⎜⎜ w ⎟⎟⎝ γβ z ⎠)((⎠) ⋅ P 1 2 / I ⎞ ei (k zq +δk j )L
b⎟
⎠

b

2

⋅

L2
Aem

(18.4))

Δ = δk δk − θ − θ pr δk − θ + θ pr + Γ 3

2~v z (0, ω )

)

2
2
2
1
~
H FEL = e 3Γ L ⋅ e −(ω −ω0 ) (Δω HG )9(19.1)

for a current (density) pre-bunched FEL:⎞⎟⎟
⎝ IbΓ L ⎠1

Δω HG =

2

Γ
33 4
λw
ω0
2π
L

(19.5)

is the full width of 1/e of maximum of the high gain FEL
gain curve and

SASE FEL

2 ~
2
2
~
~
Pq ( L, ω ) = H FEL ⋅ C q (0, ω ) = H FEL Pq (0, ω )2⎛~
P pb− I ( L, ω ) = H FEL ⋅ Pb ⎜⎜(19.4)

is the power transfer function of the high gain FEL, and(18.5)In these formulas we use the “conventional”
parameters: θ - detuning parameter; Γ – gain parameter;θpr – space-charge parameter with reduction factor; L –interaction length; Ib – electron beam current, Aem –effective mode area. Here δk = kz-kzq is the modification
to the wavenumber of mode q (at fixed frequency ω) due
to the interaction. Solution of the Pierce cubic dispersion
equation 18.5 and substitution into (17, 18.1-18.3) resultsin the output radiation field amplitude for all gain regimes
and any initial conditions.
In the high gain tenuous beam regime (Γ3 >> θ,θpr,1)
one gets for an FEL amplifier:2~
I (0, ω )(19.2)

The current and velocity modulation amplitudes in(19.2, 19.3) may be deterministic (prebunching) or
random (noise). The video presentation in thetransparencies demonstrates the meaning and significanceof the current and velocity coherent modulation and noise
processes.
The SASE FEL is based on amplification of electron
beam noise in the FEL high gain regime. To analyze thiscase it is proper to calculate spectral energy and spectral
power parameters instead of the single frequency gain andradiative power parameters (19.1-19.3):

dWq
dω

dPq
dω

=

=

2

π

(

C q (ω )2(20.1)

1 dWq
T dω

(20.2)

where the averaging is over the electrons random entrance
times and T is an averaging time duration longer than theslippage time tsl.
The SASE FEL is nothing but a single path high gain
FEL with an effective beam-prebuncing input signal due
to current shot noise and velocity shot noise. Near thesynchronism frequency its spectral power is a sum of theamplified current and velocity shot noise sources:

for a velocity pre-bunched FEL:

(

dPq I
dω

8

2

Here

(18.3)
Ib2

kzL(19.3)(18.2)H I (ω ) = ∑ Res⎜⎛2~
( L, ω ) = H FEL ⋅ Pb ⎜⎟⎠3

H v (ω ) = ∑ Res⎜

P

pb −v

⎛
1 ⎞
⎟
= H FEL ⋅ Pb ⎜⎜⎟π⎝ IbΓ L ⎠22

I (0, ω )T

2

(21.1)FEL Prize and New LasingProceedings of FEL 2006, BESSY, Berlin, Germany

dPq v
dω

⎛
⎞
kz L
⎟
= H FEL ⋅ Pb ⎜
2 ⎟
⎜v
π
Γ
L
⎝ 0z
⎠

2

(

)

2

(

v z (0, ω )2

T(21.2)

where(2

I (0, ω )= eI b

(22.1)

e
2
δv z
Ib

(22.2)T2(v z (0, ω)T=relatively high bandwidth of the averaged radiation
spectrum (1/Tcoh) is related to the characteristic durationof the spikes (Tcoh). It is also noteworthy, that the single
pulse spectrum contains spectral lines that are very
narrow (1/Tb) – corresponding to the duration of the ebeam micro bunch - but appear at random centre
frequencies.
Since the shot noise spectrum is uniform, the average
spectrum of the SASE is determined merely by thetransfer functions (18.2, 18.3). Consider now only thecurrent shot noise. It is useful to expand the logarithm of
the exponentially growing term in (18.3) (including thephase, namely the imaginary part) to second order interms of frequency ω around the synchronism frequency
ω0. In the high gain (tenuous beam limit) this results in:~
H I ( z, ω ) ≅Here δvz is the axial velocity spread of the electron beam.
Usually the current shot noise is considered the main
source for SASE input power and the velocity noise isneglected. This is not self evident. For this assumption to
be valid (21.1) should exceed (21.2). Considering (22.1,
22.2) this leads to the condition

δv z
v oz

<

Γ
kz

(23)

MOAAU01

×e (

)

Pb
e − iπ 12 e ( 3 + i )Γz 2 ×
3 I b Γz

3 (ω − ω 0 )2 2(Δω HG )2− 1+ i

e

(24)

ikz

where ΔωHG is the width of the high gain FEL gain curve.
Indeed this spectral width is the linewidth ΔωHG ~ 1/Tcohof the SASE average spectrum shown in Fig.12b.
It is instructive now to calculate the "impulse response
function" corresponding to the complex transfer function(24). This is straightforwardly found by applying an
inverse Fourier transformation on (24):()

E ( z , t ) = Re{⎛⎜ Pb Δω HG / 3 3 4 2π i + 3 I b Γz ⎞⎟ ⋅SPIKING IN SASE-FEL AND THE
IMPULSE RESPONSE FUNCTION
Since the SASE-FEL is a wide band amplifier of a wideband incoherent signal (the shot noise), it is no wonderthat the spectrum of its radiation output is relatively wide
and its temporal waveform is characterized by a random
sharp structure (spiky). Fig.12 [10, 17] displays the
typical spectrum of a single SASE radiation pulse(Fig.12a), the averaged spectrum over many pulses(Fig.12b) and the spiky time-domain waveform of asingle radiation pulse (Fig.12c). One should note that the

⎝

[

]

⎠

exp − iπ / 12 + ( 3 + i )Γz / 2 ⋅

(

)

(

exp ⎢ + i⎛⎜ ω 0 t − cz − t 0 − (Δω HG )2 t − cz − t 0
⎡
⎣

⎝

(

exp ⎡⎢ − (Δω HG )2 t − cz − t 0⎣)2 / 8⎤⎥⎦})2 8 ⎞⎟⎠⎤⎥⎦ ⋅ (25)This function is displayed in Fig.13. It depicts (within
the quadratic expansion approximation a Gaussian wave
form envelope of width Tcoh ~ 1/ ΔωHG. It also reveals an

(a)
(b)
(c)
Fig.12: Simulation data of SASE radiative emission [9, 16]:a) Single pulse spectral power, b) Spectral power averaged over many pulses, c) Time domain "Spiky" intensity
distribution of a single pulse.
FEL Prize and New Lasing

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MOAAU01

Proceedings of FEL 2006, BESSY, Berlin, Germany

inherent (negative) chirp of the centre frequencydω d 2ϕ== −(Δω HG 2 )2
2
dt
dt

(26)

The impulse response function (25) is the coherent fieldwave-form created by an impulse of charge (of durationmuch shorter than the radiation wavelength), which is

4.7/ΔωHG

E(t)t

Fig.13: The time domain charge-impulse response function of an FEL in the high gain regime (Eq. 20).
I(Lw,t)~ 1 pst

Eout(Lw,t)

CONDITIONS FOR COHERENT X-UV
FEL

t

a)
I(Lw,t)2π/ωb (< Tcoh = 2π/ΔωHG)

Tb < 2π/ω0t~ 1 psEout(Lw,t)Tcoht
2π/ω0 = 3 AttoSec (for λ = 1 nm)

It is well known that the radiation output of SASE FEL
is spatially coherent (due to the optical guiding effect).
This is the reason why SASE FELs can be so muchbrighter than any other existing radiation source in thisspectral regime. However there will be even greaterinterest in this source if it would be also temporally
coherent and stable (pulse to pulse). How can a SASE
FEL be turned into a coherent radiation source?
dP
dω

b)

Fig.14: Spikes emission in SASE FEL within the
micropulses duration: a) Random emissionb) Phase-locked coherent spikes emission initiated bysubharmonic current prebunching.
Prebunching can be produced by a train of superimposed
positive or negative current impulses or any stable periodic current waveform of high harmonic contents.
10

superimposed at entrance over a uniform e-beam current
Ib. it is quite natural to identify it with the spikes
phenomenon shown in Fig.12c. The physical picture of
the phenomenon is based on appearance of random
electron bunches (current fluctuation) on the electron
beam current entering the interaction region. This current
is uniform on the average, but fluctuates because of therandomness of electrons generation in the cathode ("shotnoise"). The random electron bunches start radiatingsuperradiantly right at start, and their radiation
wavepackets dominate over the spontaneous radiativeemission from the other uniformly (but randomly)
injected electrons. Due to the forward slippage effect of
the radiation wavepacket and the high gain stimulated
emission process, the random electrons, that are flowing
within a cooperation length vzTcoh ahead of the initialradiating random bunch, are induced to emit at the same
frequency and phase (except for the inevitable chirp
effect), and consequently a coherent wavepacket (Fig.13)
is emitted. The output wavepacket duration
Tcoh = π/ ΔωHG (determined by the high gain FEL
bandwidth 19.4) is the minimal width of the spike. Spikes
that are excited by random bunches in time always shorter
than Tcoh merge into one spike. Assuming there are always
enough random bunches to negate presence of long"silent" spaces between the spikes; one can estimate thatthe average number of spikes in a bunch of duration Tb isTb/Tcoh [10]. Fig.14a displays the spikes waveforms of thisphysical model. It should be compared to the simulation
spiky pattern of Fig.12c. If Tb ≅ Tcoh then there is only
one spike in the macropulse duration [17]. In this case the
SASE radiation is as coherent as can be (Fouriertransform limited). Its spectral width is ≅ π Tcoh = π Tb .
It can be narrowed down only if pulse stretching
techniques can be employed.

dPs/dω
ΔωS

ΔωHG

ω

Fig.15: Spectral power of the coherent radiation outputof the FEL amplifier (red) and the SASE (shot noise)radiation (blue).
FEL Prize and New LasingProceedings of FEL 2006, BESSY, Berlin, Germany

Realizing that the SASE-FEL is an amplifier of noise, itis evident that what is required is a coherent input signal.
The input signal can be a coherent radiation wave (this issometimes called seed radiation injection), and there has
been intensive studies of developing an appropriate
coherent seed radiation sources based on high harmonic
multiplication of intense laser pulses in gas. Anotherscheme is based on filtering the undulator synchrotron
radiation after a few sections of the undulator, andreinjecting the narrower bandwidth radiation into theundulator for high gain amplification.
Another approach for attaining coherent emission from
SASE-FEL is based on coherent prebunching of theelectron beam (within the duration of its pSec
microbunches) at the radiative emission frequency of ahigh power optical laser or its subharmonics. This process
can be repeated in several steps, in which the bunchedradiation is amplified at high gain, and then highharmonics of the electron bunching are filtered out andamplified again, and so on (High Gain High Harmonic
Generation – HGHG [21]).
In all of these schemes the condition for attaining
coherent high power output radiation is that the coherent
input signal will be significantly larger than the noise. In
the first case of seed radiation injection (coherent
amplification) a simple criterion can be inferred bycomparing (19.2) to (21.1-22.2). Assuming the current
shot noise is dominant, this condition is:Ps (0) >> Pbe
Ib (ΓL )2

Δω

(27.1)

Here Δω is the frequency bandwidth of the detection
system in which inevitable (now undesirable) SASE
radiation is collected. If there are no means of filtering
available, then Δω = ΔωHG - the SASE radiation
bandwidth. In any case Δωs, π/Tb < Δω < ΔωHG, whereΔωs is the linewidth of the injected input radiation and
π/Tb is the Fourier limited bandwidth of the finite pulse.
Similar condition can be derived for the required
prebunching current required to dominate the current
shot-noise by comparing (19.2) to (21.1, 22.1):

2~2
I (0, ω ) >> eI b Δωπ(27.2)PHASE LOCKING THE SPIKES
If sufficient coherent seed radiation input power isattainable it makes the output power of the FEL amplifiercoherent as well. But other aspects of the seed radiation
injection approach, as tunability and operating
wavelengths range still need to be addressed. The current
prebunching approach may provide more options offrequency tunability and short wavelengths availability.

FEL Prize and New Lasing

MOAAU01

But its realization requires more intricate conceptual
schemes.
Much insight into this problem may be gained from thephysical description of the radiation processes in theprevious section. In particular it is worth noting the
striking correspondence between the emission of single
mode undulator radiation wavepackets by a single
electron (or single bunch) (10) (in the frequency domain)and (11) (in the time domain) and the corresponding
expressions of spectral transfer function (24) and impulse
response function (25) in the case of FEL in the high gain
regime. In the first case the wavepackets emission process
is spontaneous (or superradiant in the case of a bunch)and no supporting medium is required for the wavepacket
emission. In this case Eq.11 (Fig.4) is the explicit timedomain expression of the wavepacket emitted in theundulator from a particulate charge of one electron (e). In
the second case, (Eq.25) (Fig.13) is the radiation
wavepacket emitted by a current impulse of a unit charge,
and the excitation of this wavepacket is conditioned on
the presence of an electron beam medium (assumed
uniform) in front of the beam current impulse. Itsemission process involves stimulated emission andbunching of the e-beam, in contrast to the first case.
In both cases the coherence of the total radiation of thee-beam depends on the phase relation between the emitted
respective wavepackets by the charged particles or by thebunches. In the first case, when the electrons enter into
the undulator at random, the superposition of the radiation
wavepackets (11) in (5) produces incoherent radiation (ormore correctly - partially coherent radiation withcoherence time tsl). Analogously, in the SASE case, thesuperposition of the impulse response waveforms (23)from random bunches (the “spikes”) produces partiallycoherent radiation of coherence length Tcoh ~ 1/ΔωHG.
How can we turn the SASE radiation to be coherent? In
analogy to the case of superradiant emission from aperiodic train of bunches it is suggested that periodic
superposition of current impulses on top the uniform
current of the microbunch will phase-lock the spikes into
a coherent train of wavepackets with distinct phaserelation of the “carrier” radiation waves along the entire
microbunch (see Fig.14b as opposed to Fig.14a). Thissituation is analogous to the one described by Fig.5.
How to create the sub optical period current impulses isstill an open challenge. It is important to note that thecurrent perturbation does not have to be positive (see third
pulse in Fig.15b). It can be of any shape, as long as it is
kept periodic along the pulse with accuracy (stability)
better than one optical period (which may be AttoSeconds
in the X-UV regime!), and as long as it is “sharp” enoughto produce significant current amplitude of Fourier
harmonics to satisfy (27.2).
It is noteworthy that the prebunching frequency does
not need to be equal to the radiation emission frequency
and it can be a high sub-harmonic of this frequency. In
this case the coherent spectrum may contain several
harmonics as in Fig.5c, however as discussed in that
context, each harmonic would be coherent throughout the11

MOAAU01

Proceedings of FEL 2006, BESSY, Berlin, Germany

entire duration of the pulse, and its linewidth is Fouriertransform limited (2π/Tp). In principle the harmonics canbe filtered out by physical means or by numerical
processing of the data acquired by a coherent detection
system data in a spectroscopic application.
Note that if single harmonic operation is desired it is
not necessary that the prebunching frequency be equal to
the radiation frequency. It is only required that thebunching frequency ωb (sub-harmonic nH of the radiation
frequency ω0) will be larger than the FEL high gain
bandwidth (compare to (15)):

ωb =

ω0
nH

> Δω HG =or n H 〈

Γ
33 4
λw
ω0
2π
L

2π

Γ

3/ 4

L

3

2
1

θ 0
1
2

3

2

0

1

2

3

ψ

a)

40
I(t)/e

(28)
20

λw
0
0

The spectrum will look then as in Fig.5b, but with asingle harmonic frequency of linewidth 2π/Tp under theamplifier gain curve. In time domain the radiation
waveform will look then as in Fig.14, without spacing
between the overlapping phase locked spikes. In theextreme limit of (25) the waveform would be a single
coherent wavepacket along the entire pulse (microbunch)
duration Tp.
As mentioned above, realization of the high harmonicbunching schemes is still a challenge. We examine in
principle (Fig.16) a scheme of optical laser bunching,employed on a uniform electron beam, which is trappedby the ponderomotive wave of a wiggler and an external
coherent bunching laser. Fig.16a displays the θ-ψ phasespace electron distribution of one pondermotive period
exactly after one quarter period of synchrotron oscillation[16]. The current distribution along one bunching period
is shown in Fig.16b and its Fourier harmonic amplitudes
are shown in Fig.16c. Notice that significant amplitudes
can be attained even at very high harmonics. However, inpractice realizing the sharp current waveform structure of
Fig.16b may be difficult, because of the electron beamenergy spread and finite emittance. One should also bearin mind that in this scheme also velocity (energy)
modulation of the beam is generated collaterally, and thiscontribution of to the radiation power (18.2) should betaken into account, including the consideration of therelative phase between the velocity and the current
modulation.
A third scheme that should be considered for phaselocking and increasing the coherence of the radiation in a
SASE FEL consists of imposing periodic perturbation on
the wiggler (e.g. periodic dispersive sections) [20]. The
filtering effect of the periodic structure may be viewed as
the analogue of linewidth narrowing of radiation emitted
in a Fabri-Perot resonator. It is speculated (but needs
further study) that if the SASE FEL in such a structure
arrives to saturation within the wiggler length, nonlinear
process of mode competition between the filtered spikes
will lead to further increase of coherence and stability in

12

1

0.2

0.4

ωb/2π

0.6

0.8

1

b)

I(ω, a.u)
1

0

0

50

100

n

c)
Fig.16: Bunching of a cold beam by the pondermotive wave (pendulum equation model [15]):a) Electron detuning phase distribution in one period after
one quarter period of synchrotron oscillationb) Corresponding current waveform in one bunching periodc) Fourier harmonic amplitude of the waveform in (b).
analogy to the CW FEL oscillator case discussed
previous.
Acknowledgement: This presentation was dedicated tothe memory of Josef and Sofia Pietrowski (Yad-Vashem
Righteous among Nations awardees) who saved the life of
the parents of A.Gover during the Hollocaust.

REFERENCE
1. A. Gover, PRL, 96, 124801 (2006); A. Gover,Phys.Rev ST-AB, 9, 060703, (2006).
2. A.A. Barybin, “Modern electrodynamics and coupledmode theory: application to guided-wave optics”, Rinton
Press, (2002).
3. A. Gover, Phys.Rev. ST–AB, 8, 030701 (2005).
4. R.H. Dicke, Phys.Rev., 93, 99 (1954).
5. G.L. Carr et al, Nature, 420, 153 (2002).
6. A.Gover, P. Sprangle, QE-17, 1196 (1981).
7. A. Gover et al, Phys.Rev.Lett., 72 1192 (1994).

FEL Prize and New LasingProceedings of FEL 2006, BESSY, Berlin, Germany

MOAAU01

8. S.E. Korbly et al, PRL, 94, 054803/1 (2005).
9. A. Abramovich et al, Phys.Rev.Lett., 82, 5257 (1999).
10. S. Krinski and R.L. Gluckstern, Phys.Rev. ST-AB, 6,050701, (2003).
11. Gordon, Zeiger, Townes, Phys.Rev., 99, 1264 (1955).
12. Schawlow and Townes Phys.Rev., 112, 1490 (1958).
13. A. Gover A. Amir, L. Elias, Phys.Rev.-A, 35, 164(1987).
14. J.R. Pierce, “Traveling-Wave tubes”, Toronto,Van
Nostrand, (1950).
15. I. Schnitzer, A. Gover, NIMPR A237, 124 (1985).
16. A. Gover, “Lasers: Free Electron Lasers” Encyclopedia of Modern Optics, Ed. R. D. Guenther, D. G. Steeland L. Bayvel, Elsevier, Oxford (2005).
17. R. Bonifacio et al, PRL, 73, 70 (1994).
18. E. L. Saldin, E. A. Schneidmiller, and M.V. Yurkov,
The Physics of Free Electron Lasers, Chap. 6 (SpringerVerlag, Berlin, 2000).
19. H.H. Weits, D. Oepts, IEEE QE, 35, 15, 1999.
20. Y.C. Huang – private communication.
21. L.H. Yu et al, Phys.Rev.Lett., 91, p 74801/1, 2003.
22. M. Arbel et al, Nucl.Inst.Meth.Phys.Res., A445, 247(2000).

FEL Prize and New Lasing

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Proceedings of FEL 2006, BESSY, Berlin, Germany

EVOLUTION OF FELS OVER THE LAST 34 YEARS
W.B. Colson, NPS, Monterey, California

Abstract
The concept of the free electron laser (FEL) started 34 years
ago with Madey’s 1972 paper. The basic mechanism which
employs a beam of free electrons to amplify co-propagating
light has remained essentially the same as further developments have demonstrated high peak power, high average
power, high gain, optical guiding, continuous tunability andreliability. FELs have operated at wavelengths from the far
infrared, infrared, visible and down to the ultraviolet. The
realization of high gain has lead to the generation of soft xrays and soon hard x-rays where there are no mirrors. Abouta hundred FELs and user facilities are distributed aroundthe world, and in many ways the FEL has become a "perfect" source of coherent electromagnetic radiation. FELs
are in encyclopedias, in laser textbooks, with several textbooks specifically on FELs, and have clarified several physical principles for stimulated emission and laser physics.
Today a Google search on "free electron lasers" producesnearly 13 million hits. The accomplishments during thistime have been many, but none so important as establishinga community. Prospects for future directions are also briefly
considered.

PAPER NOTAVAILABLE14

FEL Prize and New LasingProceedings of FEL 2006, BESSY, Berlin, Germany

MOAAU03

LASING AT 13 NM OF THE SASE FEL AT FLASH
E. Schneidmiller, M.V. Yurkov, DESY, Hamburg

Abstract
We present the recent result from FLASH (VUV FEL at
DESY): lasing at 13 nm, the shortest wavelength ever generated in free electron lasers.

PAPER NOTAVAILABLE

FEL Prize and New Lasing

15

MOAAU04

Proceedings of FEL 2006, BESSY, Berlin, Germany

FIRST LASING AT SCSS
Tsumoru Shintake# and SCSS TeamRIKEN/JASRI/SPring-8, Hyogo 679-5148 Japan.
Abstract
On 20 June, the first lasing was observed at 49 nm in
SCSS prototype accelerator for Japanese XFEL project. A
challenging approach: 500 kV gun using CeB6 single
crystal thermionic cathode generates low emittance beamfrom 500 kV gun, followed by velocity bunching, andmagnetic chicane bunch compression, the measured
emittance at 50 MeV was 3 π.mm.mrad normalized.
When we firstly closed undulator, we observed narrowspectrum of amplified SASE signal. Radiation energy perpulse is around 1 μJ/pulse at moment.

INTRODUCTION
Unique combination of three key technologies: the invacuum short period undulator, the C-band high gradientaccelerator and low emittance injector using thermionicelectron source make possible to realize SASE-FEL at 1
Å within available site length at SPring-8 less than 800 m.
It was named as SCSS: SPring-8 Compact SASE Source[1]. From year of 2001, we have been carrying out R&D
on the key components: the electron gun, injector, C-band
klystron modulator with oil-filled compact design, highresolution beam position monitor, digital rf signal
processing system, etc.

of 250 MeV, the shortest wavelength of VUV-radiation at
50 nm can be obtained.
We commissioned beam operation in November 2005
and spent a few months to repair some hardware andsoftware. From May 2006, we started dedicated beamtuning to demonstrate first lasing.

FIRST LASING EVENT
Two in-vacuum undulators were installed, whose
undulator period is 15 mm, minimum gap is 3.5 mm,
nominal K value is 1.3 and one undulator length is 4.5 m.
In the beam tuning, we firstly opened the gap to 20 mm
and passed the e-beam through gap and transported into
the beam dump. We tuned the beam optics upstream of
the undulator. We setup the optics, in coming betamatching and focusing Q-magnet in between two
undulators.

TEST ACCELERATOR
In order to test this challenging scheme, and check all
hardware components developed in our R&D [2], weconstructed prototype accelerator in 2004-2005 as shownin Fig. 1. Beam line layout is shown in Fig. 4. We use four
C-band accelerating structures, 1.8 m long each, energy
gain 32 MV/m maximum. With maximum beam energy

Fig. 1 Tunnel view in SCSS prototype accelerator.
____________________________________________#

shintake@spring8.or.jp

16

Fig. 2 Radiation spectrum at the lasing condition, 0.25 nC
per bunch and 250 MeV. Peak at 49 nm is the coherently
amplified signal (6000 times) from the spontaneous
undulator radiation (blue line).

Fig. 3 Peak output power v.s. bunch charge. Using photo
diode, peak height was detected from averaged pulses.
FEL Prize and New LasingProceedings of FEL 2006, BESSY, Berlin, Germany

MOAAU04

As shown in Fig. 3, when we varied thebunch charge, the lasing power drasticallychanged. This threshold phenomenon
indicates high FEL amplification. The power
has not yet reached the saturation. Further
tuning is required. Detail analysis is now
undertaken.

EMITTANCE MEASUREMENTAt the injector end, the velocity bunching
and chicane bunch compression have been
completed, where the beam energy reaches
to 50 MeV, bunch charge is 0.25 nC and thebunch length is 1 psec or less, which
Fig. 4 SCSS prototype accelerator, two undulators of 15 mm pitch, 250 dependingon
operation
condition,
MeV e-beam, generates VUV-radiation.
specifically phase & amplitude tuning of
238 MHz and 476 MHz cavities.
We measured projected emittance right before the Cband accelerators, using Q-scan method. By reversing
polarity of one of the Q-magnets to provided strong
focusing in X- and Y-direction, and measured theminimum beam width. By varying focusing power, thebeam width response was measured as Fig. 5. By fitting
the beam size data as a function of the Q-magnet focusing
strength as shown in Fig. 6, we found the normalized
projected emittance of around 3 π.mm.mrad for both Xand Y- directions. The slice emittance was also measured
at 50 MeV beam dump, it was 2 π.mm.mrad, where themeasurement was limited by spatial available resolutionof profile monitor. Probably, the slice emittance is still
lower than 1 π.mm.mrad [3], but we do not have
Fig. 5 Beam profile during Q-san emittance measurement.
instrument to measure it at moment.
Transition radiation from Au coating of optical mirror
We repeated many measurements in this kind, always
was monitored by CCD camera.
observed emittance around 3~4 π.mm.mrad. This
experimental data indicates that the velocity bunching in
our system does not largely deteriorate the projected
emittance for compression ratio exceeding 100 times.

CONCLUSION & SCHEDULE
We measured the e-beam emittance and observed firstlasing in the SCS prototype accelerator. From thisexperiment, superior performance of the thermionic gun
and injector system has been demonstrated.
Analysing the experimental data carefully, we refine
hardware design, and start XFEL construction this year.

REFERENCES
Fig. 6 Beam width as a function of focusing power. At
beam energy 50 MeV, charge 0.25 nC, length <1 psec.
On 15 June, evening, we firstly closed the gap in the
upstream undulator, and measured radiation spectrum,
where the spectrum width was already quite narrow
peaked at 49 nm, and totally different from the natural
spontaneous radiation, as shown in Fig. 2. The spectrum
width is around 1% FWHM, which is much narrower than
the spontaneous undulator radiation, while it is dominatedby e-beam energy fluctuation, at moment.

FEL Prize and New Lasing[1] T. Shintake, et. al, "SPring-8 Compact SASE Source",
SPIE2001, San Diego, USA, June 2001.
[2] T. Shintake, Status of SCSS Project, 3rd Asian
Particle Accelerator Conference, APAC2004,
Gyeongju, Korea, March 2004.
[3] K. Togawa et.al., "Emittance Measurerment on the
CeB6 Electron Gun for the SPring-8 Compact
SASE Source", FEL2004, Trieste Italy.

17

MOAAU05

Proceedings of FEL 2006, BESSY, Berlin, Germany

THE FIRST LASING OF 193 NM SASE, 4TH HARMONIC HGHG AND
ESASE AT THE NSLS SDL*
X.J. Wang, Y. Shen, T. Watanabe, J.B. Murphy, J. Rose and T. Tsang, BNL, Upton, NY 11973, USA
Abstract
The first lasing of three types of single-pass high-gain
FELs, SASE at 193 nm, 4th harmonic HGHG at 199 nm
and ESASE at the Source Development Lab (SDL) of
Brookhaven National Laboratory (BNL) is reported. The
saturation of 4th harmonic HGHG and ESASE FELs wasobserved. We also observed the spectral broadening andinstability of the 4th harmonic HGHG.

INTRODUCTION
After the successfully experimental demonstration of
Self-Amplified Spontaneous Emission (SASE) and HighGain Harmonic Generation (HGHG) around the world[14], great progress was made recently in reducing the
SASE wavelength [5-6]. We present recent progress inboth SASE and HGHG at the the National SynchrotronLight (NSLS) Source Development Lab (SDL). The newlasing of three types of the single-pass high-gain FELs at
the NSLS SDL, SASE at the 193 nm, the first lasing of
the 4th harmonic HGHG and ESASE is reported in thispaper.
After a short description of the SDL facility, we will
present the preliminary experimental characterization of
new lasing of three types of single-pass high-gain FELs.
We will first discuss the experimental characterization of
the new lasing of a SASE FEL at 193 nm. The first lasing
and saturation of the 4th harmonic HGHG at 199 nm witha 795 nm seed laser is presented. With the same
experimental setup of the 4th harmonic HGHG, weobserved first lasing of the laser enhanced SASE at 210
nm after detuning the electron beam energy. The firstsuccessful demonstration of ESASE [7-8] not only will
open a new avenue to improve the performance of a
SASE FEL, but will also greatly expand the HGHG
tunability.

current of a few hundred amperes. The high brightness
electron beam transits the three magnets used for the
HGHG and laser seeded FEL amplifier (Fig.1): a
modulator undulator, a dispersion magnet and the 10 mlong radiator undulator (named NISUS) (Table 1).
One of the unique features of the SDL laser system isthat it was designed in such a way that a single laser
system is used to drive both the photocathode RF gun andto provide a seed laser pulse. This setup make it possible
to achieve sub-ps timing jitter between the seed laser andthe electron beam. The seed laser used for the experimenthas a bandwidth of 7 nm (FWHM), the pulse length canbe adjusted from 100 fs to 6 ps (FWHM). Table 1 lists theundulators, seed laser and electron beam parameters used
for the single-pass high-gain FELs presented here. The
matching optics for the seed laser focuses the seed laser
into the HGHG modulator on axis while a mini-chicane isused to manipulate the electron beam to by-pass the seedlaser mirror. There are 16 beam profile monitors (BPM)
uniformly distributed along the NISUS and they havebeen used both for e-beam matching and trajectorystudies. There is a dipole magnet after the NISUS
undulator which bends the electron beam to the beam
dump. The beam profile monitor in front of the beam
dump was used to monitor the electron beam energy andenergy modulation. The FEL radiation can also betransported by a periscope to the diagnostic station forcharacterization. The diagnostics station allows us tocharacterize the FEL output.
Table 1: the SDL accelerator, seed laser and HGHG
magnet parameters.
e-beam Energy (MeV)

180 - 210e-beam peak current (A)300 - 400

e-beam bunch length (FWHM, ps)~1

THE NSLS SDLEmittance (rms, mm-mrad)

2-4

The SDL is a laser linac facility dedicated for linac
based light source technology R&D and applications. The
main components of the SDL are a high-brightness
electron accelerator, an RF synchronized Ti:Sapphirelaser system, a High Gain Harmonic Generation (HGHG)
FEL, together with sophisticated electron and photon
beam instrumentation. The accelerator system of the SDL
consists of a 1.6 cell BNL photo-injector driven by the
Ti:Sapphire laser system and a S-band traveling wave
linac. After the recent electron beam energy upgrade [9],the maximum electron beam at the SDL is about 250
MeV. The magnetic chicane bunch compressor at the
SDL produces sub-ps long electron bunches with a peak

Seed laser wavelength (nm)795

Seed laser pulse length (FWHM, ps)~2-3

HGHG modulator period (cm)8

HGHG modulator length (m)0.8

HGHG modulator K

1.67 -3.02

HGHG dispersion magnet R56 (mm)0-5

HGHG radiator period (cm)3.89

HGHG radiator length (m)10Undulator parameter of the radiator

1.1___________________________________________#

xwang@bnl.gov

18

FEL Prize and New LasingProceedings of FEL 2006, BESSY, Berlin, Germany

199 nmMOAAU05

Dispersion

Radiator

795 nmModulator

Resonant at 795/4 =199 nm

Resonant at 795 nm

Figure 1: The SDL HGHG magnets and schematic of the 4th harmonic HGHG.

FEL CHARACTERIZATION
The major steps of the single-pass FEL experiment areelectron beam and trajectory optimization, seed laser ande-beam synchronization, and FEL output characterization.

193 nm SASE Characterization
We first present the experimental characterization of a
SASE FEL generated by the HGHG radiator – NISUS
undulator. SASE was first used to optimize the electron
beam and its trajectory inside the NISUS undulator. For
the NISUS undulator, the shortest SASE FEL wavelength
at the SDL should be about 150 nm when the electron
beam energy chirped is taken into consideration. The UV
Ocean Optics spectrometer and joulemeter used forcharacterizing the FEL are in the open air, which limits
the minimum observable SASE wavelength to about 193
nm. Fig.2 is the shortest single-shot SASE spectrum
obtained. The spectrometer resolution is about 0.7 nm.
The maximum SASE energy is about 1 µJ when 5%transmission is assumed.

As part of the recent electron beam energy upgrade [9],extensive modification of the HGHG modulator was done
to make it possible to achieve HGHG at harmonics ashigh as seven . A new vacuum chamber and a stronger
motor drive were installed. After the successful lasing of
SASE at 193 nm, the electron beam energy was tuned to202.5 MeV for the 4th harmonic HGHG with the seedlaser at 795 nm. The synchronization of the seed laser andelectron beam was realized in two steps. First we
observed the SASE and seed laser using a fast photodiode at the diagnostics station to make the two of themwithin 100 ps. The final synchronization was realized byobserving the electron beam energy modulation while
adjusting the seed laser delay line. With the seed laser
pulse length at about 2 ps (FWHM) and a peak power of
50-100 MW, we successfully observed the first lasing of
the 4th harmonic HGHG at 199 nm (Fig. 3). The slightdifference of the measured central spectrum from the 199
nm could be explained by the seed laser bandwidth, andthat will be discussed in more detail later.
4

6

7000

Intensity (a.u.)

5

6000

Intensity (a.u.)

x 10

5000
4000

4
3
2
1

3000
194

2000
185

196

198

200

202

204

Wavelength (nm)
190

195

200

Figure 3: The 4th harmonic HGHG spectrum.

Wavelength (nm)Figure 2: The shortest SASE spectrum at the SDL.

The First Lasing of the 4th Harmonic HGHG
To improve the performance of the SASE FEL, BNL
has been performing R&D on laser seeded and HGHG
FELs. Prior to April 2006, the shortest wavelengthachieved is the 3rd harmonic HGHG at 266 nm [4].

FEL Prize and New Lasing

The HGHG dispersion magnet was adjusted to optimize
the output of the 4th harmonic HGHG. The HGHG energy
was measured at the diagnostics station while the electron
beam was steered off the trajectory along the NISUS
undulator. Fig. 4 plots the maximum energy of the 4th
harmonic HGHG along the NISUS using the techniques
just described. It can be clearly seen that the energy
growth of the HGHG deviates from the exponential

19

MOAAU05

Proceedings of FEL 2006, BESSY, Berlin, Germany

growth which indicates the saturation of the 4th harmonic
HGHG.
2

HGHG Energy (a.u.)

10

0

10

-2

10

-4

10

4

6
8
Undulator Length (m)10Figure 4: The log plot of the 4th harmonic HGHG energy
along the NISUS undulator.

Experimental Characterization of the HGHG
Spectrum Broadening and Instability
As we pointed out earlier, the HGHG spectra stability
and width are not as stable and narrow as we expected.
We decided to explore this more by taking hundreds ofsingle-shot HGHG spectra using the UV spectrometerwith 0.7 nm resolution. Fig. 5 plots four of the typical
HGHG spectrums obtained. The electron beam energy
stability is one of the first considerations for the source of
this instability. We measured the shot-to-shot electron
beam energy fluctuation to be about 0.2% (Full width),
which could contribute to about 0.4% fluctuation in the
HGHG spectrum. But we observed as large as a 2%
fluctuation of the HGHG spectrum. After carefully
analyzing the data, we concluded that the dominant sourceof the HGHG spectrum fluctuation is the seed laser
bandwidth.
4

7

x 10

bunch length. The effective seed laser bandwidth sampled
by the electron beam is much narrower than the seed laser
bandwidth. So the HGHG bandwidth observed in earlier
experiments is dominated by the electron beam bunch
length. In our 4th harmonic HGHG experiment, to increase
the seed laser power, the seed laser pulse length employed
is comparable to the electron beam bunch length (2 ps vs.
1 ps). When timing jitter and drifting are taken into
consideration, the electron beam will sample the fullrange of the seed laser bandwidth. Fig. 5 shows the
HGHG spectral fluctuation is about 2%, which iscomparable to the seed laser bandwidth. The spectral
broadening shown in Fig. 5 is well above the spectrometer
resolution, which could be explained by the electron beam
distribution and mismatch between the electron beamenergy and the seed laser [10].

The First Lasing of ESASE at 210 nm
We also explore the tuning range of the HGHG
modulator undulator. For this study the seed laser
wavelength and power were kept constant while theelectron beam energy was adjusted. We observed nosignificant change in electron beam energy modulation as
the electron beam energy was adjusted from 190 MeV to
208 MeV. This corresponds to ± 5% energy tuning. Since
our modulator has only 10 periods, the observed tuning
range is well within our expectation.
Taking advantage of the large tuning range of the
HGHG modulator, we moved the electron beam energy to
197 MeV to demonstrate ESASE [7-8]. The resonancewavelength of the HGHG radiator at 197 MeV is about
210 nm, which is beyond the seed laser bandwidth. We
successfully observed first lasing of a laser enhanced
SASE FEL at the 210 nm (Fig. 6) using the same HGHG
arrangement. The intensity of the ESASE is a couple
orders of magnitude stronger than SASE without the seedlaser.

∆λHGHG ≤ ∆λSEED/4

1

Normalized Intensity

Intensity (a.u.)

6
5
4
3
2
1
0
195

200
Wavelength (nm)

ESASE
0.6
0.4
0.2

205

th

Figure 5: The 4 harmonic HGHG spectra.
In all of the previous HGHG experiments [4], the seedlaser pulse length is much longer than the electron beam

20

0.8 HGHG

0

195

200

205

210

Wavelength (nm)Figure 6: ESASE Spectrum vs. 4th harmonic HGHG.

FEL Prize and New LasingProceedings of FEL 2006, BESSY, Berlin, Germany

MOAAU05

SUMMARY AND ACKNOWLEDGMENT

REFERENCES

We present the new lasing of a SASE FEL at 193 nm,
and the first ever lasing of the 4th harmonic HGHG and
ESASE. We have experimentally investigated the spectral
instability and broadening of the HGHG FEL; thebandwidth of the seed laser is one of the major sources ofthe HGHG spectral instability. This observation could
have important implications for a future X-ray FEL basedon a cascaded HGHG concept, where a short broad band
seed laser will be employed. By taking advantage of thelarge tuning range of the HGHG modulator we havesuccessfully demonstrated the first lasing of the so called
ESASE. Our experiment shows that ESASE not only will
open a new avenue to improve the performance of a
SASE FEL, but will also greatly expand the HGHG
tunability. More detailed analysis and simulation of theexperiments presented here will publish in the future.
We are grateful for support from the NSLS and its staff,
and this work is partially supported by the Office of Naval
Research (ONR) and U.S. Department of Energy undercontract No. DE-AC02-98CH1-886.

[1] S. Milton et al., Science 292, 2037 (2001).
[2] A. Tremaine et al., Phys. Rev. Lett. 88, 204801-1(2002).
[3] V. Ayvazyan, et al., Phys. Rev. Lett. 88, 1048021(2002).
[4] L.H. Yu, et al, Phys. Rev. Lett. 91, 074801-1 (2003).
[5] E. Schneidmiller, et al, “Lasing of FLASH at 13 nm”,
this proceedings.
[6] T. Shintake, “First Lasing at SCSS”, this proceedings.
[7] Y. Liu et al, Phys. Rev. Lett. 80, 4418 (1998).
[8] A.A. Zholents, Phys. Rev. ST Accel. Beams 8, 040701(2005).
[9] X. J. Wang et al, Proceeding of the 2004 FEL conf.,
Trieste, Italy, 209-211 (2004).
[10] W. Fawley, “Output Bandwidth Effects in Seeded
Harmonic Cascaded FELs“, this proceedings.

FEL Prize and New Lasing

21

MOBAU01

Proceedings of FEL 2006, BESSY, Berlin, Germany

STATUS OF THE LINAC COHERENT LIGHT SOURCE
D. Dowell, SLAC, Menlo Park, California

Abstract
The world’s first x-ray free electron laser, the Linac Coherent Light Source (LCLS), is currently under construction
at the Stanford Linear Accelerator Center (SLAC). This facility uses the last kilometer of the SLAC 3 km Linac to
produce 1.5 to 15 angstrom photons in a 100 meter long undulator with up to 15 GeV electrons. The production of thehigh-brightness electron beam requires the construction of a
new RF photocathode gun and a 135 MeV injector at the 2/3
point of the SLAC Linac. In addition, two stages of chicane
compressors will be installed for compressing the electrons
to a 22 micron bunch length, boosting the peak current to
3.5 kiloamperes. The bright, dense electron bunches thenradiation via the SASE process in the long undulator. The
coherent x-ray beam propagates through a gas attenuatorand various diagnostics, before delivery to the experimental stations in the Far Hall. The design features and statusof this novel facility will be presented.

PAPER NOTAVAILABLE22

The Angstrom ChallengeProceedings of FEL 2006, BESSY, Berlin, Germany

MOBAU02

RESULTS AND LESSONS FROM FLASH
B. Faatz, DESY, Hamburg

Abstract
Since first lasing beginning of 2005, we have continuously
extended the wavelength range and improve the performanceof FLASH. With regular blocks of accelerator and FEL studies and user beam time, we have now covered a wavelength
range between 13 and 45 nm, at power levels between 5
and 50 µJ. Depending on user demands, we have delivered
single bunch or multiply bunches at repetition rates of 1
MHz or 250 kHz. The latest results of the machine performance will be shown. In addition, the specific problems thathave been encountered and our solutions during the past 18
months will be discussed. Finally, future plans for FLASH
will be presented.

PAPER NOTAVAILABLE

The Angstrom Challenge

23

MOBAU03

Proceedings of FEL 2006, BESSY, Berlin, Germany

THE EUROPEAN XFEL PROJECT
R. Brinkmann, Deutsches Elektronen-Synchrotron (DESY), D-22607 Hamburg, Germany
for the XFEL Team
Abstract
The European X-ray Free Electron Laser XFEL is a 4th
generation synchrotron radiation facility based on the
SASE FEL concept and the superconducting TESLA
technology for the linear accelerator. This multi-user
facility will provide photon beams in a wavelength
regime from 0.1nm to 5nm in three FEL beam lines andhard X-rays in two spontaneous radiation beam lines,
serving in total 10 experimental stations in the first stage.
The project is in an advanced planning and technicalpreparation stage and its construction as aEuropean/International facility near DESY in Hamburgwill start in 2007. This talk gives an overview of theoverall layout and parameters of the facility, withemphasis on the accelerator design, technology andphysics.

INTRODUCTION
The XFEL was originally proposed as part of the
TESLA facility, first in a version integrated with the linear
collider using the same linac [1,2], in a later version with
its own separate linac [3]. In February 2003 the German
Government announced the decision that the XFEL
should be realized as a European project, with 60% of thefunding provided by Germany (Bund and Länder
Hamburg and Schleswig-Holstein) and 40% requested
from partner countries. In mid-2003 an XFEL projectgroup was established at DESY which, together withpartner institutes, pushed forward the preparation work
necessary to achieve the status of readiness for start ofconstruction by 2006. Besides the optimization of theoverall design, main objectives in this phase arepreparations for the site and civil construction (including
the legal procedure for construction permission),
industrialization of major technical components anddetailed studies of beam physics and the FEL process.
The XFEL has a strong link to the FLASH (VUV-FEL)
facility at DESY [4 – 6], which is in nearly all respects(accelerator technology, FEL operation, photon beamlines and user experiments) truly a pilot facility for the
future project.
The project organization at the international level issupervised by a steering committee (ISC) with members
from all countries interested in participating in the project.
Up to date, 13 countries (Figure 1) have signed the XFEL
Memorandum of Understanding for the preparation phase.
The ISC is supported by two working groups: STI for
scientific and funding issues and AFI for administrativeand funding issues. In 2005 ISC nominated a European
Project Team (EPT), with the main charge to deliver thetechnical and administrative documents required for the24

process of negotiations and decisions at the political leveltowards achieving the final go-ahead for the project.

CH CN DE DK ES

FR

GB

GR HU

IT

PL

RU S

Figure 1: Signature countries of the European XFEL MoU
as of August 2006.
In July 2006, an updated Technical Design Report(TDR) was completed [7] and delivered to ISC. The
report had previously been reviewed and endorsed by STI
and additional experts from the international scientificcommunity. In addition, the administrative documents
have been essentially completed and reviewed by AFI.

LAYOUT AND PARAMETERS
The main components of the XFEL Facility are theinjector, the linear accelerator, the beam distribution
system, the undulators, the photon beam lines, and the
instruments in the Experiments Hall (see Figure 2).
These components are distributed along an essentiallylinear geometry, 3.4 km long, starting on the DESY
campus in the northwest part of the city of Hamburg, andending in the neighbouring Federal State of SchleswigHolstein, south of the city of Schenefeld, where theExperimental Hall is located. Permission for construction
and operation on this site was recently (July 2006)
obtained (concluding a so-called Plan Approval
Procedure) and publicly announced by the authority incharge (LBEG Clausthal-Zellerfeld).

Figure 2: Site and schematic layout of the European
XFEL Facility.

The Angstrom ChallengeThe basic functions of the main components areschematically described in the following: In the injector,
electron bunches are extracted from a solid cathode by alaser beam, accelerated by an electron RF gun anddirected towards the linear accelerator with an exit energyof 120 MeV. In the linear accelerator, consisting of a
1.6 km long sequence of superconducting accelerating
modules, magnets for beam steering and focusing, anddiagnostic equipment, the electrons are accelerated toenergies of up to 20 GeV (17.5 GeV is the energy
foreseen for the standard mode of operation of the XFEL
facility at 0.1nm FEL wavelength). Along the accelerator,
two stages of bunch compression are located, to produce
the short and very dense electron bunches required toachieve saturation in the SASE process. At the end of thelinac follows a beam transport section with collimation,
stabilization feedback and diagnostics systems, after
which the individual electron bunches are fed into one or
the other of two electron beam lines by the beam
distribution system. The linac and beam transport line arehoused in a 2.1 km long underground tunnel (Figure 3).

Figure 3: Layout of the 5.2 m diameter linac tunnel.
In the initial configuration the user facility has 3 SASEFEL and two spontaneous radiation undulator beam lines(Figure 4) with in total 10 experimental stations. The sitelayout permits a later extension of the facility by another5 beam lines. Independent wavelength tuning by
undulator gap variation is foreseen and, together withelectron beam energy variation, a total wavelength rangeof 0.1 – 5 nm (FEL) and 0.014 – 0.2 nm (spontaneousradiation) can be covered. The peak brilliance of FEL
radiation (Figure 5) is in the range 1032 - 5⋅1033
photons/0.1%bw/s/mm2/mrad2. The baseline operating
point for 0.1nm wavelength (SASE1) at 17.5 GeVelectron energy has been chosen on the basis of extensive
studies of the FEL process with a relatively conservative
assumption on the minimum undulator gap (10mm). At
the design electron beam emittance (εN = 1.4 mrad⋅mm,see below) very good transverse coherence of the FEL
radiation is predicted [8]. The magnetic lengths of theundulators (105 – 210 m) include a safety margin of atleast 20% w.r.t. the calculated saturation lengths.

The Angstrom Challenge

MOBAU03

SASE 2tunable, planar
0.1 – 0.4 nm

electrons

U2

e-

U1

17.5 GeVe-

SASE 1

Experiments

Proceedings of FEL 2006, BESSY, Berlin, Germany

SASE 3tunable, planar
0.1 nmtunable, helical
0.4 – 1.6 nm

Figure 4: Schematic layout of the beam lines in the user
facility.

FLASH(seeded)

FLASH

Figure 5: Peak brilliance of X-ray FELs versus 3rd
generation SR light sources. Blue spots show
experimental performance of the FLASH facility.

ACCELERATOR COMPLEX
The layout of the accelerator is schematically shown in
Figure 6 and its main parameters are summarized in Table
1. The beam energy required for 0.1 nm photon
wavelength in the SASE1 and SASE2 beam lines is 17.5
GeV. The linac design energy of 20 GeV thus alreadyincludes the potential to reach a lower wavelength ofabout 0.08 nm. The required peak power per RF station iswell below the limit of the 10 MW multibeam klystrons.
This de-rated mode is beneficial for highly reliable
operation on one hand and for an upgrade potential
regarding beam energy or duty cycle on the other.
Likewise, the cryogenic system is laid out with an
overhead of 50% with similar operational benefits.
The electron beam is generated in a laser-driven
photocathode RF gun and pre-accelerated in a single
superconducting accelerator module. The injector ishoused in an underground enclosure separate from thelinac tunnel, so that it can be commissioned at an earlystage, well before installation work in the linac tunnel is25

MOBAU03

Proceedings of FEL 2006, BESSY, Berlin, Germany

completed. Furthermore, there is space foreseen for acompletely separate and radiation-shielded second
injector, which can be constructed, commissioned andmaintained independently from the operation of the first
injector.
beam lines

Collimation
Diagnostics
Feedback

0.4 kmBeam distr.

116 m odules
29 RF stations

23+2 RF stations

LINAC
BC-II

1.7 km

20GeV

2 GeV

2+1 RF stations
BC-I
0.5GeV
3rd h., 2 m odules
1 RF station
Injector

originally expected, as measurements performed at the
PITZ facility (DESY-Zeuthen) indicated [9]. A highpriority of the future program [10] at PITZ will be on theverification of the XFEL gun design parameters, withimprovements expected from higher cathode field andoptimized laser profile.
After transfer to the main accelerator tunnel (see thelayout sketched in Figure 7), the beam is further
accelerated by one linac unit (4 accelerator modules with
8 cavities each, driven by one RF station) to an energy of
0.5 GeV before entering the first bunch compression
stage. A third harmonic (3.9 GHz) RF system is foreseen
to optimize the longitudinal phase space properties. After
acceleration to 2 GeV with three linac units the beam
enters the second (final) compression stage, after which
the 1nC bunch peak current has increased to 5 kA (σz =23μm for a 1nC bunch), a factor of 100 higher than theinitial peak current from the RF gun. Considerable
attention has been paid to foresee beam diagnostics
stations in order to assess the beam phase space properties
after the compression process in great detail [11]. Beamsimulation studies of the compression system (see [12] fora recent overview of simulation code developments) showthat the slice emittance growth due to space charge andCSR effects can be kept at a low level and there is roomfor further parameter optimization beyond the nominal
design bunch parameters [13].

2 RF stations

Figure 6: Schematic layout of the accelerator.

Table 1: Main parameters of the XFEL accelerator.
Energy for 0.1 nm wavelength17.5 GeV(max. design energy)(20 GeV)# of installed accelerator modules
116# of cavities
928
Acc. Gradient (104 act. mod.) at 20 GeV 23.6 MV/m
# of installed RF stations
29
Klystron peak power (26 active stations) 5.2 MW
4.6 × 106
Loaded quality factor Qext
RF pulse length
1.4 msBeam pulse length
0.65msRepetition rate
10 Hz
Max. average Beam power
600 kW
1010
Unloaded cavity quality factor Q0
2K cryo load (incl. transfer line losses)
1.7 kW
Max. # of bunches per pulse (at 20 GeV) 3,250 (3,000)
Min. bunch spacing
200 nsBunch charge
1 nC
Bunch peak current
5 kA
Emittance (slice) at undulator
1.4 mm×mrad
Energy spread (slice) at undulator
1 MeV
The results from simulation studies of the RF gun showthat a normalized beam emittance below 1mrad⋅mm at thedesign RF field of 60MV/m on the cathode is achievable,
even if the thermal emittance is somewhat larger than

26

Figure 7: Layout of the XFEL bunch compression system.
The large compression factor and resulting shortbunches (70fs rms) require timing, synchronization anddiagnostics devices at the fs level. A considerable R&D
program is ongoing in this field, see e.g. [14 – 16] forrecent developments. Furthermore, extremely accurate RF
control is required in the low-energy part of theaccelerator [17].
Final acceleration to a nominal maximum beam energy
of 20 GeV takes place in the main part of the linac,
consisting of 25 RF stations and 100 accelerator modules
in total. Downstream from the linac follows aconventional beam line for installation of the beamcollimation and trajectory feedback systems, as well as
providing distribution of the beam into the different
undulator beam lines, including the connection to a future
upgrade of the user facility with more beam lines. A
combination of slow and fast switching devices permits togenerate bunch trains of different time patterns for

The Angstrom ChallengeProceedings of FEL 2006, BESSY, Berlin, Germany
different experiments without having to generate andaccelerate bunch trains with strongly varying transient
beam loading. A fraction of each bunch train will be used
to accurately stabilize the following bunches in positionand energy by means of a fast feedback system [18]. After
having passed through the undulators, the “spent” beam is
stopped in radiation shielded solid absorbers. An
additional beam dump is installed in the beam distribution
shaft XS1, just upstream from the undulator beam lines. It
allows to commission or to operate the accelerator while
installation or maintenance work is ongoing in theundulator tunnels.
The layout of the linac includes precautions for energy
management in case of RF component failure. The section
between the two bunch compression stages consists ofthree RF units with four accelerator modules each, out of
which only two have to be active to accelerate the beam
to 2 GeV at the design gradient. Likewise, the main
section of the linac (from 2 to 20 GeV) has an overheadof two RF stations. This guarantees that in case of an RFunit failure there is sufficient energy reserve to maintainboth the beam energy at the second bunch compressor
stage as well as at the end of the linac. Tunnel access forrepair of RF stations during scheduled operation time canthus be safely avoided. In practice, the reserve stations
will not be left idle when not needed. Instead, allavailable stations will be operated with reduced gradientand in case a station fails the gradient will be increased in
the other sections such as to keep the beam energy
constant.

MOBAU03possible parameters for CW operation is shown in Table
2.
Table 2: Sketch of possible parameters for a future optionof operating the linac in CW mode.
Beam energy
7 GeV
Accelerating Gradient
7.5 MV/m# of CW RF stations
116
RF power per accelerator module ≈20 kW
Beam current
0.18 mA
2 ×107Loaded quality factor Qext
Bunch frequency
180 kHz
Unloaded quality factor Q0
2⋅10102K cryogenic load
≈3.5 kWPROJECT COST AND SCHEDULE
An in-depth re-evaluation of project construction costs
has been performed as part of the project preparation
work (see the TDR [7] for more details). In year 2005
prices, the construction costs are 986 M€, out of which
736 M€ are capital investment and 250 M€ personnel
costs (including overhead). A breakdown of theconstruction costs is shown in Figure 8 and the budget
time profile in Figure 9.

XFEL construction cost distribution

Operational Flexibility
The single set of basic reference parameters in Table 1
does not cover the full range of operational flexibility of
the linac. There is, within certain limits, a considerable
flexibility regarding operation parameters, based on builtin performance reserves of its technical components.
Operation at lower beam energy, thus extending thephoton wavelength range to softer X-rays, is an obvious
possibility. On the other hand, based on the experience
gained with the superconducting TESLA cavities, it canbe realistically expected that the linac can be operated at
an accelerating gradient somewhat above the specified
design value of 23.6 MV/m at 20 GeV. An increase of thegradient to about 28 MV/m would permit a maximum
beam energy of 24 GeV, thus significantly extending thephoton wavelength range to harder X-rays, provided thatsimultaneously also an improved injector beam quality
becomes available to be able to maintain saturation of the
SASE FEL process. In addition to the possibility ofhigher beam energies, the available reserve in the RF andcryogenic systems can also be used for increasing thelinac repetition rate and thus the duty cycle of the pulsed
linac. At sufficiently low beam energy, a 100% duty
cycle, i.e. continuous wave (CW), mode of operation isconceivable, an option which is only possible with asuperconducting linac. This option is viewed as not being
part of the first stage of the XFEL facility but isconsidered as a future option. A preliminary set of

The Angstrom Challenge

17%

27%

Linac
Acc sub-systems
Undulator & photon
Control & operation

19%

9%
4%

24%

Infrastructure
Civil construction

Figure 8: XFEL construction cost distribution.
The project schedule assumed for the profile of Figure
9 is based on an expected project go-ahead decision in the
beginning of 2007. After a construction period of 6.5
years, beam through the linac and the first beam line
(SASE1) is scheduled for 2013 and first user operation for2014. There will be a transition phase until end of 2015,
during which operation of beam lines takes place inparallel with completion of construction andcommissioning of others. By 2016 the entire facility will
be operational. The yearly operation budget (in 2005
prices) has been estimated at 83 M€, including
administrative overhead and user support.

27

MOBAU03

Proceedings of FEL 2006, BESSY, Berlin, Germany

y2
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y2
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6
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1
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kEURO

[12] M. Dohlus, “Modeling of Space Charge and CSR
Effects in Bunch Compressor Systems”. Proc. EPAC,
European XFEL budget profile
Edinburgh 2006.
250,000[13] T. Limberg et al., “Optimized Bunch Compression
System for the European XFEL”, Proc. PAC,
200,000
Knoxville 2005.
Operation
150,000[14] A. Winter et al., “High Precision Master Oscillator
Comm issioning
for Optical Timing Distribution Systems”. Proc.
Construction
100,000
Preparation
EPAC, Edinburgh 2006.
[15]
J.-W.
Kim, “Femtosecond Synchronization and
50,000Stabilization
Techniques”,
thisconference
TUBAU02.
0[16] B. Schmidt, “Overview on Diagnostics for X- and
VUV-FELs”, this conference THCAU01.
[17] F. Ludwig et al., “Phase Stability of the Next
Figure 9: XFEL budget profile, including preparation phase
Generation RF Field Control for VUV- and X-ray
and transition from construction to operation.
Free Electron Lasers”, Proc. EPAC, Edinburgh 2006.
[18] V. Schlott et al., “An Intra Bunch Train Feedback
System for the European XFEL”, Proc. EPAC,
ACKNOWLEDGEMENT
Edinburgh 2006.
The paper presented here is based on the recently
published XFEL Technical Design Report. The author
would like to express his thanks to the co-editors and coauthors of the TDR, who contributed and shaped a vast
amount of material for that comprehensive report, ofwhich this paper can be viewed as a short summary.

REFERENCES[1] R. Brinkmann, et al., “An X-Ray FEL Laboratory asPart of a Linear Collider Design”, Nucl. Instr. Meth
A393, (1997) 86-92.
[2] R. Brinkmann et al. (eds.), ”TESLA Technical
Design Report”, DESY-2001-011, March 2001.
[3] R. Brinkmann et al. (eds.), “TESLA XFEL Technical
Design report – Supplement”, DESY-2002-167, Oct.
2002.
[4] J. Roßbach, “Results from the VUV-FEL”, Proc.
EPAC, Edinburgh 2006.
[5] H. Weise, “The TTF/VUV-FEL (FLASH) as thePrototype for the European XFEL Project”, Int. Linac
conf., Knoxville 2006.
[6] B. Faatz, “Results and Lessons from FLASH”, Thisconference MOBAU02.
[7] “XFEL Technical Design Report”, DESY 2006-097,
http://xfel.desy.de.
[8] E. Saldin et al., “Transverse and Longitudinal
Coherence Properties of the Radiation from X-ray
SASE FELs”, this conference MOPPH069 .
[9] J. H. Han et al., “Emission Mechanisms in a
Photocathode RF Gun”, Proc. PAC, Knoxville 2005.
[10] A. Oppelt et al., “Upgrade of the PITZ Facility andFirst Beam Measurements”, this conference
THPPH022 .
[11] C. Gerth, “Layout of the Diagnostic Sections for
Emittance and Energy Spread Measurements at theEuropean XFEL”, this conference THPPH010.

28

The Angstrom ChallengeProceedings of FEL 2006, BESSY, Berlin, Germany

MOBAU04

OPTICAL KLYSTRON ENHANCEMENT TO SASE X-RAY FELS
Yuantao Ding∗ , Paul Emma, Zhirong Huang† , SLAC,Menlo Park, CA 94025, USA
Vinit Kumar‡ , ANL, Argonne, IL 60439, USA.
Abstract
The optical klystron enhancement to self-amplified
spontaneous emission (SASE) free electron lasers (FELs)
is studied in theory and in simulations. In contrast to aseeded FEL, the optical klystron gain in a SASE FEL is notsensitive to any phase mismatch between the radiation andthe microbunched electron beam. The FEL performancewith the addition of four optical klystrons located at theundulator long breaks in the Linac Coherent Light Source(LCLS) shows significant improvement if the uncorrelated
energy spread at the undulator entrance can be controlled toa very small level. In addition, FEL saturation at shorter xray wavelengths (around 1.0 Å) within the LCLS undulator
length becomes possible. We also discuss the applicationof the optical klystron in a compact x-ray FEL design that
employs relatively low electron beam energy together witha shorter-period undulator.

INTRODUCTION
An x-ray free electron laser (FEL) operated in the selfamplified spontaneous emission (SASE) mode is the primary candidate for the next-generation light source and isunder active development around the world [1, 2, 3]. Insuch a device, based on the achievable electron beam qualities such as peak current and transverse emittances, the total length of the undulator required to reach the x-ray intensity saturation usually exceeds 100 m. The electron beamenergy spread is typically too small to affect the SASE performance.
To enhance the FEL gain, the optical klystron concept
has been invented by Vinokurov and Skrinsky [4] and has
been successfully implemented in many FEL oscillator facilities such as the Duke FEL [5]. An optical klystronconsists of two undulators, separated by a dispersive section (a magnetic chicane). The dispersive section converts beam energy modulation into density modulation andhence speeds up the gain process. Theoretical studies ofthe optical klystron in high gain FEL amplifiers show thatits performance depends critically on the electron beamenergy spread [6, 7, 8]. More recently, Neil and Freund[9] have studied a distributed optical klystron configuration using the LCLS parameters. Based on the FEL amplifier simulations that start with a coherent seed, they pointout that the performance of the optical klystron for shortwavelength FELs is very sensitive to the exact slippage of∗ Electronic address:

ding@slac.stanford.edu. On leave from IHIP,
Peking University, Beijing, China.
† Electronic address: zrh@slac.stanford.edu.
‡ Current address: G-20, ADL Building, Raja Ramanna Centre for Advanced Technology, Indore-452013, INDIA.

The Angstrom Challenge

the electron beam relative to the radiation in the dispersive
section. Thus, the magnetic fields of the chicane must be
carefully designed and controlled to very high precision.
Motivated by the very small uncorrelated energy spreadof the electron beam that has been measured in a photocathode RF gun [10], we study the possible optical klystronenhancement to SASE x-ray FELs. We show that a SASE
optical klystron is not sensitive to the relative phase of theelectron beam to the radiation as long as the electron slippage length in the dispersive section is much longer thanthe coherence length of the radiation. Based on extensive
SASE simulations, we illustrate the gain enhancement of
the optical klystron to the LCLS and a compact x-ray FEL
scheme.

ONE-DIMENSIONAL ANALYSIS
In this section, we analyze an optical klystron configuration with a magnetic chicane between two high-gain FEL
undulators and extend the previous theoretical treatments[6, 7, 8] to the high-gain SASE operating mode. A detailed
description may be found in [11].
A magnetic chicane introduces an energy-dependent longitudinal delay of the electron relative to the radiation,
which can be expressed as a change of the radiation phase“seen” by the electron:Δθ = −

kr R56+ kr R56 δ
2(1)

Here λr = 2π/kr = 2πc/ωr is the FEL resonant wavelength, R56 is the momentum compaction of the chicane,and δ = (γ − γ0 )/γ0 is the relative energy deviation. The
first term in Eq. (1) describes the overall phase slippage between the FEL radiation and the reference electron having
the energy γ 0 mc2 , and the second term describes the relative phase change for an electron with a slightly different
energy. Following the one-dimensional (1D) theory of Kim[8] but keep the overall phase slippage, we write down the
optical klystron (OK) enhancement factor to the radiation
field Eν at the scaled frequency ν = ω/ω r :EνOKEνno OK(ξ)/(dξ) −iρkr νR56 ξ ikr νR56 /2ee
1 − dξ dV(μ−ξ)
2
=

V (ξ)
1 + 2 dξ (μ−ξ)3R(ν) ≡(2)

where ξ = δ/ρ is the normalized energy variable, ρ is the
FEL Pierce parameter [12], μ is the complex growth √rate ofthe radiation field in each undulator, μ = (−1 + i 3)/2
for a beam with a vanishing energy spread, and V (ξ) is the29Proceedings of FEL 2006, BESSY, Berlin, Germany

energy distribution of the electron beam with the normalization V (ξ)dξ = 1.
The first term in the numerator of Eq.(2) represents thecontribution from the radiation in the first undulator, while
the second term in the numerator represents the contribution of the microbunched electron beam. For a seeded FEL
with ν = 1, kr R56 /2 = 2πn(n = 1, 2, 3, . . .) yields anearly matched phase (i.e., constructive interference between two terms). The optical klystron is then optimized
for a matched phase. However, in the hard x-ray wavelength range, changing R 56 of the chicane by a fractionof 1 Angstrom can result in a complete phase mismatch.
Thus, there can be large fluctuations in the radiation power
due to small fluctuations in the magnetic fields as observedin Ref. [9]. Even when the magnetic fields are held constant, a small energy jitter (on the order of 10 −4 ) can also
mismatch the phase.
Nevertheless, SASE FELs start from shot noise and havea relatively wide bandwidth. For a given value of R 56 ,the phase may be mismatched for one particular wavelength but may be properly matched for another wavelength
within the SASE bandwidth. Thus, we should integrate
over the SASE spectrum S(ν) to obtain the optical klystronpower gain factor as:2
G = dν|R(ν)| S(ν)(3)
For an electron beam with a Gaussian energy distributionof rms width σδ  ρ (i.e., σξ  1), we can integrate Eq.
(1) over energy and Eq. (3) over frequency (assuming a
Gaussian average SASE spectrum) to obtain



√
1
D2 σξ 22
2
2
G=
5 + D exp(−D σξ ) + 2 3Dexp −
9
2


 

√
D
−D2 σξ 2cos(4)+ 4 + 3Dexp
2
2ρ

 



D
−D2 σν 2−D2 σξ 2sinexp− Dexp22ρ
8ρ2
where D = kr R56 ρ. The power gain factor G as a functionof the chicane strength R 56 is shown in Fig. 1 for two typical values of the rms energy spread σ δ , assuming a typicalrms SASE bandwidth σ ν = ρ.
When R56 is very small, the optical klystron operates asa phase shifter, and the FEL power is oscillatory dependingon the relative phase between the radiation and the electron
beam. As kr R56 σδ → 1 , the optical klystron gain peaks
and starts to decay exponentially due to the smearing effectof the intrinsic energy spread. Thus, the phase matching
is no longer important when the optical klystron is near its
peak performance.
A simple physical picture emerges in the time domain.
The path length difference between the SASE radiation andthe electron beam passing the dispersive section is about
R56 /2 ≈ 1/(2kr σδ ) = λr /(4πσδ ) at the optimal chicane

30Power gain factor

MOBAU04ΣΔ  0.1
0.1Ρ

64
ΣΔ  0.2
0.2Ρ

2

0
0

0.5

1
kr R56 ΣΔ

1.5

2

Figure 1: (color) 1D power gain factor with relative energy
spread σδ = 0.1ρ (red line) and σ δ = 0.2ρ (blue line)
setting. Since the typical SASE coherence length is on theorder of λr /(4πρ) [13, 14], it is much smaller than the path
length difference introduced by the chicane when the beamenergy spread σ δ  ρ (a necessary condition for the operation of the high-gain optical klystron). Therefore, there isno place for the electron beam to match the radiation phase
after the beam is slipped from the SASE radiation morethan a few temporal spikes. The radiation power averaged
over many statistically independent spikes is then not sensitive to the exact slippage introduced by the chicane.

UNCORRELATED ENERGY SPREAD
Since the uncorrelated energy spread plays a crucial role
for the gain enhancement of the optical klystron, we analyze here two main sources of energy spread. One is fromthe gun and the linac, which forms the initial energy spreadat the entrance of the FEL undulator; while the other is thequantum diffusion due to spontaneous radiation along theundulator, which leads to an increase of energy spread after
the electron beam is injected into the undulator. The uncorrelated energy spread of electron beams generated froma photocathode rf gun can be extremely small, at an rms
value of 3 to 4 keV from both measurements [10] and simulations. Nevertheless, a microbunching instability driven
by longitudinal space charge and coherent synchrotron radiation in the accelerator system may be large enough tosignificantly degrade the beam qualities including the energy spread [15, 16]. This microbunching instability occurs
at much longer wavelengths than the FEL microbunching
and requires much larger R56 (from bunch compressor chicanes) than the optical klystron chicanes. To maintain arelatively small energy spread after compression and acceleration, a laser heater [15, 16] will be used in the LCLS
injector to increase the rms energy spread from 3 to 40 keV.
After a total compression factor of about 30, the slice rms
energy spread at the undulator entrance can be controlled
to 1 × 10−4 at 14 GeV, which is tolerable for the SASE
FEL at 1.5 Å. However, considering the gain enhancementof the optical klystron (see Fig.1), a smaller energy spread(e.g., 5 × 10−5 or 0.1ρ) is desirable. This may be achiev-

The Angstrom ChallengeProceedings of FEL 2006, BESSY, Berlin, Germany

THREE DIMENSIONAL SIMULATIONS
Three-dimensional (3D) simulation code Genesis 1.3[18] is used to explore the LCLS gain enhancement witha distributed optical klystron configuration for two different radiation wavelengths of 1.5 Å and 1.0 Å and a very
compact x-ray FEL at 1.5 Å.
We place four 4-dipole chicanes in the first four long
breaks between LCLS undulator sections (at 12, 24, 36,
and 48 m) to form a distributed optical klystron configuration. For each chicane, the optimal gain enhancement
is obtained by scanning the chicane dipole magnetic fieldstrength. Two initial rms energy spread values of 1 × 10 −5
and 5 × 10−5 at the entrance of the undulator are used inthe 3D simulations. While we consider the energy spreadof 5 × 10−5 may be achievable in the LCLS with a reasonably smooth drive-laser profile or with the low-charge option [19], the energy spread of 1 × 10 −5 requires to switch
off the laser heater completely and is probably not allowedby the microbunching instability in the linac. It is still included in the simulations in order to study the best possible
optical klystron performance and the influence of spontaneous energy diffusion in the undulator.
Fig. 2 shows the FEL power gain along the undulator
with and without optical klystrons at the resonant wavelength of 1.5 Å for K = 3.5 (the current LCLS design parameters), with an electron peak current of 3.4kA and normalized rms emittance of 1.2 μm. The saturation lengthis shortened by 13 m using these optical klystrons with an
initial energy spread of 5 × 10 −5 and R56 of the chicanes ataround 0.25μ m (with a small variation for each chicane).
Note that a 10% variation of the chicane R 56 values does
not make a visible difference for the FEL output power.
To allow for the LCLS to reach 1.0 Å without increasing
the beam energy, the undulator gap may be increased by
2 mm to reduce the undulator parameter to K= 2.7. The
3D simulation results are presented in Fig. 3, using a peakcurrent of 3.4kA and normalized rms emittance of 1.2 μm.
Without any optical klystron, the nominal LCLS beam cannot reach SASE saturation at this wavelength. With theaddition of four optical klystrons as described here, the sat-

The Angstrom Challenge

10

10

9

power [W]

10

8

10

7

10

6

10

0

20

40

60

80

100

120

z [m]

Figure 2: (color) SASE FEL power along the undulator
without any optical klystron (blue solid curve), and with 4
optical klystrons for the initial rms energy spread of 1 ×
10−5 (magenta dashed curve) and 5 × 10 −5 (green dottedcurve). The FEL wavelength is 1.5 Å, and the undulator
parameter K = 3.5.
10

10

9

10

power [W]able by dropping the heater-induced energy spread to 20
keV at the expense of the increased microbunching instability gain. For a smooth enough photocathode drive laser
profile, this higher instability gain may still be tolerable
after acceleration and bunch compression. Thus, the final
slice energy spread at the undulator entrance may be kept
at 5 × 10−5 for the LCLS.
The energy diffusion due to spontaneous radiation along
the undulator was discussed by Saldin et al [17]. This energy diffusion rate increases with γ 4 and K 3 for K 2  1.
For the LCLS at λr = 1.5 Å and K = 3.5, the rms energy
spread increases from initial value of 5×10 −5 to 1×10−4at
the undulator position of 40 m due to the spontaneous radiation. We will include this effect in the FEL simulations to
be discussed below.

MOBAU04

8

10

7

10

6

10

0

20

40

60

80

100

120

z [m]

Figure 3: (color) SASE FEL power along the undulator
without any optical klystron (blue solid curve), and with
4 optical klystrons for the rms energy spread of 1 × 10 −5(magenta dashed curve) and 5 × 10 −5 (green dotted curve).
The FEL wavelength is 1.0 Å, and the undulator parameter
K = 2.7.
uration distance is shortened by about 26 m and is wellwithin the LCLS total undulator length. At this K value
and using a lower beam energy (11.0 GeV), simulations
also show the FEL at 1.5 Å approximately save 25 m ofsaturation length compared to that without any optical klystron.
It is clear from these numerical examples that a simultaneous reduction in beam energy and undulator parameterfor the same radiation wavelength is beneficial for the optical klystron enhancement, where the energy diffusion due

31MOBAU04

Proceedings of FEL 2006, BESSY, Berlin, Germany

910

power [W]

8

10

7

10

6

10

0

20

40

60

80

z [m]

Figure 4: (color) SASE FEL power along the undulator at apeak current of 2kA without any optical klystron (blue solid
curve) and with 4 optical klystrons (magenta dashed curve),
and at peak current of 3kA without any optical klystron(green dotted curve). The FEL wavelength is 1.5 Å and theundulator parameter K = 1.3.

distributed optical klystron configuration show significant
gain enhancement if the slice energy spread at the undulator entrance can be controlled to a very small level. The
improved performance can be used to obtain the FEL saturation at shorter x-ray wavelengths for a fixed undulator
length or to relax the stringent requirement on the beamemittance. The exploration of optical klystrons in a very
compact x-ray FEL also indicates promising results. Therefore, we think that the optical klystron configuration can be
an easy ”add-on” to SASE x-ray FELs provided that electron beams with very small energy spreads are obtainable
at the final beam energy.
We thank J. Wu and S. Reiche for useful discussions, J.
Galayda and R. Ruth for their encouragement on this work.
This work was supported by Department of Energy Contracts No. DE-AC02-76SF00515.

REFERENCES[1] Linac Coherent Light Source (LCLS) Conceptual Design
Report, SLAC Report No. SLAC-R-593, 2002.
[2] Technical Design Report, DESY TESLA-FEL Report,
2002.
[3] SCSS X-FEL conceptual design report, RIKEN, 2002.

to spontaneous radiation in the undulator is much reduced.
Inspired by the Spring-8 Compact SASE Source (SCSS)
design [3], we study the possibility of using a relatively
low energy electron beam together with a short-period undulator to drive a compact x-ray FEL with the aid of the
distributed optical klystrons. A 1.5-cm period in-vacuum
undulator with K = 1.3 is used according to the design
parameters in SCSS. To produce 1.5- Å FEL radiation, thenecessary electron energy is about 5 GeV. Rather than astandard peak current of 3 kA as described in Ref. [3],we assume a lower peak current of 2 kA and an rms energy spread of 100 keV (or 2 × 10 −5 ) at the undulator entrance. A smaller peak current allows for a smaller energy
spread and may also help reduce the microbunching instability gain in the accelerator, as well as any wakefield effectin the small gap, in-vacuum undulator. Fig. 4 shows thesimulation results for the SASE mode without any optical
klystron (for both 3-kA and 2-kA bunches) and with four
optical klystrons (for a 2-kA bunch). The latter saturates ataround 50 m of the undulator distance, which is still about
10 m shorter than the higher-current case without any optical klystron.

SUMMARY
The small, experimentally measured uncorrelated energy
spread from RF guns offers the opportunity to consider
applications of optical klystrons in x-ray FELs. In contrast to a seeded FEL, our study shows that the optical klystron gain is not sensitive to the relative phase between the
SASE radiation and the electron beam, and that the radiation power is very stable with a relatively large tuning range
of optical klystrons. 3D simulations of the LCLS with a32[4] N.A. Vinokurov and A.N. Skrinsky, Preprint of INP 77-59,
Novosibirsk, (1977).
[5] Y. K. Wu et al., Phys. Rev. Lett. 96, 224801 (2006).
[6] R. Bonifacio, R. Corsini, and P. Pierini, Phys. Rev. A 45,
4091 (1992).
[7] N.A. Vinokurov, Nucl. Instrum. Methods Phys. Res. A 375,
264 (1996).
[8] K.J. Kim, Nucl. Instrum. Methods Phys. Res. A 407, 126(1998).
[9] G.R. Neil and H.P. Freund, Nucl. Instrum. Methods Phys.
Res. Sec. A 475, 381 (2001).
[10] M. Huning and H. Schlarb, in Proceedings of the 2003 Particle Accelerator Conference, Portland, 2074 (2003).
[11] Y. Ding, P. Emma, Z. Huang, V. Kummar, Phys. Rev ST
Accel. Beams 9, 070702 (2006).
[12] R. Bonifacio, C. Pellegrini, and L.M. Narducci, Opt. Commun. 50, 373 (1984).
[13] R. Bonifacio, L. De Salvo, P. Pierini, N. Piovella, and C.
Pellegrini, Phys. Rev. Lett. 73, 70 (1994).
[14] E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov, Opt.
Commun. 148, 383 (1998).
[15] E. Saldin, E. Schneidmiller, and M. Yurkov, TESLA-FEL2003-02, DESY (2003).
[16] Z. Huang et al., Phys. Rev. ST Accel. Beams 7, 074401(2004).
[17] E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov, Nucl. Instrum. Methods Phys. Res. A 381, 545 (1996).
[18] S. Reiche, Nucl. Instrum. Methods Phys. Res. A 429, 243(1999).
[19] P. Emma et al., the Proceedings of 2005 Particle Accelerator
Conference, Tennessee, 344, (2005).

The Angstrom ChallengeProceedings of FEL 2006, BESSY, Berlin, Germany

MOBAU05

STATUS OF JAPANESE XFEL PROJECTAND SCSS TEST ACCELERATOR
Tsumoru Shintake# and SCSS TeamRIKEN/JASRI/SPring-8, Hyogo 679-5148 Japan.
Abstract
On 20 June, the first lasing has been observed at 49 nm
in SCSS test accelerator, which is prototype machine forJapanese XFEL project. A challenging approach is
employed in injector system: a low density electron beam
is generated from 500 kV gun using thermionic cathode,followed by velocity bunch compression by factor of afew 100 times, and magnetic chicane bunch compression.
The injector created high quality and high density
electron bunch, whose measured emittance was 3π.mm.mrad normalized with 800 A peak current and 1
psec pulse width or less. When we firstly closed the gap
in one undulator in 15th June, we observed the SASE
signal at 49 nm. Using two undulators, the signal
amplification gain reached 105, which is close to thesaturation level. The average radiation energy is 1 microJ/pulse at moment, we need more beam tuning.
The XFEL project aiming at generating 1 Å coherent
intense X-ray laser based on SASE using 8 GeV normalconducting accelerator has been funded. The constructionis scheduled 2006-2010, and beam operation will start in2011.

INTRODUCTIONSCSS project has started in 2001 [1]. Unique
combination of three key technologies: the in-vacuum
short period undulator, the C-band high gradientaccelerator and low emittance injector using thermionicelectron source make possible to realize SASE-FEL at 1
Å within available site length at SPring-8 less than 800 m
as shown in Fig. 1. It was named as SCSS: SPring-8
Compact SASE Source because of this reason. From yearof 2001, we have been carrying out R&D for key
components: the electron gun, injector, C-band klystron
modulator with oil-filled compact design, high resolution
beam position monitor, digital rf signal processing system,
etc [2]. In order to check performance of developed
hardware components and verify system performance,
especially the low emittance electron injector, weconstructed prototype accelerator for XFEL in 2004-2005
as shown in Fig. 2. The tunnel length is 60 m long, themaximum electron beam energy is 250 MeV, the shortest
lasing wavelength is around 50 nm. From May 2006, westarted dedicated beam tuning to demonstrate first lasing.
In 2006, the Japanese MEXT: Ministry of Education,
Culture, Sports, Science and Technology has decided
construction of XFEL at SPring-8 site. The project isaiming at generating 1 Å coherent intense X-ray laser,which is based on SASE using 8 GeV normal-conducting
accelerator. Figure 2 shows the computer image of the
facility, the XFEL will be constructed right next to the 1
km beam line. The construction is scheduled 2006-2010.
One big benefit to have XFEL at SPring-8 site is toshare human resources and sample preparation facilities
in the existing 8 GeV synchrotron light source.

CHOICE OF ACCELERATORTECHNOLOGY
We have decided to use normal conducting linear
accelerator technology at C-band frequency (5712 MHz).
It is “warm” technology, not super conducting “cold”
technology. The reason why we chose this technology is(1)
Since C-band accelerator can generate highFig. 1: The XFEL will be build at SPring-8 site.
____________________________________________#

shintake@spring8.or.jp

The Angstrom Challenge

Fig. 2: Tunnel view in SCSS test accelerator.
33

MOBAU05(2)

Proceedings of FEL 2006, BESSY, Berlin, Germany

gradient, as high as 35 MV/m, with reasonable
cost. Technology is available right now.
Pulse repetition frequency of C-band accelerator
is limited to 60 pps maximum, and average flux
becomes quite lower (about 1/100 times) thanthe case of super conducting machine. The
special feature of XFEL radiation is extremely
high peak power (~ 2 GW) and short pulse
duration (~30 femot-sec), and most of allscientific case to make use these features does
not request high average flux. The existing
SPring-8 3rd generation light source provides
high average flux, thus XFEL and SPring-8 arecomplementary facilities in the same site.

CHOICE OF ELECTRON SOURCEThe SASE-FEL at 1 Å wavelength region requires highquality electron beam of extreme parameter: peak current> 2 kA, low slice emittance ~ 1 π.mm.mrad, and low slice
energy spread < 10-4. Additionally, it requires fairly longundulator line, near 100 m long, where the beam
trajectory has to be guided in a straight line within small
error < 10 μm. In this alignment, we use high resolution
e-beam position monitors, and relay on beam-basedalignment. To perform this alignment, the electron beam
has to be very stable, and also the beam hallow
component and dark-current must be negligibly small(clean beam).
The transverse electron beam size at the undulator
section is order of 30 μm, from this beam the X-ray isradiated with diffraction limited condition, thus the X-ray
beam spot is also quite small, which is order of 100 μm at
the sample located 30 m or 100 m downstream from theundulator. Pointing of the radiated X-ray beam follows ebeam trajectory, therefore, e-beam trajectory angle has tobe fairly stable, such as, 3 μrad, and otherwise X-ray does
not hit small samples.
In order to make such a stable and clean beam, first ofall, the initial condition of electron beam trajectory, or theemission condition of the electron from the source has tobe very stable. One candidate to meet this requirement is
the thermionic cathode.
The LaB6 or CeB6 have been widely used in thescanning electron microscope, because of its highbrightness and superior performance of quick recovery
from contaminations [3]. Since they operate at hightemperature near 1800 K, no any residual gases cancondensed on the cathode surface. Additionally, there isconstant rate of cathode material evaporation from thesurface, which provides continuous activation, and also
self-cleaning process. If we use a high quality single
crystal, a very flat surface is formed in a single atomic
layer after evaporation, which provides very uniform
emission density and ensures no emittance breakassociated with rough cathode surface or non-uniform
emission density sometimes observed in Ba-oxide
cathode materials.
34

It should be noted that the pin-shaped cathode iscommonly used in electron micro scope, since it provides
extremely high brightness, i.e., small emission area
provides small emittance while high current density,
which meets imaging optics in microscope. However, it
can emit fairly low current beam, typically less than 1 μA.
In contrast, the SASE-FEL requires a few Ampere beamfrom the cathode, thus we use a flat surface. We chose
CeB6 rather than LaB6, because of longer life time. At
1700 K operation temperature, expected lifetime is 20,000
hours for 100 μm material loss due to evaporation.
We use rod shape CeB6 of 3 mm in diameter as shownin Fig. 3. We extract 1 A beam via 10 MV/m acceleration
field in the gun (500 kV/5cm), which is in the temperature
limited condition. The theoretical normalized emittancedue to thermal motion at the cathode is 0.4 π.mm.mrad.
The emittance was carefully measured at the gun using
double slits, it was 1.1 π.mm.mrad including tailcomponent for 1 A beam current. Eliminating tailcomponents from the data, we estimated the net emittanceof core beam as 0.6 π.mm.mrad [3].

Fig. 3: CeB6 single crystal thermionic cathode for low
emittance electron source.

BUNCH COMPRESSION
In the X-ray FEL for 1 Å wavelength, very high peakcurrent is required for e-beam to obtain high SASE-FEL
gain. Nominal beam current value of 3 kA is required inour design. We can not generate such beam from any kindof electron sources, therefore we compress the bunch
length in longitudinal direction by means of velocity
bunching in injector and magnetic chicane bunch
compressor. We designed the compression factor as 20, 18,
8 in velocity bunching at injector, the first and second
bunch compression system, respectively. Big question is
how we maintain low emittance value from the gun to
undulator through these compressions.
In the injector and bunch compressors, if the following
conditions are satisfied, the slice emittance can beconserved.
(1) Radiation damping or excitation throughsynchrotron radiation is small.
The Angstrom ChallengeProceedings of FEL 2006, BESSY, Berlin, Germany

MOBAU05

EMITTANCE MEASUREMENTAt the injector end, the velocity
bunching
andchicanebunch
compression complete, where the beamenergy reaches to 50 MeV, bunch charge
is 0.25 nC and the bunch length is 1 psecor less, which depending on operation
condition,
specificallyphase&amplitude tuning of 238 MHz and 476
MHz cavities.
We measured projected emittanceright before the C-band accelerators,
using Q-scan method. By reversing
polarity of one of the Q-magnets toprovided strong focusing in X- and YFig. 4: SCSS prototype accelerator, two undulators of 15 mm pitch,
direction, and measured the minimum
250 MeV e-beam, generates VUV-radiation.
beam width. By varying focusing power,
the beam width response was measured(2) There is no highly nonlinear optics, which mix
as
Fig.
5
and
6.
We found the normalized projectedparticle in radial direction, resulting in non laminar
emittanceofaround3 π.mm.mrad for both X- and Yflow.
directions.
The
slice
emittance
was also measured at 50(3) There is no over-bunching process, which mixes
MeV
beam
dump,
it
was
2
π.mm.mrad, where theand overlaps two or more slice components frommeasurement
was
limitedbyspatialavailable resolutiondifferent z-positions.
ofprofilemonitor.
To satisfy above condition, we designed the injector
We repeated many measurements in this kind, always
system based on “adiabatic compression” scheme: the gun
with beam chopper generate 1 A x 1 nsec x 500 kV beam, observed emittance around 3~4 π.mm.mrad. This
then velocity modulation by 238 MHz sub-harmonic experimental data indicates that the velocity bunching inbuncher cavity, followed by velocity bunching along a our system does not largely deteriorate the projected
drift section, then the space charge effect becomes severe emittance for compression ratio exceeding 100 times. For
as raising peak current, then 476 MHz booster cavity more detail, refer the report by H. Tanaka [6].
accelerates beam energy to 1 MeV, relativistic effect
FIRST LASING EVENT
lowers the space charge effect, followed by velocity
bunching, and inject into the S-band standing wave
Two in-vacuum undulators were installed, whose
accelerator, and capture single bunch.
undulator period is 15 mm, minimum gap is 3.5 mm,
In order to test this challenging scheme, and check all nominal K value is 1.3 and one undulator length is 4.5 m.
hardware components developed in our R&D [4], we In the beam tuning, we firstly opened the gap to 20 mmconstructed prototype accelerator in 2004-2005 as shown and passed the e-beam through gap and transported into
in Fig. 2. Beam line layout is shown in Fig. 4. We use four the beam dump. We tuned the beam optics upstream ofC-band accelerating structures, 1.8 m long each, energy the undulator. We setup the optics, in coming betagain 32 MV/m maximum. With maximum beam energy matching and focusing Q-magnet in between twoof 250 MeV, the shortest wavelength of VUV-radiation at undulators.
50 nm can be obtained.

Fig. 5: Beam profile during Q-san emittancemeasurement. Transition radiation from Au coating of
optical mirror was monitored by CCD camera.
The Angstrom Challenge

Fig. 6: Beam width as a function of focusing power. At
beam energy 50 MeV, charge 0.25 nC, length < 1 psec.
35

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Fig. 7:Radiation spectrum at the lasing condition, 0.25 nC
per bunch and 250 MeV. Peak at 49 nm is the coherently
amplified signal (6000 times) from the spontaneous
undulator radiation (blue line).
th

On 15 June evening, we firstly closed the gap in the
upstream undulator, and measured radiation spectrum,
where the spectrum width was already quite narrow,peaked at 49 nm, and totally different from the natural
spontaneous radiation, as shown in Fig. 7. The spectrum
width is around 1% FWHM, which is much narrower than
the spontaneous undulator radiation, while it is dominatedby e-beam energy fluctuation, at moment.
As shown in Fig. 8, when we varied the bunch charge,
the lasing power drastically changed. This thresholdphenomenon indicates high FEL gain. The power has not
yet reached the saturation.
By varying K-value of undulator, response of the power
gain was measured. Comparing to numerical simulation
we determined the electron beam brightness as 270 ~ 310
A/(π.mm.mrad)2 in the undulator.

FROM TEST ACCELERATOR TO XFEL
To obtain enough FEL-gain at 1 Å, we need ten times
higher brightness than the test accelerator case, i.e., 3 kA
at 1 π.mm.mrad. This will be easily obtained by thesecond stage bunch compressor at high energy (designed
compression factor is x 8, at 1.8 GeV).
On the other hand, about the X-ray energy, we need
improvement. The lasing pulse energy in the test
accelerator is 1 micro-J/pulse average, which is about ten
times lower than theoretically predicted value for 0.25 nC
charge. This is partly due to the fact that the second
undulator field is not perfectly matched with requirement,
and may be also due to non-uniform charge distribution inelectron bunch [6]. While we do not have enough data to
determine amount of charge contributed to lasing, it may
be 10% or less.
In XFEL machine, to raise fraction of charge for lasing
and increase total charge, we improve injector design asfollows.
(1) Run the electron gun at 2 A beam current (twice
higher than test accelerator case). The cathodeand gun handle this beam without loosing cathodelifetime and breaking emittance.
36

Fig. 8: Peak output power v.s. bunch charge. Using photo
diode, peak height was detected from averaged pulses.
(2)

Use L-band accelerator instead of S-band at thebuncher cavity, which makes beam acceptance 8times larger. In the test accelerator, acceptance islimited upstream end of the S-band standingwave buncher. Lowering frequency twice, all
structure dimensions will scale twice larger,
resulting in larger acceptance in x, y, z-directions.
(3) Flat-topping cavities will be used in the injector.
Since we use rf-field to compress bunch, the nonlinear curve associated with cosine-function
creates non-uniform charge distribution after
bunching. Applying higher harmonic cavity, we
can obtain a linear response function. This
technique is well known as “flat-topping cavity”
in traditional cyclotrons.
With this improvement, we will be able to generatebunch to drive FEL with 1 nC charge, with emittance 1π.mm.mrad and with uniform charge distribution.

CONCLUSION & SCHEDULE
We measured the e-beam emittance and observed firstlasing in the SCSS prototype accelerator. From thisexperiment, superior performance of the thermionic gun
and injector system has been demonstrated.
Analysing the experimental data carefully, we refine
hardware design, and start XFEL construction this year.

REFERENCES[1] T. Shintake et al., "SPring-8 Compact SASE Source",
SPIE2001, San Diego, USA, June 2001.
[2] http://www-xfel.spring8.or.jp[3] http://www.feibeamtech.com[4] K. Togawa et al., "Emittance Measurerment on the
CeB6 Electron Gun for the SPring-8 Compact SASE
Source", FEL2004, Trieste Italy, August 2004.
[5] T. Shintake, Status of SCSS Project, 3rd Asian
Particle Accelerator Conference, APAC2004,
Gyeongju, Korea, March 2004.
[6] H. Tanaka et al., “Low Emittance Injector at SCSS”,
FEL2006 conference, Berlin, August, 2006.

The Angstrom ChallengeProceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH001

COHERENT HARMONIC GENERATION EXPERIMENT ON UVSOR-II
STORAGE RING
M. Labat, CEA, Saclay, France
G. Lambert, CEA, Saclay, France, RIKEN SPring-8 Harima, Hyogo, Japan
M.E. Couprie, Synchrotron Soleil, Saint-Aubin, France
D. Nutarelli, LAC, Orsay, France
M. Hosaka, A. Mochihashi, J. Yamazaki, M. Shimada, M. Katoh, IMS, Okazaki, Japan
Y. Takashima, Nagoya University, Nagoya, Japan
T. Hara, RIKEN SPring-8 Harima, Hyogo, Japan.
Abstract

experiment.

In the Coherent Harmonic Generation Free Electron
Laser configuration, an external seed signal, a commercial laser source, is focused inside the first undulator. Theinteraction between the electron beam and this seed leads
to a more coherent light emission. Such devices are very
promising for short wavelength operation with a rather
compact facility. Experiments have been performed on the
UVSOR-II Storage Ring (Okazaki, Japan) with electrons
stored at 600 MeV, and using a 2.5 mJ Ti:Sa laser at 800
nm wavelength, 1 kHz repetition rate, and 150 fs up to
2 ps pulse duration, allowing emission at 266 nm. This
third harmonic has been characterised versus various parameters. Optimizations have been realized on the electron beam and laser synchronisation. The dependency ofthe harmonic signal on the gain (undulator gap, magnetic
functions) has also been studied. Theory is compared toexperiment using analytical model. These encouraging results make UVSOR-II storage ring an active test facility for
Coherent Harmonic Generation scheme, as well as a potential VUV source for users experiments.

INTRODUCTION
Recent Free Electron Lasers aim at reducing the radiatedwavelength to the X-ray domain, the time duration to the
femto-second domain, and at improving the coherence ofthe source. FELs based on linear accelerators are mainly
experimenting SASE [1], HGHG, and seeded configurations. Coherent Harmonic Generation (CHG) is a seeded
FEL configuration based on storage ring [2, 3]. The seed
can be either the own spontaneous emission of the electrons
as demonstrated on DUKE [4] and ELETTRA [5] storagerings, or an external source [6] such as a commercial laser.
This paper presents the successful generation of the third
coherent harmonic of a Ti:Sa laser in USOR-II.
In the Coherent Harmonic Generation configuration, thelaser is focused in the modulator [7], and synchronized withthe circulating electron bunch. The electron beam is micro
bunched at fundamental and sub harmonic wavelengths ofthe seeded laser. The light emission of the electrons is thenenhanced in the radiator at the third harmonic of the seed,i.e. 266 nm. Figure 1 presents the general scheme of the

FEL Prize and New Lasing

Figure 1: Coherent Harmonic Generation scheme on a storage ring
The seeding laser used for the CHG experiment was initially optimized for Slicing and Coherent Synchrotron Radiation experiments (CSR) [8], requiring high repetition
rate (1 kHz) and short pulse duration (150 fs), and therefore
not perfectly adapted for generation of the third harmonic.
UVSOR-II facility can now provide coherent, short duration and intense light in the far infra red (using CSR) andin the VUV range (using CHG) simultaneously, using one
single high power laser. Figure 2 illustrates a burst of CSR
emission observed in CHG operation.

Figure 2: Oscilloscope trace of CSR signal detected by abolometer observed in CHG operation.
Throught out this paper, an analytical model for CHG
will be reminded, followed by a description of the components of the experiment. The first results and optimisationon the third harmonic are finally presented.

37

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Proceedings of FEL 2006, BESSY, Berlin, Germany

ANALYTICAL MODEL FOR CHG
In 1982, R. Coı̈sson and F. De Martini [9] proposed ananalytical model to describe the Coherent Harmonic Generation process in an optical klystron. The intensity of thelight emitted by a relativistic electron bunch in an optical
klystron can be expressed as the sum of an incoherent and acoherent term. The coherent term equals zero for randomly
distributed electronic phases. In the case of CHG process,and assuming that the energy modulation only occurs in thefirst undulator, the interaction between the electric field E L
and the electrons induces an additional energy spread given
by:eKN EL λ0(J0 (ξ) − J1 (ξ)),(1)Δγ =2γ 2 mc2
where J are Bessel functions, depending of ξ =K2
4(1+K 2 /2) . K is the undulator deflexion parameter, λ 0 the
spatial period, N the number of periods, c the velocity oflight, e the electrons charge, m their mass, and γ their normalized energy. This energy spread results into an additional phase difference at the exit of the dispersive section,equal at its maximum to: Δα = 4π(N + N d )Δγ. Nd isthe number of equivalent periods of the dispersive section.
The intensity of the coherent emission no longer averages
to zero, and is given by the following expression:
δWcoh
n2 e2 Ne2 fn2 Jn2 (nΔα) KN λ0 2 2=) An .
(
δwδΩ
16π0 cλ2Lγ(2)n is the harmonic number, N e the number of electrons in
the bunch, f n the modulation rate, λ L the seeded laser
wavelength, and:An = 1/2(Jn+1 (nξ) − Jn−1 (nξ)).

(3)

The intensity of the incoherent emission is given by:
n2 e 2 N e
KN λ0 2 2
δWincoh=) An .
(1 + fn )(2δwδΩ
16π0 cλLγ

Figure 3: UVSOR-II storage ring

Table 1: Characteristics of the electron beam on UVSOR-II
Storage Ring for CHG operation.
Parameter (Unit)
SymbolValue
Energy (MeV)E
600
Circumference of the Ring (m)C
53.2
Cavity voltage (kV)V RF
100
RF Frequency (MHz)
f RF
90.1
Harmonic numbernH
16
Number of bunches storednb
1
Period of revolution (ns)T0
178
Momentum compaction
α
0.028
Synchrotron frequency (kHz)fS
19.4
Current (mA)I
0 - 40Natural Energy spread
σγ
0.00034(4)This model, already used for ACO [2] and Super-ACO [3]storage rings configurations, allows apprehending Coherent Harmonic Generation process and its dependency toelectron beam and seeded laser parameters. In addition,
calculations performed before the experimental sessions
provided with reasonable expectations on the generation of
the third coherent harmonic with UVSOR-II storage ring,and its laser parameters.

CHARACTERISTICS OF THE
EXPERIMENTAL COMPONENTSElectron Beam
For CHG experiment, UVSOR-II [10] facility (see Figure 3) was used in single bunch mode. The characteristicsof the electron beam delivered are given in Table 1. Experiments have been performed with beam current up to
40 mA, since no beam instability occurs below this value.

38

The modulator and radiator of UVSOR-II’s optical klystron[11] are identical and made up of 9 periods of 11 cm, separated by a 33 cm long dispersive section.

Beam diagnostics
Four different diagnostics have been used to characterize
the output radiation of the radiator (which includes electron
beam radiations, and IR laser), and therefore the coherent
emission. For spectral selection, the light is sent to an interferometric filter (CVI-F25-265), centered at 266 nm with25 nm bandwidth. The detection of the UV light is thenperformed using a solar blind PhotoMultiplier (PM, Hamamatsu, R759). In order to observe the coherent emission
at 1 kHz, among incoherent emission at 5.6 MHz, the PM
signal is observed on an oscilloscope, triggered by the laser
timing system. A streak camera (Hamamatsu, C5680) has
also been used. It allows to follow the longitudinal distribution of the electron bunch, and to measure relative positionin the time domain between laser pulse and electron bunch.
The light was spectrally characterised using a spectrometerfor spontaneous emission, and a monochromator followedby the photomultiplier for the coherent emission.

FEL Prize and New LasingProceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH001

Seeding Laser

Alignment

The characteristics of the seeding laser system used are
given in Table 2. This system includes a mode-lockedtitanium-sapphire (Ti:Sa) laser oscillator (Coherent, Mira
900-F) and a regenerative amplifier (Coherent, Legend HE)
driven by a Q switched pump laser, which delivers high intense femto-second pulses. Those elements are shown in
Figure 4.

Spatial overlap is an other key step in Coherent Harmonic Generation. An accurate alignment of the IR laseron the electrons trajectory has to be performed in the modulator. The electronic orbit of the FEL oscillator at 800 nm
has been selected for this trajectory. Auto collimation wasthen used to mark the seeded laser path from the laser hutchthrough out the FEL cavity. Three periscopes made of two
flat mirrors at 45o incidence allowed the transport of the IR
and a 5 m long focal lens its focusing inside the modulator.
This allows to optimize the overlapping with the e-beamand to increase the local energy. Both beams have horizontal polarization. Figure 5 illustrates the experimental setup
for transport and alignment of the seeding laser.

Table 2: Seeded Laser characteristics
Parameter
Value
Unit
Wavelength
800
nm
Spectral width
12nm
Repetition rate
1
kHz
Pulse duration (Δt)
0.15 to 2
ps
Average Power (P L )1.8
WDiameter
11.5
mm
Gaussian quality factor
1.25
Polarization
Horizontal

Figure 5: Setup of the laser transport to the FEL cavity.

OBSERVATION OF THE THIRDCOHERENT HARMONIC
Figure 4: Photograph of the laser system used for CHG
experiment.

Synchronisation
The overlap in the modulator for the micro bunching of
the electronic distribution, requires a precise synchronisation of the laser pulse and the electron bunch, and therefore a specific timing system for UVSOR-II facility [12]organized as following. The mode-locked Ti:Sa laser is
synchronised with the RF signal (f RF ) of the storage ring.
In addition, the repetition frequency f Q of the Q switchedlaser is based on the sub-harmonics of the revolution frequency of the bunches f rev =fRF /nH =5.6 MHz, leading to
fQ =frev /5632=1kHz. To select and fix the electron bunchwith the laser pulse cuts, an RF bucket selector is used formaking the Q switching trigger signal. The timing of thelaser pulse within the bunch spacing time is adjusted usinga phase shifter modifying the phase of the RF signal. The
condition of synchronisation is observed using in first stagea photodiode, receiving both laser pulses and synchrotron
radiation (SR). More accurate tuning is further performed
using the streak camera, which temporal resolution reaches
10 ps.

FEL Prize and New Lasing

A picture of the oscilloscope screen is presented in
Figure 6, illustrating the output radiation of the undulators. Central peak corresponds to the radiation of the laser
heated electron bunch. The intensity at 266 nm is dramatically enhanced thanks to the coherent emission at the third
harmonic of the seeding laser.

Figure 6: Oscilloscope trace of of the optical klystron out
put radiation. Central peak corresponds to the laser heatedbunch emission, and edged peaks to unheated bunch emission. PL =1.78 W, Δt= 1.12 ps, I=4.29mA. Time scale: 40
ns/division.
Figure 7 shows the streak camera image of CHG signal. This diagnostic confirms the enhancement of the intensity at 266 nm radiated by the heated electron bunches (see39

MOPPH001

Proceedings of FEL 2006, BESSY, Berlin, Germany

bright blue spots). In addition, the vertical axis of the image
allows to evaluate the duration of the heated bunch radiation: it is much shorter than unheated one’s, and measurment of the pulse duration is limited by the streak camera
resolution. The temporal coherence achieved with Coherent Harmonic Generation allows to expect pulse durations
below 2 ps.

CONCLUSION
Using a 1 kHz Ti:Sa laser, a Coherent Harmonic Generation FEL configuration has been successfully set up at
UVSOR-II facility. Short (below 2 ps), UV (266 nm), coherent laser pulses are delivered. In addition, both CHG
and CSR can be operated in parallel, using the same laser
system and experimental setup: an important step in thedevelopment of the fourth generation light sources.
More Coherent Harmonic Generation experiments on
UVSOR-II are to be performed in order to study the influence of the seeding laser characteristics: energy, diameter, pulse duration, as well as shaping inside the modulator.
Observation of the fifth harmonic is also foreseen.

ACKNOWLEDGMENTS
Figure 7: Photograph of the streak camera image. The
bright spots correspond to laser heated bunch emission (coherent emission). Full scales are 85 ms for the horizontal
and 700 ps for the vertical axis.

We would like to thank all the UVSOR-II staff for its
help during experimental sessions. This work was supported by International Collaboration program of IMS.

REFERENCES[1] F. Ciocci et al., IEEE Jour. Quant. Elec. 31 (1995) 1242.

Once the Coherent Harmonic Generation systematic andreproducible, the harmonic radiation was studied as a function of various parameters.

[2] R. Prazeres, J.M. Ortega, C. Bazin, M. Bergher, M. Billardon, M.E. Couprie, M. Velgue and Y. Petroff, Nucl. Inst.
Meth. A 272 (1988) 68-72.

According to the analytical model previously mentioned,
the number of coherent photons produced is proportional to
the square of the number of electrons heated by the laser,
linearly related to the peak current, assuming that the electron bunch duration is much wider than the laser pulse duration (by two orders of magnitude). First results seem toconfirm the expected quadratic behaviour.

[3] R. Prazeres, P. Guyot-Sionnest, J. M. Ortega, D. Jaroszynski, M. Billardon, M. E. Couprie, M. Velghe and Y. Petroff,
Nucl. Inst. Meth. A 304 (1991) 72-76.

The third harmonic has then been studied versus synchronisation. Using a 3 mA beam current, the laser pulse
position in time was shifted back and forth by 200 ps
from its initial position: where maximum UV intensity isrecorded. Coherent emission could be detected over 360
ps, with total disapearing for delays longer than 200 ps,
giving an rms width of 70 ps. This result is in good agreement with the rms bunch length measured at this current:
85 ps. Indeed, since the coherent emission is linked to theelectronic density, maximum emission is obtained when theseeding laser heats the centre of the bunch, and a scan withthe laser pulse in the time domain gives back the longitudinal distribution of the bunch.

[7] N.A. Vinokurov and A.N. Skrinsky, Preprint 77-59, Nuclear
Physics Institute of Novossibirsk (1977).

The undulator gap has also been studied as a varying parameter. CHG process is based on the amplification by theradiator of the sub harmonics of the seeding laser wavelength. To be properly amplified, this sub harmonic wavelength must correspond to a resonant wavelength of the optical klystron, defined by the undulator parameter K, andtherefore by its gap. Consequently, a detuning of this parameter might kill the radiation at 266 nm. Indeed, CHG
emission is maximum for an undulator gap of 40.8 mm andthe signal vanishes for gaps of 39.7 and 42.5 mm.

40[4] V. Litvinenko, Nucl. Inst. Meth. A 507, 265 (2003).
[5] G. De Ninno, M. B. Danailov, B. Diviacco, M. Ferianis and
M. Trovo, FEL’04, August 2004, p. 237-240.
[6] P.L. Csonka, Part.accele. 8, 225 (1978).

[8] M. Katoh, M. Hosaka, S. Kimura, A. Mochihashi, M. Shimada, T. Takahashi, Y. Takashima and T. Hara, to be published in the Proceedings of EPAC’06, THPLS041.
[9] R. Coı̈sson, F. De Martini, Phys. of Quant. Electron., 9, p.
939, Addison-Wesley (1982).
[10] M. Katoh, M. Hosaka, A. Mochihashi, J. Yamazaki, K.
Hayashi,Y. Hori,T. Honda, K. Haga, Y. Takashima, T.
Koseki, S. Koda, H. Kitamura, T. Hara, T. Tanaka, AIP’04,
2004, (708) p. 49-52.
[11] H. Hama, K. Kimura, M. Hosaka, J. Yamazaki and T. Kinishita, Nucl. Instr. and Meth. A393 (1997) 23.
[12] A. Mochihashi, M. Hosaka, M. Katoh and Y. Takashima,
UVSOR ACTIVITY REPORT 2005 (2006).

FEL Prize and New LasingProceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH005

GENERATION REGIMES OF FEL WITH VOLUME DISTRIBUTEDFEEDBACK∗
K. Batrakov† , S. Sytova‡ , INP BSU, Minsk, Belarus.
Abstract
This paper discusses different generation regimes of Volume Free Electron Lasers (VFELs) which utilize Volume
distributed feedback (VDFB). Dependence of VFEL operation on VDFB parameters is studied.

ENERGY TRANSFER IN VDFB SYSTEMS
Let’s study energy exchange between electron beam andradiation in the system with VDFB. Electromagnetic fieldin this case can be expressed as

INTRODUCTIONVDFB significantly extends operation possibilities ofFree Electron Lasers (FELs). It was shown in [1] that properly parameters choice of VDFB geometry lowered down
the threshold current magnitude of generation. VDFB cansolve the problem of mode discrimination at great electromagnetic power generation in oversized systems. The
beam cross section in such systems significantly exceeds
wavelength. Large sizes of electron beam cross section allow to distribute power and to lower local load of system elements. However, standard oversized system suffers fromexcitation of great number of parasitic undesired modes.
As a result, the destructive interference takes place, the coherence of radiation degrades and the generation efficiency
significantly reduces. So, analysis of electron beam dynamics dependence on VDFB parameters is of great importance. Partly, threshold parameters of electron beam instability in VFEL can be investigated by using linear theory. For example, the first threshold point j 1 corresponds
to beginning of the electron beam instability. At this point
the first radiating mode appears. Instability stage corresponding to regenerative amplification is in the range ofparameters j1 < j < j2 when generating mode is already appeared, but the radiation gain of this mode is lessthan radiation losses of the coupled feedback mode. Suchsystem can amplify incident wave. Parameters at whichradiation gain becomes equal to absorption correspond to
the second threshold point. When magnitude of beam current exceeds the second threshold value, generation process occurs without incident wave. For current density jin the range j2 < j < j3 the beam instability in short period of time changes into the stationary nonlinear saturation
regime. If current exceeds the third threshold value j > j 3 ,the nonlinear stage becomes non-stationary. The thresholdcurrents mentioned above depend on parameters of VDFB.
So, variation of VDFB can change the type of generation.
For providing VFEL experiments and their interpretation itis necessary to have theoretical description and numericalsimulation of effects considered. Here some such theoretical results are presented.
∗ Worksupported by Belarus Foundation for Fundamental Research,
Grant F06R-101.
† batrakov@inp.minsk.by‡ sytova@inp.minsk.by

FEL Theory

E

=



aα exp {ikα r − iωt} {e + ..

α+ei si exp [iτi r] + ..} ,(1)

where τi are the set of reciprocal vectors, e i are unit polarization vectors, s i are coupling coefficients between waves,aα are mode amplitudes which are determined from initialand boundary conditions. Using the equation of electron
motion in the electromagnetic field and averaging over initial electron phases the following expression for mean electron energy can be obtained 2
e2 (ue)2kukΔγ = −−
L3∗ F,(2)
2m2 u3 c2 γ ωc2where L∗ is the length of interaction region,⎡
exp {i (νβ − να )} − 1∗
F = Im ⎣aα aβ+(νβ − να ) νβ2αβexp [−iνα ] − 1 exp [−iνα ] (iνα + 1) − 1,++να νβ2iνα2 νβνi = (ω − ki u)L∗ /u are parameters of detuning from synchronism.

Control of Emission Line Shape by VDFBGenerally in the case of n-wave VDFB the energy transfer (2) between electron and electromagnetic field depends
on n detuning parameters. This gives additional possibilities to regulate the shape of emission line in comparison
with one-wave synchronism case.
Shapes of one-wave and different two-wave synchronism lines is illustrated in Fig. 1. It is seen that corresponding selection of parameter a = ν 1 − ν2 increases thewidth of amplification region by two times (compare thecurves ”one-wave” and ”a=7”). Due to this fact, electron
beam will be synchronous with electromagnetic wave fora longer time. So, more energy is transferred to electromagnetic wave that raises the laser efficiency. On the other
hand emission line can be narrowed by properly choice of
detuning parameters.

41

MOPPH005

Proceedings of FEL 2006, BESSY, Berlin, Germany
F
0.2

0.1

-5

-10

a4

Ν1

5

a5
-0.1
a7
-0.2

a8
onewave

Figure 1: Emission line dependence on the relation between detuning parameters a = ν 1 − ν2 for one and two-wave
synchronism.

REGENERATIVE AMPLIFICATION(LINEAR STAGE)
Eigenmodes for two-wave VDFB are obtained from thedispersion equation [1]
2

2 2

2

kτ2 c2 − ω 2 ε0k c − ω ε0
(ω − ku)
2
2
(ue)
ωL
4
ω r =−
k 2 c2 − ω 2
γ

I
I0

−

τ

Representing solutions of (3) as k = k 0 + nδω/c, wherek0 satisfies to the condition ω − k0 u = 0 the following
boundary conditions for mode amplitudes a i can be written:ai = a,si ai exp {ikδi L} = b,
i

i

δi

i

=

0,

 ai
i

= 0.
δi2

=
where

2

2

γ0 |E0 | + γ1 |Eτ |=γ0 |a| + γ1 |b|
 γ c 3
16π 2 n20,2nu
−β (kχτ L∗ ) (Γth − Γ)
2

2

(6)




γ0 c 3 16π 2 n2nu
+ Imχ0 1 − β ± χ Imr
Γth =2
τ Imχ0−β (kχτ L∗ ) kL∗
2 2

Γ = π4γnωL 2 k 2 L2 χ ± √−β |χ | − γ −2 ·0τ∗ω· χ0 ±

f (y) = sin y
2(5)

The first and the second equalities in (5) correspond to thecontinuity of electromagnetic field at the input (z = 0) andthe output (z = L) of VDFB structure, a and b are amplitudes of incident waves. The third and the fourth equations

42=kτ2 c2 − ω 2 ε0 .

(3)Here kτ = k + τ , ε0 = 1 + χ0 , r = χτ χ−τ , χ0 andχτ are polarizabilities of periodical structure with VDFB
which appear in the expansion of permeability:ε (r, ω) = 1 +χτ exp {−iτ r} .
(4)

 ai

correspond to the density and current density continuity ofunperturbed at the input electron beam. Solving system(5) one can obtain the following expression for intensity ofoutput electromagnetic waves:√−β |χτ | f (y),(2y + πn) sin y − y(y + πn) cos y.
y 3 (y + πn)32

I0 = γ0 |E0 | + γ1 |Eτ | is the intensity of incident waves.
y = ν1 /2, β is diffraction asymmetry factor, γ 0 and γ1are diffraction cosines. Expression (6) is derived in the low
gain approximation.
It follows from (6) that I/I 0 > 1 when Γ >Imχ0 (1 − β ± Imr/ (χτ Imχ0 )) (j > j1 is the firstthreshold point) and the amplification process starts. Fig. 2

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH005II020∂E0 + γ ∂E0 + 1 lE − 1 χ E − 1 χ E
0∂ (ωt)∂ (kz) 2 0 2 1 1 2 2 2

15
10

 2π
= 2πjΦ/ω 0 2π−p8π 2 (exp(−iΘ(t, z, p)+5exp(−iΘ(t, z, −p))) dp,
2

4

6

8

10

Β

Figure 2: Dependence of regenerative amplification coefficient on asymmetry factor β of VDFB.

∂E1 + γ ∂E1 − 1 χ E + 1 l E −1∂ (ωt)∂ (kz) 2 −1 0 2 1 1(7)1
2 χ2−1 E2 = 0,

∂E2 + γ ∂E2 − 1 χ E − 1 χ E
2∂ (ωt)∂ (kz) 2 −2 0 2 1−2 1demonstrates amplification dependence on VDFB geometry factor β. So, VDFB can control amplification process.
When current reaches some critical value j > j 2 the oscillation regime develops. Dependence of the second threshold current on VDFB asymmetry is illustrated in Fig. 3.
It is seen that VDFB allows to control the second thresh-

Here li = kτ2i c2 − ω 2 ε0 /ω 2 . γ0 , γ1 , γ2 are three VDFB
cosines.
System (7) must be supplemented with equations for thephase dynamics:3d2 Θ(t, z, p)dΘ(t,z,p)= eΦ
·2
3 2 kz −
dz
dz
mγ ω

j2
200
180

·Re (E0 exp(iΘ(t, z, p)) ,160

dΘ(t, 0, p)= kz − ω/u,
dz

140
120
100
2

4

6

8

10

Β

Figure 3: Dependence of the second threshold current j 2
on asymmetry factor β of VDFB.
old current too. Regenerative amplification (j 1 < j < j2 )is stationary and can occur in linear or nonlinear regime
depending on magnitudes of I (nonlinear regime will be
discussed bellow). In contrary, oscillation regime has thenon-stationary character and the linear stage rapidly transfers to the nonlinear one. To study nonlinear regime thenumerical simulation of VFELs must be carried out.

NUMERICAL SIMULATION OF THE
SYSTEM WITH VDFBFor n-wave VDFB from Maxwell equations in the approximation of slow varied amplitudes the system of nequations for n strong coupled waves can be obtained Here
we restrict ourselves by considering three-wave VDFB.
The system for n-wave VDFB can be written by evident
generalization.
 So, using the field representation in theform E = τi ei Ei exp {ikτi r − ωt}, i = 0, 1, 2 we obtain the following nonlinear equations:

FEL Theory+ 12 l2 E2 = 0.

(8)
Θ(t, 0, p) = p.

In (8) it was proposed that the electron beam is synchronous with the wave E 0 only. The integral form ofbeam current in the right hand side of (7) is obtained byaveraging over the following initial phases of electrons in
the beam: entrance time of electron in interaction zone ωt 0
and transverse coordinate of entrance point in interaction
zone k⊥ r⊥ .
Equation (8) depends on these two initial phases only in
combination k⊥ r⊥ − ωt0 (that appears in initial condition
for phase at z = 0). Therefore, in the mean field approximation double integration over two initial phases can be reduced to the single integration. As the result, the averaged
current in right hand side of the first equation of (7) differsfrom expressions frequently used in literature (in which the 2πcurrent is used in the form 0 dΘ0 exp {−iΘ}).

Regimes of VFEL Generation (Nonlinear Stage)
VFEL dynamics simulated on the basis of the system(7) and (8) is illustrated in Fig. 4 - 7. In the Fig. 4 theregimes of regenerative amplification and stationary generation are presented. It follows from this Fig., that the regionof regenerative amplification is rather narrow. This region
j1 < j < j2 is marked by two dotted lines. Therefore,
the idea to control amplification by regulating VDFB parameter β (and other VDFB parameters) seems to be very
useful. Let’s note, that the region of regenerative amplification by corresponding choice of VDFB parameters can be

43

MOPPH005

Proceedings of FEL 2006, BESSY, Berlin, Germany

|E|

A

1E+3
1E+2
10
1
0.1
0.01
1E-3
1E-4
1E-5
1E-6
1E-7
1E-8
1E-9

|E|

B

4E+3

E00= 1

3E+3

2E+3

|E0|
|E1|
|E2|

E00= 0

300

400

500

600

j, A/cm

2

700

1E+3

800

900

0

Figure 4: Amplification and oscillation regimes for threewave VDFB. Vertical dotted lines (A and B) shows positions of the first and the second threshold currents.

|E|

2

0

1E+3

5E-8

1E-7

t, s

1.5E-72E-7

Figure 6: Chaotic oscillation regime.
6

4

IFT

increased for three-wave VDFB in comparison with twowave VDFB ([2]).
When electron beam current increases, generation remains stationary up to the third threshold current j 3 . Then
at j > j3 non-stationary periodic regime of generation
starts. Fig. 5 demonstrates temporal dynamics of generation in this region (j > j 3 ).

|E0|
|E1|
|E |

2

0

1200

0

100

w , arb. units

200

300

Figure 7: Fourier transform of E 0 corresponding to chaotic
generation in Fig. 6 .

800

400

|E0|
|E1|
|E |
2

0
0

5E-8

1E-7

t, ns

1.5E-72E-7

Figure 5: Current exceeds third threshold value (j > j 3 ).
Periodic regime of oscillation for three-wave VDFB.
Oscillations appear at discrete number of frequencies atfurther current increase.
At some current value dynamics becomes chaotic andthe regions with continuous frequency spectrum appears(Fig. 6 and Fig. 7).

between different regimes. In addition n-wave VDFB allows to discriminate parasitic modes at generation of great
power in large volume. First experiments with VFEL generation was presented in [3, 4] and the following papers.
So, VFEL has great future prospect.

REFERENCES[1] V. Baryshevsky, K. Batrakov, I. Dubovskaya, J. Phys. D. 24(1991) 1250.
[2] K. Batrakov, S. Sytova, Nonlinear Phenomena in Complex
Systems, 8 (2005) 359.
[3] V. Baryshevsky, K. Batrakov, A. Gurinovich et al., NIM 483A
(2002) 21.
[4] V. Baryshevsky,
K. Batrakov,
N. Belous et
al.,
LANL
archive,
physics/0409125(2004),
http://arxiv.org/pdf/physics/0409125, 3 p.

CONCLUSION
In the paper presented it was shown that VDFB allows
to regulate the generation regime. Changing VDFB parameters at given current value can transfer generation process

44

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH006

EXTRACTING INFORMATION FROM SMITH-PURCELL FELSIMULATIONS
J.T. Donohue, Centre d'Etudes Nucléaires de Bordeaux-Gradignan, BP 120, 33175 Gradignan,
FranceJ. Gardelle, CEA CESTA, BP 2, F-33114 Le Barp, France
Abstract
Simulations of coherent Smith-Purcell radiation using 2D
particle-in-cell codes have provided insight into the natureof the process, and have generally provided support to theviewpoint of the Vanderbilt University FEL group.
However, if one is interested in terahertz frequencies, theneed for small meshes and short time intervals makes thecalculations exceedingly long. In particular, the S-P
correlation between frequency and angle is only valid at
distances large compared to the grating size, and may not
be apparent if the simulation area is too small. With thehelp of the multipole expansion, we show how simulation
data obtained with a small area may be extended to anarea of arbitrary size. This enables us to confirm thepresence of coherent higher order S-P peaks at theappropriate angles. We also isolate the forward andbackward surface Floquet waves. Evidence for thepresence of unsuspected components is presented.

INTRODUCTION
In attempting to simulate Smith-Purcell (S-P) radiation
at terahertz frequencies with a 2D particle-in-cell code,
one is confronted with problems of time and memory, atleast if the simulation is performed on a PC. The reasonsare easy to understand. Typical wavelengths are hundredsof μ m, which means that mesh sizes must be tens of μ m.
The time step is tied to the mesh size Δ through stability
conditions, and is, typically Δ/c, where c denotes the
speed of light. Finally, the overall size of the simulation
area is determined by the experimental circumstances.
For example, the Dartmouth College experiment[1]using a
low energy continuous electron beam has a grating about
12.7 mm long, and we perform our simulation in an areaof approximately 20 mm μ 5 mm, with Δ = 10 μ m. To
follow the system through one ns takes about 10 hours of
calculation with the commercially available code we use,
MAGIC[2]. In contrast the MIT experiment using a 15
MeV pre-bunched beam[3](at 17.1 GHz) had a grating 10cm long, which means that our simulation area must be
considerably larger than for the Dartmouth set-up.
However, two ns are all that is needed to get a satisfactory
simulation, since the beam is already bunched. At FEL
2005,[4]we reported our first attempts to simulate coherent
S-P radiation in these two experiments. While we didfind some interesting results, we used an unrealisticallylarge current in the Dartmouth case, which led to copious
emission of radiation from the ends of the grating at a

FEL Theory

frequency less than any allowed S-P frequency. This
corresponded to the evanescent surface wave predicted by
the theory of Andrews and Brau (AB)[5] but it obscured
the true S-P signal that we sought. In the MIT simulation,
we found that there remained a substantial emission ofradiation even when we removed the grating.
Furthermore, although we observed up to 20 harmonics ofthe bunching frequency, we didn’t see the usual S-P
relation between wavelength and angle. This is given by
λ = L(1/ β − cosφ )/ n , where λ is the wavelength, L thegrating period, β the relative velocity (in a plane parallelto the grating and perpendicular to the direction of thegrooves), φ the angle of emission (with respect to thebeam direction), and the integer n denotes the order.
While this relation is true, it only holds precisely when
the radiation is observed at distances large compared toboth the wavelength and the grating size. Given theconstraints of small mesh size, it is impractical tosimulate in an area large enough to see the wavelengthangle correlation.
Another problem we encountered was the presence on
the grating surface of two distinct surface waves. One ofthese, according to the AB theory, is in resonance with theelectron beam, while the other, of the same frequency but
propagating in the opposite direction, is generated byreflection at the grating ends. It is of some interest to
isolate these two Floquet waves, in order to obtain a directverification of the AB theory, and to determine thereflection coefficient when such a wave reaches thegrating end. This coefficient may be used in a refinementof the AB theory proposed by Andrew, Boulware, Brau
and Jarvis[6]in order to estimate the start current needed to
produce coherent S-P radiation in the Dartmouth
experiment. In reference 6 an estimate of 50 A/m was
made, while Kumar and Kwang-Je Kim[7] obtained aslightly smaller value of 36.5 A/m.
In this paper we describe two methods we havedeveloped to address these problems. The first method
we call the Small BoxØBig Box transformation, since itallows us to simulate in a small area and extrapolate to amuch larger area, so as to see the S-P wavelength-angle
correlation. While the near-to-far-field transformation is
the subject of a chapter of Taflove’s monograph[8],our
simple method uses Finite Fourier Transforms (FFT) andfitting procedures readily available in such high-level
programs as Mathematica and MAPLE, and thus involves
relatively little effort on the part of the user. The second

45

MOPPH006

Proceedings of FEL 2006, BESSY, Berlin, Germany

method has been developed to extract from a simulation
the two oppositely moving Floquet evanescent waves,which are important only in the neighborhood of thegrating. Again, the FFT and fitting capacities ofMathematica or MAPLE may be used to execute the task.
In Section II we describe the Small BoxØBig Box
transformation as applied to a MIT simulation. In Section
III we show how to separate the Floquet components froma simulation of the Dartmouth set-up. The anomalies
observed in our fitting procedure reveal an unsuspected
presence of higher temporal harmonics in the field, as
well as incipient coherent S-P radiation. Our conclusions
are given in Section IV.

SMALL BOXÆBIG BOX
TRANSFORMATION
In a source-free half-plane region extending to infinity,
the magnetic field in the z-direction may be written as∞∞⎛ ωρ ⎞Bz (ρ , φ , t ) = ℜ ∫0 dωe −iωt ∑ sin (mφ )H m1 ⎜⎟bm (ω ) ,
⎝ c ⎠
m=1
where the standard Hankel functions H m1 are used and thecomplex quantities bm (ω ) are the coefficients of themultipole field. They may be written as∞π2
bm (ω ) =dteiωt ∫ dφ sin (mφ )Bz (ρ0 , φ , t ) .
∫0−∞⎛ ωρ ⎞
π 2 H m1 ⎜⎜ 0 ⎟⎟⎝ c ⎠The azimuthal component of the electric field (cgs units)
may then be written as∞∞′ ⎛ ωρ ⎞Eφ (ρ , φ , t ) = −ℜ ∫0 dωe −iωt ∑ i sin (mφ )H m1 ⎜⎟bm (ω )⎝ c ⎠m =1
The total energy/cm radiated across a semicircle of radiusρ is thendW ⎛ cρ ⎞ ∞=⎜⎟ dt Eφ (ρ , φ , t )Bz (ρ , φ , t )dz ⎝ 4π ⎠ ∫−∞which reduces, after some manipulations involving theWronskian, tobm (ω )
dW c ∞
dω ∑
=
,
∫
0
4
ω
dz
m =1
which is independent of the radius.
In the context of our simulation, we calculate
Bz (ρ 0 ,φk , t r ) , with φk = (2k − 1)π / 180, 1 ≤ k ≤ 90 and∞

22t r = t1 + (r − 1)T / N , 1 ≤ r ≤ N , where the time step T/N ischosen by MAGIC. Accordingly, we use FFT rather thancontinuous Fourier transforms, and we perform a FFT at
each of the 90 angles, obtaining~b (s, φ k ) = FFT(B z (ρ 0 , φ k , t r )) , where ω → 2π (s − 1) / T .
Then at fixed s, we write85 ~~b (s, φk ) = ∑ bm (s ) sin (mφk )
m=1

46

~
and we apply a fitting procedure to determine the bm (s )for 1 ≤ m ≤ 85 . Finally we introduce the normalized
multipole coefficients bˆm (s ) ,~bˆm (s ) = bm (s ) / H m1 (2π (s − 1)ρ 0 / cT ) .
We may now calculate the magnetic field and theazimuthal component of the electric field at any point in
the source-free region by taking the Inverse FFT of thesequence of sums
⎧ 85⎫
Bz (ρ ,φ , t ) = IFFT(⎨∑ bˆm (s )sin (mφ )H m1 (2π (s − 1)ρ / cT )⎬)
m
=
1
⎩
⎭
⎧ 85
⎫
′
Eφ (ρ ,φ , t ) = IFFT(⎨∑ − ibˆm (s )sin (mφ )H m1 (2π (s − 1)ρ / cT )⎬)⎩m=1⎭
It is often desirable to examine the fields in a given
frequency range, and this may be accomplished byintroducing a filter in the Inverse FFT. We should pointout that since the FFT assumes a periodic function, thetime behavior we obtain at an arbitrary point may violatecausality. However, an ad hoc translation in time allows
one to find the true pulse shape at the new radius.
The energy radiated during the interval of time T isgiven by (ergs/cm if bˆm (s ) is in Gauss)2⎞⎞dW ⎛ c 2T 2 ⎞ N ⎛ ⎛ 85 ˆ
= ⎜ 2 ⎟∑ ⎜⎜ ⎜ ∑ bm (s ) ⎟ / (s − 1)⎟⎟ .
dz ⎝ 4π N ⎠ s =2 ⎝ ⎝ m=1⎠⎠

To illustrate this procedure, we plot in Figure (1) our
simulated Bz (t ) (for the MIT set-up) vs. t at a distance 5.5
cm from the center of the grating, and at angle 89°, with
its FFT.
BHGL

f = 89°, r = 5.5 cm

120

B

10
80

5
0

40

-5

0.5

1

1.5

2

f HGHzL

tHnsL

100

200

300

Figure 1. Bz (t ) vs. t and its FFT, φ = 89°, ρ = 5.5cm.

After performing the operations indicated above, we
obtain the extrapolated function Bz (t ) vs. t at a distance 50
cm from the center, again with its FFT, which are shownin Figure (2).
BHGL

f = 89°, r = 50 cm

B

2

40

0

20

-2

1.5

2

2.5

3

tHnsL
3.5

f H GHz L
100

200

300

Figure 2. Bz (t ) vs. t and its FFT, φ = 89°, ρ = 50 cm.
The reconstructed signal is smaller than the original, as
expected, since the fields decrease asymptotically as ρ -1/2.
Even taking into account the overall reduction in size, thereconstructed FFT is quite different from that at small
radius. This must be attributed to the fact that for the

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

second harmonic, there is a broad S-P first order peak at
82°, close enough to our angle of 89° to favor thefrequency near 34 GHz.
To indicate how the small box Ø big box
transformation affects the angular distribution of energy,
we show in Figure (3) the energy radiated during our 2 ns
pulse as a function of angle for a band of frequencies
centered around the sixth harmonic, near 103 GHz.
d2Eêdzêdf Hergs êcmLr = 5.5 cm, band 103 GHz

500
400
300
200
100
45

90

fHdegL180

135

as free radiation. The magnetic field in the neighborhoodof the grating is then a sum of two Floquet evanescentwaves propagating in opposite directions, and one may
write,∞Bz (x, y, t ) = ℜ ∑ e −α y {B p ei ((k + pK )x −ωt ) + B′p ei ((− k − pK )x −ωt ) }pd2Eêdzêdf Hergs êcmL r = 50 cm, band 103 GHz
S-P order 1

500
400

2

300

3

200

4

5

6

100
45

90

135

fHdegL180

where α p =119.3 ergs/cm, calculated by numerical integration. Thisin good agreement with the direct formula for the energy
radiated in that band. Results similar to these wereobtained for the first 20 harmonics. The prominent peakat small angles (8° here) is not S-P radiation but isassociated with the appearance and disappearance of shortcurrent pulses, even in the absence of a grating.

ISOLATING FLOQUET WAVES
In the AB approach the electron beam interacts with acomponent of an evanescent Floquet wave. In theDartmouth configuration, the wave has a negative groupvelocity, and the mechanism is that of a Backward Wave
Oscillator. Upon reaching the end of the grating, thewave is partly reflected, and some of its energy is emitted

FEL TheoryF( k F + pK ) + (ω / c ) .
2

2

The reflected wave is not in resonance with the beam, andessentially traverses the grating without change, until it isalso reflected at the other end, again emitting radiation.
To better understand this, we have developed a simple
method for isolating the Floquet waves. We use the“range” command of MAGIC, which measures acomponent of the electromagnetic field along somestraight line in space (along the x-direction here), at a
fixed time. An example is shown in Figure (5).

BHGL

40
xHcmL

20
0
- 20
- 40
- 0.6- 0.4- 0.2 0 0.2 0.4 0.6

Figure 5. Bz vs. x at fixed t and y. Dartmouth Grating.
By performing three ranges separated by short timeintervals, obtaining the spatial FFTs and fitting the threecomplex amplitudes for each wave number k to anassumed form α k e −iωt + β k e iωt , we can empiricallydetermine the coefficients αk and βk. An FFT is shown in
500 B
400

kF

300

Figure 4. The reconstructed angular distribution ofenergy at 50 cm in a frequency band centered at 103 GHz.

F

p = −∞

Figure 3. The angular distribution of energy at 5.5 cm ina frequency band centered at 103 GHz.
For comparison we show in Figure (4) thereconstructed distribution of energy as predicted by oursmall box Ø big box transformation with ρ = 50 cm. The
angles at which coherent S-P radiation is expected in the
MIT experiment at this frequency are indicated. For both
distributions we find the same total energy radiated

MOPPH006

K+kF

B μ 20
2K-kF

2HK-kFL

3HK -kFL

K-kF

200

2K+kF

kH cm-1L

100
200

400

600

800

1000

Figure 6. FFT of signal in Figure 5.
Figure (6). The prominent peaks are indicated by red
arrows, and the right-hand side of the figure has been
multiplied by 20 to make details visible. The blue arrows
indicate second and third harmonics of K-kF, thecomponent resonant with the beam. Here the frequency ω
is known (2πf, with f = 432 GHz). By comparing with thegeneral expression for Bz, we see that the components of
the Forward Floquet wave have peaks at kF + pK, while
the Backward Floquet wave has support at pK-kF. If we
multiply the αk by a filter that includes only the peaks at
kF + pK, and perform the Inverse FFT, we obtain the47

MOPPH006

Proceedings of FEL 2006, BESSY, Berlin, Germany

Forward Floquet waves at each of the three instants.
Similarly, by filtering around pK-kF, we find the backward
wave, and both are shown in Figure (7).

BH GL

40

Fwd
Bkwd

20
0

xH cmL-20-40- 0.6 - 0.4 -0.2

0

0.2

0.4

0.6

Figure 7. Forward (blue) and backward (red) Floquet
waves extracted from signal in Figure 5.
It is clear from this figure that the forward Floquet wave
shows little or no growth across the grating, while thebackward wave shows considerable growth, indicating an
imaginary part of k of order 4 cm-1. We note also that at
both ends of the grating the ratio of the incident to thereflected wave is approximately 3:1.
As a check on our empirical method, which uses aleast-square method to fit all the FFT components, we
attempted to see whether the fit is adequate. This led to asomewhat serendipitous discovery that we now discuss.
If we defineΔBk (t ) = FFTk (t ) − α k e −iωt − β k e iωt ,the complex number that is a measure of the validity of
our fit, we may plot its absolute value as a function ofwave number. The results are shown in Figure (8). The
1.4 »DBHGL»
1.2
1

S-P 2,1
2,2

2w
3,3 3,1

3w
3,4

0.8
0.6
0.4

kHcm-1L

0.2
200

400

600

800

Figure 8. Discrepancy ΔB vs. wave number k.
major anomalies occur at 520 and 780 cm-1, which arejust the second and third harmonics, respectively, of theresonant wave number, 260 cm-1. They appear also in
Figure (6). Upon examining the data, we found that theseanomalies disappear if we fit using 2ω and 3ω instead of
ω in our fitting procedure. That means that there arecomponents of the form e im (( K −k )x−ωt ) , with m = 2, 3, etc.
Such components are readily found in the FFT analysis of
the current, and they follow from the non-linear nature of
the bunching phenomenon. By an argument based on
Ampère’s law, modulation of the current must appear as

modulation in the magnetic field, and that is what we see.
Aside from these two major anomalies, there appear to be
several smaller ones. We attribute these to the presence,in small amounts, of the coherent S-P signal
corresponding to various harmonics and orders. From theS-P relation and the fact that all coherent radiation will
occur at a multiple of the frequency of the evanescentwave, one may derive the following expression,k =mω / βc−2πn/ L ,where n denotes the order, m the harmonic, the period L is
173 μm, and ω =2π ×4.32×1011 s-1. Using it we havedrawn arrows to indicate the wave numbers associatedwith some pairs m, n. It must be noted that our FFT issymmetric, and peaks that should occur for negative kvalues are shown at positive values.

CONCLUSIONS
We have presented results concerning our attempts to
extract information from simulations of coherent SmithPurcell Radiation, using a 2-D PIC code. Two distinct
methods have been discussed. One permits results
obtained in a small area to be extended to a larger area.
In doing so, we see more clearly the coherent S-P
radiation produced in the MIT experiment with a highenergy pre-bunched beam. The second method involves
fitting the FFT data at three closely spaced times, in order
to separate the forward and backward Floquet surface
waves postulated in the approach of Andrews and Brau.
As a by-product, the presence of second and third
harmonics of the fundamental bunching component were
demonstrated, and evidence for tiny amounts of coherent
S-P radiation was provided.

REFERENCES[1] A. Bakhtyari, J. E. Walsh, and J. H. Brownell, Phys.
Rev. E 65, 066503 (2002).
[2] MAGIC, Mission Research Corporation.
[3] S.E. Corbly, A. S. Kesar, J. R. Sirigiri, and R. J.
Temkin, Phys. Rev. Lett. 94, 054803 (2005).
[4] JT. Donohue and J. Gardelle, Proceedings of the 2005
FEL Conference, Stanford,California USA p. 262(http://www.JACoW.org).
[5] H.L. Andrews and C.A. Brau, Phys. Rev. ST Accel.
Beams 7, 070701 (2004).
[6] H.L.Andrews, C. H. Boulware, C. A. Brau and J. D.
Jarvis, , Phys. Rev. ST Accel. Beams 8, 050703(2005).
[7] Vinit Kumar and Kwang-Je Kim, Phys. Rev. E 73,
026501 (2006).
[8] A.Taflove, Computational Electrodynamics, (Artech
House, Boston, 1995), p. 203.

F

48

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH007

SIMULATION OF SMITH-PURCELL FELS AT TERAHERTZFREQUENCIES
J.T. Donohue, Centre d'Etudes Nucléaires de Bordeaux-Gradignan, BP 120, 33175 Gradignan,
FranceJ. Gardelle, CEA CESTA, BP 2, 33114 Le Barp, France
Abstract
Our previous work on the 2D simulation of a coherent
Smith-Purcell FEL operating in the terahertz domain isextended to a systematic study of the dependence onvarious parameters. The important question of the starting
current required to produce coherent radiation isaddressed, and our new results are presented. As in ourprevious work we concentrate on two configurations, one
similar to the Dartmouth S-P FEL, with a low energy
continuous beam, and the other similar to the MIT
experiment that used a pre-bunched 15 MeV beam.

INTRODUCTIONAt FEL 2005[1]we reported on simulations of coherent
Smith-Purcell (S-P) radiation at terahertz (THz)frequencies using a two-dimensional (2D) particle-in-cellcode, MAGIC. Two quite different experimental set-ups
were considered; one similar to the long-running
Dartmouth College experiments initiated by Walsh[2],while the other was similar to the MIT experiment thatused a pre-bunched 15 MeV electron beam[3].The results
we presented were rather preliminary and a fuller accounthas recently appeared[4].We remind the reader of the S-P
relation, λ = L(1/ β − cosφ )/ n , where λ is the wavelength,
L the grating period, β the relative velocity (in a plane
parallel to the grating and perpendicular to the directionof the grooves), φ the angle of emission (with respect tothe beam direction), and the integer n denotes the order.
One of our aims was to verify the analytical model
proposed by Andrews and Brau[5](AB) and subsequently
extended by Andrews, Boulware, Brau and Jarvis[6]toexplain coherent Smith-Purcell radiation. Our results did
indeed support the viewpoint of Brau and co-workers, thatthe mechanism for coherent radiation is the bunching of
the initially continuous beam by an evanescent wave thatis significant only in the vicinity of the grating. The
frequency of this wave is always less than the minimum
allowed S-P frequency. The process is unstable in thesense that the wave bunches the beam, the beam drives
the wave and growth occurs, both in time and along thegrating. Our simulation of the Dartmouth set-up foundthat this is indeed what happens. In particular, thefrequency and axial wave number (in the first Brillouinzone) of the simulated grating wave were very close towhat the model predicts. Since the bunching is inherently
non-linear, once it becomes significant the current ismodulated at harmonics of the fundamental frequency,
and these may correspond to allowed S-P frequencies.

FEL Theory

The radiation emitted then shows both intrabunch (since
the bunches are small compared to a wavelength) andinterbunch (since the fields of all bunches over the grating
add up) coherence. Consequently, the coherent radiation
occurs only at integer multiples of the fundamental, andonly at the corresponding S-P angles. However, thesimulation also revealed a major unexpected effect,
namely the copious emission of radiation at thefundamental frequency. Indeed, this unforeseen radiation
made the direct observation of the S-P radiation quitedifficult. Our simulated grating has a finite length. Whenthe evanescent wave reaches the end of the grating, partof its energy is emitted as free radiation of the same
frequency, and part of it is reflected back in the opposite
direction. The result is that there are two evanescentwaves on the grating, which propagate with equal andopposite wave numbers. Only one of these waves isresonant with the electron beam, and since the beam-wave
instability is absolute in the Dartmouth configuration, it
displays growth both in space and time. The other
Floquet wave grows in time only (through reflections),
but not in space. In a companion paper we show how
both of these Floquet waves may be extracted from thesimulation data.
For the MIT experiment, since the beam was alreadybunched, the bunching mechanism referred to played norole, and the simulation was expected to bestraightforward.
However, the simulation failed todisplay unambiguous S-P radiation. In fact, there were
two distinct problems, first the emission of considerable
radiation even when no grating was present, and secondly,
the expected frequency-angle correlation was notapparent. The former has been understood to be aconsequence of standard electrodynamics. It is associatedwith the appearance and disappearance of a relativistic
short bunch of electrons. The latter was caused by the factthat the S-P relation is valid only at distances large
compared to the grating size. Since the MIT grating was
10 cm long, S-P radiation can be seen clearly only at
distances of order 40 cm or more from the center of thegrating. Since we are dealing with radiation whose
wavelength is a few hundred μ m, the mesh size in thesimulation must be kept on the order of tens of μ m.
Under such circumstances, the computing time andmemory needed become unreasonable, at least for a PCbased simulation. In the companion paper we outline a
simple method we call the Small Box→Big Box
transformation, which enables us to circumvent thisdifficulty. While techniques for passing from the near49

Proceedings of FEL 2006, BESSY, Berlin, Germany

zone fields to the far zone based on Green’s theorem arewell known[7],our method appears to work quite well. It
makes use of Finite Fourier Transforms (FFT) and fitting
tools available with symbolic manipulation programs
such as Mathematica or MAPLE.
Once thistransformation is performed, we see clearly the expected
coherent S-P radiation at a large number of angles andfrequencies.
Since the last FEL conference, other work on coherent
S-P radiation has appeared, notably by Dashi Li andcollaborators[8],who also use MAGIC for simulations, andby Kumar and Kwang-Je Kim[9]. In their simulations Li
and co-workers studied the effects both of a single shortbunch and a periodic train of such bunches passing over a
grating of the Dartmouth type. The former showed
intrabunch coherent S-P radiation, followed by theemptying of the evanescent wave from the grating after
the passage of the bunch. The latter illustrated interbunchcoherence, since the second harmonic of the imposed
bunch frequency was S-P allowed and indeed emerged at
the expected angle. The extensive analysis of Kumar and
Kim, based on the traditional approach of diffraction by
the grating of the incident electron’s field, yielded adispersion relation quite similar to that obtained byAndrews and Brau. The analysis included a treatment ofcoherent S-P radiation similar to that of a Backward Wave
Oscillator (BWO), for which a start current is known toexist. Using both numerical and analytical methods, they
estimated a start current (minimum current needed to
produce the instability) of 36.5 A/m for a sheet beam 10
μm above the grating. This is similar to the estimate of 50
A/m found in reference 6.
Our attempt to find the start current for the Dartmouth
configuration is discussed in the second Section, andsome results on our simulation of the MIT set-up arepresented in the third Section. Simulation parameters areshown in the Table 1.
Table 1. Parameters of the Simulations
Parameters
Dartmouth MIT
beam energy

35 keV

15 MeV

Current (peak for MIT) variable

25 kA/mBeam thickness

δ = 10 μm

1 mm

Beam-grating distancee = 10 μm

0.7 mmGrating period

L = 173 μm 1 cm

Max. wave number

K = 363 cm-1 2π cm-1

Grating groove depth

H = 100 μm echelette

Grating groove width

A = 62 μm

Number of periods

N = 7410

External magnetic field Bx = 2 T

0Mesh size

50

8.65 × 8̓ μm2 (100̓μm)2

START CURRENT FOR DARTMOUTHIn Figure (1) we show a contour map of the magnetic
field Bz in the area of our MAGIC simulation. The beam
appears as a red line, and one sees cylindrical waves ofwavelength ≈ 700 μm radiating from the grating ends.
This is the evanescent wave, predicted by AB.

y(mm)

MOPPH007x(mm)Figure 1. Contour map of Bz.
In contrast to our earlier simulations, we have raised thegrating slightly. This is more consistent with the physicalsituation, where the grating is not flush with a groundplane. Upon doing so, we found that the height of thegrating plays a significant role in the reflection at the endsof the grating. In the Dartmouth set-up the systembehaves like a BWO, with two Floquet waves proceedingin opposite directions. The backward wave has acomponent in resonance with the beam, and it displays an
absolute instability, with growth both in time and inspace. The forward wave shows no growth in space, butsince it is fed by reflection at the upstream end, it doesgrow in time. We found this to be the case in our earliest
simulations, with a very large current. In fact, moresophisticated analyses, such as those of references 6 and 9
point out that the boundary conditions at the grating ends
play an important role in determining the start current. In
our companion paper[10],we separate the two Floquet
waves, and we see that the forward wave is essentiallyconstant across the grating, while the backward wave
grows strongly in the negative x-direction. However, thiswas for a current of 175 A/m, which reached saturation inabout 1 ns. In order for the BWO mechanism to work,
the gain must be sufficient to allow the ratio of the
backward wave to forward wave be small at thedownstream end and large at the upstream end. The
greater the reflection the less is the gain needed to close
the loop, and in principle the smaller the starting current.
In order to estimate the start current, we monitor thevariation with time of the current at the middle of thegrating. We filter the signal, and then estimate the gain
by fitting a logarithmic plot of the summits. We also notethe time required to reach saturation, tsat, defined by the
first maximum of the bunched current. Finally we notethe ratio of the peak current at saturation to the direct
current, Isat/I. Once the details of the simulation havebeen fixed, such as mesh size, beam width, beam height
above grating, kinetic energy, we then repeat thesimulations for various currents. To our surprise, we
obtained the curves shown below.

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

MIT SIMULATION

tsat

Isat / I

Gain
10

5
12

2.0x1010

1.2x109

8.0x10at 50Ano saturationin 10 ns83Isat / I-1

Gain (s )4from 80 A to 95 A
no saturation in 10ns

2

t sat

10

1.6x109MOPPH007

41

4.0x10

0.0

0
40

60

80

100

120

140

160

180

200

220

I (A/m)Figure 2. Gain, tsat and Isat/I vs. current I.
In the shaded region running from 80 to 95 A/m, andincluding three runs at 80, 90 and 95 A/m, no instability
was observed, even for times of 10 ns. In contrast for
currents > 100 A/m, the system always saturated in just a
few ns. More astonishingly, at 75 and 76 A/m, the systemreached saturation. However, at 50 A/m, it again failed.
We are unable to understand these results, but clearly
more work is needed. As additional evidence, we show
the MAGIC phase space densities (kinetic energy-x) for
the 76, 95 and 100 A/m runs.

In our first simulation of the MIT experiment, we
encountered a major difficulty in trying to identify thecoherent S-P radiation that was produced. The beam
consisted of short pulses (1 ps) produced by a linear
accelerator functioning at 17.14 GHz. Consequently, theonly frequencies allowed are integer multiples of thatfrequency. Since the beam energy was 15 MeV, and thegrating period was 1 cm, it is straightforward to computethe frequencies predicted by the standard S-P relation. If
we keep only the first six orders, and concentrate on
angles in the forward direction, we find the curves shownin Figure (4). The harmonics are shown as horizontal
lines, and each intersection of any of them with any of thecurves marked “order” corresponds to coherent S-P
radiation at the angle shown. Clearly there are a great
number of possibilities, and for some angles like 49, 65
and 82 degrees, several frequencies may occur. The
problem of observing S-P radiation is thus quite complex.

300
16
250

14
12

f ( GHz )

200

36

10

Order
1
2
3
4
5
6

150

Kinetic Energy (keV)

100
35

50

8
6
4
2

0
0
34

20

40

60

80

φ (deg)Figure 4. Intersections of the harmonics of 17.14 GHzwith the first six S-P orders.

I = 100A ; t = 2ns
I = 95 A ; t = 10 ns
I = 76 A ; t = 4 ns

33

-8

-6

-4

-2

0

2

4

x (mm)

Figure 3. Phase space density plots in the Kinetic
Energy-x plane, for 76 (blue), 95 red and 100 (black)
A/m.
The oscillations correspond to an axial wave number of
260 cm-1, which is what the AB theory suggests. For the
76 and 100 A/m runs, the average energy losses areroughly 0.5 and 0.8 keV, respectively, while the red curveshows neither oscillation nor energy loss. Again, we canonly express our surprise at this result.

FEL Theory

The situation was complicated further when we foundthat even if we removed the grating, we still observed
substantial radiation. This was clearly not S-P radiation
but it was present in our simulation. As we indicated inreference 4, the radiation we observed without grating
may
becalculated
exactlyusingclassical
electrodynamics, at least for a sheet beam of infinitesimal
width. We show in Figure (5) the results of such a
calculation. The contour map of Bz in a 120 mm ×100 mmregion of the x-y plane bears a strong resemblance to theresults of our simulation without grating. A «plume» inwhich the magnetic field is mainly concentrated
accompanies each bunch. The tiny red dots visible
beneath each bunch indicate a large positive magnetic
field between the beam and the ground plane. This
component is an important contribution even when agrating is present, and no attempt to understand oursimulation can avoid taking it into account.

51

MOPPH007

Proceedings of FEL 2006, BESSY, Berlin, Germany

B
60
40

r = 50 cm, f = 65°
f HGHzL

20
100

200

300

Figure 7. FFT of Bz following extrapolation. Third, sixthand ninth harmonics are more apparent.
It is clear that the relative importance of the third, sixth,
ninth and twelfth harmonics, all of which are S-P allowed
at this angle, has increased.
Figure 5. Contour map of Bz following the predictionsof classical electrodynamics.
The area shown
corresponds to 12 cm in x, and 10 cm in the y direction.
In order to illustrate the difficulty of interpreting thesimulation directly, we show in Figure (6) the Finite
Fourier Transform (FFT) of Bz (t) as observed directly in
our simulation, which was made in a relatively small area,
12 × 6 cm2. The observation point is at 5.5 cm from thecenter of the grating, and placed at 65°. The mostprominent lines in the spectrum are the forth, sixth andeighth harmonics, but only the sixth is an S-P frequency
at this angle.

120 B
80

r = 5.5 cm, f = 65°40

f HGHzL
100

200

300

REFERENCES[1] J.T.Donohue and J. Gardelle, Proceedings of the 2005
FEL Conference, Stanford, California USA, p. 262(http://www.JACoW.org).
[2] A. Bakhtyari, J.E. Walsh, and J. H. Brownell, Phys.
Rev. E 65, 066503 (2002).
[3] S.E. Corbly, A. S. Kesar, J. R. Sirigiri, and R. J.
Temkin, Phys. Rev. Lett. 94, 054803 (2005).
[4] J.T. Donohue and J. Gardelle, Phys. Rev. ST Accel.
Beams 9, 060701 (2006).
[5] H.L. Andrews and C. A. Brau, Phys. Rev. ST Accel.
Beams 7, 070701 (2004).
[6] H.L. Andrews, C. H. Boulware, C. A. Brau and J. D.
Jarvis, , Phys. Rev. ST Accel. Beams 8, 050703(2005).
[7] A.Taflove, Computational Electrodynamics, (Artech
House, Boston, 1995), p. 203.
[8] Dashi Li, Z.Yang, K. Imasaki and Gun-sik Park, Phys.
Rev. ST Accel. Beams 9, 040701 (2006).
[9] Vinit Kumar and Kwang-Je Kim, Phys.Rev. E 73,
026501 (2006).
[10] J. T. Donohue and J. Gardelle, these Proceedings.

Figure 6. FFT of Bz at position indicated.
As outlined in reference 10, we have developed aprocedure for extrapolating the results of our simulation
to larger distances from the grating. Shown in Figure 7 isthe result of applying our procedure to the data obtainedin the small area simulation, after extrapolation to a larger
distance from the center, but at the same angle.

52

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH008

A BEAM SHAPER FOR THE OPTICAL BEAMLINE OF RF
PHOTOINJECTORS
G. Klemz#, I. Will, Max-Born-Institute, D-12489 Berlin, Germany.
Abstract
The paper reports on first results on beam shaper for thegeneration of a flat-top beam profile in the ultraviolett(UV). The shaper can be integrated into the opticalbeamline of the PITZ facility [1]. This will improve theefficiency of the optical beamline significantly.

INTRODUCTION
A high performance of SASE FELs requires a low
emittance of the electron bunches that emerge from thephotoinjector. This in turn can be favoured by irradiating
the cathode by a laser beam with a spatial and temporal
flat-top profile [2]. A simple way to illuminate thephotocathode with a uniform beam profile is to strongly
expand the laser beam with a telescope and select the very
central region of the magnified beam by means of a small“beam shaping aperture”. This method which is presently
implemented at PITZ, inherently gives rise to a large lossof the incident UV-laser power. At PITZ the transmission
amounts to approximately 20%, and 80% of the UV laser
radiation are lost at the beam shaping aperture.
Thus, a more efficient technique for optical beamshaping is desirable.

BEAM SHAPING TECHNIQUES
Conceivable technical solutions can be associated with
one of the following methods:
Field mapping: The input beam is transformed into thedesired output beam by refraction at appropriately
designed aspherical surfaces in a prescribed manner. This
technique works well for diffraction-limited beams andcan be nearly lossless. A plane wavefront, i.e. a collimatedbeam can be generated at the ouptut of the shaper byadding a second aspherical lens. Both, the temporal shapeof the pulse and the coherence of the laser beam are
maintained, which is particularly important for the opticalbeamline of photoinjectors. Field mapping permits toprecisely control the final intensity profile. For thesereasons it is the method of choice for our beam shapercompared to the alternatives outlined below.
We suggest the setup of Fig. 1 for integration of thebeam shaper into the optical beamline. Two magnifying
telescopes are used to match the beam diameter to therequirements of the individual components. The former
beamshaping aperture remains in place. It is needed toincrease the edge steepness in the wings of the flat-top.
Another alternative are beam integrators which split
the input beam by a lens array into a large number offacets. Subsequently, the energy within each facet isdispersed over the cross section of the desired output
beam. The output profile is the sum of the diffraction
patterns of each individual aperture of the lens array.
That’s why the output beam exhibits strong, small-scaleintensity modulations (speckles) and the beam integrators
work satisfactory only for multimode beams. They are
lossless as well.
However, due to their principle of operation they
destroy the spatial coherence of the laser beam. There isalso no condition of constant optical path, so some
temporal broadening of the pulse duration results.
A third medthod is the radial intensity filter (RIF) [3].
This filter can be realized based on birefringent crystals
with a curved surface that provides a radial variation ofpolarization retardation. One or more such radialbirefringent elements in combination with polarizers form
a RIF. They are lossy due the absorption of light in thepolarizers. As a further disadvantage, flattening of thenearly Gaussian infrafred (IR) laser beam can only
approximately be obtained due to limited degrees of
freedom in its design parameters.
Beam shaping elements based on by internal conicalrefraction are commercially available [4]. These systems
require depolarized or circular polarized monochromaticradiation and contain a biaxial/trigonal crystal. The crystal
three times more energy
than without pre-shaping"pre-shaped"
beam<--- 10...25 m --->

aspheric
lens pair

Photocathodelaser with
flat-toppump profiles

Gaussianlaser beam
D = 2 mmtransmission ~ 70 %losses ~ 30 %overfilled
beam-shaping
apertureD = 1...4 mm

beamline telescopeor spatial filter
with pinhole

photocathodeFigure 1: Proposed scheme of an optical beamline for the rf-photoinjector at PITZ that integrates a refractive beam
shaper.
Bildbreite: 15.93 cm, bis zu#
klemz@mbi-berlin.de
17.03 cm möglich

FEL Theory

53

MOPPH008

Proceedings of FEL 2006, BESSY, Berlin, Germany

length has to be adapted to wavelength and diameter ofthe input beam. Since no polarizers are needed, thissystem can be highly transmissive. Unfortunately, there
are no suitable biaxial birefingent crystals available for
the UV at present. That’s why the technique cannot be
used in the UV beamline of a photocathode laser.

EXPERIMENT
We have designed a beam shaper that consists of a
Galilean telescope made of two refractive asphericallenses. Fig. 2 shows how the input rays from the laser
system are redirected into a uniform distribution within a
Galilean telescope. The Fig. 3 shows our measured beamprofiles at the input, in the middle and the exit of the lenspair when using a HeNe-laser. The absence of a focus
between the aspheres is important for application at the
PITZ beamline, since this excludes possible opticalbreakthrough due to high UV peak powers.
Our beam shaper is presently designed for 4 mmdiameter (FWHM) of the flat-top and 2.8 mm (1/e2)
diameter of the Gaussian input. The aspheres are 100 mm
apart. There diameters were chosen for a nominal powertransmission of 99.9%. Following [5], a smooth Fermidirac profile instead of a step function was chosen to
represent the flat-top profile, since this reduces diffraction
effects along the propagation path of the output profile.

CCØ = 4 . 2 mm
FWHM

Sensitivity against beam size fluctuations
For application of the shaper in a beamline of aphotocathode laser, the beam profile at the cathode should
be stable as far as possible, even if the diameter of the
input beam varies slightly. That’s why we have carefully
examined the sensitivity of of the otput beam against a
10% fluctuation of the input beam diameter for ourspherical lens pair. The results are depicted in Fig. 4.
The amount of the deviations on the edge of the flat-top
depends approximately linear on the dimensionless shapeparameter ß of the Fermi-dirac profile. ß represents theratio of the radius of the flat-top and the total width of thesoft transition region where the intensity returns to zero[5]. With increasing ß the profile becomes gradually flat
. In theand square, approaching a step function as ß
example shown in Fig. 4 the overshoot amounts to 15%.
We conclude from our experience with the current
beam shaper that a design tolerant against fluctuation of
the input beam diameter is more important than an almost
perfectly flattened output profile with steep edges. Thismeans that ß should be reduced considerably, a future
value of ß = 6 seams to be suitable for our application.

C

Figure 3: Mesasured beam profiles at the entrance,
midway and at the exit of the beam shaper
fractional power
1→∞

Figure 2: Basic scheme of the refractive field mapping
beamshaper (Galilean design)

54

0.5

-4

-2

0
2
cross section (mm)4βFigure 4: Output profile for varying beam radius w at the
input (shape parameter = 16): w = 0.9·w0 (red), w = w0
(blue), w = 1.1·w0 (green), design value: w0 = 1.422 mm(1/e2)
With the additional option of a spatial light modulator
that might preceed the aspherical lens pair the remaining
error at the edges as well as some remaining radial
variation of the intensity might be corrected.

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

Propagation of the UV beam
Fig. 5 shows the beam profile produced by therefractive beam shaper in a matched UV beam (left). The
present realization of the nonlinear frequency conversion
produces a slight elliptical beam in the UV. Its horizontal
cross section is slightly larger than in the verticaldirection. This is responsible for the observed overshootin the horizontal cross section at the output plane of theaspherical lens pair. The beam profile was reasonable
preserved by relay imaging over a distance of about 1 m,
see Fig. 5 (right).

MOPPH008

significant reduction of the overall costs of the laser due
to its reduced power requirements.

ACKNOWLEDGEMENT
This work is in part supported by the European
Community, Sixth Framework Programme, Research
Infrastructure Actions EUROFEL Design Study, contract
number 011935. Further support comes from the German
ministry of Education and Research (BMBF), contract
number 05ES4 BR1/8.

REFERENCES[1] J. Bähr et al., “Upgrades of the laser Beam-Line at
PITZ”,Proc. FEL2005, JaCoW/eConf C0508213,
p.110-113.
[2] M.Krasilnikov, “Experimental Characterization andNumerical Simulation of the Electron Source at
PITZ”, ICAP2004, St. Petersburg.
CC

Figure 5: Output beam profile of the aspherical lens pairat 262 nm wavelength (left) and its relay image in a
distance of approx. 1 m with (right).

CONCLUSION AND OUTLOOKThe suggested integration of a refractive beam-shaper
into the optical beamline of the PITZ photocthode laser
has the potential to form a flat-top beam profile andsimultaneously improve the energy efficiency of thecomplete beam-line. Consequently, the application of an
appropriately designed beam shaping system can lead to a

FEL Theory[3] M. Yun et al., “Transformation of Gaussian touniform or annular beams by radial birefringent
filters”, Proc. of SPIE 5525 (2004), p.182-187.
[4] “Laser beam sahping with only one element”, OLE(October 2004), p. 18, http://www.vct-ag.de.
[5] J.A. Hoffnagle and C.M. Jefferson, “Design andperformance of a refractive optical system thatconverts a Gaussian to a flattop beam”, Appl. Opt. 39(2000), p.5488-5499.

55

MOPPH009

Proceedings of FEL 2006, BESSY, Berlin, Germany

Beam Dynamics Experiments and Analysis on CSR Effects at FLASH
Bolko Beutner, Winfried Decking, Martin Dohlus, Torsten Limberg
and Michael Röhrs,
Deutsches Elektronen-Synchrotron DESY, D-22603 Hamburg, Germany.
Abstract
The Free Electron Laser in Hamburg (FLASH) is a linac
driven SASE-FEL in the vacuum-ultra-violet (VUV) wavelength range [1]. High peak currents are produced using
magnetic bunch compressor chicanes. In these magnetic
chicanes, the energy distribution along an electron bunch ischanged by the emission of Coherent Synchrotron Radiation (CSR). Energy changes in dispersive sections lead totransverse displacements along the bunch. Measurementsof CSR induced transverse displacements are presented andcompared with simulations.

INTRODUCTION
The peak current of an electron bunch emitted by an rf
gun is about 50-100 A. For SASE operation at FLASH,
the necessary peak currents of 1-3 kA are reached using
longitudinal bunch compression. A two stage bunch compression system with the magnetic chicanes BC2 and BC3
is employed (see Fig.1).

corresponding to about 50 A peak current. The integrated
effect of space charge from the exit of BC2 to LOLA is thensmall compared to the centroid offsets caused by CSR.

MEASUREMENTS AND ANALYSIS
For our measurements, we vary the ACC1 phase andkeep ACC2/3 on crest. The expected CSR effects are
created during over-compression in BC2. Downstream,
the transverse deflecting rf structure is passed at the zerocrossing phase. The particles are kicked transversely witha strength proportional to their longitudinal offset to thebunch center. The bunch is thus tilted and its longitudinaltransverse projection is observed on a screen.
Fig.2 shows a LOLA measurement. The red curve shows
the longitudinal beam profile, the white dashed lines indicate the fwhm points.

−3

x 10

ACC1 Phase φ = −16.8°

12
ACC1

BC2

ACC2

ACC3

BC3

ACC4

Dump
Bypass(ACC6)(ACC7)
Undulators
LOLA

10

ACC5

PhotonBeamlinehorizontal [m]

Gun

8
6
FWHM = 2.84953e−003m
RMS = 1.23692e−003m

4
2

Dump

Figure 1: Sketch of FLASH. The blue triangles indicate dipole magnets, the yellow boxes TESLA acceleration
modules.
A transverse deflecting rf-structure (LOLA) [2] is used
to take ”top view” pictures of the bunch - the projection
into the longitudinal-horizontal plane. Thus, centroid shifts
along the bunch, for instance caused by CSR fields, can beobserved.
However, other forces like space charge cause transverse
shifts of beam centroids as well. For an undisturbed measurement of CSR effects, space charge effects have to be reduced. To that purpose, we over-compress the bunch. The
longitudinal energy correlation (chirp) introduced in themodule ACC1 is chosen to reach minimum bunch lengthand a peak current beyond 2 kA towards the end of the second magnet in the BC2 chicane. The bunch will exit thechicane roughly with its incoming length of about 2 mm,

56

1

2

3
4
5
longitudinal [m]

6

7
−3

x 10

Figure 2: An example of a LOLA measurement. Longitudinal charge profile (red line), fwhm and rms bunch length
are shown.
Fig.3 shows measured bunch length at LOLA as a function of the ACC1 phase as well as simulation results. The
measured bunch length agrees well with the simulation
downstream of BC3, as it should. The calculated bunch
length downstream of BC2 (green line) is, for small phaseoffsets, longer, since the bunch is further compressed in
BC3. At about 12 degrees, the bunch is fully compressed inBC2. Above 12 degrees, the bunch is over-compressed, thechirp changes its sign and the BC2 bunch length is shorter.
Fig.4 shows measured longitudinal-horizontal projections of the bunch for different compression scenarios. In
the uppermost picture, the ACC1 phase is on crest, no com-

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany
x 10

Bunch length vs. ACC1 off−crest phase

7
6
Bunch length [m]ACC1 Phase φ = 0°

−3

x 10
horizontal [m]

−3

8

5
4

10
5
0

1

2

3

10
15
ACC1 off−crest phase [deg]20

Figure 3: Measured fwhm bunch length at LOLA (blueline) are compared with simulations. Red line: calculated
bunch length at LOLA. Green line: calculated bunch length
after BC2.

pression occurs and the horizontal centroid positions line
up straight. Close to full compression (middle picture), thebeam is heavily distorted by CSR and space charge effects.
This is understood and simulated [3], but would be very
challenging as a starting point for quantitative CSR studies.
The bottom picture shows the over-compressed case,where the space charge effects are negligible and strong
CSR occurs only in BC2. The beam centroids are still ona smooth line. Its shape and sag will be compared withsimulations in the next paragraph.
Fig.5 reflects the bunch shape changes described abovein plotting the peak to peak bunch centroid shift as a function of ACC1 phase offset.

horizontal [m]

5

x 10

5

6
−3

x 10

10
5
0

0.5

1
1.5
longitudinal [m]

2
−3

x 10

ACC1 Phase φ = −19.2°−3

horizontal [m]

0
0

3
4
longitudinal [m]ACC1 Phase φ = −9.6°

−3

2
1

MOPPH009

x 10
10
5
0

2

4
6
longitudinal [m]

8
−3

x 10

Figure 4: Measured top view for different ACC1 phase offsets. Top: no compression. Middle: near full compression.
Bottom: over-compression.

on the screen. The cause of this is under investigation. The
linear correlation as indicated by the magenta line in Fig.2
is subtracted from the centroid curve.
For error analysis, a series of pictures is taken for each
ACC1 phase setting. The different centroid curves are

Comparison with Simulations

FEL Theory−3

3
peak to peak centroid shift [m]Tracking calculations were done to simulate
longitudinal-horizontal beam projections at LOLA.
Beam transport through ACC1 was calculated with thespace charge tracking code ASTRA [4]. After ACC1,
wake fields are applied as a discrete effective kick [5].
The tracking code CSRTrack [6] is used to simulate CSR
effects in BC2. The 1D projected model is used [7]. Thelong bunch length after BC2 in the over-compression caseallows the simulation of the beam transport to LOLA by afirst order matrix.
To compare the simulated longitudinal slice centroid positions with the measurements these data have to be extracted from the measured distributions. In a first step
each distribution is divided into slices along the longitudinal axis. The horizontal charge profiles of these slices
are then calculated. Gaussian fits are used to determine thecenter of each profile. An example for the resulting centroid curve is the dashed black line in Fig.2.
At big ACC1 phase offsets, the bunches start to be tilted

x 10

2.5
2

over−compression
range

1.5
1
0.5
0
0

5
10
15
20
ACC1 off−crest phase [deg]Figure 5: The peak to peak centroid shift along the bunchis plotted vs. the phase offset in ACC1. Phase range used
for the experiment: 14 to 24 degrees.

57

MOPPH009

Proceedings of FEL 2006, BESSY, Berlin, Germany
ACC1 Phase φ=0°51horizontal [m]

−3

10

x 10

2
3
4
longitudinal [m]

5

x 10

2
0
−2
−4

6

−3

°

x 10

10

x 10

2

3
4
5
longitudinal [m]

6

−3

−2

3
−3

x 10

−1
0
longitudinal [m]

1

2

x 10

3
−3

x 10

ACC1 Phase φ=19.2°−4

10aligned to their individual centre of mass. The curves arethen fitted with a polynomial and their mean value and rms
spread are calculated for different longitudinal positions. In
Fig.7, these results are compared with the tracking calculations.

2

0

7

Figure 6: Simulated top view after BC2 for different ACC1
phase offsets. Top: no compression. Bottom: overcompression.

1

5

−5
−4

1

−1
0
longitudinal [m]ACC1 Phase φ=16.8°−4

ACC1 Phase φ=−21.6

5
0

−2

−3

horizontal [m]0ACC1 Phase φ=14.4°−4

4
horizontal [m]10horizontal [m]horizontal [m]

−3

x 10

5
0
−5
−4

−3

−2

−1
0
longitudinal [m]

1

2

3
−3

x 10

Figure 7: Experimental centroid curves are compared withsimulated data. The blue lines represent the data taken with
LOLA and the dashed red curves represent the results ofsimulations. Linear correlations are subtracted.

CONCLUSION AND OUTLOOK[7] M. Dohlus: ”Two Methods for the calculation of CSR
Fields”,TESLA-FEL-2003-05.

CSR effects in the first bunch compressor chicane in
FLASH were observed using the transverse deflecting rfstructure LOLA.
The offsets of the centers of the longitudinal bunch slices
for different over-compression scenarios were measured
and compared with simulation calculations.
Next steps in the experimental program are studies ofslice emittance growth due to CSR effects and dependenceson bunch charge and beam optics in the chicanes [8].
The observed beam tilt will be investigated to improve
both SASE operation and CSR measurements.

[8] M.Dohlus, T. Limberg: ”Impact of Optics on CSR-related
Emittance Growth in Bunch Compressor Chicanes”, PAC
2005, 2005.

REFERENCES[1] E. Schneidmiller and M. Yurkov: ”Lasing at 13 nm of the
SASE FEL at FLASH”, this conference.
[2] M. Röhrs et. al.: ”Investigations of the Longitudinal Electron
Bunch Structure at the FLASH Linac with a Transverse Deflecting RF-Waveguide”, this conference.
[3] M. Dohlus:”CSR Calculation for TTF-II”,
http://www.desy.de/xfel-beam/talks a.html#dohlus.

2005,[4] K.
Flöttmann:”ASTRAuser
manual”,
http://www.desy.de/mpyflo/Astra dokumentation.
[5] I. Zagorodnov: private communication.
[6] M. Dohlus, T. Limberg: ”CSRtrack: Faster Calculation of 3D
CSR effects”, FEL 2004, 2004.

58

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH011

FELO: A ONE-DIMENSIONAL TIME-DEPENDENT FEL OSCILLATOR
CODE
B.W.J. Mc Neil, G.R.M. Robb, SUPA, Department of Physics, University of Strathclyde, Glasgow, UK
D. Dunning and N.R. Thompson, ASTeC, CCLRC Daresbury Laboratory, UK.
Abstract
A one-dimensional, SDDS compliant time-dependent
FEL oscillator code has been developed in Fortran 90. The
code, FELO, solves universally-scaled FEL equations tosimulate oscillator FELs operating from the low to highgain regime. The code can simulate start-up from shotnoise, different electron pulse current distributions, the effects of cavity length detuning and temporal jitter between
electron bunches. Cavity detuning curves for both the lowgain IR-FEL and the regenerative amplifier VUV-FEL of
the 4th Generation Light Source (4GLS) proposal at Daresbury Laboratory are modelled. The code predictions for
the VUV-FEL output are compared with simulations performed with the parallel implementation of Genesis 1.3 andare found to be in good agreement.

INTRODUCTION
Several computational codes are available to the FEL
community to aid with the simulation and design of FEL
amplifiers e.g. Genesis 1.3 [1]. The authors have developed a simulation package containing FEL simulation
code and pre and post-processors that models a FEL withcavity feedback. The code, called FELO, solves a onedimensional spatio-temporal set of equations which areable to model much of the physics relevant to such FELs.
The design of two of the UK 4GLS project FELs wereaided by FELO and examples from the 4GLS Conceptal
Design Report [2] are presented.

THEORETICAL MODEL
The 1D equations governing the spatio-temporal evolution of the pulsed FEL interaction are well known and in
the the universal scaling of [3, 4] may be written:
dθj
dz̄
dpj
 dz̄
∂
∂ z̄

= pj

(1)

=

(2)

− (A (z̄, z̄1 ) exp (iθj ) + c.c.)∂+
A (z̄, z̄1 ) = χ (z̄1 ) b (z̄, z̄1 )
∂ z̄1

(3)

where θj = (k + ku ) z − ωtj is the phase of the jth electron with respect to the particular ponderomotive potential
well in which it evolves and (γj − γr ) /ργr is its
 pj =
scaled energy, b (z̄, z̄1 ) ≡ e−iθ(z̄) z̄1 is the bunching factor and is the average over the electrons contained within
the ponderomotive well centred at z̄1 at distance through

FEL Theory

the interaction region z̄. The weight factor χ (z̄1 ) =I (z̄ = 0, z̄1 ) /Ipk where I (z̄ = 0, z̄1 ) describes the electron pulse current distribution of peak value Ipk at theentrance to the FEL interaction region and A (z̄, z̄1 ) is
the scaled complex radiation field envelope with magnitude defined by the radiation and electron beam powers as
2|A| = Prad /ρPbeam .
The scaled independent variables may be written [4]:z
= 2ρku z
(4)
z̄ =
lg
z̄1

=

z − cβ̄z t.
lg 1 − β̄z(5)where lg = λu /4πρ is the nominal gain length of the FEL
interaction, the initial z-component of the mean electron
velocity within the interaction region is cβ̄z = vz0  and ρ
is the fundamental FEL, or Pierce, parameter [3]. The latter
may be written in practical units for a planar undulator as1/3
where fB is theρ ≈ 5.7 × 10−3 γr−1 Iā2u λ2u fB2 /σb2
usual difference of Bessel function factor associated withplanar undulators and σb is the RMS electron beaM radius
which for an electron beam of normalised emittance n ina focussing channel of beta-function β is given by σb =n β/γr .
For the case of small gain FELs typical to those encountered in high-Q cavity FELs, previous studies [5] haveshown that the effects of emittance and energy spread, electron/radiation pulse slippage effects and the relative transverse overlap between electron beam and cavity modes
may be accounted for in correction factors to the expressions for the FEL gain. A small signal gain coefficient was
defined which in the universal scaling of the above equations may be written:
z̄ 3
.
(6)
π
The maximum single pass gain is then approximated by thefitting formula:
Gmax = g0 F 0.85 + g0 F 0.19 + 4.12 × 10−3 g0 F
g0 =where the factor F = Finh Ff Fc is a product of correction factors that that respectively account for the effects ofinhomogeneous broadenning due to emittance and energy
spread; a filling factor for the transverse overlap; and theeffects of relative slippage between the radiation and electron pulses. The inhomogeneous broadening factor is given
by:
1

(7)
Finh = 
1 + 1.7μ2γ (1 + μ2 )59

MOPPH011

Proceedings of FEL 2006, BESSY, Berlin, Germanywhere μγ = 4Nu σγ /γ and μ = 2Nu n āu /λu 1 + ā2u .
The filling factor is given by:
Ff =1
1 + w̄2 /4σb2(8)where w̄ is the mean optical mode size, defined by theradius at which the intensity drops to 1/e2 of its on-axis
value, averaged over the length of the undulator.
Noting from (4 & 6) that g0 ∝ ρ3 and that the expression
for Gmax contains only factors g0 F allows the inhomogeneous fitting factor Finh and that for the filling factor Ff
to be incorporated into the definition of an effective FEL
parameter
1/3(9)ρef f ≡ (Finh Ff ) ρto replace that of ρ in the definitions and working equationsof (2..5). Note that the factor that accounts for slippage effects, Fc , is not used in the definition of ρef f as slippage
is directly modelled by the partial derivatives of the wave
equation (3). It is interesting to note that from the definitions of g0 and the filling factor Ff that the product g0 Ff ,can be expressed as
g0 Ff ∝

1.
σb2 + w̄2 /4

Hence, if the electron beam radius σb  w̄, as for example
in a long wavelength FEL, the gain is independent of theelectron beam radius.
When used with the ρef f scaling the above equations(2..3) will then estimate the effects of inhomogeneous
broadening due to electron energy spread and emittance,
and also the effects of transverse electron-radiation coupling, without the need for increased number of computational particles required in 2-D and 3-D models. The FELO
code which uses these equations is therefore significantly
faster to run than these codes and yet, as will be shown in
the following work, gives results which are in good agreement with 3-D simulations.

COMPUTATIONAL MODEL
The working equations (2..3) are solved using themethod of characteristics as described in [6] using a code
written in Fortran-90. The metod of characteristice allows the resultant equations to be integrated via a 4thorder Runge-Kutte method with slippage effects between
electrons and radiation modelled using simple array shifts.
Because the effects of electron energy spread, emittanceand transverse coupling are simply accounted for in themodified FEL parameter ρef f , no electron macroparticle
distribution in the scaled energy parameter p is required
and pj = 0 ∀ j to describe a resonant FEL interaction.
Thus, only a relatively small number of macroparticles are
required per ponderomotive well (typically ∼ 100) distributed uniformly in θ. The option to include shot-noise
effects is included using the method of [7]. Although othershot-noise models more correctly describe the physics [8],60the method of [7] is sufficient here. The FEL cavity length
can be varied to allow investigation of cavity detuning effects and the effects of a random temporal jitter in the electron arrival into the cavity can be simulated by introducing
a small random variation about the mean cavity length [9].
The FELO source code is written in Fortran-90 and isfreely available [10]. The code has been tested using theopen-source g95 compiler [11]. A parameter spreadsheet isavailable to assist the user in preparing the relatively simple input file for the code. Output from the code is written
into SDDS formated files [12]. Post-processing and plotting routines are provided using both SDDS toolkit functions in Tcl script files and MATLAB and are described in
more detail in the user-manual provided for the code.

EXAMPLE SIMULATIONSThe FELO code has been used in the design of two of
the three FELs of the UK 4GLS project [2]. Both the IRFEL and the VUV-FEL are cavity FELs. The IR-FEL is
designed to operate in the wavelength range 2.5-200 μm.
It has a relatively low gain and needs a relatively high Q
cavity to lase. The VUV-FEL is designed to generate photon energies of 3-10 eV and will operate in the intermediate
gain regime (z̄ ∼ 4) where the FEL interaction evolves exponentially but cannot achieve saturation withou seeding ina single pass. Saturation is made possible by introducing asmall amount of feedback via a low Q cavity [13]. This also
has the advantage of cleaning up the spectral quality of theoutput over that of SASE [14]. FELO simulations for bothof these designs are presented and, in the case of the VUVFEL, comparison is made with the results of the 3-D code
Genesis 1.3 [1]. No such comparison is available for the
IR-FEL due to the large number of cavity round-trips required to achieve saturation and the prohibitively long simulation time this would require.

4GLS IR-FEL
The IR-FEL simulations presented are for 2.5 μm operation of the IR-FEL. From the detailed specifications of [2],with an electron energy of 60 MeV, charge 200 pC and
RMS duration of 2 ps the IR-FEL operates at 2.5 μm.
The undulator has 50 periods, so that the approximate efficiency η ≈ 1/4Nu gives a peak power output at saturationof Ppk ≈ 12 MW. A more detailed estimate of the efficiency that accounts for passive cavity losses due to mirror
reflectivity and all diffraction losses has been derived andreduces the efficiency from that above [2]. Including theseeffects gives the optimised power estimate for operation of
the IR-FEL from 2.5-25 μm as shown in Fig. 1. A FELO
simulation at 2.5 μm operation with cavity length detuningof δc = 9 μm, so that the output pulse width is close to
its maximum, gives good agreement with these estimatesas shown in Fig. 2. (Note that positive values of δc correspond to a shortened cavity length.) Fig. 3 plots the resultsof FELO simulations for both the peak power and FWHM

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH011

Figure 3: Peak power and FWHM pulse width as a functionof cavity length detuning, for the 4GLS IR-FEL at 2.5 μm
with 2 ps electron bunches.
Figure 1: The peak output power for the 4GLS IR-FEL, assuming 2 ps RMS electron pulses and an outcoupling fraction optimised for every wavelength to give the maximum
output power. Calculations for helical and planar mode areshown in green and red respectively.

Figure 2: 4GLS IR-FEL pulse power as a function of timefor 2.5 μm operation with a cavity length detuning of 9 μm.
pulse width for 2.5 μm operation as a function of cavity detuning δc . As cavity resonance is approached at δc = 0 it isseen that the peak output power increases and pulse width
decreases, typical of superradiant behaviour in an FEL cavity [15].

4GLS VUV-FEL
FELO simulations have also been used in the conceptual design of the 4GLS VUV-FEL. This FEL operates withan intermediate gain of z̄ ∼ 4 and uses a low Q cavity.

FEL Theory

Saturation then occurs after only a few cavity passes, typically ∼ 10, which allows multi-pass simulation to saturation using the 3-D code Genesis. For 10 eV operation in a planar undulator, the VUV-FEL conceptual design uses a 600 MeV, 300A peak current electron beamand gives an FEL parameter of ρ ≈ 1.5 × 10−3 . Although utilising cavity feedback, the VUV-FEL still saturates as a high-gain FEL [13] so that the efficiency isη ≈ ρ. Hence, the saturated power can be approximatedas Psat ≈ ρPbeam ≈ 270 MW. Fig. 4 plots the resultsof FELO simulations for both the peak power and FWHM
pulse width for 10 eV photon energy operation as a function of cavity detuning δc . There are clear similarities with
the IR-FEL cavity detuning curve of Fig. 3. As with the IRFEL, assuming the greatest pulse width approximates mostclosely to the steady-state, the saturated power for cavity
length detuning of δc ≈ 18 μm agrees well with the saturated power estimate of ≈ 270 MW of above. The plotof Fig. 5 shows a comparison of the pulse power as the
VUV-FEL pulse energy saturates for the case of a FELO
(blue) and Genesis (red) simulation for a cavity detuning of
12 μm. The number of cavity passes for the Genesis simulation was 8 while that for the FELO was 30. Although the
FELO simulation approached pulse energy saturation after
8 caivity passes, the shape of the pulse power underwent
a transition from a narrower, higher peak power pulse tothat shown. This accounts for the higher peak power andnarrower pulse width of Fig. 4 where τF W HM ≈ 65 fs ⇒s ≈ 20 μm in the units of Fig. 5. This effect of higher
peak power and narrower pulse width of the FELO simulation appears to be a transiatory superradiant phase. It is notthought that the Genesis simulations show this behaviour,
although this will need to be investigated further. As cavity
resonance is approached, the radiation pulse width shortens
to approximately an order of magnitude less than the electron pulse width of 250 fs FWHM (75 μm). Also, pulse

61

MOPPH011

Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 4: Peak power (red) and FWHM pulse width (blue)
as a function of VUV-FEL cavity detuning. The parameters
are for 10 eV photon output.

Figure 6: FELO simulation showing the 10 eV radiation
power at saturation as a function of time for near-zero cavity detuning. The pulse shape demonstrates a spiking behaviour typical to FEL superradiance.
[2] 4GLS Conceptual Design Report, Council for theCentral Laboratory of the Research Councils, UK,
http://www.4gls.ac.uk/documents.htm#CDR (2006)[3] R. Bonifacio, C. Pelligrini and L.M. Narducci, Opt. Commun. 50, 373 (1984)[4] R. Bonifacio and B.W.J. Mc Neil, Nucl. Instrum. Methods A
272, 280 (1988)[5] F. Ciocci, A. Torre, G. Dattoli and A. Renieri, Insertion Devices for Synchrotron Radiation and Free Electron Lasers,
World Scientific Publishing, Singapore (2000)

Figure 5: Comparison between FELO radiation power output pulse (blue) with that of a Genesis simulation (red) approaching saturation of the output energy. The parameters
are for 10 eV photon output.
peak powers are significantly greater than the predicted by
the steady-state simulations [2]. A plot of the shape of thepulse output close to cavity resonance is shown in Fig. 6.
This pulse shape is typical of superradiant radiation witha narrow, high peak power spike followed by secondary
pulses or ringing [15].

CONCLUSIONSThe FELO code package has been developed to allow
reasonably quick and accurate simulations of cavity FELs
operating from the low to high gain. The package has beenused succesfully in the development of the design of two
cavity FELs for the UK 4GLS project. Some of these simulation results were presented. The code including manualis freely available for general use [10].

[6] R. Bonifacio, B.W.J. Mc Neil and P. Pierini, Phys. Rev. A 40,
4467 (1989)[7] C. Penman and B.W. J. Mc Neil, Opt. Commun. 90, 82(1992)[8] B.W.J. Mc Neil, M.W. Poole, and G.R.M. Robb, Phys. Rev.
ST Accel. Beams 6, 070701 (2003)[9] D. Dunning et al., First Tolerance Studies for the 4GLS FEL
Sources, ibid.
[10] Currently available from http://www.astec.ac.uk/id mag/IDMag Software.htm[11] Currently available from http://www.g95.org/[12] M. Borland, L. Emery, H. Shang and R. Soliday, Proceedings of the IEEE 2003 Particle Accelerator Conference
2003, Portland, Oregon[13] B.W.J. Mc Neil, IEEE Journal of Quantum Electronics 26,1124 (1990)[14] N.R. Thompson, B.W.J. Mc Neil and M.W. Poole, A VUVFEL for 4GLS:Design Concept and Simulation Results, Proceedings of the 27th International Free Electron Laser Conference, Stanford (2005)[15] D.A. Jaroszynski et al., Phys. Rev. Lett. 78, 1699 (1997)

REFERENCES[1] S. Reiche, Nucl. Inst. and Meth. A 429, 243 (1999)

62

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Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH012

THE CONCEPTUAL DESIGN OF THE 4GLS XUV-FEL
B.W.J. Mc Neil, SUPA, Department of Physics, University of Strathclyde, Glasgow, UK
N.R. Thompson, ASTeC, CCLRC Daresbury Laboratory, UK
B. Sheehy, Sheehy Scientific Consulting, New York, USA.
Abstract
The Conceptual Design Report for the 4th Generation
Light Source (4GLS) at Daresbury Laboratory in the UK
was published in Spring 2006 [1]. A key componentof the proposal is an XUV-FEL amplifier directly seededby a High Harmonic source and operating in the photon energy range 8-100eV. Numerical modelling shows
the FEL may generate 50fs (FWHM) pulses of variablypolarised, temporally-coherent radiation with peak powers
in the range 2-8 GW.

INTRODUCTION
Synchronised free-electron laser (FEL) sources which
operate in the XUV, VUV and IR regions of the spectrum
are fundamental components of the 4GLS design. Thesesources will deliver ultra-short pulses of temporally coherent photons with peak brightness at least 108 greater thanthat available from the best 3rd-generation light sources.
4GLS is intended to be a beyond state-of-the-art facility
that must operate over extended periods, generating stable, synchronous and reproducible radiation pulses over thewide spectral range to end-user stations. In the conceptual
design of 4GLS, therefore, the aim has been to create a robust design that does not overly stretch the specification of
its individual components. This mildly cautious approachshould minimise the risk in proceeding to the future designphase and enable further, more advanced, designs to be incorporated as technological progress permits. Here details
mainly relating to the choice of undulator and electron focussing specifications and their relation to the FEL output
are presented for the conceptual design of the XUV-FEL
covering the 8-10eV photon energy range of the spectrum.
The effects of FEL seeding by High Harmonic pulses are
discussed in [2, 3] and the temporal seed/electron pulse offset due to jitter is discussed in [4].

GENERAL SPECIFICATIONThe XUV-FEL baseline design will generate short, tunable, high-brightness pulses of 8-100 eV photons froman undulator system directly seeded by an external laser
source. The radiation output will have good temporal andtransverse coherence and also have variable polarisation.
These specifications are expected to satisfy a wide range ofcurrent user requirements and also open up many new areas of science for exploration. It is also possible to utilise
the exhaust electrons of the XUV-FEL in a spontaneous
spent-beam undulator source, before the electron beam is

Seeded FELs

dumped. The radiation from this source is then guaranteed
to be synchronous with the XUV-FEL output for pumpprobe type experiments. A schematic of the conceptual design for the 4GLS XUV-FEL is given in [3] of these conference proceedings.
Photon energy tuning in the XUV-FEL will be achievedby a combination of both undulator gap tuning and energy
tuning of the electron bunches between 750 and 950 MeV.
The electron bunches are assumed to have a rep-rate of 110 kHz, to be Gaussian of width σt = 266 fs and total
charge of 1 nC giving a peak current of 1.5 kA, and withnormalised emittance n = 2 mm mrad and fractional RMS
energy spread of 0.1%. The FEL undulator will consist ofa lattice of individual undulator modules allowing electron
beam focusing elements and diagnostics to be placed in between. The final undulator modules of the FEL will be of
APPLE-II design that will enable the generation of variable elliptically polarised radiation. Existing HHG laser
systems can provide seed energies of 10 - 100 nJ with pulse
widths of 30 fs FWHM over the photon energy range [2, 3].
The quality of XUV-FEL output can be expected to be similar to that of the input seed pulse which has a high degreeof both spatial and temporal coherence [5]. The amplified
pulse widths will also be only slightly longer than the seedpulse.

UNDULATOR AND FOCUSSING LATTICE
The design for the XUV-FEL undulator consists of a lattice of undulator modules containing both planar and variable polarisation undulator modules. For the planar undulators a relatively simple pure permanent magnet (PPM)
was chosen and an APPLE-II design was chosen for thevariable polarisation undulators. Each type of module will
have a fixed period and a variable magnetic gap, g, thatallows tuning of the RMS undulator parameter āu via theundulator magnetic field. A minimum undulator magnetic
gap is assumed for the design of both planar and variable
undulators. Note that the gap between the vacuum vessel walls will be (g − 3) mm, the 3 mm reduction fromthe magnetic gap being the estimated thickness of the vacuum vessel walls and the clearance between magnets andvacuum vessel. A schematic giving further detail of theundulator lattice and incorporating BPMs, phase matching
devices and the focussing quadrupoles is shown in Fig. 1.
The variable polarisation undulator sections, VU1..VU5,
ensure that variably polarised photons may be generated
across the full design spectrum. In practice, operation
at higher photon energies will require a longer undulator

63

MOPPH012

Proceedings of FEL 2006, BESSY, Berlin, Germany
ability to step-vary the full undulator length by opening theindividual module gaps. For these reasons a simpler FODO
focussing lattice of module length ≈ 2 m is the chosen design option.
In order to investigate the effect of β-function variation
due to the discrete focussing quadrupoles of the FODO lattice, the 3-D code Genesis 1.3 [7] was used to determine
both the saturation length Lsat and power Psat as a function of average β-function. This was carried out for a planar undulator system of module length ≈ 2 m. The respective results are shown in Fig. 2. It is seen that β ≈ 3.5

Figure 1: Schematic of the modular undulator system of the
XUV-FEL. Undulator modules PU1..8 (blue) are planar undulators; VU1..5 (red) are variable polarisation undulators.
The gap between undulator sections may contain a beam
position monitor, quadrupole and radiation/electron phasematching unit.

64

3.5
Lsat (m)Psat (GW)

3

24

2.5

23

2

22

1.5

21
3

4

5
β (m)

6

7

Psat (GW)

25

Lsat (m)length to achieve saturation. The effective undulator length
may be varied by opening the magnetic gaps of individual undulator modules to their maximum. Those modules
that have maximum magnetic gap generate only small onaxis magnetic fields and are effectively switched off for the
purpose of the FEL interaction. For example, when operating for 100eV photon energy generation all undulator
modules PU1..VU5 would be functional to achieve saturation, whereas for 50 eV operation only modules PU5..VU5
would need to be functional to achieve saturation, with
PU1..PU4 gaps fully opened. This method of operation
should allow a tapered vacuum vessel to be used along theundulator modules which will assist with reducing diffraction effects of HHG seed injection at lower photon energies [1, 3]. The minimum undulator parameter due to undulator gap tuning is taken to be āu ≈ 1 to ensure sufficient
FEL coupling. With this constraint then for a beam energyof 950 MeV the maximum planar undulator period that canachieve 100 eV FEL resonance is λu ≈ 45 mm with a gapof g ≈ 28 mm. At the lower beam energy of 750 MeV
and for λu ≈ 45 mm, the resonant photon energy is ≈ 10
eV for the minimum magnetic gap of g ≈ 10 mm. The
period of λu ≈ 45 mm is then the optimum for the beamenergy, magnetic gap and photon tuning range. A similar
analysis for the variable polarisation APPLE-II undulators
gives them an optimum period λu ≈ 51 mm
A FODO focussing lattice has been chosen for the conceptual design. Other systems based upon quadrupole doublet and triplet focussing were investigated [5] and rejected. Although these latter designs allow longer, andtherefore fewer, undulator modules of up to 4-5 m in length
to be used, the quadrupole field strengths must be significantly greater by a factor of 3-4 than those required for a
FODO lattice distributed between more modules. Tighter
quadrupole alignment tolerances would therefore be required for the doublet and triplet positioning [6]. Monitoring of the electron beam transverse position, critical to
the FEL interaction, would also be limited as would the26

1

Figure 2: Genesis simulation of the saturation length,Lsat ,and power, Psat , as a function of the β-function in a FODO
lattice for 100 eV operation.
m minimises the saturation length whereas β ≈ 5.5 m
maximises the output power. The nominal value of the βfunction is chosen to be that which gives the maximum output power: β = 5.5 m. This is motivated by the fact that theplanar modules PU1-PU8 produce a seed pulse (and prebunched beam) which will be amplified to saturation in the
APPLE-II modules VU1-VU5, so maximising the power ofthe seed into the VU modules reduces the required lengthof the more technologically challenging APPLE-II modules. For the parameters used here a β-function of 5.5 m
is satisfied by quadrupoles of magnetic length 0.09 m andof strength =13 T/m. The
 RMS electron beam radius may
be calculated as σb = n β/γ = 77 μm for beam energy
950 MeV and the design normalised emittance n = 2 mm
mrad.

UNDULATOR MODULE & GAP LENGTH
The modular construction of the combined undulator
and FODO focussing lattice requires choice of the lengthof each undulator module, LP U for planar and LV U forvariable undulators, and Lgap the spacing between modules. The FEL performance has a functional dependence onthese parameters so optimisation is needed. The energy dispersion induced into the electron beam by the FEL interaction, and the natural homogeneous energy spread, are trans-

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Proceedings of FEL 2006, BESSY, Berlin, Germany
formed into a spatial dispersion in proportion to the gap between undulator sections, Lgap which may disrupt the FELbunching process. Furthermore, it is seen from Fig. 1 thatthe undulator module length and gap define the FODO focussing lattice period, λF ODO = 2(LP U + Lgap ). In a
FODO lattice, the β-function varies about its mean value
by ±λF ODO /2 so affecting the electron beam radius via
the relation above for σb . Thus if λF ODO is too large (asdetermined principally by the module length) the electron
beam radius variation may also adversely affect the FEL
coupling. Alignment of the electron beam through the undulators is of critical importance to maintain the electronradiation coupling. This requires both beam alignment between undulator modules and careful construction of theundulators to ensure that the beam wander due to magnetic field errors and pole alignment are minimised. Ideally, beam wander off the optical axis should be no greaterthan 20% of the electron/radiation beam radius.
Genesis 3-D simulations were carried out to simulate the
FEL operating at 100 eV. Only the planar undulator modules were used with the nominal design parameters. Fig. 3
plots the results of Genesis steady-state simulations for thesaturation power, Psat , as a function of the gap between undulator modules, Lgap , for three different module lengths,
LP U . It is seen that the saturation power is nearly indepen-

MOPPH012

Figure 4: Simulation of the saturation length Lsat for
XUV-FEL planar undulator operation at 100 eV as a function of the undulator module gap, Lgap for three module
lengths: LP U =2, 3 and 4 m. (The saturation length is theundulator length only: gaps between modules are not included.
dulator module length, with the 4 m module having a saturation length longer than that of the 2 m module. This
is attributed to the greater variation in the β-function forthe longer module as discussed above. For this reason, andthe greater opportunities for beam monitoring and control
afforded by the greater number of undulator modules, themodule lengths for the design specification are chosen to
be LV U ≈ LP U ≈ 2 m. Hence, for the baseline designfor 8 - 100 eV operation, each planar PPM undulator will
have 45 periods of 45 mm giving a module length LP U =2.025 m and each variable undulator APPLE-II undulator
will have 40 periods of 51 mm giving a length LV U = 2.04
m.

3D STEADY-STATE SIMULATIONS

Figure 3: Simulation of the saturation power, Psat , for
XUV-FEL planar undulator operation at 100 eV as a function of the gap between undulator modules. The results areplotted for three module lengths: LP U =2, 3 and 4 m.
dent of the undulator module length and decreases almost
linearly with the undulator gap. A gap of Lgap = 0.6 m
is chosen for the design specification. This is the estimatedminimum length into which the quadrupoles, BPMs andphase matching units can fit.
Simulations of the saturation length Lsat of a seeded amplifier interaction, starting from a seed power of 30 kW at
100 eV, are shown in Fig. 4. For each length of undulator module Lsat is seen to increase with the module gap.
However, there is a significant difference between each un-

Seeded FELs

The design choices and optimisations discussed may besummarised by plotting both the saturation powers andlengths across the operating spectrum of the XUV-FEL. It
has been assumed that the XUV-FEL is operating in an amplifier mode with a seed power equal to 10% of the peak
power currently available from seed pulses as describedin [2, 3]. The reduction in seed power by a factor of approximately ten conservatively estimates the power available
following transmission and focussing losses from the seedlaser into the undulator. The seed is focussed to the centreof the first in-use undulator module with Rayleigh length
equal to half the module length. For seed pulses of 30 fs
FWHM and of energy 3 nJ for 10 to 40 eV photons and 1
nJ for 40 to 100 eV give corresponding approximate peak
powers of 100 kW and 30 kW. The saturation power over
the operational spectral range as calculated by both Genesis (in steady state mode) and Xie formulae [8] are shown

65

MOPPH012

Proceedings of FEL 2006, BESSY, Berlin, Germanyin Fig. 5. Both planar and helical mode results are shown.

Figure 5: Summary of saturation power estimates for the
XUV-FEL across its spectral operating range. 3-D Genesis
steady-state (SS) simulations and the Xie formulae are inexcellent agreement.
Note that the Xie design formulae cannot take into accountmixed planar/helical undulators, so the ’Xie Helical’ estimates assume a helical-only undulator for the equivalent
length of the planar-helical combination. The Xie estimatesalso do not include the effects of gaps between undulator
modules. These differences account for the small discrepancy of the ‘Xie Helical’ estimates from the other simulations, in the slightly higher saturation power estimation.
Notwithstanding this, the 3-D numerical and Xie estimates
are in excellent agreement. In Fig. 6, the length of undulator required for saturation is plotted as a function of photon
energy. Note that the gaps between undulator modules are
not included in this length and must be added on to obtain the total length of the combined undulator-focussing
lattice.

CONCLUSIONS
A robust conceptual design for the XUV-FEL has beendeveloped. Established FEL theory and state-of-the-art
simulation codes predict this free-electron laser will generate 8-100 eV photon energies at giga-watt power levels
and, as shown elsewhere [3], in pulses of duration 40-60 fs
FWHM. The pulses will have very good temporal and spatial coherence with time-bandwidth products close to the
Fourier transform limit for a Gaussian pulse [3, 5]. Unlike
the SASE mode of operation, which effectively self-starts
from intrinsic noise, the FEL interaction here is truly acting
as a simple, bandwidth limited amplifier. So long as the radiation input seed pulses have sufficient spectral purity, theoutput radiation is very nearly a simple amplified versionof the input. Recent advances in the High Harmonic seed
sources of choice ensure that the seed requirements for the
XUV-FEL already exist [2, 3]. Research in the next de-66

Figure 6: Summary of steady-state 3-D Genesis simulation estimates for the XUV-FEL undulator saturation length
across the spectral operating range.
sign phase will require full start-to-end simulations fromthe electron gun through to the end of the undulator. This
will allow the modelling of the FEL interaction with more
realistic electron pulses than that used here which assume
a Gaussian variation of most variables. Investigation of tolerances, for example in quadrupole position and undulator
field errors, will also be required, as will a more detailed
study of the effects of relative electron-seed pulse jitter than
the initial results presented at this conference [4]. Extension of the operational range down to 6eV photons may bepossible and will be investigated further in the next designphase.

REFERENCES[1] 4GLS Conceptual Design Report, Council for theCentral Laboratory of the Research Councils, UK,
http://www.4gls.ac.uk/documents.htm#CDR (2006)[2] B. Sheehy et al., High harmonic seeding and the 4GLS XUVFEL, 37th ICFA Advanced Beam Dynamics Workshop on
Future Light Sources, Hamburg, Germany (2006)[3] B.W.J. Mc Neil, The Use of HHG at 4GLS, (ibid.) (2006)[4] D. Dunning, First Tolerance Studies for the 4GLS FEL
Sources, (ibid.) (2006)[5] B.W.J. Mc Neil et al., Design considerations for the 4GLSXUV-FEL, Proceedings of the 27th International Free Electron Laser Conference, Stanford, USA (2005)[6] B. Faatz and J. Pflger, Nucl. Inst. Meth. Phys. Res. A, 475,
603 (2001)[7] S. Reiche, Nucl. Inst. Meth. Phys. Res. A, 429, 243, (1999)[8] Ming Xie, Proc. Of 1995 Part. Accel. Conf., 183 (1996)

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Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH014

OPTIMIZATION OF PARAMETERS OF SMITH-PURCELL BWO ∗Vinit Kumar† ,RRCAT, Indore, M.P. 452013,INDIA
Kwang-Je Kim, ANL, Argonne, IL 60439,USA.
Abstract
We study the dependence of start current in SmithPurcell backward wave oscillator (SP-BWO) on grating parameters and electron beam parameters. The attenuation
due to finite conductivity of the grating material is taken
into account and three-dimensional effects are included in
an approximate way in the analysis. We find that the start
current can be significantly reduced by optimizing the grating parameters.

INTRODUCTION
The Smith-Purcell free-electron laser (FEL) is a backward wave oscillator (BWO) for low energy electron beam
[1,2]. In a BWO, like any oscillator system, the electron
beam current needs to be higher than a threshold value,
known as the start current, in order to produce coherent
electromagnetic oscillation. In a recent paper [2], we have
performed a calculation of start current for the case of sheet
electron beam skimming over the grating surface in a SPBWO. The attenuation of the backward wave due to finite conductivity of the grating was not taken into accountin this calculation. The issue of attenuation becomes important while optimizing the parameters of SP-BWO. Recently, Andrews et al. [3] have discussed the calculationof attenuation coefficient for the backward wave supportedby the grating. They have also studied the dependence ofgain and attenuation in SP-BWO as a function of group velocity as the energy of the co-propagating electron beam isvaried, keeping the grating parameter fixed. In this way,
they have calculated the net gain. However, gain does nothave a straightforward meaning in a BWO. In this paper,
we therefore present a calculation of start current taking
into account the effect due to attenuation. We use this calculation to study the dependence of start current on grating
parameters as well as electron beam parameters.

START CURRENT CALCULATION
In a SP-BWO, the electron beam interacts with the copropagating surface electromagnetic mode supported by
the grating. The co-propagating surface mode has a groupvelocity in the direction opposite to the electron beam. We
consider a sheet electron beam in the (y, z) plane propagating at a height b from the grating top surface along thez-axis. The grating grooves are in the y-direction and perpendicular to the grating is in the x-direction. Due to the∗ Work supported by U.S. Department of Energy, Office of Basic Energy Sciences, under Contract No. W-31-109-ENG-38.
† vinit@cat.ernet.in

FEL Theory

finite conductivity of the material of the grating, the surface
electromagnetic mode suffers attenuation. The attenuation
coefficient can be calculated as per the prescription given
by Andrews et al. in Ref. 3. Attenuation occurs in the direction in which the energy is flowing. Here, the phase velocity of the resonant surface mode is along the positive zaxis and the group velocity v g is along the negative z-axis.
Let the longitudinal component of the the electric field of
the backward wave be given by E(z, t) exp(ik 0 z − iωt).
Including attenuation in the analysis, the equation for theevolution of the amplitude E(z, t) of the backward wave
described in Ref. 2 gets modified to∂E
1 ∂E
IZ0 χ −2Γ0 b −iψ−=ee + αE,
∂z
vg ∂t
2βγΔy

(1)

where α is the complex attenuation coefficient having positive real part. Note that we are here closely following
the notations and derivations given in Ref. 2. Here, I is
the electron beam current, Δy is the beam width in the ydirection assumed to be so large that two-dimensional approximation is valid, β is the electron velocity in the unitof speed of light c, γ is the electron energy in unit of rest
energy, Z 0 = 377 Ω is the characteristic impedence of freespace, Γ0 = k0 /γ, ψ is the electron phase and χ is theresidue of the singularity associated with the surface modeas defined in Ref. 2. Converting to dimensionless variables,
this equation can be transformed to the following form
∂E
∂E−
= −J e−iψ  − αLE,
∂τ
∂ζ

(2)

where L is the length of the grating, E is the dimensionlesselectric field, J is the dimensionless beam current, τ is thedimensionless time and ζ = z/L is the normalised distancealong the grating [2]. The second term in the right handside of the above equation is the contribution due to attenuation. The above equation for the evolution of surface mode
electric field will be coupled to equations for the electron
beam dynamics as discussed in Ref. 2. We then linearise
the equations and look for the solution for the electric fieldgrowing as eντ . For a given value of J and αL, we can obtain the complex growth rate ν by simultaneously solving
the following set of two equations
κ3 − (ν + αL)κ2 + iJ = 0.
κ21 (κ2 − κ3 )eκ1 + κ22 (κ3 − κ1 )eκ2
+κ23 (κ1 − κ2 )eκ3 = 0.

(3)
(4)

Note that we have ignored the space charge parameter Q
defined in Ref. 2, and assumed Q = 0. Here, κ 1 , κ2 andκ3 are three solutions for κ in Eq. (3). For a particular

67

Proceedings of FEL 2006, BESSY, Berlin, Germany

value of αL, by solving these equations numerically, we
can find out the minimum value of J for which the realpart of ν is positive. Let us call this as dimensionless start
current denoted by J s , which is a function of αL. For thecase when there is no attenuation (αL = 0), we had earlier
obtained that Js =7.68 [2]. Here, by numerically solving
Eqs. (3) and (4), we obtain the dependence of J s on αL.
This is shown in Fig. 1. Note that J s depends only on thereal part of αL.
The expression for the start current density dI s /dy isgiven bydIs
IA β 4 γ 4 2Γ0 b= Js (αL)
e,dy2πχ kL3(5)

where IA = 17 kA is the Alfvén current. Here, k = ω/c= 2π/λ and λ is the free space wavelength of the surface
mode. In the next section, we use the above formula tocalculate and optimize the start current.

First, we calculate the attenuation coefficient for different values of groove depth d and groove width w. For w =62 μm, we vary the groove depth d and find out the attenuation coefficient α for each groove depth. This is shownin Fig. 2(a). Note that for the calculation of the attenua1000(a)Attenuation (per m)

MOPPH014

100

1000

10
50

75

100

125

150

175

200

Groove depth, Groove width (μm)
100

(b)

Js

1000

1
0

2

4

6

8

10

χ (per cm)

10

100

Re(αL)

Figure 1: Plot of threshold dimensionless current J s as afunction of the real part of the attenuation coefficient αL.

OPTIMIZATION OF GRATINGPARAMETERS
In the past, many authors [1-5] have used the parameters
corresponding to the Dartmouth experiment [6] for studying the performance of SP-BWO. For the Dartmouth experiment, the grating parameters and the electron beam parameters are given in Table 1. Note that we interpret theelectron beam radius in Table 1 as the parameter b in ourmodel. Using the formula derived in the previous section,
we optimize the grating parameters for this case to minimise the start current.
Table 1: Parameters for the Dartmouth experiment
Groove width (w)Groove depth (d)Period (λg )Grating length (L)Electron beam radius (b)Electron beam energy

68

62 μm
100 μm
173 μm12.7 mm
10 μm
35 keV

10
50

75

100

125

150

175

200

Groove depth, Groove width (μm)

Figure 2: Plot of the real part of attenuation coefficient α(a), and the χ parameter (b) as a function of groove depth(solid curves) for groove width = 62 μm, and as a functionof groove width (dashed curves) for groove depth = 150μm.
tion coefficient, we have chosen Aluminum as the materialof the grating and used the prescription given by Andrews
et al. in Ref. 3. Then, keeping w = 62 μm, we calculate χ for different values of d as shown in Fig. 2(b). For
the calculation of χ, we have used the prescription given in
our earlier paper [2]. Next, knowing the value of α and χ,
we use Eq. (5) to obtain the start current density as a function of groove depth for w = 62 μm. As the groove depth
increases from 100 μm, the χ parameter increases, whichmeans that the start current density decreases. However, as
the groove depth is increased beyond 100 μm, the attenuation also increases, which tends to reduce the start current

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

1000
950

Resonant wavelength (μm)

density. Consequently, there is an optimum groove depth atwhich dIs /dy is minimum. As we find in Fig. 3, the start
current density is minimum for d = 150 mm. The value of
dIs /dy reduces from 40 mA/mm to 7.7 mA/mm when thegroove depth is changed from 100 μm to 150 μm.
After optimizing the groove depth, we next optimize thegroove width. Keeping d = 150 μm, we vary w from 50 μm
to 150 μm and obtain the attenuation coefficient and theχ-parameter as shown in Fig. 2. Then, using Eq. (5), we
obtain the value of dI s /dy for different values of groove
width, keeping groove depth fixed at 150 μm. This isshown in by the dotted curve in Fig. 3. We find that the
optimum value of groove width is 110 μm for which thestart current density is 5.6 mA/mm.
Hence, we find that the parameters for the Dartmouth
experiment are not optimized for the minimum value ofthe start current. The optimized value of the groove depth
and the groove width are 150 μm and 110 μm respectively. For these parameters, the start current density is 5.6
mA/mm, which is a substantial reduction compared to start
current density of 40 mA/mm corresponding to the parameters given in Table 1.

MOPPH014

900
850
800
750
700
650
50

75

100

125

150

175

200

Groove depth, Groove width (μm)

Figure 4: Plot of the free-space resonant wavelength λ withgroove depth (solid line) as well as groove width (dashedline). For the solid line, we have kept grove width = 62 μm.
For the dashed line, groove depth = 150 μm.

50

DISCUSSIONSdIs/dy (mA/mm)

40

30

20

10

0
60

80

100 120 140 160 180 200

Groove depth, Groove width (μm)

Figure 3: Plot of the start current density dI s /dy withgroove depth (solid line) as well as groove width (dashedline). For the solid line, we have kept groove width fixedat 62 μm. For the dashed line, the groove depth is fixed at
150 μm.
In the above calculations, when we change the groove
width and the groove depth, the resonant wavelength λ ofthe surface mode also changes. The value of λ can be obtained by finding out the location of the singularity of thereflection matrix associated with the surface mode, as discussed in Ref. 2. Fig. 4 shows the variation of the resonant
wavelength. We find that for w = 110 μm and d = 150 μm,
for which the start current is minimum, the resonant wavelength is 819 μm. Note that for the calculation of dI s /dy,
one needs to put the value of the free-space resonant wavelength λ of the surface mode in Eq. (5), which has beentaken from Fig. 4.

FEL Theory

We would now like to discuss the dependence of the start
current on the length of the grating. It is important to include three-dimensional effects for such an analysis [7]. A
fully three-dimensional analysis of SP-BWO does not exist yet. However, we will attempt an approximate analysis
here. The surface mode in the (y, z) plane is expected todiffract freely as an optical packet of wavelength βλ since
the grating is open in y-direction. The minimum average
rms beam size of the optical beam
 over the length L due todiffraction effects is given by βλL/4π. In order to maximize the overlap between the electron beam and the optical beam, the rms electron beam size σ y in the y-direction
should be chosen equal to this. Putting the electron beam
size in the y-direction in Eq. (5), we obtain that the start
current Is should be proportional to J s (αL)/L5/2 . As we
increase the length, the start current increases due to increase in Js . This is however counterbalanced by the L 5/2
factor in the denominator. For αL < 1, J s can be assumed
to be slowly varying. Hence, the start current should decrease as 1/L5/2 . For the larger values of αL, the attenuation effects will be dominating since J s becomes exponential as shown in Fig. 1. In this case, the start current
increases with grating length.
One of the important requirements for the operation of
SP-BWO is that the electron beam should be sufficiently
close to the grating surface. As the electron beam size inthe x-direction increases, the start current increases exponentially due to the exp(2Γ 0 b) factor in Eq. (5). Hence,
the rms electron beam size σ x in the x-direction should bearound 1/4Γ 0. In order that the electron beam size in the

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Proceedings of FEL 2006, BESSY, Berlin, Germany

x–direction is maintained around this value over a length
L, we need that the normalised electron beam emittance2
x is less than βγ/L(4Γ0 ) . We therefore notice that although the start current reduces by increasing the grating
length, the requirement on electron beam emittance in thex-direction becomes more stringent.
One should also confirm that the space charge effect does
not blow up the emittance. For this to be valid, the spacecharge term in the envelope equation should be less thanthe emittance term. This leads to the following conditionin the x-direction [7]
σx3
4 I
< 1.
βγ IA (σx + σy )2x

(6)

P/Δy (mw/mm)

It is important to point out here that for the Dartmouth parameters given in Table 1, the above inequality is not satisfied. After optimizing the grating parameters, the start
current is reduced and then the above inequality is satisfied.
10

3

10

2

10

1

10

0

10

-1

10

-2

10

-3

obtain P/Δy = 14.3 W/mm at saturation. This translates
to a power conversion efficiency of 0.56%.

CONCLUSIONS
We have derived a simple formula for the start current
density in a SP-BWO taking the attenuation due to finite
conductivity of the grating material into account. This formula has been used to optimize the parameters of the grating. We find that for the parameters corresponding to theDartmouth experiment, the start current can be reduced bysix times by optimizing the grating parameters.

ACKNOWLEDGMENTS
It is a pleasure to thank Charlie Brau for many helpful
discussions.

REFERENCES[1] H. L. Andrews and C. A. Brau, Phys. Rev. ST Accel. Beams,
7 (2004) 070701.
[2] V. Kumar and K.-J. Kim, Phys. Rev. E 73 (2006) 026501.
[3] H. L. Andrews et al., Phys. Rev. ST Accel. Beams, 8 (2005)
050703.
[4] J. T. Donohue and J. Gardelle, Phys. Rev. ST Accel. Beams,
9 (2005) 060701.
[5] D. Li et al., Phys. Rev. ST Accel. Beams, 9 (2005) 040701.
[6] J. Urata et al., Phys. Rev. Lett. 80 (1998) 516.
[7] K.-J. Kim and V. Kumar, under preparation.
[8] V. Kumar and K.-J. Kim, these proceedings.

0

2

4

6

8

10

12

14

Time (ns)Figure 5: Plot of power per unit beam width in the surface
mode as a function of time at the entrance of the grating forthe optimized grating prameters.

We would like to point out that for the optimized grating
parameters that we discussed, although the start current isreduced significantly compared to the grating parametersin Table 1, the attenuation is increased as seen in Fig. 2.
This means that the heat loss in the grating will be more
for the optimized parameters, which implies that the power
conversion efficiency of SP-BWO will be reduced. For example, for the optimized grating parameters that we discussed, Is /Δy = 5.6 mA/mm. For this case, if we take
I/Δy = 7 mA/mm, we obtain P/Δy = 900 mW/mm at
saturation as shown in Fig. 5. This translates to a power
conversion efficiency of 0.37%. Note that this calculationis performed by numerically solving the coupled MaxwellLorentz equations as discussed in Ref. 8. On the other
hand, for the Dartmouth parameters, we have I s /Δy = 40
mA/mm. For this case, if we take I/Δy = 50 mA/mm, we

70

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH015

ANALYSIS OF SMITH-PURCELL BWO WITH END REFLECTIONS ∗Vinit Kumar† ,RRCAT, Indore, M.P. 452013,INDIA
Kwang-Je Kim, ANL, Argonne, IL 60439,USA.
Abstract
We present a one-dimensional time-dependent analysis
and simulation of Smith-Purcell (SP) backward wave oscillator (BWO) taking end reflections and attenuation into
account. In the linear regime, we obtain an analytic solution and calculate the start current. The dependence of start
current on end reflections is studied taking the attenuation
due to finite conductivity into account.

INTRODUCTION
The Smith-Purcell (SP) free-electron laser in the terahertz (THz) regime using a low energy electron beam isa backward wave oscillator (BWO) [1,2]. Previous analyses of SP-BWO [1-3] have ignored the reflection at theends of the grating. However, there will in general be somereflection at the end of the grating due to discontinuity inthe medium. One can, if desired, also add external mirrors to enhance reflection. In the presence of reflection,
the start current, which is defined as the minimum valueof the electron beam current needed to produce coherent
electromagnetic oscillations, can be reduced. In this paper, we present a self consistent nonlinear analysis of SPBWO including end reflections and attenuation. We set up
Maxwell-Lorentz equations equations and develop a computer code to solve these equations. We present the results of numerical simulation and discuss the evolution of
power. In the linear regime, we solve the coupled MaxwellLorentz equations analytically and calculate the start current taking end reflection and attenuation into account.

MAXWELL-LORENTZ EQUATIONS
In a SP-BWO, the electron beam interacts with the backward surface wave co-propagating with the electron beam.
We assume that the electron beam is in the form of athin sheet moving along the z-axis above a metal gratingwith rectangular grooves, the direction of the grooves isalong the y-axis and the outward normal to the grating surface is along the x-axis. The plane of the sheet electron
beam is at x = 0, and the top surface of the grating is
at x = −b. We have earlier studied the interaction between the electron beam and the backward surface modeusing Maxwell-Lorentz equations where we ignored the reflection at the end of the grating [2]. The backward surface mode supported by the grating is a linear combination of infinite number of Floquet-Bloch harmonics hav∗ Work supported by U.S. Department of Energy, Office of Basic Energy Sciences, under Contract No. W-31-109-ENG-38.
† vinit@cat.ernet.in

FEL Theory

ing the z-component of propagation vectors differing fromeach other by an integral multiple of k g , where kg = 2π/λg
and λg is the period of the grating. The y-component H yof the magnetic
 field of the backward surface mode can be
written as
An exp(ik0 z + inkg z − Γn x − iωt), where
the summation is implied over all n from -∞ to +∞ [2].
Here, ω is the frequency, k 0 is thepropagation vector of2

the backward surface mode, Γ n = (k0 + nkg ) − ω 2 /c2
and c is the speed of light. The zeroth-order componentof this mode has the longitudinal electric field given by
E− (z, t) exp (ik0 z − iωt) at x = 0. The amplitude of
all other components of the backward surface mode haveto maintain a fixed ratio with the amplitude of the zerothorder component such that the electromagnetic field satisfies the required boundary conditions. Hence, as the zerothorder component of the surface mode evolves due to interaction with co-propagating electron beam, the amplitudeof all other components also evolve proportionately. One
can calculate the group velocity, which is dω/dk, fromthe dispersion relation of the backward surface mode. For
low energy electron beam, the group velocity of the copropagating surface mode having ω/k 0 = βc is along thenegative z-axis [1,2]. Let us denoted the magnitude of thegroup velocity by v g . Here, βc is the velocity of electrons.
For a grating with rectangular grooves considered here,a wave going along the positive z-axis will see the same
boundary as the wave going along the negative z-axis.
Hence, if we construct a mode having H y given by
An exp(−ik0 z − inkg z − Γn x − iωt), it will satisfy
the Maxwell equations and the required boundary condition for the reflection grating. This is actually the forward surface mode supported by the grating. This has
the propagation vector -k 0 and the group velocity v g along
the positive z-axis. Hence, the grating supports forward
as well as backward surface mode. However, none of
the components of the forward surface mode co-propagate
with the electron beam. Consequently, the forward surface
mode does not interact with the electron beam. It however arises due to reflection of the backward wave at theend of the grating. As the backward surface mode extracts
energy from the electron beam and grows, it gets reflected
at the end to the forward surface mode and consequently
the forward surface mode also grows. Let us denote thezeroth-order component of the forward surface mode as
E+ (z, t) exp(−ik0 z − iωt) at the location of sheet electron beam.
In our previous work [2], we had set up Maxwell equation for the backward wave, which is coupled to Lorentz
equations for the beam dynamics. We will now add theMaxwell equation for the forward wave to this set of equa-

71

MOPPH015

Proceedings of FEL 2006, BESSY, Berlin, Germany

tions. We will be following notations used in Ref. 2. Theenergy flows along the negative z-axis for the backward
wave and hence, it gets attenuated along the negative zaxis. Similarly, for the forward wave, the energy flows
along the positive z-axis and it gets attenuated along thepositive z-axis. The complex attenuation coefficient α forthe backward wave supported by a rectangular reflection
grating can be obtained as per the prescription given in
Ref. 3. For the forward wave, the complex attenuation coefficient will be simply −α. Taking the attenuation into account, the equation for the evolution of the amplitude E +of the forward wave becomes
1 ∂E+
∂E+
+
= −αE+ .
∂z
vg ∂t

(1)

The equation for the evolution of the amplitude E − of the
backward wave as derived earlier is given by [2,4]
∂E−
1 ∂E−
IZ0 χ −2Γ0 b −iψ−=ee + αE− , (2)
∂z
vg ∂t
2βγΔy
where I is the electron beam current, Z 0 = 377 Ω is thecharacteristic impedence of free space, χ is the residueof the singularity associated with the surface mode as defined in Ref. 2, γ is the energy of the electron beam inunit of rest energy, ψ is the electron phase and Δy is thewidth of the sheet electron beam in the y-direction. Boththese equations are coupled through boundary conditionat the end of the grating. Let ρ 0 and ρL be the complex reflection coefficient at the entrance and exit end of
the grating. The boundary conditions will then given by
E+ (z = 0) = ρ0 E− (z = 0), and E− (z = L)eik0 L =ρL E+ (z = L)e−ik0 L , where L is the length of the grating. The entrance and the exit of the grating are at z = 0
and z = L respectively.
In order to further simplify the analysis, we define a new
amplitude of the forward wave given by E + = −ρ0 Ẽ+ . The
boundary conditions, in term of this definition can then be
written as Ẽ+ (z = 0) = −E(z = 0) and E− (z = L) =Re−i2k0 L Ẽ+ (Z = L), where R = −ρ0 ρL . As discussed
in Ref. 2, we can define dimensionless variables and makea transformation from (z, t) to (ζ, τ ) to simplify the analysis. Here, ζ = z/L is the normalised length and τ is thedimensionless time defined in Ref. 2. We define dimensionless amplitude of the forward and the backward wave
denoted by E + and E− respectively as
E± =2

4π k0 LẼ± ,IA Z0 β 2 γ 3(3)where IA = 17 kA is the Alfvén current and Ẽ− = E− .
After making these transformations, the equation for evolution of E+ and E− are given by
∂E−
∂E−
−
∂τ
∂ζ
∂E+
∂E+
+ d1
∂τ
∂ζ

72

= −J e−iψ  − αLE− ,(4)= −d1 αLE+ ,(5)

where d1 = (vp + vg )/(vp − vg ). The boundary conditions
now become E + (ζ = 0) = −E− (ζ = 0) and E− (ζ = 1) =Re−i2k0 L E+ (ζ = 1). These equations are coupled to theelectron beam dynamics equations
∂ηi
∂ζ
∂ψi
∂ζ

=

(E− + Esc )eiψi + c.c.,

(6)

=

ηi ,

(7)

where the Esc is the dimensionless longitudinal electricfield due to space charge given by E sc = iQe−iψ , andQ = (J /χL)(χ1 − e2Γ0 b ). The χ1 -parameter appears
in the analysis of singularity associated with the surface
mode and can be calculated as per prescription discussed
in Ref. 2. Here the subscript i stands for i th electron andηi = (γi − γ)/γ is the relative energy deviation of the i thelectron. Eqs. (4-7) along with the boundary conditions
form the complete set of differential equations needed todescribe the one-dimensional time-dependent behavior of
SP-BWO with end reflections and attenuation. In the next
section, we discuss the analytic solution of these equationsin the linear regime.

LINEAR ANALYSIS
We can linearize Eqs. (4-7) around an equilibrium solution and perform a stability analysis to find out the parameter regime in which the instability for exchange of energy
from electron beam to electromagnetic oscillation can be
excited. For simplicity, let us assume that the injected beam
is monoenergetic, and η i = 0 for all the electrons at ζ = 0.
Further, we assume that the injected beam is unbunched,i.e., e−iψ0  = 0, where ψ0,i is the phase of the i th particleat ζ = 0. An equilibrium solution of the system of Eqs. (47) is obviously E − = 0, E+ = 0, ηi = 0, and ψi = ψ0,i . Let
us define the perturbative solution by E − = ˜− , E+ = ˜+ ,ηi = δη i , and ψi = ψ0,i + δψ i . We introduce the following collective variables as done by Bonifacio et al. [5] forconventional FELs:x̃ = δψe−iψ0 ,

ỹ = δηe−iψ0 .

(8)In terms of these variables, Eqs. (4-7) can be linearized andwritten as
∂˜−
∂˜−
−
∂τ
∂ζ
∂˜+
∂˜+
+ d1
∂τ
∂ζ
∂ x̃
∂ζ
∂ ỹ
∂ζ

=

iJ x̃ − αL˜
− ,

(9)

=

−d1 αL˜
+ ,

(10)

=

ỹ,

(11)

=

˜− + Qx̃.

(12)

The boundary conditions for these equations are: (1) x̃ =0 at ζ = 0 at all τ since the injected beam has no phasemodulation, i.e., it is injected unbunched. (2) ỹ = 0 at ζ =FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany
0 at all τ since the injected beam has no energy modulation,
− at ζ =i.e., it is injected monoenergetically. (3) ˜+ = −˜
0 for all τ , and ˜− = Re−i2k0 L ˜+ at ζ = 1 for all τ .
Assuming a solution of the type e ντ , we can find out thegrowth rate ν for the above linearised equations with theboundary conditions. In order to find out the growth rate ν,
one has to first solve the following cubic equation
κ3 − (ν + αL)κ2 − Qκ + νQ + iJ = 0.

(13)

Then, the three roots of the above cubic equation κ 1 , κ2 andκ3 should satisfy the following transcendental equation
Re−αL e−i(2k0 L−i d1 ) [(κ21 − Q)(κ2 − κ3 )+(κ22 − Q)(κ3 − κ1 ) + (κ23 − Q)(κ1 − κ2 )]MOPPH015

given set of parameters, if we make a slight change in theelectron beam energy, the value of ξ changes accordingly
and affects the value of start current. For our parameters, Q
is very small, and we take Q = 0. Figure 1 shows the variation of dimensionless start current J s with ξ for R = 0.8.
We find that that the value of J s oscillates between 11.1
and 14.2. Note that the start current density corresponding
to J = 11.1 is 4.7 mA/mm. The value of J s is 12.7, when
we neglect end reflection. When the attenuation is smaller,
the effect of end reflection is more pronounced.

NUMERICAL SIMULATIONν+(κ21 − Q)(κ2 − κ3 )eκ1 + (κ22 − Q)(κ3 − κ1 )eκ2+(κ23 − Q)(κ1 − κ2 )eκ3 = 0.

(14)

By solving the above two equations, we can find out theminimum value of J , called the dimensionless start current
Js for a given Q, R, α and L, for which the real part of thecomplex growth rate ν is positive.
14.5
14.0
13.5

Js

13.0
12.5
12.0
11.5
11.0
0.0

0.5

1.0

1.5

2.0

2.5

3.0

ξ

Figure 1: Variation in the dimensionless start current with
ξ for R = 0.8 (solid curve) and R = 0 (dashed curve).
Next, we use Eqs. (13-14) for the calculation of start current. In a companion paper [4], we have optimized the parameters corresponding to Dartmouth experiment [6] taking attenuation into account, but excluding end reflection.
We use those parameters for calculation of start current
here. For the grating, we use groove depth d = 150 μm,
groove width w = 110 μm, period λ g = 173 μm and length
L = 12.7 mm. For the 35 keV sheet electron beam, we use
b = 10 μm. From our calculation [2], for these parameters, we obtain the free-space wavelength λ = 819 μm,
χ = 120 per cm, χ 1 = 3.9, αL = 0.94(1 − i) and v g /c =0.0925. Note that in Eq. (14), for a given grating length,
when we change the electron beam energy, the value of
k0 will change, which will change the phase factor term
e−2ik0 L . Let us define ξ = mod(k 0 L, π). Hence, for a

FEL Theory

For numerically solving Eqs. (4-7), we use the approach
used by Ginzburg et al. [7] and later also by Levush
et al. [8] for BWO. The electron dynamics equations fora given field distribution along the interaction region aresolved by the predictor-corrector method. Then, knowing
the modified electron distribution in phase space, the field
distribution at the next time step is obtained by solving thepartial differential equations (Eqs. 4-5) by the finite difference method. The method is stable for Δτ < Δζ for the
backward wave and for Δτ < (1/d 1 )Δζ for the forward
wave. Here, Δτ and Δζ are the step sizes in τ and ζ respectively, used in the finite difference method.
For initializing the electron beam in phase space, we
simulate the shot noise using the algorithm given by Penman and McNeil [9], which is commonly used in FEL
codes.
We performed a couple of tests on the code we developed. We first checked for the convergence of the solution
by increasing the number of particles and also by reducing
the step size. Based on this convergence test, we chose thenumber of particles to be used in the simulation as 1024 andthe step sizes as Δτ = 0.01 and Δζ = 0.02. We also confirmed that the energy conservation equation along with thedamping term due to attenuation is satisfied in the code ateach integration step.
Figure 2 shows the evolution of power in the backward
wave at the entrance of the grating for J = 11.6 and J =10.6. The parameters used in the calculation are same as
mentioned in the last section. We have chosen ξ = 2.5 forwhich Js is minimum as shown in Fig. 1. For these parameters, Js = 11.1 and hence for the case J = 10.6, there
is no build-up of power, whereas for the case J = 11.6,
we find that the power grows exponentially and saturates.
Note that I/Δy = 4.9 mA/mm for J = 11.6. After saturation, the variation of the amplitude of electric field for theforward as well as the backward wave along the length of
the grating is shown in Fig. 3.
Let us now discuss the calculation of outcoupled power.
Power in the backward and the forward surface mode denoted by P− and P+ respectively can be obtained by thefollowing expression
2βγ mc2 β 3 γ 3P2=2e2Γ0 b |E| ,ΔyZ0 χ
ek0 L2(15)73

MOPPH015

Proceedings of FEL 2006, BESSY, Berlin, Germany

2

10

1

P/Δy (mW/mm)

10

0

10

-1

10

-2

10

-3

10

-4

10

0

20

40

60

80

Time (ns)Figure 2: Evolution of power in the backward wave at theentrance of the undulator for J = 11.6 (solid curve), and J= 10.6 (dashed curve). We have used R = 0.8 and ξ = 2.5
in the calculation.

1.8

Electric field amplitude (arb. unit)

1.6
1.4
1.2
1.0

at higher value of beam current. Our emphasis here is toshow that including reflection, it is possible to reduce thestart current surface density to as low as 4.7 mA/mm.
In our calculation, we have not calculated the value of reflectivity, instead we have assumed a value for reflectivity.
In a realistic situation, there will be some reflectivity at theend of the grating due to change of boundary, which needs
to be calculated. However, we can put an external mirror
and the reflectivity R can be adjusted to a desired value.
By introducing a reflectivity, the start current is reduced,
but the outcoupled power may not be optimized. Using our
calculation in the saturation regime, one can optimize theparameters to obtain optimum combination of start current
and outcoupled power.

CONCLUSIONSIn this paper, we have set up Maxwell-Lorentz equations for the one-dimensional time-dependent analysis of
SP-BWO including end reflection and attenuation due tofinite conductivity. We have obtained a solution in thelinear regime and extended the analysis to the nonlinear
regime by solving the Maxwell-Lorentz equations numerically. Our analysis can be used for detailed optimization ofoutcoupled power and start current in SP-BWO taking end
reflection and attenuation into account.

REFERENCES

0.8[1] H. L. Andrews and C. A. Brau, Phys. Rev. ST Accel. Beams,
7 (2004) 070701.

0.6
0.4

[2] V. Kumar and K.-J. Kim, Phys. Rev. E 73 (2006) 026501.

0.2[3] H. L. Andrews et al., Phys. Rev. ST Accel. Beams, 8 (2005)
050703.

0.0
0

2

4

6

8

10

12

z (mm)

Figure 3: Variation of the amplitide |E − | of the backward
wave (solid curve) and the amplitude |E + | of the forward
wave (dashed curve) along the length of the grating for J= 11.6. Other parameters are same as those used in Fig. 2.

[4] V. Kumar and K.-J. Kim, these proceedings[5] R. Bonifacio, C. Pelligrini, and L. M. Narducci, Opt. Commun. 40 373 (1984).
[6] J. Urata et al., Phys. Rev. Lett. 80 (1998) 516.
[7] N. S. Gingburg, S. P. Kuznetov, and T. N. Fedoseeva, Sov.
Radiophys. Electron., 21 (1979) 728.
[8] B. Levush et al., IEEE Trans. Plasma Sci. 20, (1992) 263.

where P = P− for E = E− and P = P+ for E = ρ0 E+ . The
outcoupled power P 0 at the entrance of the grating is givenby P− (z = 0) − P+ (z = 0) and at the exit, the outcoupled power P1 is given by P+ (z = L) − P− (z = L). If
we assume ρL = 1, the power will be outcoupled only atthe entrance of the grating. For the case of Fig. 3, the outcoupled power is calculated to be 54 mW for Δy = 1 mm.
The total power in the electron beam for this case is 171.5
W for 35 keV, 4.9 mA electron beam current. Hence, theoverall efficiency is only 0.03%. Such a low efficiency isthere beacuse we have chosen the electron beam current
very close to the start current and also the heat loss occurring in the grating due to attenuation deteriorates the efficiency. We have checked that the efficiency is improved74[9] C. Penman and B. W. J. McNeil, Opt. Commun. 90 (1992)
82.

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH016

MODE COUPLINGS IN A RAMAN FREE-ELECTRON LASER WITH IONCHANNEL GUIDING
B. Maraghechia,b,* , T. MohsenpouraaDepartment of Physics, Amirkabir University of Technology, Tehran, Iranb
Institute for Studies in Theoretical Physics and Mathematics (IPM),
P.O. Box 19395-5531, Tehran, Iran.
Abstract
The free-electron laser (FEL) theory in the collective or
Raman regime relies on the unstable coupling between
the radiation and the negative-energy space-charge wave.
Due to the high density and low energy of electron beama focusing mechanism like an axial magnetic field is
usually required to guide the beam. It is found that the
wiggler has direct effect on the right and left waves andthe wiggler effect on their dispersion relations are of thesecond order in the wiggler amplitude. Due to the fully
relativistic treatment the dispersion relation is to fourthorder in wiggler amplitude and it can be used to study
new couplings between the negative and positive-energy
space-charge waves as well as between the right and left
circularly polarized electromagnetic waves.

INTRODUCTION
Relativistic electron bean injected into an ionizedplasma channel ejects plasma electrons leaving a positiveion core which attracts and confines the beam electron.
There are important applications in this subject such asadvanced accelerators >@ and free-electron lasers (FELs)>@. Ion-channel guiding as an alternative to theconventional axial magnetic-filed guiding, was first
proposed for use in FELs by Takayama and Hiramatsu>@. Experimental results of a FEL with ion-channel
guiding have been reported by Ozaki at al. >@ Also, Yu et
al. >@ have reported that the combination of ion focusing
and beam conditioning would lead to high gain FEL
operation in the soft x-ray regime. Jha and Wurtele >@developed a three-dimensional code for FEL simulationthat allows for the effects of an ion channel. The
theoretical studies of this problem with a helical wiggler
are carried out in the low-gain >@ and high-gain >@regimes. In Ref 10, the relativistic Raman backscattering
theory is used to find the FEL dispersion relation with
ion-channel guiding, in the beam frame of electrons, withthe left circularly polarized backscattered wave neglected.
This DR was used to find the growth rate of the FEL
resonance due to the coupling of radiation with the slow
space-charge wave.
The purpose of the present investigation is to obtain thedispersion relation (DR) for the interaction of all possible
waves in a relativistic electron bean that passes through a
one-dimensional helical wiggler magnetic field with ionchannel guiding. The motion of a relativistic electron* Electronic mail: behrouz@aut.ac.ir
FEL Theory

through the wiggler is analyzed. Three coupled equations
are derived and a formula for the general DR is obtained.

ELECTRON MOTION
Consider a relativistic electron moving along the z axisof an idealized helical wiggler magnetic field describedby
B B w xˆ cos k w z  yˆ sin k w z ,(1)
where Bw denotes the wiggler amplitude, andkw

2S O w is wiggler wave number. In the presence ofan ion channel, with its axis coincident with the wiggler
axis, the following transverse electrostatic field is acted
on the electron beam
E i 2 S e ni x xˆ  y yˆ ,(2)where ni is the number density of positive ions withcharge e. The steady-state motion of an electron in theabove field consists of an axis centred helical motion,with radius R 0 v w k w v|| , given by Eq. (16) with >@vw: w k w v||2

Z i2  k w2 v||2,(3)

where : w { e B w J m c , Z i2 2S ni e 2 J m , m is theelectron rest mass, e is the magnitude of the charge of anelectron, and c is the speed of light in vacuum. Thisvelocity is related to the axial velocity v|| throughJ 0 2

v w2

v||2

.
(4)
c
c2
Equation (4) is cubic in v||2 c 2 and describes two classes12

of trajectories propagating along the positive z axis of the
FEL.

DISPERSION RELATION
An
analysisofthepropagationofelectromagnetic/electrostatic waves in the electron beam
may be based on the continuity equation,wn   nv 0,(5)
wt
the relativistic momentum equation
dv
1
1
e §
·
(6)

¨E  2 v v E  v u B¸ ,J m0 ©
dt
c
c
¹

75

MOPPH016

Proceedings of FEL 2006, BESSY, Berlin, Germany

and the wave equation
1 w2 Eu uE  2
c wt2

w 4S e n v
.
wt c2

(7)

Here n is the electron density, v is the electron velocity,
J is the Lorentz factor corresponding to v , E is theelectric field, and B is the magnetic field. With theunperturbed electron density n 0 taken to be independentof position and time and the self-fields of the unperturbed
state neglected, the electron and field variables may be
expressed in the formnn 0  G n,v

v 0  G v,

(8)
(9)

E E i  G E,

(10)

B

(11)

B w  G B,

R R0 G R(12)
The linearized equations for the continuity equation, therelativistic momentum equation, and the wave equation
may be derived as
wG n
(13)
 n 0   G v  v 0  G n 0 ,
wt
wG v
1
e ª
 v 0  G v  G v   v 0 
G E  2 v 0 v 0 G E
wt
J 0 m 0 «¬
c



1
c

2

v 0 G v E i 

1
c

2

1
c

J2 §
1
 02 ¨ E i  v 0 u B w cc ©

 u  uG E 

1 w 2G E21c

G v v 0 E i  G v u B w  v 0 u G B2º·v 0 v 0 E i ¸ v 0  G v » ,
c
¹
¼»
1

2

(14)

w 4S eG n v 0  n 0 G v . (15)wt c 2c wt
By introducing a new set of basis vectorseˆ xˆ  i yˆ
2 , eˆ * xˆ  i yˆ
2 , and eˆ zˆ , theunperturbed magnetic field, electron density, andtransverse electrostatic field can be written as
B w B w 2 exp (ik w z )eˆ  B w 2 exp (ik w z )eˆ * , (16)v0Eiv w 2 exp (ik w z )eˆ  v w
 v|| ê z ,2 exp (ik w z )eˆ *i 2 S e ni R0 exp(ik w z )eˆ  exp(ik w z )eˆ ,(18)

The perturbed state is assumed to consist of alongitudinal space-charge wave and right and left
circularly polarized electromagnetic waves, referred here
as radiation, with all perturbed waves propagating in thepositive z direction. Accordingly, solution of the systemof equations (13)-(15) may be assumed as
G v G v R eˆ  G v L eˆ *  G v Z eˆ z ,
(19)

GE

2 S e ni G R R  G E R eˆ  2 S e ni G R L  G E L eˆ *
G EZ ê z ,(20)

G B G B R eˆ  G B L eˆ * ,76k  kw ,

kR

(26)
(27)

kL k  kw .
The linearized wave equation yield§ v·~
k R2 c 2  Z 2 E R 4S i eZ ¨¨ n~ w  n 0 v~R ¸¸ ,
2
©
¹
§
·
v
~
k L2 c 2  Z 2 E L 4S i eZ ¨¨ n~ w  n 0 v~L ¸¸ ,
2
©
¹
2 ~
~
~
Z E
4S i eZ n v  n v .
z

||

(28)
(29)
(30)

0 z

Similarly, the linearized continuity and momentum
equations yield(31)
n~ Z  k v|| n 0 k v~z ,ªºv 2 · Z 2 v w2
Z i2 §¨«Z  k R v|| 
1  w2 ¸  i A1 » v~R2¨¸Z  k R v|| © 2c ¹ k w v|| 2c«¬»¼ª Z 2 v w2
º
Z i2
v w2
i e ª§
« i A1 » v~L «¨12
2
Z  k L v|| 2c
J 0 m0 «¬¨©
¬« k w v|| 2c¼»

v w2 ·¸ k R v|| º ~i e v w2 ~i e v w v|| ~» ER 

EL 
Ez
2 ¸
2
J 0 m 0 2c
J 0 m 0 2c 2
2c ¹ Z »¼
 A2 v~z 0 ,
(32)


ª
º
v 2 · Z 2 v w2
Z i2 §¨«Z  k L v|| » v~L
1  w2 ¸  i
A

1
2
¨
¸

k
v
k
v
Z
2c ¹
«¬
»¼
L || ©
w || 2cª Z 2 v w2
º~
Z i2
v w2
i e ª§
Av
 « i


»
«¨1
R
1
2
Z  k R v|| 2c 2
J 0 m0 ¬«¨©
¬« k w v|| 2c¼»

v w2 ·¸ k L v|| º ~i e v w2 ~i e v w v|| ~» EL 

ER 
Ez
2 ¸
2
J 0 m 0 2c
J 0 m 0 2c 2
2c ¹ Z »¼
 A v~ 0 ,
(33)


(17)
*

G R G R R eˆ  G R L eˆ *(22)~
G n n exp[i (k z  Z t )] ,(23)
G v R v~R exp[i (k R z  Z t )] ,(24)~
G v L v L exp[i (k L z  Z t )] ,(25)
G v z and G E z are analogous to G n ; G E R , G R R , andG B R are analogous to G v R ; G E L , G R L , and G B L areanalogous to G v L ; the wave numbers are related to by

(21)

2

z

 i Z  k v|| v~z 2e §¨ v|| ·¸ ~e ª v w v||
1 2 Ez «
J 0 m0 ¨ c ¸
J 0 m 0 ¬ 2c 2©
¹

k R c vw º ~e ª v w v|| k L c v w º ~

»EL
«
»ER 
Z 2c ¼
J 0 m 0 ¬ 2c 2Z 2c »¼ª§ Z 2
Z i2 ·¸ v w v|| : w º ~» vR
 i «¨ i «¬¨© k w v|| Z  k R v|| ¸¹ 2c 2
2 »¼ª§ Z 2
Z i2 ·¸ v w v|| : w º ~» vL
 i «¨  i «¬¨© k w v|| Z  k L v|| ¸¹ 2c 2
2 »¼
where

0,

(34)

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

v||2

J || 2

1

,
2

(35)

AL

k L2 c 2  Z 2 ,k R2 c 2  Z 2 ,

(36)

AR

c

(37)

Z i2

·
v||
§ 1 · 2 v w §¨ v w
 :w ¸ ,¨ ¸J 0¨¸c © c k w v|| c
©2¹
¹

A1

(38)

§ 1 ·
§ 1 · 2 v|| § v w Z i2¨¸ k wvw  : w  ¨¸J 0 ¨¨¸¨¸c ¨© c k w v||
© 2¹
© 2¹
v||
·
(39)
 : w ¸¸ .
c¹
The electron density n~ may be eliminated in (30) by useof (29) to obtainZ  k v|| ~(40)
v~z iEz .
4S en 0with the use of Eqs. (28)-(31) and (40), v~R , v~L and v~z
may be eliminated in the three components of the
momentum equation (32)-(34) to obtain~~
D R0  \ R v w2 c 2 E R  \ L v w2 c 2 E L  [ R1 v w c~
 M  v w3 c 3 E z 0 ,
(41)
 2
 2
2 ~
0
2 ~
\ R v w c E R  D L  \ L v w c E L  [ L1 v w c~
 M  v w3 c 3 E z 0 ,
(42)
A2

>

@

@

§v · ~
© c ¹

@

>

>

§v · ~
© c ¹

@

>

@

>

ª

§ Z i2¨ Z  k L v||©

[ R 2 ¨¨ w ¸¸ E R  [ L 2 ¨¨ w ¸¸ E L  Z «H 0  k v|| ¨

Z i2· v w2 º ~¸» Ez 0 ,Z  k R v|| ¸¹ 2c 2 ¼»«¬

H 0 are defined in the appendix. Here, DR0 , DL0 , and H 0
are the uncoupled dispersion relations, i.e., in the absenceof the wiggler, for the right and left circularly polarized
electromagnetic waves, and the space-charge wave,
respectively. Equations (41) and (42) show that the DR
for the right and left waves, alone, in the absence of theother two waves, are
D R D R0  \ R v w2 c 2 0 ,(44)
D L D L0 \ L v w2 c 2 0 ,(45)which indicate that the wiggler has direct effect on theright and left waves and the wiggler effect on their DRs
are of the second order in the wiggler amplitude. On theother hand, Eq. (43) Shows that the DR for the spacecharge wave in the absence of the right and left wave is
H 0 0 , which indicates that the wiggler has no direct
effect on the space-charge wave. The reason is that thetransverse helical motion of electrons, due to the wiggler,
has no effect on the longitudinal oscillations of the spacecharge wave. Therefore, if the electromagnetic waves are
removed the wiggler effect on the space-charge wave will
FEL Theory

also be removed and the space-charge wave will be
unaffected by the wiggler in the absence of the transverse
electromagnetic waves.
The necessary and sufficient condition for a nontrivial
solution consists of the determinant of coefficients in Eqs.
(41)-(43) equated to zero. Imposing this condition yields
the dispersion relation
ª
§ Zi2
ª
Zi2 ·¸º» DR DL  « DR [ L 2Z «H 0  Z k v|| ¨¨ Z  k L v|| Z  k R v|| ¸»
¬«
©
¹¼
¬«
2 ·
2 ·º 2ª§§¨ [ L1  M  v w ¸  D L [ R 2 ¨ [ R1  M  v w ¸» v w  «\ L [ R 2¨¨c 2 ¸¹c 2 ¸¹»¼ c 2 «¬
©
©

2 ·
2 ·
§
§
¨ [ L1  M  v w ¸ \ R [ L 2 ¨ [ R1  M  v w ¸  Z H 0\ L \ R¨¨c 2 ¸¹c 2 ¸¹©
©
§ Z i2
Z i2 ·¸º v w4.
(46)»
 \ L \ R Z k v|| ¨¨ Z  k L v|| Z  k R v|| ¸» c 4©
¹¼
Equation (46) is the DR for coupled electrostatic andelectromagnetic waves propagating along a relativistic
electron beam in the presence of a wiggler magnetic field
and an axial guide magnetic field. A numerical analysis of
the general dispersion relation can be used to study
interactions among all possible waves. In group II orbits,with relatively large wiggler induced velocities, newcouplings between the negative and positive-energy
space-charge waves as well as between the right and left
circularly polarized electromagnetic waves are expected
to be found. These instabilities are distinct from the usual
FEL resonance.

APPENDIX: DEFINITION OF
QUANTITIES(43)

where DR0 , DL0 , \ Rr , \ Lr , M r , [ R1 , [ R 2 , [ L1 , [ L 2 ,MOPPH016

The following quantities are used in equations (41)-(43)§Z i2 ·¸
D R0 ¨ Z  k R v|| AR  Z 2p (Z  k R v|| ) ,
¨
¸
Z

k
v
R || ¹©
2§·Zi¸ AL  Z 2p (Z  k L v|| ) ,DL0 ¨ Z  k L v|| 
¨
¸

Z
k
v
L || ¹
©

\ Rr

2
º
·
Z2
§ 1 · ª§¨ Zi
 i r J 02k wv|| ¸ AR  ZZ 2p » ,¨ ¸«¸© 2 ¹ «¬¨© Z  k R v|| k wv||
»¼
¹

2
·
Z2
Z i2
§ 1 · ª§¨ Z i
 i# J 02 k w v|| ¸ AL¨ ¸«¨¸© 2 ¹ «¬© Z  k L v|| k w v|| Z  k L v||¹º
 ZZ 2p »»¼·
Zi2§ Z k c · § Zi2r 2 J 02 kw v|| ¸ ,
Mr ¨
¨
¸¨
¸
© 2 2 ¹ © Z  k R v|| Z  k L v||¹
2·v§ Z ·ª §Zi¸  Z 2p ||¸ «k c¨ Z  k R v|| [ R1 ¨¨¸ ¨¸Z  k R v|| ¹c© 2 ¹ «¬ ©

\ Lr

77

MOPPH016

Proceedings of FEL 2006, BESSY, Berlin, Germanyº§ Z 2 c J 02 k w v|| ·¸ Z  kv » ,¨ i 2 
||
¨k v
c ¸
»
© w ||¹¼[ L1v§ Z ·ª §Z i2 ·¸2 ||¸ «k c¨ Z  k L v|| 
¨
Z

p
¸ ¨
¨
Z  k L v|| ¸¹c© 2 ¹ «¬ ©

º
§ Z 2 c J 02 k w v|| ·¸ Z  kv » ,¨ i 2 
||
¨k v
c ¸
»
© w ||
¹
¼

[ R2

§ Z2
§ 1 ·ªZ 2c
Z i2 ·¸¨¸ «  AR ¨ i  i  k w c ¨¸¨ k wc k v 2
Z  k R v|| ¸¹© 2 ¹ «¬w ||©
º
 Z 2p k R c  Z v|| c » ,
¼»

[ L2

H0

ª
§ Z2
Z 2c
Z i2 ·¸§ 1 ·«¨ ¸  AL ¨  i  i 2  k w c ¨ k wc k v
Z  k L v|| ¸¹© 2 ¹«w ||©
¬º Z 2p ( k L c  Z v|| c) » ,»¼(Z  kv|| ) 2  Z 2p J ||2 .
REFERENCES>@ E. Esarey, P. sprangle, J. Krall, and A. Ting, IEEE
Trans. Plasma Sci. 24 (1996) 252.
>@ D.H. Whittum, A.M. Sessler, and J.M. Dawson, Phys.
Rev. Lett. 64 (1990) 2511.
[3] S. Wang, C.E. Clayton, B.E. Blue et al., Phys. Rev.
Lett. 88 (2002) 135004.
>@ K. Takayama and S. Hiramatsu, Phys. Rev. A 37
(1988) 173 .
>@ T. Ozaki, K. Ebihara, S. Hiramatsu, Y. Kimura, J.
Kishuro, T. Monaka, K. Takayama, and D.H.
Whittum, Nucl. Instrum. Methds Phys. Res. A 318(1992) 101.
>@ L.H. Yu, A.M. Sessler, and D.H. Whittum, Nucl.
Instrum. Methods Phys. Res. A 318 (1992) 721.
>@ P. Jha and J.S. Wurtele, Nucl. Instrum. Methods
Phys. Res. A 331 (1993) 477.
>@ P. Jha and P. Kumar, IEEE Trans. Plasma Sci.
24 (1996) 1359.
>@ P. Jha and P. Kumar, Phys. Rev. E 57 (1998) 2256.
[10] A.A. Kordbacheh, B. Maraghechi, B. Farokhi, andJ.E. Willett, Phys. Plasmas 12 (2005) 113106.
>@ S. Mirzanejhad, P. Maraghechi, and B. Maraghechi,
Phys. Plasmas 11 (2004) 3047.

78

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH020

ENHANCEMENT OF A COHERENT (SUPER-RADIANT) EMISSIONIN FEL BY MEANS OF ENERGY MODULATION OF AN EMITTINGSHORT ELECTRON BUNCH
Yu. Lurie and Y. Pinhasi, The College of Judea and Samaria, Ariel, Israel
A. Gover, Tel-Aviv University, Tel-Aviv, Israel
Abstract
Super-radiant emission from a wiggling short electron
bunch, is strongly suppressed at high frequencies in comparison with radiation, obtained in a FEL if an ultra-short-beam pulse of the same total charge is available. However, radiation intensity of a wiggling short electron bunch
can be greatly enhanced by means of energy modulation. In
this way, a super-radiant FEL source driven by short electron bunches and operating in the Tera-Hertz regime can berealized. Analytical evaluations and numerical simulations
utilizing a space-frequency 3D model show, that a linear
energy modulation enables one to increase the power ofsuper-radiant emission by few orders of magnitude. Possible limitations in application of this method are also discussed, as well as a spectral purity of enhanced radiation.

It was suggested that emission of a short electron bunchof some finite duration may be greatly enhanced by meansof its proper energy modulation [3]. In this work, the effect of energy modulation on SR emission of a wiggling
short electron bunch is analyzed in a space-frequency 3D
approach and demonstrated by numerical simulations carried out using WB3D code [4].

ANALYTICAL EVALUATIONS
The total electromagnetic field emitted by a wiggling
electron bunch may be found in the frequency domain
in terms of expansion over transverse eigenmodes of themedium (free-space or waveguide) in which the radiation
is excited and propagates [5]: 

INTRODUCTION
Development of experimental set-ups utilizing mechanism of short bunching of relativistic electron beams
enables construction of high-power free-electron lasers(FELs) operated by a single short pulse or by a train of such
pulses. Optimal efficiency of such radiation sources may
be achieved with ultra-short beam pulses, when a superradiant (SR) emission occurs (see [1, 2] and references
therein).
Unfortunately, a beam pulse duration obtained in practice is still relatively long, leading to a dramatic reduction in SR emission at high frequencies. For example, in acase of Gaussian electron pulse, the super-radiant to spontaneous emission ratio at a synchronism frequency  is decreases with the beam duration as fast as the Gauss function
[1]:
SNR

    

×  ¾

 -mail: ylurie@yosh.ac.il

FEL Theory

½




      ÞÕ  





(2)



where     is the transverse profile (Hermitte-Gaussian
free-space mode or waveguide mode) of the mode  and    is its wavenumber. (Although the form of mode
presentation given in Eq. (2) is not valid in the far-field freespace propagation, it is still applicable to most electron devices in which the interaction takes place within a Rayliegh
length of the Hermitte-Gaussian modes, where the diffraction is small).     is the propagating mode amplitude,
which may be found from the excitation equation (see [4, 5]
for details).
Neglecting the influence of the emitted electromagnetic
field on the emitting electrons, the mode expansion coefficients     of electromagnetic field emitted by a single
wiggling electron may be found in the following simple analytical form:







(1)

(here  is a number of electrons in the bunch and  is thestandard deviation of the electron Gauss distribution, whichcorresponds to the bunch duration    ). It meansthat to provide an intense high frequency SR emission,ultra-short electron bunches of time duration 
have only to be applied. For example, with ultra-short femtoseconds bunches, intense SR emission may be obtainedat radiation frequencies up to approximately 100 THz only.





 

 

 sinc

 





  ¼  ½¾ Õ Û 

(3)where  is some normalization coefficient, sinc ,  is the time that the electron enters into the interaction region,  is the length of the interaction region,
and


(4)
   is the detuning parameter ( is the wiggler wave numberand  is the electron longitudinal velocity in  -direction).

79

MOPPH020

Proceedings of FEL 2006, BESSY, Berlin, Germany

In the low-gain regime, electromagnetic field emitted bya bunch of  electrons may be given in the terms of a summation of (3) over all the electrons in the bunch:



 

 



 sinc  ¼Ô  ¾½ ÕÔ Û  Ô 

(5)
here the coefficient   is supposed to be approximately aconstant for all the electrons in the bunch. At some synchronism frequency  , a coherent summation in (5) may
only be obtained when sinc  Ô   (or Ô  ,what defines the synchronism frequency  ), and the phase
matching condition   Ô
is satisfied.
  
 Ô
 )
A SR emission from a single ultra-short (bunch takes place in this situation, when the radiated field
is simply proportional to a number of the electrons in thebunch (to the total charge of the driving bunch):     , and energy flux spectral density of the emitted radiation may be given as

where we assume that       . Substitution of (8)into (7) provides the following limitation on the maximal
bunch duration:


(9)


Therefore the considered enhancement of SR emission may
be obtained with as long as    beam bunches.
Condition (8) actually requires an energy modulation of
the driving electron bunch as follows:    

here 
cause






     






The phase shifts  Ô
The first condition means, that:


 Ô


 


 
 Ô

remains constant.

º 



Õ



Introducing
 Õ





 

(6)

where   is some bunch mean longitudinal velocity in -direction, the previous equation may be rewritten as:


 Ô







(7)

here  is the radiation wave length and  Ô   Ô . The
phase-matching condition may only be satisfied, if the driving electron bunch is pre-modulated so that the longitudinalvelocities of the electrons are distributed as follows:   80  (8)¾

Þ   Þ  Û 



 









  (10)

¾









 

where
 

 










  


and the modulation rate isThe most part of sinc-functions in (5) save their sign:
sinc  Ô   , to prevent the terms compensation in the summation; and





¾
Û



the distribution (10) may be linearized:

As mentioned above, this energy flux is drastically reduced if the driving bunch duration is increasing comparedwith period  of the emitted radiation. But also in thiscase of “finite-duration” beam bunches, the summation in(5) may still remain a partly coherent in the vicinity of synchronism frequency  , if the previous conditions are fulfilled in a bit modified form:







    is the wiggler parameter. Be-



 





!











(12)

 
 













(11)



 !  here  









(13)








(14)

So, energy modulation of a wiggling electron bunch according (10) or (11) may considerably enhance its SR emission, even if the driving bunch is as long as    .
Obviously, energy modulation of the beam reduces the
spectral purity of the emitted radiation in comparison withthat of SR emission, emitted by an unmodulated ultra-shortelectron bunch. The reason is that the synchronism frequencies of radiation emitted by individual electrons aredifferent due to difference in there kinetic energies. Therefore a bandwidth of radiation, emitted by energy modulated bunch is supposed to be more wide by a factor of        , so that the radiation band width
may be evaluated by


 

















(15)

revealing a linear growth with the energy chirp rate .

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

NUMERICAL SIMULATIONS

Table 1: Operational parameters for THz FEL.
Accelerator
Electron beam energy:=2.8 MeV
Total charge:#  $      pCl
WigglerMagnetic induction:
Period:Number of periods:

 =20 mm
 =20

Waveguide
Rectangular waveguide:

5 5 mmFEL Theory=3 kGauss ( " )10 1

W [nJ]

10 0

10 -1

fs Tb = 0.5
fs Tb = 1.0

10 -2

10 -3

0.00

0.05

0.10

0.15

dE

0.20

0.25

0.30

0.35

0.40

/dt [MeV / pSec]

Figure 1: Total energy flux emitted by   " pSec (boxsymbols) and   " pSec (circle symbols) bunches asa function of the energy chirp rate   .
develops while propagating in the wiggler to a density compression and the -beam pulse becomes an ultra-short one,
generating a strong super-radiant emission. At this moment, the most intensive radiation is emitted, as may beseen from the time-domain dependence of electric component of the emitted field given in figure 5.

CONCLUSIONSIn a practical case of FEL driven by a single short bunchor by a train of such bunches, a super-radiant emission isstrongly suppressed at high frequencies. It was shown thatit can be greatly enhanced by means of a proper energy
modulation of the driving beam. The effect is studied in theframework of space-frequency model and is explained in a

SR emission
dE/dt=0.08 MeV/pSec
dE/dt=0.12 MeV/pSec
dE/dt=0.20 MeV/pSec

400

dW/df [pJ/GHz]To demonstrate the effect, a number of numerical simulations with the code WB3D [4] were carried out for a
THz-regime free-electron laser with operational parameters given in the table 1. Simulations demonstrate, that
extremely short electron bunches (  º  ) have tobe applied in order to produce a strong super-radiant emission. With such ultrashort bunches, the total energy flux ofsuper-radiant emission may be as large as    " nJ.
With a longer unmodulated bunches, the total energy fluxof emitted radiation is drastically reduced and it is justabout   " pJ when   " pSec unmodulated
bunches are applied. In accordance with analytical evaluations, a linear energy modulation (11) of the electron bunch
enables one to enhance this radiation by more than a threeorders of magnitude, as demonstrated in the figure 1. It isevident, that the energy modulation causes the emitted total energy flux to increase rapidly, saturating at the energy
chirp rate    of about 0.12 MeV/pSec (resulting in
the energy flux of     nJ) and slowly reducing fora higher values of the energy chirp rates. Note, that equation (13) provides the value of     " MeV/pSec.
With a longer bunches (  " pSec,    " ), theobtained effect is even more strong (circle symbols at the
picture).
Energy spectrums of the radiation emitted by energy
modulated  =1.0 pSec bunches are given in the figure 2, comparing to that emitted by an unmodulated ultrashort bunch (solid line) and by unmodulated  =1.0 pSec
bunch. A spectral purity of the emitted radiation is
obviously reduced if the driving electron bunch is energy modulated. At high energy chirp rates, the radiation band width grows linearly with   , as demonstrated at the figure 3, in accordance with above evaluation (15). It’s interesting to note some non-linear dependence near the “optimal” value of the energy chirp rate =0.12 MeV/pSec, when a high-power radiation isemitted.
To explain the effect, a microscopic analysis of trajectories of emitting electrons was carried out (see figure 4).
As easily seen from the picture, a non-modulated bunchpropagates through the undulator saving its initial temporal duration. Initial energy modulation of the driving bunch

MOPPH020

300

200Long pulse(T f = 0.5)

100

0
850

900

950

1000

1050

1100

1150

1200

Frequency [GHz]

Figure 2: Total energy flux emitted by   " pSec
bunch as a function of the energy chirp rate 
 .

81

MOPPH020

Proceedings of FEL 2006, BESSY, Berlin, Germany

dE/dt=0.00 MeV/pSec
20
200

10
150

Ex [V/m]

FWHM BW [GHz]

15

100

0
−5

fs Tb = 0.5 Q=10 pCl
fs Tb = 1.0 Q=10 pCl
fs Tb = 0.5 Q=100 pCl

50

5

−10
−15

0
0.00

0.05

0.10

0.15

dE

0.20

0.25

0.30

0.35

0.40

−20

/dt [MeV / pSec]

1.4

1.6

1.8

2

2.2

2.4

t [nSec]dE/dt=0.12 MeV/pSec
300

Figure 3: Full-width half-maximum radiation bandwidth asfunction of the energy chirp rate   .

200

100

Ex [V/m]dE/dt=0.00 MeV/pSec
40
35

−100

30
25

z [cm]

0

−200

20
−300
1.33

15

1.335

1.34

1.345

1.35

1.355

1.36

t [nSec]

10
5
0
−1.5

−1

−0.5

0

Δ t [pSec]

0.5

1

1.5

Figure 5: Time-domain electromagnetic field, emitted by unmodulated (top) and by energy modulated(  =0.12 MeV/pSec, bottom) bunches.
simple analytical approach as well as by numerical simulations with WB3D code. The considered principal scheme
may be realized in a construction of a pulsed FEL, whichenables to provide intensive high-frequency radiation witha reasonable spectral quality.

dE/dt=0.12 MeV/pSec
40
35
30

z [cm]

25

REFERENCES

20[1] Y. Pinhasi, and Yu. Lurie, Phys. Rev. E 65, 026501 (2002).
15[2] A. Gover, Phys. Rev. ST Accel. Beams. 8, 030701 (2005).
10[3] A.Doria et al., PRL 80, 2841 (1998).

5[4] Y. Pinhasi, Yu. Lurie and A. Yahalom, Nucl. Instr. and Meth.
in Phys. Res. A, 475, 147 (2001).

0
−1.5

−1

−0.5

0

Δ t [pSec]

0.5

1

1.5

[5] Y. Pinhasi and A. Gover, Phys. Rev. E 51, 2472 (1995).

Figure 4:
Trajectories of the emitting electronsin unmodulated (top) and energy modulated with =0.12 MeV/pSec (bottom) bunches.

82

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Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH022

CONTROL OF THE INTENSITY OF A WAVE INTERACTING WITH
CHARGED PARTICLES
R. Bachelard, C. Chandre, X. Leoncini, M. Vittot
CNRS Luminy, Case 907, F-13288 Marseille Cedex 9, France
A. Antoniazzi, D. Fanelli∗
Dipartimento di Energetica and CSDC, Universitá di Firenze, INFN, Italy

Abstract

0

10

−2

10

I

The interaction of a wave with a beam of particles is ofparamount importance in a great number of physical applications. We here focus on the case of a Free Electron Laserand review two control strategies aimed at re-shaping theinner topology of the single-particle phase-space to stabilize the oscillations of the laser intensity in the deep saturated regime.

−4

10

0

50

100

150

t

The interaction between a wave and a bunch of charged
particles plays a central role in many branches of applied
physics ranging from particle accelerators to laser physics.
Generically, this self-consistent interaction leads to an exponential increase of the intensity of the wave, followed byan oscillating saturation. Oscillations are generated by therotations in phase space of a clustered bunch of particles.
The wave-particle interaction can be cast in a Hamiltonian form with N +M degrees of freedom, where N and M
are resprectively the number of charged particles and electromagnetic waves. Examples include the so called electron beam-plasma instability, a phenomenon of paramountimportance in the wide realm of kinetic plasma turbulence,and single-pass high-gain Free Electron Lasers (FELs). In
the following we shall refer to the latter case, focusing inparticular on seeding schemes where a small laser signal
is injected at the entrance of the undulator and guides thesubsequent amplification process [1]. Basic features of thesystem dynamics are successfully captured within a simplified one-dimensional framework discussed in the pioneering work by Bonifacio and collaborators [2]. The Hamiltonian reads:

N
N

p2j
I 
H=
− δI + 2
sin(θj − ϕ),
(1)
2
N j=1
j=1
where I and ϕ stands respectively for the intensity andphase of the wave, while the N conjugated pairs (p j , θj ) refer to the electrons. The detuning parameter δ measures theaverage relative deviation from the resonance condition.
As previously anticipated, the theory predicts a linear exponential instability and a late oscillating saturation for the∗ duccio.fanelli@ki.se

FEL Theory

Figure 1: Normalized intensity calculated from the dynamics of Hamiltonian (1).
4
3
2
1

p

INTRODUCTION

0
−1
−2
−3

−3

−2

−1

0
θ + φ [2π]

1

2

3

Figure 2: Snapshot of the N particles at t = 1000, with
N = 104 . The grey points correspond to the chaotic particles, the dark ones refer to the macro-particle

amplitude of the radiation field, Fig. 1. Inspection of theasymptotic phase-space, see Fig 2, suggests that a bunch ofparticles gets trapped in the resonance and forms a clumpthat evolves as a single macro-particle localized in space.
The remaining particles are almost uniformly distributed
between two oscillating boundaries, and populate the socalled chaotic sea [3].
The macro-particle rotates around a well defined fixed
point and this microscopic dynamics is shown to be responsible for the macroscopic oscillations observed at the intensity level. Qualitatively similar observations have beenreported for the case of a Travelling Wave Tube (TWT)[4],a specially designed apparatus that mimics the plasma in-83Proceedings of FEL 2006, BESSY, Berlin, Germany

i=1

where
H1p (θ, p, t) =

p2
−2
2



3
2
1
0

−1
−2
−3
−4
−3

−2

−1

0

θ

1

2

3

Figure 3: Poincaré sections of a test-particle of Hamiltonian H1p (θ, p, t).
4
3
2
1
0
−1

I(t)
cos (θ + φ(t)).
N

−2

(3)

In conclusion, the dynamics of a FEL can be adressed bymonitoring the evolution of a test particle, obeying the
Hamiltonian (3) where the functions I(t) and φ(t) act asexternal fields and are here imposed by assuming their simplified asymptotic behaviour as obtained by a frequency
analysis [5] :KI(t) iφ(t)e≈F −Wk eiωk t ,
(4)
2
N
k=1

in the reference frame of the wave.

TOWARD STABILIZATION: TWO
ALTERNATIVE APPROACHES
Two different control strategies are here shortly discussed and shown to produce beneficial effects on stabilityof the system at saturation. For a detailed account on thetechniques and an extensive report of the main findings, theinterested reader may refer to [6] and [7].

Hamiltonian control of a test particle
First let us consider a Hamiltonian control technique.
The method is based on the introduction of a small and apt
modification of the potential that enables to recreate (alternatively destroy) invariant (KAM) tori in phase space.
The Hamiltonian control addresses systems which are close
to integrable, i.e. whose Hamiltonian can be written as
H = H0 + V , where H0 is integrable and V a perturbation of order  (compared to H 0 ). The results we use

84

4

p

stability and enables to accurately investigate the non linear regime of the self-consistent wave-particles interaction.
Given the above, it is an interesting problem to define dedicated strategies aiming at regularizing the saturated dynamics that could eventually contribute to improve the performance of the aforementioned devices.
The goal of this paper is to show that it is indeed possible to influence by an external perturbation the dynamics
of the particles and enhance the stability of the system. To
this end we shall consider a mean field type of approach
which constitutes the natural reduction of the original N body formulation (1). According to this simplified picture,
the conjugated variables (φ, I) are replaced by two functions of time φ(t) and I(t), the latter being obtained fromdirect simultations of the self-consistent dynamics. This inturn amounts to formally neglecting the action of the electrons on the field, an assumption that holds true in the latesaturated regime.
The N -body Hamiltonian (1) can therefore be reduced
to
N

H˜N =
H1p (θi , pi , t),(2)p

MOPPH022

−3
−4
−3

−2

−1

0

θ

1

2

3

Figure 4: Poincaré sections of a controlled test-particle of˜ p, t) (right).
Hamiltonian H1p (θ, p, t) + f(θ,here have been proven rigorously [8, 9]. In practice, it canbe shown that a suitable control term f of order  2 exists
such that H0 + V + f has an invariant torus at a given frequency ω 0 . In the present case, and focusing on the latesaturated regime, the perturbation term is associated withthe oscillating part of the intensity.
The calculation of the control term [6] is carried on into
action-angle variables (ϕ, J) and the derivation is not esplicitly reported here due to space limitations 1 . Instead,
we shall present results of numerical experiments whichclearly demonstrate (see Figs.3 and 4), that, in (θ, p) variables the analytical control term derived in [6] is successful in reconstructing some invariant tori around the macroparticle. In other words, it enlarges the macro-particle
which in turn corresponds to enhancing the bunching factor, a quantity of paramount importance in FEL context.
Finally, it is worth emphasising that according to this approach the form of the control term is derived and not imposed a priori.
1 As a side remark, note that the exact change of variables from (ϕ, J)
to (θ, p) presents a singularity at the pendulum separatrices. In orderto implement our control on the whole space, a simplified, but regular,change of variables is used which mimics the exact one in the region of
the invariant torus predicted by the control

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

The residue method

4





0 −I2
, and
I2
0
I2 being the two-dimensional identity matrix. In order toanalyze the linear stability properties of the associated periodic orbits, we also consider the tangent flow written as

where z = (p, E, θ, t) ∈ R4 and J =d t
J (z) = J∇2 H(z; λ)J t ,dtwhere J 0 = I4 and ∇2 H is the Hessian matrix (composedof second derivatives of H with respect to its canonicalvariables). For a given periodic orbit with period T , thelinear stability properties are given by the spectrum of themonodromy matrix J T . These properties can be synthetically enclosed in the definition of Greene’s residue :4 − trJ T.
4
In particular, if R ∈]0, 1[, the periodic orbit is elliptic; if
R < 0 or R > 1 it is hyperbolic; and if R = 0 and R = 1,
it is parabolic.
Since the periodic orbit and its stability depend on the setof parameters λ, the features of the dynamics will change
under apposite variations of such parameters. Generically,stability od periodic orbits is robust to small changes of parameters, except at specific values when bifurcations occur.
The residue method [11, 12, 13] detects these rare events
thus allowing one to calculate the appropriate values of theparameters leading to the prescribed behaviour in the dynamics. This method yield reduction as well as enhancement of chaos.
To illustrate the potentiality of method we shall introduce a parametrized perturbation, in the form [7]:R=

2 At this level λ represents any generic family of parameters that influ-

ence the dynamics of the system

FEL Theory

3
2

p−Ω

An alternative strategy can be elaborated that enables
to modifying the intrinsic characteristics of the macroparticle. Contrary to the above technique, a (generic)parametrized perturbation is here a priori introduced,
which allows to modify the topology of phase-space, by
tuning appropriately the parameters. The residue method[10, 11, 12, 13] is used to predict the resulting local bifurcations, by an analysis of linear stability of periodic orbits. Information on the nature of these orbits (elliptic, hyperbolic or parabolic) is provided using e.g. an indicatorlike Greene’s residue [10, 14], to monitor local changes ofstability in a system subjected to an external perturbation[11, 12, 13, 15]. As we shall see, this approach enables
one to tune the size, gyration radius and internal structureof the macroparticle, thus resulting in an effective tool forthe stabilization of the intensity.
Consider an autonomous Hamiltonian flow with two degrees of freedom which depends on a set of parameters 2
λ ∈ Rm :ż = J∇H(z; λ),

MOPPH022

1
0
−1
−2
−3
−3

−2

−1
0
1
θ + Ω t [2π]23Figure 5: Poincaré section of a test-particle, described by
Hamiltonian (3). The periodic orbits with r.n. 7 are marked
by plus (elliptic orbit) and crosses (hyperbolic orbit). Ω
stands for the wave velocity.

I(t)cos (2θ + φ(t)).
N(5)
Here λ controls the amplitude of the injected wave. Focus then on λ = 0, which corresponds to the original
Hamiltonian H1p , and consider two coupled Birkhoff periodic orbits, i.e. orbits having the same action but different
angles in the integrable case and having the same rotation
number (r.n.) on the Poincaré section, one elliptic O e andone hyperbolic O h (see Fig. 5) 3 .
Call Re and Rh the residues of these orbits: We have
Re (0) > 0 and Rh (0) < 0. We then modify the parameterλ until the following condition is matched :c
H1p(θ, p, t; λ) = H1p (θ, p, t) − 2λRe (λc ) = Rh (λc ) = 0,(6)

at λc = −0.0370 [7]. Bifurcation (6) is associated with thecreation of an invariant torus [13]. This diagnostic is confirmed by the Poincar section (see Fig.6) of the controlled
Hamiltonian (5), at λ = λ c : The elliptic islands with r.n.
7 have been replaced by a set of invariant tori, leading toan enlargement of the macro-particle. Note that elliptic islands with r.n. 6 are now present around the regular core.
The associated couple of elliptic/hyperbolic orbits can betreated similarly as those of r.n. 7, in order to gain further
enlargement of the macro-particle (not reported here).
The control is naturally introduced in the self-consistent
dynamics as :c
HN(I, φ, pi , θi , λ)= HN (I, φ, pi , θi )I 
cos (2θi + φ),(7)−2λN i

3 Let us recall that the rotation number (or winding number) of a pe-

riodic orbit is the number of times it crosses the Poincaré section before
closing back on itself

85

MOPPH022

Proceedings of FEL 2006, BESSY, Berlin, Germany
proaches are utterly general and could be eventually considered to define innovative strategies aimed at adjusting
the size of the macro-particle, and consequentely enhancing the bunching factor. In this respect, it is worth stressingthat an experimental test of the Hamiltonian control method
on a modified Travelling Wave Tube has been performed[16] in absence of self-consistency. Exploring the possibility of experimentally implementing the above control terms
in both FEL and TWT contexts will be addressed in future
research.

4
3

p − Ω

2
1
0
−1
−2
−3

−3

−2

−1
0
1
θ + Ω t [2π]23Figure 6: Poincaré section of a controlled test-particle ofHamiltonian (5), with λ = λ c ≈ −0.0370. The periodic
orbits with r.n. 6 are marked by plus (elliptic orbit) andcrosses (hyperbolic orbit). Ω stands for the wave velocity.

REFERENCES[1] L.H. Yu et al., Science 292, 2037 (2003).
[2] R. Bonifacio, et al., Rivista del Nuovo Cimento 3, 1 (1990).
[3] A. Antoniazzi, Y. Elskens, D. Fanelli and S. Ruffo, Europ.
Phys. J. B, in press (2006).
[4] Y. Elskens, D. Escande, Microscopic Dynamics of Plasmas
and Chaos IoP Publishing, Bristol (2003).

1[5] J. Laskar, Proc. of NATO ASI Hamiltonian Systems withThree or More Degrees of Freedom, (C. Simò Ed, Kluwer) 134(1999).

I

0.8
0.6
0.4
0.2
0

λ=0
0

λ=−0.0370200

λ=−0.0746

400
t[6] R. Bachelard, A. Antoniazzi, C. Chandre, D. Fanelli, M. Vittot, Comm. in Nonlinear Sci. and Num. Simu. in press (2006).

λ=−0.132600

800

Figure 7: Intensity of the wave at saturation, in the four
regimes : λ = 0, −0.037, −0.0746 and −0.1321 . Further
improvements over this condition are discussed in [7]where HN is given by Eq. 1. The behaviour of the system is investigated in correspondence of the critical values(λc , λc , λc ) which have been calculated in the frameworkof the test-particle model, and identifying successive corrections as outlined in the precedding discussion. Importantly, the macro-particle is shown to increase also when
operating within the relevant self-consistent context. As
concerns the wave, the control results in a stabilization of
its intensity (see Fig.7) [7].

CONCLUSIONS[7] R. Bachelard, A. Antoniazzi, C. Chandre, D. Fanelli,
X. Leoncini, M. Vittot, preprint nlin/0609030 (2006).
[8] Vittot, M. (2004). Perturbation theory and control in classicalor quantum mechanics by an inversion formula. J. Phys. A:
Math. Gen., 37, pp. 6337-6357.
[9] Chandre C., M. Vittot, G. Ciraolo, Ph. Ghendrih, R. Lima(2006). Control of stochasticity in magnetic field lines. Nuclear Fusion, 46, pp. 33-45.
[10] J.M. Greene, J. Math. Phys. 20, 1183 (1979).
[11] J. Cary, J.D. Hanson, Phys. Fluids 29(8), 2464 (1986).
[12] J.D. Hanson, J. Cary, Phys. Fluids 27(4) 767 (1984).
[13] R. Bachelard, C. Chandre, X. Leoncini, Chaos 16 023104(2006).
[14] R.S. MacKay, Nonlinearity 5 161 (1992).
[15] J.E. Howard, R.S. MacKay, J. Math. Phys. 28 1036 (1987).
[16] Chandre, C., G. Ciraolo, F. Doveil, R. Lima, A. Macor and
M. Vittot (2005). Channeling chaos by building barriers. Phys.
Rev. Lett., 74, 074101.

In this paper, we focus on the physics of the waveparticle interaction and consider in particular the case ofa FEL. Control techniques are developed in the frameworkof a simplified mean-field description aiming at stabilizing the laser behavior at saturation. In both cases, the sizeof the macro-particle is shown to be increased by adding
a small pertubation to the system. These procedures result in a low–cost correction in term of energy 4. Both ap4 As concerns the method of residues, the fact that the applied corrections are indeed small is confirmed by the values of λ that are calculated
for the various setting considered above.

86

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Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH025

FREE ELECTRON LASER AS A PARADIGMATIC EXAMPLE OFSYSTEMS WITH LONG-RANGE INTERACTIONS
A. Antoniazzi, D. Fanelli, S.Ruffo
Dipartimento di Energetica and CSDC, Universitá di Firenze, INFN, Italy
J. Barré, T. Dauxois, ENS, Lyon, France
G. De Ninno, Sincrotrone Trieste, Trieste, Italy
Abstract
We here shortly review the field of long-range interactions and presents selected issues of fundamental interest for statistical mechanics and dynamical systems theory. Applications to the case of a Single-Pass Free Electron
Laser are discussed.

INTRODUCTION
Physical systems are constituted by interacting elements,
point particles or atoms. In presence of short-range couplings, every element is solely sensitive to the adjacent environment, being therefore uniquely subjected to the interaction with local neighbors. Conversely, when long-range
forces are to be considered, the direct coupling of each element to every other element in the system must be taken
into account (the system is dominated by mean-field effects). This crucial distinction is responsible for the enhanced degree of complexity in the treatment of long-range
systems when compared to short-range ones.
Moreover, basic concepts in physics, notably in theframework of equilibrium statistical mechanics, have beendeveloped only for short range interactions. The potential
interest of such tools is however very broad since for all
fundamental interactions in nature (with the exception ofgravity), screening mechanisms manifest, resulting in effective short-range couplings. For this reason, it has essentially only been in the context of astrophysics and cosmology that the very specific and difficult features of longrange interactions have been tackled. Recently, however,a growing number of physical laboratory systems haveemerged in which the interactions are truly long-range,e.g. unscreened Coulomb interactions, vortices in twodimensional fluid mechanics, wave-particle systems relevant to plasma physics and Free-Electron Lasers (FELs).
These developments gave new impetus [1] to attempts aiming at describing the peculiar behaviour of long-range interacting systems, in a context where, in contrast to astrophysics, laboratory experiments are possible. Moreover, anumber of “ toy models“ have been proposed that provide
the ideal ground for theoretical investigations. Among others, the Hamiltonian Mean Field (HMF) model [2] is nowadays widely analyzed for pedagogical reasons, because of
its intrinsic simplicity.
In presence of long-range interactions, physics is in fact
very peculiar and a wide range of striking and curious phe-

FEL Theory

nomena appears. Importantly, energy is non additive, hence
the system under scrutiny cannot be divided into independent macroscopic parts, as it is usually the case for shortrange interactions. This fact leads to unexpected consequences when performing the analysis in terms of statistical mechanics.
Single-pass FELs constitute an example of systems withlong-range interactions, where the interplay between collective (wave) and individual (particles) degrees of freedom
is well known to be central. This interplay being essentially non dissipative, its prototype is described by a selfconsistent Hamiltonian [3], which provides a clear and intuitive picture of the basic mechanisms that drive the process of light amplification and saturation. In this respect,
FELs provides a very general experimental ground to investigate the universal features that characterize systems withlong range interactions.
In this paper we shall present a short review of recent
progress in this field of research by focusing in particular on the relevant case of a Single Pass FEL. A wider
overview on long range systems can be found in Ref. [1].

DEFINITION OF LONG-RANGESYSTEMSLet us consider the potential energy U of a given particle
positioned in the center of a sphere of radius R. Assume
that the matter is homogeneously distributed with density
ρ and introduce a lower cut-off ε << R, as depicted inFig. 1. Focusing on the case where the interaction potential
decays at large distances with a power-law with exponent
α, one gets:U== R  1
ρ α 4πr2 dr =
r
ε
 R
R

r2−α dr ∝ r3−α ε ∼ R3−α ,4πρεClearly, the above energy diverges with R if the exponent α is smaller than 3, which in turn corresponds to thedimension of the physical space where the interaction isembedded.
This argument holds true in any dimension d, implyingthat similar divergences are found when α ≤ d. We hence
define the interaction to be long-range if α ≤ 3 (resp. α ≤d). Equivalently, it can be said that the contribution to the87MOPPH025

Proceedings of FEL 2006, BESSY, Berlin, Germany
I

II

+

_

Figure 2: A microscopic configuration with total zero magnetization, illustrating the lack of additivity in the CurieWeiss model.
Figure 1: The energy in a sphere of radius R diverges asR3−α if the interaction is long-range and α ≤ 3.
energy due to the surface of the sphere with respect to thebulk can be safetly neglected only if α > 3. In the latter
case, the interaction is of the short-range type.
As anticipated in the preceding discussion, long-range
forces arise in many different contexts. Few physical examples of broad relevance are listed below:• Gravity: α = 1, d = 3. In addition to the long range
nature of the interaction, the system displays a singularity at the origin that needs to be carefully tackled
by involving dedicated regularization schemes.
• Coulomb interactions: α = 1, d = 3.
• Dipolar interactions: α = 3, d = 3. The shapedependence phenomenon is found, which makes theenergy dependent on the form of the sample.
• Onsager’s 2D vortex systems or 2D Coulomb systems. Here α = 0, because the interaction decays
logarithmically, and d = 2.
• Mean-Field: α = 0, due to the infinite-range interaction, and any d. This latter cathegory does not reflect a pure physical example, but rather a useful (andcommon) approximation to which one resorts whentreating complex problems. In fact, it provides theideal setting to gain insight into a number of different physical problems and eventually enables to perform analytical calculations. As we shall see, Single
Pass FELs can be effectively described by resorting toa mean-field type of approach .

THE PROBLEM OF ADDITIVITY
The long range nature of the interaction reflects in a
number of peculiar phenomena which will be shortly reviewed in the forthcoming sections. Such curious behaviours are intrinsically connected to the non additivityof the system, a crucial concept that one can illustrate withreference to a specific case, namely the Curie-Weiss modelof magnetism. Consider the following Hamiltonian:
H=−

88

J 
Si Sj ,
2N i,j(1)where Si = ±1 labels a spin variable, J is the ferromagnetic coupling and the sum extends over all pairs spins, N
being their total number. Note that Hamiltonian (1) is extensive, since H ∝ N , but, as we shall see, not additive.
Refer, in fact, to the situation schematized in Fig. 2
where all the spins in the left portion of the space are equal
to 1, whereas the ones in the right are assumed to be −1.
Under this conditions the energy of the two regions reads
EI = EII = −(J/8)N = 0. Conversely, when computing the total energy, one finds E = −J/(2N )(N/2 − N −2)2 = 0. The relation E = EI + EII does not hold, andconsequently the system is not additive. The underlying
reason is that the above Hamiltonian is long range, since
every spin interacts with all the others. This in turn implies
that the energy at the interface cannot be neglected, the latter being of the same order of the energies in the two bulks.
As a side remark, we shall note that the lack of additivity
affects dramatically the usual construction of the canonicalensemble, and therefore peculiar behaviours are to be expected for a long-range system in contact with a thermal
reservoir. Next paragraph is devoted to a short account on
this topic.

THERMODYNAMICS PECULARITIESAs previosuly pointed out, the non-additivity issue is responsible for a number of important and non trivial consequences. As soon as first order phase transitions arepresent, “convex intruders” in the microcanonical entropy
appear [4, 5]. A typical situation is displayed in Fig 3.
Only if interactions are short-range and, hence, the additivity property holds, the states in the convex entropy region
1 <  < 2 of Fig 3a are unstable, when compared tothose obtained by combining, in appropriate portions, thetwo limiting states with energies  1 and 2 . This is not thecase if long-range interactions are to be considered and additivity is violated. The presence of stable, non-concave,entropy regions implies the appearance of negative specificheat in the microcanonical ensemble. As an immediate
consequence statistical ensembles are not equivalent, since
the specific heat is always positive in the canonical ensemble. Note that, large deviation techniques allow one tosolve, both in the microcanonical and in the canonical ensemble, a large class of mean-field models and constitutetherefore a powerful tool to detect possible discrepancies.
Another intriguing effect is related to temperature jumps,
as depicted in Fig. 3b. In this case, two branches of the

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Proceedings of FEL 2006, BESSY, Berlin, Germany
s

a)

s

MOPPH025

0.35

b)

(a)

0.3

M(t)

0.25
0.2
0.15
0.1

ε1

ε2

ε

ε1

ε2

0.05

ε

0

Figure 3: (a) Entropy s() can be non-concave in the
microcanonical ensemble, giving rise to negative specificheat. (b) In the non-concave region, entropy can develop
kinks in the slope, creating temperature jumps.
entropy exist, respectively a high and a low energy ones.
When crossing each other, they generically form an angle:
this sets the origin of the temperature jumps, the derivativeof the entropy with respect to energy being different on thetwo sides of the intersection point.

NON-LINEAR DYNAMICAL ASPECTS
In this Section we shall shortly report about a selectionof peculiar dynamical features, which are generically encountered when dealing with long-range interacting systems. First, the existence of quasi-stationary states has
been often discussed in the literature with reference to various test models. Particularly important is the case of theso called Hamiltonian Mean Field (HMF) model [2], which
describes the motion of N coupled rotators and is characterized by the following Hamiltonian
N
N
1 2
1 
H=
pj +
[1 − cos(θj − θi )]2 j=1
2N i,j=1

FEL Theory

0

1

2

3

4

5

6

7

8

lo
g10t

Figure 4: Temporal evolution of the magnetization M (t)for different particles numbers: N = 10 2 (103 ), 103 (102 ),2.103 (8), 5.103 (8), 104 (8) and 2.104 (4) from left to right(the number between brackets corresponding to the numberof samples).
troduced in the astrophysical and 2D Euler turbulence contexts [7, 8].
Finally, let us mention that recently [9], in analyzing aIsing model with both short and long-range interactions on
a ring, it has been realized that the accessible region of extensive parameters (energy, magnetization, etc.) may be
non convex. This implies that broken ergodicity can appear,
due to the fact that the accessible magnetization states at agiven energy can be disconnected.

THE CASE OF A SINGLE-PASS FELFor Single-Pass FEL amplifiers, the Colson-Bonifacio[3] model applies:
dθj
dz̄
dpj
dz̄
dA
dz̄

(2)

where θj represents the orientation of the j-th rotor andpj is its conjugate momentum. Note that the HMF model
correpsonds to the XY model with J = 1, K = 0. To monitor the evolution of the system, it is customary to introduce the magnetization,a global order parameter defined
as M = |M| = | mi |/N , where mi = (cos θi , sin θi )is the local magnetization vector. A second order phasetransition is found at  c = Ec /N = 0.25 (Tc = 0.5).
For energy close to the transition value, the finite N system can remain trapped in quasi-stationary states whose
life-time increases with a power of N . An example of theevolution of magnetization from an initial homogeneous(non-magnetized) water-bag state to the final maximum entropy state is displayed in Fig. 4. As N is increased thelifetime of the non-equilibrium quasi-stationary state increases: curves with growing N go from left to right. Importantly, in this intermediate regime, the magnetization islower than predicted by the Boltzmann–Gibbs equilibrium
and the system apparently displays non Gaussian velocity
distributions. The above phenomena can be successfullyinterpreted in the framework of the statistical theory of the
Vlasov equation [6], a wide general approach originally in-

−1

=

pj

=

−Aeiθj − A∗ e−iθj

=

iδA +

(3)

1 
N

e−iθj

(4)
(5)

j

The complex field amplitude A is the degree of freedom
associated to the wave, while θ i , pi are the conjugate variables related to the electron position and “momentum”. z̄
is the (rescaled) longitudinal position along the undulator,
N is the number of electrons and δ stands for the so-called
detuning parameter. The above model can be derived fromthe mean-field Hamiltonian
HN =

N

p2j
j=1

2

− N δI 2 + 2IN
sin(θj − ϕ) ,

(6)

j=1

where A = I exp(−iϕ). In this respect, FELs fall naturally in the realm of systems with long-range interactions.
The microcanonical equilibrium entropy of this model
can be obtained using large deviation techniques [10]. Ensembles are equivalent, no negative specific heat or temperature jump appears. However, the evolution towards
the maximum entropy equilibrium state is highly non trivial, as shown in Fig. 5, and shares many similarities with89

MOPPH025

Proceedings of FEL 2006, BESSY, Berlin, Germany

CONCLUSIONS
0.6

0.4

0.6

Laser intensity

Laser intensity (arb. units)

0.8

0.2

3
2

0.4

0

0

20

40

1

0.5

60

0

500

80

100

z

1000

120

1500

140

160

z

2000

180

200

Figure 5: Typical evolution of the radiation intensity using
Hamiltonian (6). The detuning δ is set to 0, the energy perelectron H/N = 0.2 and N = 10 4 electrons are simulated.
The inset presents averaged simulations on longer times fordifferent values of N : 5 · 10 3 (curve 1), 400 (curve 2) and100 (curve 3).

0.7

Intensity

Laser Intensity, Bunching

0.6

0.5

0.4

Bunching

0.3

0.2

0.1

0

0

0.05

0.1

e

0.15

0.2

0.25

Figure 6: Comparison between theory (solid and longdashed lines) and simulations (symbols) for a non monoenergetic beam when the energy (e) characterizing the initial velocity dispersion of the initial electron beam, is varied. The dottedlines represent the intensity and bunching (b = | j eiθj |/N ) predicted by the full (BoltzmannGibbs) statistical equilibrium, not very appropriate here,
whereas the solid line and long-dashed lines refer to the
Vlasov equilibrium [10]. The discrepancy between theory
and numerical experiments is small over the whole rangeof explored energies.

the case of the HMF. After the initial exponential growth,
the system converges to a quasi-stationary state that gets
more pronounced when increasing the number of simulated electrons N . Finally it relaxes to the BoltzmannGibbs equilibrium, driven by granularity. The intermediate quasi-stationary state is indeed the only experimentally
relevant regime, due to the finite extension of the undulators. As already pointed out, the latter state, is a Vlasov
equilibrium, sufficiently well described by Lynden-Bell’s
Fermi-like distribution arising from “violent relaxation”(constrained maximum entropy principle) [7, 8, 10, 11].
Results reported in Fig. 6 provide a clear support to thisconclusion.

90

In this paper, we discussed the concept of long-range
interactions and shortly reviewed the fundamental properties of such systems. In particular, microcanonical andcanonical ensembles disagree for long range interactions
at canonical first order transitions. Negative specific heatand temperature jumps are typical signatures of this ensemble inequivalence. Dynamical non equilibrium featuresarise, and more specifically, quasi-stationary states, where
the system gets trapped for long times. Their life-time increases in fact with the system size N . Moreover, as anindirect signature of non-additivity, broken ergodicity manifests as a generic feature of systems with long-range interactions.
Further we focused on a simple model of the Free Electron Laser dynamics, which shares many similarities withthe so called Hamiltonian Mean Field model, a paradigmatic toy-model often referred to for theoretical applications. For the case of the FEL, we have shown that collective phenomena for wave-particle interactions can be succesfully interpreted through a constrained maximum entropy principles of the associate Vlasov system. Given
the above, it is here anticipated that FELs will constitutea promising experimental set up to investigate the universal pecularities that characterize systems with long range
interactions.

REFERENCES[1] T. Dauxois, S. Ruffo, E. Arimondo and M. Wilkens (eds),
Dynamics and thermodynamics of systems with long-range
interactions, Lecture Notes in Physics 602 (Springer, Berlin,
2002).
[2] M. Antoni and S. Ruffo, Phys. Rev. E 52 (1995) 2361.
[3] W. B. Colson, Phys. Lett. A 59, 187 (1976); R. Bonifacio etal., Opt. Comm 50, 373 (1984).
[4] J. Barré, D. Mukamel and S. Ruffo, Phys. Rev. Lett. 87(2001) 030601.
[5] D. H. E. Gross, Microcanonical Thermodynamics: Phase
Transitions in Small Systems, Lecture Note in Physics, 66,
World Scientific, Singapore (2001).
[6] A. Antoniazzi, D. Fanelli, J. Barré, P.H. Chavanis, T.
Dauxois, S. Ruffo, submitted to Phys. Rev. Lett., condmat/0603813 (2006)[7] D. Lynden-Bell, Monthly Notices of the Royal Astronomical
Society 136, 101 (1967).
[8] P.H. Chavanis, J. Sommeria, R. Robert, Astrophys. J., 471,
385 (1996).
[9] D. Mukamel, S. Ruffo and N. Schreiber, Phys. Rev. Lett.. 95,
240604 (2005)[10] J. Barré, T. Dauxois, G. De Ninno, D. Fanelli, S. Ruffo,
Phys. Rev. E, Rapid Comm. 69 (2004) 045501.
[11] F. Curbis, A. Antoniazzi, G. De Ninno, D. Fanelli, submitted
to Phys. Rev. E (2006)

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH026

OVERVIEW OF PERSEO,
A SYSTEM FOR SIMULATING FEL DYNAMICS IN MATHCAD
L. Giannessi, ENEA C. R. Frascati, Via E. Fermi 45, 00044 Frascati (Rome) Italy.
Abstract
Perseo is a library of functions devoted to thesimulation of FEL dynamics in the Mathcad environment.
Functions for the generation of phase space variables, forthe solution of the pendulum-like equation and for
manipulating the phase space in a number of devices areavailable. These function can be combined in order tomodel more complicated situations as time dependent
simulations,
3D
simulations,oscillator
FEL
configurations, optical klystron, cascaded FELs …

INTRODUCTION
Mathematical computer aided scratchpads which
integrate standard mathematical notation, text, graphs andprogramming capabilities in worksheets as Mathcad orMathematica and Matlab, are widespread tools in thescientific community. Nowadays computers are fastenough to execute interactively from start-up to saturation
an FEL simulation involving a few thousands macroparticles. This suggested to develop a set of basic
functions which can be called from within the Mathcad
environment, devoted to solve FEL dynamics related
problems. The result is Perseo[1], a flexible tool that canbe simply programmed to set up FEL simulations in awide variety of configurations.

THE FEL MODEL IN PERSEO
The core of the library consists of a routine solving thependulum-like FEL equations coupled with the field
equations which govern the FEL longitudinal dynamics[2,3]. This routine includes self consistently the field
variables for the higher order harmonics. In this picture
the field is the superposition of slowly varying complex
a n = a n e iϕ nfor each harmonic n,
amplitudes~~i (k n z −ωnt +ϕ n )E ( z , t ) = n En an e
. The parameters En link∑the dimensionless field amplitude an to the field at theharmonic n. They may be defined in terms of the~saturation intensity [4] as En = z 0 I s (n ) 4π where z 0 is
the vacuum impedance. In a linear undulator the nthharmonic
saturation
intensityisdefinedas4−2
3
I s (n ) = 1 (4π ) m0 c r0 (γ N ) (λu Kf b (n, ξ )) where γ is()

the beam energy in m0 c 2 units, λu is the undulator period,
N is the number of undulator periods, K is the undulator
parameter. The function f b (n, ξ ) = J (n−1) 2 (ξ ) − J (n+1) 2 (ξ )()

where ξ = K 2 4 1 + K 2 2 , is the Bessel factor arisingfrom the average over the longitudinal fast motion typical

FEL Theoryof linear undulators. The evolution of the amplitudes anis governed by the equations:∂ Re(an (τ ))= −2πg n cos(inϑi (τ )) i∂τ
∂ Im(an (τ ))= 2πg n sin (inϑi (τ )) i∂τ(1)

where the variable τ = β z ct Lu is a dimensionlessinteraction time, Lu = Nλu is the undulator length andcβ z is the longitudinal beam velocity. The phaseϑi = (k L + ku )zi − ω L t is the electron phase in the
ponderomotive bucket corresponding to the first harmonic
field (n=1, k L = ω L c = k1 = 2π λ1 is the wave-vector
corresponding to the first harmonic and ku = 2π λu is thewave-vector associated to the undulator period). The
coupling coefficients at the odd harmonics g n are given
by [3]
 3
N
g n = 2π   λu Kf b n, ξ

γ

[

(

I

)]2 peakI AΣ b(2)

where I peak Σ b is the electron current density and IA is
the Alfven current . The ith particle motion is governed by
pendulum-like equations:

dϑi
=νi
dτ
dν i
= ∑ cos(nϑi ) Re(an ) − sin (nϑi ) Im(an )
dτ
n

(3)

where ν i = 2π N (ω i − ω L ) ω i represents the frequency
shift
of
the
ith
particleresonance22
ωi c = 2γ i k u 1 + K 2 from the reference frequency
ω L . Note that the above choice for the coefficients~( En , g n ) leads to the expression (3) for the particles
dynamics, where all the harmonics in the expression ofdν i dτ have the same weight factor. Analogous
expressions for the helical undulator are easily obtained()

by substituting f b (n = 1, ξ ) = 1 , K → K helical = 2 K in(2) and in the definition of I s (n ) , and neglecting thehigher order harmonic coupling ( f b (n ≠ 1, ξ ) = 0 ) in (2).
In the following we will analyze the subset of functions
that are necessary for setting up a simple FEL simulation

91

MOPPH026

Proceedings of FEL 2006, BESSY, Berlin, Germanyin the Mathcad environment. Some knowledge of thebasic Mathcad language is assumed [5].

The function FELPendulum_h
In Perseo the coupled equations (2) and (3) are solved
by calling the function:

PHSPnew := FELPendulum_h(PHSPold, g,τ0,τ1, tol)

(4)

This function integrates the coupled system of equations(2) and (3) with the coupling coefficients g (g is indeed anarray with number of components equal to the number ofsimulated harmonics) advancing the system from τ0 to τ1with tolerance tol. The variables PHSPnew and PHSPoldrepresent the status of the system before and after the
integration and are defined as:

PHSP =

nh

not used Re(a1 )Im(a1 )

Re anh( )Im anh

ν1

ϑ1

( )

ν np

ϑn p

A quiet start distribution is obtained by setting

ϑ1 = ϑ0 +2nπ with n integer (normally ϑ0 , ϑ1 =0, 2π).
An example of the phase space distribution as returned by
FELquietstart_h is shown in Fig. 1.

A simple simulation
A simple simulation is realized by the Mathcad
sequence in Fig. 2 1 + 3i 
θ 1 := 2⋅ π a :=  0nθ := 40 θ 0 := 00P := FELquietstart_h ν 0 , σν , n ν , θ 0 , θ 1 , n θ , a 
 10 
g0 :=  0  0ν 0 := 2.6

σν := 2nν := 40

(

)

(

)

P := FELpendulum_h P , g 0 , 0 , 1 , TOL












(5)

Figure 2: Mathcad sequence integrating the epndulum-likeequation coupled to the field equations with coupling
coefficient g=10 on the first harmonic and 0 on the higher
harmonics.
The phase space in P is integrated over the undulator
length with the coupling coefficient g=10 on the firstharmonic and 0 on the higher harmonics. The resulting
phase space is plotted in Fig.3.

The first line contains the number of harmonics nh, thennh lines contain the real and imaginary part of the field at
each harmonic, followed by the coordinates (ν , ϑ ) of anarbitrary number of simulated particles np.

10

(P 0 ) n0

The function FELquietstart_h
The variable PHSP may be prepared by filling thematrix with the desired field values and particles
coordinates, but a more convenient way is that of using
the function
PHSP := FELquietstart_h(ν0, σν, nν, ϑ0 , ϑ1 , nϑ ,a)(6)

that fills the variable PHSP with n p = nν ⋅ nϑ particles,nν particles in the ν space, over a Gaussian centred in ν0with r.m.s. σν, and nϑ particles distributed uniformly in
the interval ( ϑ0 , ϑ1 ).

10



5 

0

10

15

(P 1 ) n
Figure 3: Phase space distribution at the end of thesimulation with the parameters listed in Fig. 2.
After the FEL interaction the phase space is distributedin an interval longer than (0, 2π). The periodicity in ϑ ofthe system of equations (2) and (3) can be imposed to thephase space variables with the function P :=FELBox_h(P, ϑ0 , ϑ1 ). By calling this function with
( ϑ0 , ϑ1 )=(0, 2π) we obtain the phase space distribution ofFig. 4.

10(P 0 ) n

5

10



5

(P 0 ) n

0

0

5

10

0

2



4

6

(P ) n1

Figure 1: Phase space distribution obtained by calling thefunction FELquietstart_h with ν0=2.6, σν=2, nν=40,
ϑ0 =0, ϑ1 =2π, nϑ =40.

92

0

2



4

6

(P 1 ) n
Figure 4: Phase space distribution after imposing aperiodicity condition in the interval (0, 2π).

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

Start-up from e-beam shot noise
Startup from shot noise may be simulated by using thefunction FELquasiquietstart_h(ν0,σν, nν, ϑ0 , ϑ1 , nϑ , φns,a) which is analogous to the function FELquietstart_h
except for the additional argument φn which is used todisplace the particles according to the function
$
!$
!

 "" ϑ − ϑ "
n
−
1
1
0
#i − ϑ #

ϑi = arg(φns ) + (1 − φns )

2

nϑ

(7)

MOPPH026

In an oscillator FEL or in a seeded FEL and in general,
when the transverse properties of the radiation may beconsidered as a constraint of the problem, the coupling
coefficients (2) have to be corrected by a proper filling
factor. In general when the radiation size is the result of
the balance between diffraction and focusing induced by
the gain, as in a single pass FEL, a filling factor
coefficient may be derived from the Xie scaling laws [8]by calculating the ratio between the Xie factor with andwithout diffraction effects. In a similar way a coefficientcorrecting the coupling factor g may be derived from thesemi-analytical model in [9].

In the limit of small perturbation ( φns → 0 ) andsufficiently large number of particles nϑ the distribution
has Fourier coefficients bn ≅ φns (bunching coefficients at
the harmonic n) almost independent from n (see ref. [1]).
The coefficient b1 can be estimated in a steady state
simulation using the procedure of ref.[6].

The variable ν i = 2π N (ωi − ω L ) ωi represents therelative shift of the resonance of the ith particle from agiven reference frequency ω L . According to thedefinition of the resonant frequency of the ith particle
ωi = 2γ i 2 cku 1 + K ( xi , yi ) 2 2 + γ i 2 θ x ,i 2 + θ y ,i 2 , where
we have included the dependence on the angle between
the average particle trajectory and the undulator axis
θ xy ,i = β xy β z (we use the notation θ xy ,i = θ x ,i , θ x ,i ) and())

the dependence of the undulator K parameter on thetransverse coordinates, the particles distribution in energy
and transverse phase space may be converted in a
distribution in the detuning parameter space ν. At thelowest order in xi , yi and θ xy,i we have [7]
*

'2 *

'

2γ 2 (( πK %% (( β x , yε n, xy %%σ x , y = 2π N hx , y&)& )1 + K 2 2 γλu
γ
*

'2 *
(

'
%

2γ 2 (( πK %% ( ε n, xy %σ ′x , y = 2π N)
& )&1 + K 2 2 γλu
β x , yγσ e = 4πN

Mathcad programming may be used to set up FEL
simulations in a wide variety of conditions. As an
example we analyse the case of 1D FEL simulations
including pulse propagation effects. The field is governedby the evolution equation
0
∂ ++
.. ∂
+∆
/
, a n (τ , ζ ) = −2πg n I(ζ ) exp(inϑi (τ , ζ )) ζInhomogeneous broadenings and three
dimensional effects(

TIME DEPENDENT SIMULATIONS

(8)

σγ
γ

∂τ

∂ζ

where ∆ = Nλl is the slippage length, ζ is the longitudinalcoordinate in the frame moving with the electron bunchand I(ζ ) is the normalized current shape. The average on
the r.h.s. of (10) is intended in a region λl at theposition ζ . The solution of this equation is obtained bydefining an array of variables of the type of PHSP in (5),representing the sampling of both the field and the beamphase space variables along the coordinate ζ at thepositions ζ = ζ0, ζ1, …, ζnb-1. The phase space beamlets
are defined as
P = (P0, P1, …, Pnb-1)

for n ∈ 1 .. P1
P1

where hx , y are the undulator focusing parameters (withand the β Twiss coefficients in the x and y planes
respectively. An approximated expression for standard
deviation in the ν space is obtained by combining
quadratically the standard deviations (8)σ ν ≅ σ x2 + σ y2 + σ ′x2 + σ ′y2 + σ e2

FEL Theory

(9)

(11)

The undulator is divided in time steps such that the step
length ∆τ is related to the spatial sampling ∆ζ by thecondition ∆ζ = ∆ ∆τ . With such a choice, at each time
step the field variables at the ith position in the P arrayhave to slip to the next position: ith1 ith+1. For thispurpose the function in Fig. 5 is defined.
FELSlipField ( P1 , P2 ) :=hx + hy = 2 ), ε n, xy and β x, y are the normalized emittances

(10)

P1

n, 0
n, 1

0, 0

← P2
← P2

n, 0
n, 1

P1

Figure 5: Function FELSlipField loading the field datafrom beamlet P2 to P1. Fields in P2 are overwritten.

The simulation of a single pass FEL in time dependent
mode is then simply obtained with the function shown in
Fig. 6. The first loop over the nb beamlets loads the initial
phase space array P, generating each beamlet with a

93

MOPPH026

Proceedings of FEL 2006, BESSY, Berlin, Germany

different shot noise coefficient φn,i. The initial field
amplitude a0 is multiplied by a modulating coefficient sei
which can be defined in order to simulate theζ dependence of an input seed. The second loop over thevariable nτ takes care of the integration of the phase space
beamlets P along the undulator. At each time step oflength ∆τ the array of beamlets P is stored in the matrix
OUT, particles and fields are advanced by the
FELpendulum_h and the slippage is applied by the
FELSlipField procedure defined in Fig. 5. Each columnof the matrix OUT contains the array P at time ∆τnτ . Asan example of a simulation obtained with the routine in
Fig. 6, we have considered the case of a SASE FEL withthe resonance at 200 nm, a FEL parameter ρ≈4x10-3 andgain length of about 0.3 m. In Fig. 7 the longitudinal
phase space at saturation is shown. The beamlets at thesame time frame have been joined together in the sameplot. The horizontal axis represents the beamlets position
along ζ. The phase space variable ϑ in each beamlet isexpanded by the factor ∆ζ 2π in order to give theimpression of a continuous beam. The ζ window is large

enough to contain two spikes, the red line represents
indeed the separatrix of the motion and is proportional to
the root of the field.
FELTimedep :=for i ∈ 0 .. nb − 1(

P ← FELquasiquietstart_h ν 0 , σν , n ν , 0.0 , 2 ⋅ π , n θ , φn , i , a 0 ⋅ se
i

)

i

τ←0
for n τ ∈ 0 .. n T
for i ∈ 0 .. nb − 1OUTnτ , i

←P

i

(i

)

P ← FELpendulum_h P , g ⋅ I , τ , τ + ∆τ , TOLiifor n ∈ n b − 1 .. 0

( i if ( i=0 , nb−1 , i−1) )PT ← FELSlipField P , P

P ← FELbox_h (PT , 0 , 2 ⋅ π)iτ ← τ + ∆τ
OUT

Figure 6: Function simulating the longitudinal dynamics
of a single pass FEL in time dependent mode. The result
returned by the matrix OUT contains the beamlets phasespaces composing the beam at the nT time steps.

Phase space of selected slices

Detuning

50

0

50

0

20

40

60

80

100
Phase

120

140

160

180

Figure 7: The beamlets resulting after a SASE FEL simulation at saturation have been joined together in the same plot.
The horizontal axis represents the beamlets position along ζ. The phase space variable ϑ in each beamlet is expandedby the factor ∆ζ 2π in order to give the impression of a continuous beam. The red line represent the separatrix of the
motion and is proportional to the root of the field.

CONCLUSIONS
We have provided a brief overview of the physicalmodel implemented in Perseo. The main functions
required for setting up a simple simulation have been
analysed and the algorithm for implementing timedependent simulation has been explained. With asimilar procedure fully 3D simulations can be
implemented but the cpu and memory requirements
becomes excessive for an interactive execution.
For additional information and further insight in
Perseo capabilities the reader is addressed to the web
page [1] and to the Perseo Electronic Handbook
included in the installation package.

REFERENCES[1] See www.perseo.enea.it[2] W. B. Colson, Laser Handbook vol 6, ClassicalFree Electron Laser Theory, 301 North-Holland,
Amsterdam, 1990.
[3] W. B. Colson, G. Dattoli, F. Ciocci, Phys. Rev. A
31, 828 , 1985.
[4] G. Dattoli, S. Cabrini, L. Giannessi, Phys. Rev. A
44, 8433 , 1991.
[5] Mathcad Help files – see also www.mathsoft.com[6] L. Giannessi, in Proc. of the 26th FEL conference,
Trieste 2004 , p. 37.
[7] G. Dattoli, A. Renieri, Laser Handbook vol. 4 ed.
by M.L.Stich and M.S. Bass , North Holland
Amsterdam 1985.
[8] M. Xie, in Proceedings of the 1995 Particle
Accelerator Conference, Dallas, Texas, 1–5 May
1995, IEEE, Piscataway, NJ, 1996 , p. 183.
[9] G. Dattoli et al., Journal of Appl. Phys. 95, 3206
2004.

94

FEL Theory,

Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH028

FUTURE SEEDING EXPERIMENTS AT SPARC
L. Poletto, G. Tondello, Università di Padova, Padova, Italy
S. De Silvestri, M. Nisoli, G. Sansone, S. Stagira, Politecnico di Milano, Milano, Italy
P. Musumeci, M. Petrarca, M. Mattioli, INFN Sez. Roma I, Rome, Italy
M. Labat, O. Tcherbakoff, M. Bougeard, B. Carré, D. Garzella, G. Lambert, H. Merdji, P. Salières,Service des Photons Atomes et Molécules, CEA Saclay, DSM/DRECAM, France.
M. E. Couprie, SOLEIL, Sant-Aubin, Gif-sur-Yvette CEDEX, France
D. Alesini, M. Biagini, R. Boni, M. Castellano, A. Clozza, A. Drago, M. Ferrario, V. Fusco, A.
Gallo, A. Ghigo, M. Migliorati, L. Palumbo, C. Sanelli, F. Sgamma, B. Spataro, S. Tomassini, C.
Vaccarezza, C. Vicario, INFN-LNF, Frascati, Italy
L. Serafini, INFN, Milano, Italy
S. Ambrogio, F. Ciocci, G. Dattoli, A. Doria, G. P. Gallerano, L. Giannessi, E. Giovenale, I.
Spassovsky, M. Quattromini, A. Renieri, C. Ronsivalle, ENEA C. R. Frascati, Rome, Italy
P.L. Ottaviani, S. Pagnutti, M. Rosetti, ENEA C.R. Bologna, Italy
A. Dipace, E. Sabia, ENEA C. R. Portici, Napoli, Italy.
Abstract
This communication describes the research work planthat is under implementation at the SPARC FEL facility
in the framework of the DS4 EUROFEL programme. The
main goal of the collaboration is to study and test the amplification and the FEL harmonic generation process of an
input seed signal obtained as higher order harmonics generated both in crystals (400 nm and 266 nm) and in gases(266 nm, 160 nm, 114 nm). The SPARC FEL can be configured to test several cascaded FEL layouts that will bebriefly analysed.

Table 1. List of the main SPARC beam parameters
Beam energy

155-200 MeV

Bunch Charge

1.1 nC

Rep. Rate1 – 10 Hz

Peak current (>50% bunch)

100 A

Norm. emittances (integrated)

2 mm-mrad

Norm. emitt. (slice len. 300μm)< 1 mm-mrad

INTRODUCTION

Total correlated energy spread

0.2 %The SPARC FEL experiment is based on two main
components, a high brightness photoinjector that is expected to provide a high quality beam at energies between
150 and 200 MeV (see Tab.I and ref.[1]) and a single pass
FEL, whose undulator beam-line is composed by six undulator sections of 77 periods each, with a period lengthof 2.8 cm and a gap ranging from 6 to 25 mm[2].
The FEL will operate in self amplified spontaneousemission (SASE) mode at a wavelength of about 500 nm
with an expected saturation length of about 10-12 m, according to the beam parameters listed in table 1. The
flexibility offered by the variable gap configuration of the
SPARC undulator and the natural synchronization of theelectron beam with the laser driving the photoinjector,
makes the SPARC layout particularly suited for a numberof experiments where the FEL amplifier is seeded by an
external laser source. The seed laser is driven by the same
oscillator initiating the laser cascade which is used to run
the photocathode and consists in a regenerative amplifierdelivering 2.5mJ at 800 nm with a pulse duration shorter
than 120 fs.

Total uncorrelated energy spread

0.06 %

e-bunch duration (rms)∼ 4 psSeeded FELs

Different schemes of non-linear harmonic generation
are then implemented to generate the shorter wavelength
radiation for seeding the FEL. Second and third harmonic
generation in LBO crystals will provide the powerfulpulses required to reach saturation and study the nonlinear pulse propagation in FELs and FEL cascades insuperradiant regime, at 400nm and 266nm [3], [4]. The
other method considered for the frequency up-conversionof the Ti:Sa fundamental wavelength, is based on the nonlinear higher order harmonics generation of the Ti:Sa laser in a gas-jet or in a gas-cell [5]. While at SPARC weplan to seed the FEL with the harmonics up to the 9th of
the Ti:Sa [6], the harmonic generation in gas allows toextend the seed source spectral range down to the EUV
region of the spectrum and represents a promising technique to seed FEL amplifiers at shorter wavelengths.
In the following we will review some of the plannedexperiments with the two different seed sources.

95

300

Power (a.u.)

-40

200

100
0.5

(b)

(c)

170 MeV
200 MeV
160 - 266 - 400 nm
114 - 160 - 266 nm

1

1.5
K

2

160 nm100

Power (a.u.)

Wavelength (nm)

400

(a)

Power (a.u.)

The experiment of seeding high harmonics generated ingas at SPARC is based on the installation of a gas jet interaction chamber and an in vacuum optical system whichmatches the transverse optical mode of the harmonic tothat of the e-beam in the first undulator section [6]. The
UV pulse is injected into the SPARC undulator by meansof a periscope and a magnetic chicane deflecting the ebeam from the straight path. High-order odd harmonics of
the Ti:Sa laser may be generated at the wavelengths
266nm, 160nm, and 114nm. The undulator resonancecondition is tuned at these wavelengths by varying thebeam energy and undulator strength K according to theplot shown in Fig. 1.

200
λ (nm)

300

100

200
λ (nm)

300

100

200
λ (nm)

300

Power Spectrum

SEEDING WITH HIGH HARMONICS
GENERATED IN GASPower Spectrum

Proceedings of FEL 2006, BESSY, Berlin, Germany

Power Spectrum

MOPPH02855
z (μm)

150

Figure 2 Power and spectrum of the radiation at different
positions in the undulator for the SPARC FEL seeded at
160nm. Seed signal (a), after the first undulator section(b), at the end of the undulator (c). Beam energy 200
MeV, K=1.226, the other beam parameters as in Table 1.

Figure 1: Seeded SPARC FEL operation wavelengths.
The high order harmonics result from the strong nonlinear polarisation induced on the rare gases atoms, suchas Ar, Xe, Ne and He, by the focused intense electromagnetic field of the "pump" laser. The emitted pulse is composed by a sequence of short bursts separated by one halfof the fundamental laser period (400nm) and the spectrum
contains the odd harmonics of the original laser. A simulation of the amplification of a pulse at 160nm with thetypical time structure of harmonics generated in gas has
been done with Perseo[7]. The laser pulse shape vs. thelongitudinal coordinate is shown in Fig. 2 at different positions along the undulator. The radiation spectrum is also
shown in Fig.2 and the effect of the spectral “cleaning”
associated with the limited FEL bandwidth (FEL parameter ρ ≈ 4⋅10-3) is evident. An analogous behaviour is observed at the third harmonic generated by the non-linear
FEL dynamics. More detailed simulations based on an
accurate model of the seed fields distribution and including transverse effects are under study.

96

SEEDING WITH 2ND AND 3RD HARMONICS OF TI:SA GENERATED IN CRYSTAL
The six SPARC undulators may be configured in order
to set up a single stage cascaded FEL based on a modulator – radiator configuration, similar to the one tested at
BNL [8]. The layout of this configuration is shown in
Fig.3.
λ = 400 nm

λ = 200 nm

modulator

radiator

Figure 3 Single stage cascaded FEL layout.
The number of sections of the modulator and of the radiator may be tuned depending on the intensity of thelaser seed. The availability of intense short pulses fromthe seed laser allows to test the superradiant cascade concept [4]. The seed laser power is indeed sufficient to bringat saturation a modulator made by a single undulator
segment tuned at 400 nm. The pulse generated in these
conditions propagates with the typical signature of superradiance in the following radiator composed by the re-Seeded FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany
maining five sections. The feasibility of this experiment
was studied in[9].
A second interesting configuration consists in the experimental test of the fresh-bunch injection technique[10]. The layout is shown in Fig.4. In this case the firsttwo undulators (A and B) represent the modulator andradiator sections of single stage cascade, the following
two undulators (C and D) are tuned off resonance with theseed wavelength and its higher order harmonics. These
undulators play the role of the dispersive section where
the radiation exiting the first radiator at 200 nm (B) is
longitudinally separated from the electron beam part
where the high quality beam has been heated in the previous sections, by the FEL interaction with the seed.

266 nm

MOPPH028

222 nm44 nm

Figure 5 FEL Harmonic cascade FEL configuration.
The energy of the radiation pulse at the wavelength of
44nm vs the longitudinal coordinate in the radiator isshown in Fig. 6.

0.4

(A)

(B)

400nm 200 nm

(C)

(D)

≈ 380 nm(E)(F)

200 nm 300 nm

modulator
modulator
radiator dispersion
radiator

100 nmEnergy (μJ)

0.3

0.2

0.1

Figure 4 Fresh bunch injection technique layout.

Seeded FELs

0

5

10

15

z (m)
Fig. 6 Pulse energy vs. the longitudinal coordinate in
the radiator.

A transition to superradiance where the pulse energy
grows as z3/2 occurs after about five meters of the radiator
section.
The pulse shape is shown in Fig. 7 and the relevant
spectrum is shown in Fig. 8.

1

Power (a.u.)

Section (E) is the modulator of the second stage cascade and section (F) is the radiator that is tuned in orderto match the resonance of its third harmonic with the second harmonic of the radiator (E). This is necessary since
the K parameter excursion of the undulator is not sufficient to span the 1st to 3rd harmonic range and coupling on
the higher order odd harmonics in a linear undulator
based FEL has been considered [11].
The last configuration considered in this overview consists in the harmonic FEL cascade [12]. As in the laststage of the previous configuration, the two undulators are
tuned at different, not-harmonic fundamental frequencies,
but have instead one of their higher order harmonics incommon. According to the SPARC FEL undulator properties, this scheme may be tested in configurations where
the fourth of the sixth harmonic of the 266nm signal usedas seed of the first section, are amplified as the third or
fifth harmonics in the second section. This configuration
has been analysed with numerical simulations in timedependent mode. Both the codes Perseo and a modified
version of the code Genesis 1.3 [13-14] which includes
the self consistend dynamics of the higher order harmonics have been used. In the example considered in Fig. 5,
we show the result obtained with Perseo. The cascade isdriven by a seed of 2 MW peak power at a wavelength
corresponding to the third harmonic of the Ti:Sa drive
laser. The first undulator has the fundamental resonance at
266nm and the second section is tuned at 222nm. The two
undulators have a common resonance at 44nm, corresponding to the 6th harmonic of the first section and the 5thof the second.

0.

0
38.2

9.8

57.9
ζ (μm)

106

154

Fig. 7. Longitudinal profile of the radiation power at theend of the second undulator.

97

Power spectrum (a.u.)

MOPPH028

44.2

Proceedings of FEL 2006, BESSY, Berlin, Germany

44.3
44.4
wavelength (nm)Fig. 8 Power spectrum of the radiation pulse as shown in
Fig. 7.

CONCLUSIONS
We have given a brief overview of some of the experiments that will be implemented at SPARC thanks to theflexibility of the SPARC configuration and of the variable
gap undulator. Seeding the FEL with harmonics generated
in gas and testing schemes as the fresh bunch injection
technique and the harmonic FEL cascade are among thecapabilities of the SPARC hardware. The harmonic cascaded FEL scheme is in particular a promising scheme toextend to the short wavelength the operation range of aFree Electron Laser. A wavelength of 44nm was obtainedin simulations with a beam energy of only 200 MeV.
The opportunities provided by the SPARC experimentof a deeper understanding of the amplification process
and of experimentally testing and of the FEL dynamics
through a whole cascade, may affect in the future the design of the foreseen FEL facilities aiming at the generation of radiation in the VUV-EUV region of the spectrum.

[9] L. Giannessi, P. Musumeci, in Proc. of the 27th
FEL conference, JACoW (Joint Accelerator Conference Website) at http://www.JACoW.org, p. 210(2005).
[10] I. Ben-Zvi, K.M. Yang, L. H. Yu, Nucl. Instrum. &Meth. A 318, 726 (1992).
[11] W. B.Colson, G. Dattoli and F. Ciocci, Phys. Rev.
A 31, 828 (1985).
[12] L. Giannessi and P. Musumeci, in proc. of 46th
workshop on the Physics and applications of highbrightness electron beams, Erice (Tr), 9 - 14 October 2005.
[13] S. Reiche, Nuclear Instrum. & Meth. A429, 243(1999).
[14] L. Giannessi and P. Musumeci, The Free Electron
Laser Harmonic Cascade” submitted to New Journal of Physics, June 2006.

ACKNOWLEDGMENTS
Work partially supported by the EU Commission in thesixth framework programme, contract no. 011935 – EUROFEL.

REFERENCES[1] SPARC Collaboration, Nucl. Instr. & Meth. A507
(2003) 345-349, see also http://www.sparc.it andthese proceedings.
[2] A. Renieri et al. Status report on SPARC project,in Proc. of the 26th FEL conference, Trieste 2004
JACoW (Joint Accelerator Conference Website) at
http://www.JACoW.org, p. 163 (2004).
[3] R. Bonifacio, L.De Salvo Souza, P.Pierini, and N.
Piovella, Nucl.Instrum. & Meth. A 296, 358 (1990)[4] L. Giannessi, P. Musumeci, S. Spampinati, J. Appl.
Phys. 98, 043110 (2005).
[5] T. Brabec, F. Krausz, Rev. Mod. Phys. 72, 545(2000).
[6] M. Labat et al., Seeding SPARC Facility with
Harmonic Generation in Gases, MOPPH047 theseproceedings.
[7] L. Giannessi, Perseo see http://www.perseo.enea.it[8] L. H. Yu et al. Phys. Rev. Lett. 91, 074801 (2003).

98

Seeded FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH030

X-RAYS GENERATION WITH A FEL BASED ON AN OPTICAL WIGGLER
A. Bacci, C. Maroli, L. Serafini, INFN-Sezione di Milano, 20133 Milano (Italy)
V. Petrillo , Dipartimento di Fisica dell’Università di Milano-INFN Sezione di
Milano, 20133 Milano (Italy)
M.Ferrario , INFN-LNF, 00044 Frascati, Roma, Italy.
Abstract
The interaction between high-brilliance electron beams
and counter-propagating laser pulses produces X rays via
Thomson back-scattering. If the laser source is long andintense enough, the electrons of the beam can bunch and aregime of collective effects can be established. In the caseof dominating collective effects, the FEL instability candevelop and the system behaves like a free-electron laser
based on an optical undulator. Coherent X-rays can be
irradiated, with a bandwidth very much thinner than thatof the corresponding incoherent emission. The main
quantities that limit the brilliance of the X-rays are
emittance, mean radius, current and energy spread of theelectron beam, and the distribution and intensity of thelaser beam. In this work we discuss first some ideal
examples. Secondly we present the preparation of theelectron beam by means of the use of a genetic code that
optimizes the output of the code ASTRA. The electron
beam obtained is analysed in slices and the best one isused in the 3-D radiation code.

INTRODUCTION
A Thomson back-scattering set-up can be considered inprinciple as a source of intense X-ray pulses which is at
the same time easily tunable and highly monochromatic.
Due to recent technological developments in the
production of high brilliance electron beams and highpower CPA laser pulses, it is now even conceivable to
make steps toward their practical realisation.
The radiation generated in the Thomson back-scattering is
usually considered incoherent and calculated by summingat the collector the intensities of the fields produced insingle processes by each electron. If the laser pulse is longenough, however, collective effects can establish andbecome dominant. The system in this range of parametersbehaves therefore like a free-electron laser, where thestatic wiggler is substituted by the optical laser pulse.
From the point of view of the theoretical description of
the process, it is convenient to start with the same set ofone-dimensional equations that are used in the theory ofhigh-gain free-electron laser amplifier [1,2]. To take into
account the many aspects of the process connected withthe finite transverse geometry of the electron beam and of
the laser and radiation pulses it is necessary to consider
3D equations [3].
A set of numerical results based on ideal electron beams
is first presented. Secondly we present a genetic code that
permits the optimization of the outputs of the beam
dynamics code ASTRA, in order to obtain an electron

The Angstrom Challenge

beam with suitable characteristics. The electron beamobtained is analysed in slices and the best slice is used in
the computation of the X-ray radiation under the effect of
the laser. A short discussion of the importance of thedata will be given at the end of the paper.

MODEL EQUATIONSEXAMPLES

AND

IDEAL

We start from the Maxwell-Lorentz equations that
describe both laser and collective electromagnetic fields
and from the relativistic equations of motion for theelectrons of the beam. The laser and collective fields are
given in terms of the corresponding scalar and vector
potentials in the Coulomb gauge.
We assume that the laser is circularly polarised with thefollowing form of the vector potential A L (the laser pulse
propagates along the z-axis in the negative direction):A L (r , t ) =

aL0
2

λ

( g (r , t )e − i ( k L z +ω L t )eˆ + cc) + O ( L )w0(1)

where λL = 2π/kL is the laser wavelength, w0 the laser
spot size, ωL=ckL the angular frequency andeˆ = (e x + ie y ) / 2 . The envelope g(r,t) is considered to

be a slowly varying function of all variables xyz and t andis defined as a complex number with |g(r,t)|≤1. In the caseof a laser pulse with a Gaussian transverse shape, theenvelope has the form
⎡
⎤
⎢
2
2
2
2 ⎥
x +y
x +y ⎥
exp ⎢− 4− 4ig(r, t) = Φ(z + ct)
2
2
⎢
z z ⎥
z
z
w02( + 0 ) ⎥⎢1+ 2
w02 (1+ 2 )z0 z ⎥
z0
z0
⎢⎣
⎦

1+ i

z
z0

(2)

where z0 = πw02/4λL is the Rayleigh length and the formof the (real) function Φ (with 0≤Φ(z)≤1) depends on the
shape of the pulse along the z-axis. In the case of a guided
laser pulse the quantity g(r,t) is a step function. We
suppose that ϕ (r, t ) and A(r, t ) have a slow dependence
on x and y, i.e., that they vary on a transverse scale LT
much greater than the radiation wavelength λ=2π/k andwrite, accordingly to the single-mode hypothesis
frequently used in 1D treatmentsA(r , t ) = M (r, t )eˆ + cc + O(λ / LT )(3)
= A(r, t )e i ( kz −ωt ) eˆ + cc + O (λ / LT )where M (r, t ) = A(r, t )e i ( kz −ωt ) and ω=ck is the radiation
angular frequency. In the three-dimensional equation of99

MOPPH030

Proceedings of FEL 2006, BESSY, Berlin, Germany

the model derived in details in Ref [3] a critical role isplayed

by

the

FEL

parameter

The resonant frequency is at ω ≈1
1 ⎛⎜ ωb2 a L2 0 ⎞⎟ 3.
ρ= ⎜γ 0 ⎝ 16ω L2 ⎟⎠4γ 02 ω L

. The fact that
1 + a L2 0
the quantum effects are negligible is guaranteed by< 1.
taking the quantum parameter q= hk
ρmc < γ >First, we have solved our model equations in thefollowing case: the laser has a wavelength λL=10 micronand the parameter aL0 = 0.3. The diameter of the laser
focal spot w0 has been assumed 50 μm, the length of thepulse 70-100 psec, for a total power of 40-100 GW and a
total energy of 4-10 J. The bunch of electrons has beenchosen with an average value of γ, <γ>=60, corresponding
to an energy of 30 MeV. This value of <γ> leads to aresonant wavelength λ=7.56 Angstrom. The quantum
parameter q =0.2 and the classical model is expected to
be fully valid. The collective effects appear and saturate
after 7 gain lengths which in our case correspond to timesof the order of 60-70 ps (each gain length corresponds to
Lg=1 mm), i.e., of the same order of the duration of thelaser pulse.
The electron beam has a mean radius σ0=25 micron , a
total charge of 1-5 nC and a length Lb= 1 mm, so that the
Pierce parameter is ρ=2.8 . 10-4. Its energy spread Δγ/γ
ranges from 0 to 1.5 . 10-4 and the initial normalized
transverse emittance εn has been varied up to 1.

the electron bunch at the position zm =<z> and averaged
on the transverse plane. The peak number of X coherent
photons is 2.5 .1010, while the incoherent process provides
2 .10 8 photons.
In this case w0= 50 micron, εn=0,6 mm mrad, Q=3 nC,
I=0.9 KA and the signal saturates at t=70 psec.
Figure 2 gives the first peak value of <|A|2> versusΔω/(ωρ), representing the spectrum of the signal. As canbe seen the width of the spectrum is few times ρ. In Fig 3
the peak value of <|A|2> is given as function of thetransverse emittance, showing a depletion of the emission
for emittances larger than 0.6-0.7 mm mrad.

0.1
2<|A| >peak
0.05

0
-2

-1

0

Δω/(ωρ)1

2

Figure 2: First peak value of <|A|2> versus Δω/(ωρ)
for the same parameters as Fig 1

(a)

0.5



0.5
<|A| >peak
2

0
00

50
(b)

100
(1)

2

<|A| >

(2)

-4

0
0.5
-8
0

50

100

t(psec)Figure 1 (a) |b| averaged on the transverse section vs t in
psec and (b), (1) coherent value of |A|2(zm) (b),(2)incoherent value for w0= 50 μm, εn=0,6 mm mrad
Fig 1 shows the typical growth of the bunching factor intime (a), as well as the collective potential (b) curve 1 andthe incoherent potential (b) curve 2. The amplitude of thevector potential |A|2 has been calculated in the middle of

100

εn

1

Figure 3: <|A| >peak versus εn evaluated in micron for thesame case of Fig 1 and with Δω/ω=-10-4, w0=50 micron,
aL0=0.3, Δγ/γ=10-4.
2

In Figures 4,5,6,7 a different case is shown. The laser
wavelength in this case is 0,8 μm.The electron beam has<γ>=30, for a Pierce parameter ρ=4,38 . 10-4. Other
parameters of the beam are: a mean radius σ0=10 micron,a total charge of 1 nC, a length Lb= 200 micron,corresponding to a beam current of I=1.5 KA.
In Fig 4 the bunching (a) and the collective (b) (1) and
The Angstrom ChallengeProceedings of FEL 2006, BESSY, Berlin, Germany

In Fig. 5 the spectrum of the radiation is presented, while
in Fig. 6 the dependence of the maximum of <|A|2> on thetransverse normalized emittance is shown. Curve (a) isrelevant to the situation of flat laser pulse with w0=50
micron, while curve (b) shows the more critical situation
where a Gaussian profile for the laser has been assumed.
In this case the quantity σL has been taken equal to 106
μm with aL0=0.8, increasing consequently the laser power.
We must note that we have considerable emission also in
violation of the Pellegrini criterion for a static wiggler. In
fact, the emittances considered exceed largely the value
γλ/4π, which in this case is 9 .10-4 μm. On the other hand,on the fact that ZR/Lg=1.2 .104, the criterion of Pellegrini
can be rewritten in a generalized form for both static andoptical undulators as εn ≤ α ZR / Lg λRγ / 4π [5] where

(a)
0.5



0

0

0

2

4
(1)

(b)

2

<|A| >
(2)

-4

-8

0

2
t(psec)

MOPPH0304

α= dω /(ωρ) ≈ 2 , giving the more relaxed limit εn<0,3μ.

Figure 4: Bunching (a) and log of the radiation intensity(b) vs t in the coherent (1) and incoherent (2) casefor: λL=0.8 μm, aL0=0.8, Δγ/γ=10−4,Δω/ω=-2 .10-4, εn=0.88.
incoherent (b) (2) potential amplitude are shown versus
time. Furthermore, we have assumed a focal spot ofradius w0 of about 50 μm with a laser parameter of
aL0=0.8 so that the radiation turns out to have λ= 3,64
Angstrom. With these values the gain length corresponds
to about 145 micron, the appearance and the saturation of
the collective effects (taking place in 7-12 gain lengths)
being contained in 5 picoseconds, a time of the sameorder of the duration of the laser pulse. The quantum
parameter q is 0.5.
The energy spread Δγ/γ of the electron beam has beenchosen 1. 10-4 and the initial normalized transverse
emittance has been varied from 0 up to 2.

0.5
2<|A| >peak
(a)
0.25
(b)

0
0.5

1.

εn

1.5

2.

Figure 6: <|A|2>peak ves εn, with Δω/ω=0. and: (a) flat
laser profile with w0=50 μm and aL0=0.8 and (b) Gaussianlaser profile with aL0=0.8 and σL=106 μm.
0.8

2

0,5

<|A| >peak
0.4

(a)

2

<|A| >peak
0

(b)
0,0
-3

-2

-1

0

1

Δω/(ρω)2

3

Figure 5: <|A|2>peak versus Δω/(ωρ) for the case of fig 5
and (a) εn=0,44 μm and (b) εn=0,88 μm.
The saturation level of the radiation is reached at t=4 psec
at <|A|2>peak=0,275, with a total number of photons of
1,86 1010, against the 2 108 provided by the incoherent
process.

The Angstrom Challenge

250

500 w

0

750

1000

Figure 7 <|A|2>peak vs w0 for a Gaussian laser for εn=0,44
μm, Δω/ω=-1 .10-4, aL0=0.8.
Fig 7 shows the dependence of the growth of the signal on
the transverse energy distribution of the laser in the caseof a Gaussian pulse for εn=0,44 μm, Δω/ω=-1.10-4,
aL0=0.8. In fact, in this case, a spot size with a radius
smaller than 75 micron does not permit the instauration of
the instability. The collective signal in this condition,
therefore, does not grow.

101

MOPPH030

Proceedings of FEL 2006, BESSY, Berlin, Germany

REALISTIC EXAMPLE OBTAINED BY
MEANS OF A GENETIC ALGORITHM
A realistic electron beam has been generated using thebeam dynamic code ASTRA. The sequence of theaccelerating and focalization elements in the beam line isshown in Fig 8, where the RF section works in thevelocity bunching configuration.

Injection phase in the bunching structure φb. 4) Position of
the bunching structure lb. 5) Intensity of the first solenoid
field B1, used to control the envelope in the emittancecompensation layout. 6) Intensity of the second solenoid
field B2, used to control the envelope. 7) Position of thesecond solenoid ls2.
The convergence is reached in 500 generations on anelectron beam configuration whose best slice has anemittance of 0,56 mm mrad, a radius of 15 micron, alength of 15 micron with a charge Q=0.05 nC. The genis
values for the final configuration are: φrf =9.77°, ga =17.68 MV/m, φb =-91.57°, lb =1.3868 m, B1 =0.256 T
B2=0.0532 T, ls2 =1.3685m. The energy spread of the slice
Δγ/γ is 0.15 %. The growth of the signal is shown in fig
10, while the spectrum is in Fig 11. The saturation occurs
in 6 psec, the focal spot size is w0=30 μm, aL0=0.8, for a
total laser power of W=9.77 TW.
0,102<|A| >
0,05

Figure 8: Beam line lay-out.
However, the optimization of the output is very difficult
due to the high number of parameters which have to be
fixed and to the non linear correlations existing between
them. To circumvent this difficulty we have developed agenetic code that manages to fix the values of theparameters. The optimization is made by maximizing thefollowing fitness function:

0,00
0

2

4

6
t(psec)8

Figure 10: Growth of the signal.

0,10
2<|A|sat >
0,05

0,00
-0,0015-0,0010-0,0005Δω/ω0,0000Figure 11: Spectrum of the signal.

REFERENCES
Figure 9: Bunch phase space and slice used (in blue).
F fitness =I 3.5

ε n− x, y ⋅ σ x , y ⋅⎛ Δγ ⎞
⎜
⎟
⎜
⎟
⎝ γ ⎠

as function of the following genes defining the beamline: 1)
Phase of the gun radiofrequency φrf. 2)
Acceleration gradient in the bunching structure ga. 3)

102

[1]

W.B. Colson, Phys.Lett. 59A,187,(1976). R.
Bonifacio, C. Pellegrini, L. Narducci Opt. Commun.
50 (1984) 313[2] A.Bacci, C.Maroli, V.Petrillo, L.Serafini:”Collective
effects in the Thomson back-scattering between alaser pulse and a relativistic electron beam” EPJAP(in print)[3] A.Bacci, M.Ferrario, C. Maroli, V. Petrillo, L.
Serafini PRST-AB 9 (2006) 060704

The Angstrom ChallengeProceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH031

THE SATURATED REGIME OF A SEEDED SINGLE-PASS FREE
ELECTRON LASER: A THEORETICAL INVESTIGATION THROUGH
THE STATISTICAL MECHANICS OF THE VLASOV EQUATION
F. Curbis∗ , University of Trieste & Elettra, Basovizza, Trieste, Italy,
A. Antoniazzi, Dipartimento di Energetica, Università di Firenze, Italy
G. De Ninno, Elettra, Basovizza, Trieste, Italy,
D. Fanelli, Dipartimento di Energetica, Università di Firenze, Italy.

Abstract∗ francesca.curbis@elettra.trieste.it

FEL Theory

DISPERSIVESECTION

RADIATOR

electronbeamcoherent
emissionenergymicro-bunchingmodulation

Figure 1: Schematic layout of the CHG scheme.

persive section. Finally, in a second undulator, called radiator and tuned at the n-th harmonic of the seed frequency,
the micro-bunched electron beam emits coherent radiation
at the harmonic wavelength λ/n. Such a radiation is thenamplified until saturation is reached.
Importantly, it shall be noticed that Single-pass FELs
represent an example of systems with long-range interactions [2]. When long-range forces are to be considered,a global network of connections between individual constituting elements is active, and mean − f ield effects are
dominant. Surprisingly, within the realm of long range interacting systems, a wide number of striking phenomena
appear including ensemble inequivalence, negative specificheat and emergence of Quasi–Stationary States (QSS), i.e.,
long–living states where the system gets eventually trapped
before relaxing to its final statistical equilibrium. This latter remarkable non equilibrium feature is also reported for
4b)

INCOHERENTENERGY SPREADc)

SEPARATRIX

0

2

2

0

0

1

2

3

Phase

4

5

6

4

COHERENT
ENERGYSPREAD

2

2

2
4

4

4

a)
2

EnergyIn a single-pass FEL, the physical mechanism responsible for the light emission and amplification is the interaction between a relativistic electron beam, a magnetostatic periodic field generated by an undulator and an optical wave co-propagating with electrons. Two different
schemes can be distinguished, depending on the origin of
the optical wave which is used to initiate the process. In
the SASE configuration, the initial seed is provided by the
spontaneous emission of the electron beam which is forcedby the undulator field to follow a curved trajectory. The
seed is then amplified all along the undulator until the laser
effect is reached. The SASE radiation produces tunable
signal at short (x-ray) wavelengths with several GW peak
power and excellent spatial mode. An alternate approachto SASE is Coherent Harmonic Generation (CHG) [1],which is capable of producing temporally coherent pulses.
A schematic layout of CHG is shown in Figure 1.
In this case, the initial seed is produced by an external
light source, e.g. a laser. The light-electron interaction
in a short undulator, called modulator, imposes an energy
modulation on the electron beam. The modulator is tuned
to the seed wavelength λ. The energy modulation is thenconverted into a spatial density modulation as the electron
beam transverses a magnetic dispersion. Figure 2 showsthe evolution of the electron-beam phase space (i.e. energy
vs. electrons’ phase in the undulator plus radiator field)
from the entrance of the modulator to the exit of the dis-

MODULATOR

EnergyINTRODUCTION

SEED LASER

EnergyThe quasi-stationary state characterizing the saturationof a single-pass free-electron laser is governed by the
Vlasov equation obtained by performing the continuum
limit of the Colson-Bonifacio model. By means of astatistical treatment, this approach allows to predict analytically the saturated laser intensity as well as the final
electron-beam energy distribution. In this paper we consider the case of coherent harmonic generation obtained
from a seeded free-electron laser and present predictions
for the first stage of the project FERMI@Elettra project at
Sincrotrone Trieste.

0

0

1

2

3

Phase

4

5

6

4

0

1

2

3

Phase

4

5

6

Figure 2: Electron-beam phase space at the entrance a) andat the exit b) of the modulator; c) phase space at the exitof the dispersive section. In a), the thickness of the distribution corresponds to the (initial) incoherent energy spreadof the electron beam. In c) the gap between the boundariesof the separatrix corresponds to the energy modulation induced by the seed-electron interaction (see Figure 1).

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Proceedings of FEL 2006, BESSY, Berlin, Germany

FELs, where it plays a central role, being the only stateexperimentally accessible in real devices. In this respect,
FELs provide a general experimental ground to investigate
the universal characteristics of systems with long range interactions.
Motivated by this analogy, we shall apply a maximum
entropy principle, inspired to Lynden-Bell’s theory of “violent relaxation” [3]–[6] for the Vlasov equation and analytically predict the characteristics of the laser signal atsaturation. More specifically, the above theoretical interpretative framework will enable us to estimate the expected
intensity for the case of FERMI@Elettra [7], a future userfacility based on CHG, without resorting to direct numerical simulations. Our results will be shown to correlate wellwith Genesis-based [8] estimates.

FROM THE MEAN-FIELD MODEL TO
THE LYNDEN–BELL PREDICTION
In this section we will introduce the model that is customarily employed to investigate the time evolution of asingle-pass FEL, both in SASE and CHG configurations.
By putting forward the hypothesis of one-dimensional(longitudinal) motion and monochromatic radiation, thesteady-state dynamics of a single-pass FEL is described by
the following set of equations:
dθj
dz̄
dpj
dz̄
dA
dz̄

=

pj

=

−Aeiθj − A∗ e−iθj=

1  −iθj
iδA +
e
N j

,

(1)
,

(2)
,

(3)

where z̄ = 2ku ρzγr2 /γ0 2 is the re-scaled longitudinal coordinate, which plays the role of time. Here, ρ =(aw ωp /4cku )2/3 /γr is the so-called Pierce parameter, γ r
the resonant energy, γ 0  the mean energy of the electrons
at the undulator’s entrance, k u the wave vector of the undulator, ωp = (e2 n̄/mε0 )1/2 the plasma frequency, n̄ being
the electron number density, c the speed of light, e and mrespectively the charge and mass of one electron. Further,aw = eBw /(ku mc2 ), where Bw is the rms undulator field.
Introducing the wavenumber k of the FEL radiation, thephase θ is defined by θ = (k + k u )z − 2δρku zγr2 /γ0 2 ; its
conjugate momentum reads p = (γ − γ 0 )/(ργ0 ). The
complex amplitude A = A x + iAy represents the scaled
field, transversal to z. Finally, the detuning parameter isgiven by δ = (γ 0 2 − γr2 )/(2ργr2 ), and measures the average relative deviation from the resonance condition. The
above system of equations (N being the number of electrons) can be deduced by the Hamiltonian:
H=

N

p2j
j=1

104

2


− δI + 2NI sin(θj − ϕ),
N j=1

(4)

where the intensity
 I and the phase ϕ of the wave are defined by A =I/N exp(−iϕ). Here, the canonicallyconjugated variables are (p j , θj ) for 1 ≤ j ≤ N and(I, ϕ). Besides the “energy” H, the total momentum P =j pj +I is also a conserved quantity.
Let us finally define
the bunching parameter as b(t) =exp(iθi (t))/N :=exp(iθ(t)). The latter provides a quantitative measure of
the degree of spatial compactness of the particles distribution.
Numerical simulations based on the above system of
equations show that the amplification of the wave occurs
in several subsequent steps. First, an initial exponential
growth takes place, which is successfully captured by a linear analysis. Then, as previously anticipated, the system
attains a QSS, where the wave intensity displays oscillations around a well-defined plateau. As predicted by the
Boltzmann-Gibbs statistics, for longer times a slow evolution toward the final equilibrium is found. The process isdriven by granularity and the relaxation time diverges withthe system size N . Hence, due to the constraint imposedby the typical length of an undulator, the QSS is the only
regime experimentally accessible in the case of single-pass
FELs.
When performing the thermodynamics limit, i.e., N →∞, one gets to the following Vlasov–wave picture:
∂f
∂ z̄
dAx
dz̄
dAy
dz̄

∂f
∂f
+ 2(Ax cos θ − Ay sin θ)∂θ∂p= −δAy + f cos θ dθ dp ,= δAx − f sin θ dθ dp .

= −p

, (5)
(6)
(7)

which can be shown to govern the initial growth and relaxation towards the QSS. The latter conserves the pseudoenergy per particleh(f, A) =p2
f (θ, p) dθ dp − δ(A2x + A2y ) +2(Ax sin θ + Ay cos θ)f (θ, p) dθ dp (8)and the momentum per particleσ(f, A) = pf (θ, p) dθ dp + (A2x + A2y ).

(9)In ref. [4] it was shown that the average statistical parameters of the laser (intensity and the bunching in the QSS) areaccurately predicted by a statistical mechanics treatmentof the Vlasov equation, according to prescriptions of theseminal work by Lynden-Bell [5]. The analysis developedin [4] was limited to the case of spatially homogeneous initial conditions (i.e., initial zero bunching). In [9], we extended the analysis by including initially bunched distributions. In the remaining part of this section we will review
the foundation of the analytical method and presented select numerical results.

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany
The basic idea of Lynden–Bell “violent relaxation” theory [4, 6] is to coarse-grain the microscopic single-particle
distribution function f (θ, p, t), which is filamented andstirred by the dynamics. An entropy is then associated tothe coarse-grained function f¯, which essentially counts thenumber of microscopic configurations giving rise to it.
Starting with an initial centered water-bag distribution,
which corresponds to a rectangle uniformly occupied in thephase space (θ, p) with −p 0 < p < p0 and −θ0 < θ < θ0 ,the normalization condition reads f 0 = 1/(4θ0 p0 ).
The entropy can be expressed as [5, 6]:

MOPPH031

reported in Figure 4. A direct inspection of the figures confirms the adequacy of the proposed theoretical framework:
predictions based on the Vlasov theory correlate well withnumerical curves. In the next section, starting from theseresults, we will elaborate a strategy to gain insight into thenon–linear evolution of a CGH scheme without resorting todirect numerical investigations. In particular, we will focus
on the case of the FERMI@Elettra project.

0,8

0,8

0,6

0,6

dθ dp.

0,4

0,4

(10)
The equilibrium is computed by maximizing this entropy:
max s(f¯) ,
(11)

0,2

s(f¯) = −


  ¯
f
f¯
f¯
ln
+ 1−
f0 f0
f0


f¯
ln 1 −
f0

0,2
a)

I

f¯,Ax ,Ay

while imposing the dynamical constraints:

0

0

b)
0,2

0,4

0,6

0,8

0,8

0,8

0,6

0,6

0,4

0,4

0,2



h(f¯, Ax , Ay )σ(f¯, Ax , Ay )= h0 ,(12)= σ0 ,(13)f (θ, p) dθ dp

= 1,

(14)

where h0 and σ0 stand, respectively, for the energy andmomentum (per particle) of the system. Performing the analytical calculation and introducing the rescaled Lagrange
multipliers for the energy, momentum and normalization
constraints (β/f0 , λ/f0 and μ/f0 ) one obtains the typicalFermi-Dirac distribution:

0

1

0

0,2

0,4

0,6

0,8

1

0,2

0,4

0,6

0,8

1

0,2
c)

0

d)
0,2

0,4

0,6

0

0,8

0

|b0|
Figure 3: Average intensity I¯ at undulator exit as function of the initial bunching |b 0 | for different values of theinitial average kinetic energy, respectively a) h 0 = 0.01b) h0 = 0.16 c) h0 = 0.21 d) h0 = 0.315). The continuouslines correspond to the Lynden–Bell theoretical prediction,
while symbols represent numerical results obtained averaging intensity fluctuations in the saturated regime over ten
different realizations of the initial conditions resting on thesame values of θ0 and p0 .

2

f¯ =

f0

A =

e−β(p /2+2A sin θ)−λp−μ(15)
1 + e−β(p2 /2+2A sin θ)−λp−μ
βsin(θ)f¯(θ, p) dθ dp.
A2x + A2y =βδ − λThe three constraints (12)–(14) are then imposed bymaking use of the above expression for f (θ, p) and A, andthe obtained equations numerically solved to provide an estimate of the multipliers as functions of energy h 0 and momentum σ0 of the system. Ones β, γ, μ are calculated,
one can in turn estimate the value of the intensity I and thebunching parameter b of the QSS.
To validate our findings, we performed numerical simulation for a water-bag initial distribution as specified above,
where θ0 < π. Further, label with |b 0 | the initial bunching,i.e., the positive quantity given by |b 0 | = |exp(iθ(0))|.
Numerical calculations are performed based on the discrete
system (1–3). In Figure 3 the average intensity at saturationis reported as function of |b 0 |, for different values of theinitial kinetic energy. Results are compared with the analytical estimate obtained above. Analogous plots for the
average value of the bunching parameter at saturation are

FEL Theory

0,7

0,7

0,6

0,6

0,5

0,5

0,4

0,4

0,3

0,3

0,2

0,2

0,1
0

b

0,1

a)
0

0,2

0,4

0,6

0,8

1

0

0,7

0,7

0,6

0,6

0,5

0,5

0,4

0,4

0,3

0,3

0,2

0,2

0,1
0

0,1

c)
0

b)
0

0,2

0,4

0,6

0,8

1

0

0,2

0,4

0,6

0,8

1

0,2

0,4

0,6

0,8

1

d)
0

|b0|
Figure 4: Average values of the bunching parameter | b¯0 |at the undulator exit as function of |b 0 |. Same choice ofparameters as in Figure 3.

105

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Proceedings of FEL 2006, BESSY, Berlin, Germany

CHARACTERIZING THE SATURATION
OF CHG FELS
The seed-electron interaction in the first undulator of a
CHG scheme induces a coherent modulation, Δγ, of theelectron-beam energy, which superimposes to the initial incoherent energy spread σ γ . Inside the dispersive section,
the energy modulation is converted into a spatial density
modulation. Performing a Fourier analysis of the spatial
beam distribution at the end of the dispersive section one
finds the following bunching parameters:|b0 |  Jn (n)/ exp(1/2),(16)

where Jn stands for the n-th order Bessel function 1 .
On the other hand, the total energy spread σ γ,tot at theentrance of the second undulator reads:
σγ,tot =

σγ2 +

(Δγ)2
 σγ
2


1+

n2
,
2

(17)

where n is the harmonic number. Moreover, in term of
the rescaled variables used in the formulation of the above
one-dimensional model, the associated energy profile canbe ideally schematized as a water-bag distribution, wherep0 =σγ,tot.
γρ

(18)Taking full advantage of the above theoretical analysis, we are therefore in a position to quantify the saturated(QSS) behaviour of a CHG device. In particular, we shallfocus on the case of the project FERMI@Elettra [7] and assume the experimental setting relative to the output wavelength 100 nm. In this case, n = 3 (i.e., the initial seedwavelength is 100 nm), γ = 2348, σ γ = 150 KeV andρ = 3 · 10−3 . Direct numerical simulations are performed
using GENESIS [8], a three dimensional code that explicitly accounts for the coupling between the transverse andlongitudinal dimensions. Assuming a radiator length of 16m, a horizontal and vertical (normalized) beam emittanceof 1.5 μ m and on optical waist of w  300 μm, simulations give an output power of about 3 GW.
Independently, one can calculated the value of |b 0 | andp0 by inserting the nominal values of the relevant parameters in equations 18 16. Then, Lynden–Bell theory enables us to predict the QSS value for the intensity which
are shown to correlate extremely well with Genesis based
calculation, the disagreement being quantified in at most
10 % [9] .

for a CHG setting, provided the value of the incoherent energy spread is assigned and without involving to direct numerical investigations.
The short recipe goes as follows: by knowing σ γ one
can calculate σγ,tot by means of eq.(17) and consequently
estimate both |b0 | and p0 , based on eqs.(16)–(18). The spatial width, θ0 , of the initial water-bag distribution (hereassumed to mimick the more natural Gaussian profile)is eventually obtained upon inversion of relation |b 0 | =sin(θ0 )/θ0 . Once the values of θ 0 and p0 are given, the theory of the violent relaxation allows to quantitatively predict
the saturated state of the system.
Finally let us stress that the applicability of the method
we have developed is currently limited to situations inwhich transverse effects are neglected. This in turn entails the possibility of assuming the electron-beam geometrical emittance smaller than the radiation wavelength,
the beam relative energy spread smaller than ρ and theRayleigh length of emitted radiation much longer than theradiator length. These conditions apply for instance to thecase of the whole spectral range that is to be covered by the
FERMI@Elettra FEL (100-10 nm).

REFERENCES[1] L. H. Yu, Phys. Rev. A 44 5178 (1991).
[2] T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens (Eds), Lecture Notes in Physics 602, Springer Dynamics and Thermodynamics of Systems with Long Range Interactions (2002).
[3] A. Antoniazzi, D. Fanelli, J. Barré, P. H. Chavanis, T. Dauxois, S. Ruffo, submitted to Phys. Rev. Lett. (2006).
[4] J. Barré et al., Phys. Rev. E 69 045501 (2004).
[5] D. Lynden-Bell, Mon. Not. R. Astron. Soc. 136, 101 (1967).
[6] P. H. Chavanis, J. Sommeria, R. Robert, Astrophys. J. 471,
385 (1996).
[7] See http://www.elettra.trieste.it/FERMI/.
[8] http://pbpl.physics.ucla.edu/ reiche/.
[9] F. Curbis, A. Antoniazzi, G. De Ninno, D. Fanelli, preprint
submitted to Phys. Rev. E (2006).

CONCLUSIONSThe theoretical approach outlined in this paper constitutes a novel strategy to predict the intensity at saturation
1 Note that in deriving equation (16) an optimization scheme for thebunching parameter has been put forward according to the standard experimental procedure. A detailed account on the approximations involved
is presented in [9] starting from the usual expression given in [1]106

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Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH032

ANALYSIS OF FEL OSCILLATIONS IN A PERFECTLY SYNCHRONIZEDOPTICAL CAVITY
N. Nishimori∗ , JAEA, Ibaraki, Japan.
Abstract
We analyze free-electron-laser (FEL) oscillations in aperfectly synchronized optical cavity by solving the onedimensional FEL equations. The radiation stored in thecavity can finally evolve into an intense few-cycle opticalpulse in the high-gain and low-loss regime. The evolutionof the leading slope of the optical pulse, which is definedfrom the front edge toward the primary peak, is found toplay an important role in generating the intense few-cycle
pulse. The phase space evolution of electrons on the second pass which interact with the leading slope of a SASE
output pulse is obtained in a perturbation method similar
to that used in our previous study for a SASE FEL. The resulting analytical solution of the leading slope in the second
pass is shown to be approximated by that of a SASE FEL
with FEL parameter greater than ρ. The same perturbation
method can thus be used to the subsequent passes.

INTRODUCTION
The FEL dynamics is affected by the slippage that iscaused by the velocity difference between the electron
bunch and the optical pulse inside an undulator. The groupvelocity of the optical pulse becomes slightly slower thanthe vacuum speed of light, since the trailing slope of the
optical pulse is mainly amplified due to the slippage. Thisphenomenon, called the laser lethargy (see Ref. [1] andreferences therein), can be compensated in oscillators byslightly shortening the optical cavity length from the perfect synchronism (δL = 0), where the cavity length exactly
matches with the injection period of the electron bunches.
The FEL dynamics of the oscillators with shorter cavity
length (δL < 0) has been studied extensively [2, 3]. At
δL = 0, the optical pulse centroid continues to be retarded
on successive passes through the undulator, and the optical pulse finally dissipates, as shown in theoretical studies[4, 5, 6].
An experiment of a high-power FEL driven by a superconducting linac in the Japan Atomic Energy Research Institute (JAERI) FEL facility has however showed that an
intense, ultrashort optical pulse is generated at δL = 0.0 ±0.1 μm despite the lethargy [7, 8]. The optical power curvemeasured with respect to δL is well reproduced by thetime-dependent simulation code based on one-dimensional(1D) FEL equations [9], if shot-noise effect is includedin every fresh electron bunch. A few theoretical studies
have attempted to explain the FEL oscillations at δL = 0,
proposing that sideband instability [10] or superradiance inshort-pulse FELs [11] is the fundamental physics responsi∗ nishimori.nobuyuki@jaea.go.jp

FEL Theory

ble for the lasing at δL = 0. Nevertheless, the underlying
physics responsible for the FEL oscillations at δL = 0 has
not been clearly explained yet.
In this paper, we investigate the FEL evolution at δL = 0
by analytically solving the 1D FEL equations. A set of
nondimensional parameters and the 1D FEL equations used
in Ref. [12] are employed for the present study. The opticalpulse on the first pass, which is equivalent to the output of aself-amplified spontaneous-emission (SASE) FEL and represented by the solution of the cubic equation [14, 15, 16],is reflected back into the undulator for subsequent amplifications in FEL oscillators. The phase space evolution ofelectrons on the second pass which interact with the leading
slope of the FEL pulse, which is defined from the front edge
toward the primary peak amplitude in the present paper, isobtained in a perturbation method similar to that used in
our previous work for the phase space evolution of electrons in a SASE FEL [12]. Consequently, an analyticalsolution for the optical growth of the leading slope during
the second pass is derived. The leading slope of the output
pulse is shown to be approximated by that of a SASE FEL
with FEL parameter greater than ρ. The same process canthus be applied to pass numbers greater than n = 2 and theevolution of the leading slope with respect to n is obtained
analytically. The output field similar to that of a SASE FEL
accounts for the exponential increase of the field amplitudein the leading slope from the front edge toward the primarypeak, and the amplitude gradient with respect to the longitudinal position is shown to increase with n. With theincreasing gradient, the field gain per pass decreases down
to the level of optical cavity loss α, and a self-similar radiation pulse is generated at saturation. The evolution of theleading slope leads to sustained FEL oscillations at δL = 0
and thus disappearance of the lethargy effect. More details
are described in Ref. [13].

1D FEL EQUATIONS
The dimensionless 1D FEL equations of Colson are usedin the present study under the slowly varying envelope approximation [17], while the variables used here are similar
to Bonifacio’s variables [16]. The simplest situation is considered in the present study. The electron beam energy is
given by γ0 mc2 with small energy spread. The initial electron bunch has a rectangular shape with density of n e anda uniform distribution in phase. The fundamental FEL parameter in MKSA units is given by1(1)
ρ = [eaw F ne /(ε0 m)/(4ckw )]2/3 .
γ0Here λw = 2π/kw is the period of the undulator, a w is theundulator parameter, and F is unity for a helical undulator

107

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Proceedings of FEL 2006, BESSY, Berlin, Germany

or Bessel function [JJ] for a planar undulator [16]. The
dimensionless time is defined by τ = 4πρct/λ w , so thatδτ = 1 corresponds to the transit time of light through one
gain length of λ w /(4πρ). The longitudinal position of theith electron is defined by ζ i (τ ) = 4πρ[zi (t) − ct]/λr , sothat δζ = 1 corresponds to the cooperation length definedby Lc = λr /(4πρ). Here λr = λw (1 + a2w )/(2γ02 ) is theresonant wavelength. The dimensionless field envelope isdefined bya(ζ, τ ) =2πeaw λw FE(ζ, τ ) exp[iφ(ζ, τ )],(4πρ)2 γ0 2 mc2(2)

with phase φ(ζ, τ ), which is equivalent to Bonifacio’s envelope [16]. Here E(ζ, τ ) is the rms optical field strength.
The dimensionless energy and phase of the ith electron arerespectively defined by μ i (τ ) = [γi (t) − γ0 ]/(ργ0 ) andψi (τ ) = (kw + kr )zi (t) − ωr t, where kr = 2π/λr is thewave number of the resonant wavelength λ r . The dimensionless energy μi (τ ) also means the dimensionless energychange at τ from τ = 0, since the energy spread of the initial electron beam is assumed to be small, i.e., μ i (0) = 0.
In the present definition, the evolutions of the field envelope a(ζ, τ ), the energy μ i (τ ) and phase ψi (τ ) of the ithelectron during FEL interaction are respectively given by[5]dμi (τ )dτdψi (τ )dτ∂a(ζ, τ )∂τ=a[ζi (τ ), τ ] exp[iψi (τ )] + c.c.,(3)=μi (τ ),

(4)=−exp[−iψi (τ )]ζi (τ )=ζ .

(5)

The angular bracket indicates the average of all the electrons in the volume V around ζ.

EVOLUTION OF SASE FEL PULSE
The optical field and electron phase space evolutions on
the first pass, which are equivalent to those in a SASE FEL,
are presented in our previous work [12]. The startup process known as spectrum narrowing [18] or as longitudinal phase mixing [19] leads to a uniform field in time andspace. The phase of the field φ(0) is almost uniform overthe length N λr along the propagation direction when theincident electron beam passes through N undulator periods [5, 19]. In the present study, the initial uniform field
is assumed to be given by |a(0)|e iφ(0) for simplicity. The
initial field evolves through electric interaction with undulating electrons as it passes through the undulator. The incident electron beam is assumed to be uniformly distributedin phase ψi (0) with resonant energy μ i (0) = 0 and interacts with the SASE FEL field in the steady-state region due
to the slippage [16]. The evolution of the uniform field asa function of time is derived from Eqs. (3), (4), and (5), as
described by Colson et al. in Ref. [15].
The electron phase can be expressed as ψ i (τ ) = ψi (0) +Δψi (τ ) where Δψi (τ ) is the first-order perturbation in

108a(τ ). The field at time τ for the steady-state region whereζ < −τ is given by τa(τ ) = a(0) + i
e−iψi (0) Δψi (τ  )ζi (τ )=ζ dτ  . (6)0The ith electron interacts with the field in the steadystate region due to the slippage, and the energy modulation at τ  during δτ  is given from Eq. (3) by δμ i (τ  ) =[a(τ  )eiψi (0) + c.c.]δτ  . The energy change of the ith electron at time τ , μi (τ ), is given by the sum of those modulations during τ : τ{a(τ  )eiψi (0) + c.c.}dτ  .
(7)μi (τ ) =0

The electron phase perturbation is given from Eq. (4) by τ
Δψi (τ ) =μi (τ  )dτ 
(8)
0

=

 τ
0

dτ



 τ
0

{a(τ  ) exp[iψi (0)] + c.c.}dτ  (9)Substitution of Eq. (9) into Eq. (6) leads to τ τ τ 
a(τ ) = a(0) + idτdτa(τ  )dτ  . (10)000The integral equation (10) can be written in a differential
form by taking successive derivatives.
The solution is ex3
pressed in the form a(τ ) = n=1 an exp(αn τ ) where the
αn are three complex roots of the cubic equation α 3 = i[14, 15, 16]. When the initial conditions ȧ(0) = ä(0) = 0,
the field at time τ for the steady-state region where ζ < −τ
is given by

−iπ/6
−iπ/2
|a(0)|eiφ(0)  τ eiπ/6e.
+ e−τ e+ eτ e3(11)Equation (11) is valid in the linear regime before saturation
when the incident electron beam is resonant.
a(τ ) =EVOLUTION OF OSCILLATOR FEL
PULSE
We first study the optical field and electron phase space
evolutions on the second pass (n = 2) in an analytical way
and then show that the analytical method can be applied to
the nth pass with reasonable approximations. At first thenotation n is thus used for n = 2.

FEL evolution on the second pass
The input field for the second pass, a n (ζ) = an (ζ, 0), is
the same as the output of a SASE FEL with FEL parameterρ except for a decrease of the amplitude due to the cavity
loss α. The leading slope of the input field for the second
pass is therefore given as a function of ζ byan (ζ)iπ/6= (|an (0)|eiφn (0) /3)(e−ρn ζe−iπ/6+eρn ζe−iπ/2+ e−ρn ζe

),

(12)

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany
where ρ2 = 1 and |a2 (0)| ≈ (1−α/2)|a(0)|. Equation (12)can be used where |ζ| < L s and |ζ| < Lb before the fieldreaches saturation. Here L b is the incident electron bunch
length in units of L c and Ls = 4πρNw is the slippage
distance. The phase space evolution of electrons during
interaction with the leading slope given by Eq. (12) is quite
similar to that of a SASE FEL. The perturbation method
used in Ref. [12] can be applied to a study of the optical
growth during the second pass, as long as the growth issmall and the field an (ζ) remains almost unchanged during
the FEL interaction. The electron phase can be expressedas ψi (τ ) = ψi (0) + Δψi (τ ) where Δψi (τ ) is the firstorder perturbation in a n [ζi (τ )]/ρ2n , since the field in theleading slope divided by ρ 2n is weak even after saturation
except for a narrow range near ζ p . When the ith electron ismodulated in energy by interacting with the leading slope,the energy modulation at τ  during δτ  is expressed from
Eq. (3) by δμ i (τ  ) = {an [ζi (τ  )]eiψi (0) + c.c.}δτ  . Theenergy change of the ith electron at time τ , μ i (τ ), is givenby the sum of those modulations during τ : τ{an [ζi (τ  )] exp[iψi (0)] + c.c.}dτ  . (13)μi (τ ) =MOPPH032

The field gain da n (ζ)/dτ caused by the electron microbunch in units of λ r whose initial position is ζi (0) = ζ+τ is derived from substitution of ψ i (τ ) = ψi (0) + Δψi (τ )into Eq. (5) as follows:dan (ζ)/dτ = (|an (0)|eiφn (0) /3ρ2n )×{e(−ρn ζeiπ/6 +iπ/6)−iπ/6−e(ρn ζe−iπ/6)−iπ/2+e(−ρn ζe[1 − e−iπ/6[1 − eρn τ e−iπ/2)(16)−ρn τ eiπ/6(1 + ρn τ e

iπ/6

)]

(1 − ρn τ e−iπ/6 )]−iπ/2[1 − e−ρn τ e(1 + ρn τ e−iπ/2 )]},

when |Δψi (τ )|  1.
The field an (ζ) is sequentially amplified from τ = 0 to
τ = −ζ by the electron microbunches whose initial position are ζi (0) = ζ + τ as it passes through the undulator.
The field gain per pass is given bydan (ζ)/dn = [|an (0)|eiφn (0) /3ρ3n ]iπ/6

×{−ρn ζ[e(−ρn ζe−iπ/2−iπ/2)−iπ/2)+e(−ρn ζe+e(−ρn ζe+iπ/6)−iπ/6− e(ρn ζeiπ/6] − 2[e(−ρn ζe)−iπ/6)−iπ/6+ e(ρn ζe] + 6}.

)

(17)

0

The integration of Eq. (13) after substitution of Eq. (12)yieldsμi (τ ) = [2|an (0)|/3ρn ] ×{e√− 3ρn ζi (τ )/2−ecos[ψi (0) + φn (0) − ρn ζi (τ )/2 − π/6]√
− 3ρn ζi (0)/2√

cos[ψi (0) + φn (0) − ρn ζi (0)/2 − π/6]−e 3ρn ζi (τ )/2 cos[ψi (0) + φn (0) − ρn ζi (τ )/2 + π/6]

The leading slope of the output field for the second pass isthus given byan (ζ) + dan (ζ)/dn = [|an (0)|eiφn (0) /3ρ3n ]iπ/6

×{−ρn ζ[e(−ρn ζe−iπ/2+e(−ρn ζe−iπ/6+e(ρn ζe)−iπ/2)+iπ/6)−iπ/6− e(ρn ζe−iπ/6)iπ/6] + (ρ3n − 2)[e(−ρn ζe−iπ/2+ e(−ρn ζe)] + 6}.

)

(18)

√

+e 3ρn ζi (0)/2 cos[ψi (0) + φn (0) − ρn ζi (0)/2 + π/6]
+ cos[ψi (0) + φn (0) + ρn ζi (τ ) + π/2]

The amplitude and phase of the output field given by Eq.
(18) are plotted as solid circles in Figs. 1(a) and 1(b), respectively, as a function of ζ. The solid line shows the out(14) put field of the second pass obtained in a time-dependent− cos[ψi (0) + φn (0) + ρn ζi (0) + π/2]}.
numerical calculation, which solves Eqs. (3)−(5) with an
The integration of Eq. (8) after substitution of Eq. (14)input field given by Eq. (12) with ρ n = 1 and represented
yieldsby the dotted line. In the calculation, the shot-noise effectis neglected. One can see that the field given by Eq. (18)Δψi (τ ) = [2|an (0)|/3ρ2n ] ×
agrees well with the numerical calculation where |ζ| < 3.5√{e− 3ρn ζi (τ )/2 cos[ψi (0) + φn (0) − ρn ζi (τ )/2 − π/3]
but the phase gradually deviates from the calculation where√− 3ρn ζi (0)/2|ζ| ≥ 3.5. This is because the assumption that the field re−ecos[ψi (0) + φn (0) − ρn ζi (0)/2 − π/3]√
mains almost unchanged during the passage through an un−ρn τ e− 3ρn ζi (0)/2 cos[ψi (0) + φn (0) − ρn ζi (0)/2 − π/6] dulator does no longer hold where |ζ| ≥ 3.5 for the second√pass.
+e 3ρn ζi (τ )/2 cos[ψi (0) + φn (0) − ρn ζi (τ )/2 + π/3]√−e 3ρn ζi (0)/2 cos[ψi (0) + φn (0) − ρn ζi (0)/2 + π/3]√+ρn τ e 3ρn ζi (0)/2 cos[ψi (0) + φn (0) − ρn ζi (0)/2 + π/6]

FEL evolution on pass numbers greater than 2

The output field of the second pass is equivalent to the
input field for the third pass except for amplitude decrease
due to the optical cavity loss α. If the input field for the(15) third pass is found to be approximated by Eq. (12), the−ρn τ cos[ψi (0) + φn (0) + ρn ζi (0) + π/2]},
same procedure described in the previous subsection canwhere ζi (τ ) = ζi (0) − τ is used, which is valid as long as be used for a study of the optical growth during the third
the electron energy change μ i (τ ) is small and dζi (τ )/dτ = pass. The dash-dotted line in Fig. 1 shows the field given
by Eq. (12) with ρ n = 1.28. The amplitude of this field−1 holds. Equations (14) and (15) represent the phasespace evolution of the ith electron during the second pass.
is different from that obtained in a numerical calculation− cos[ψi (0) + φn (0) + ρn ζi (τ )]+ cos[ψi (0) + φn (0) + ρn ζi (0)]FEL Theory109

Proceedings of FEL 2006, BESSY, Berlin, Germanyan (ζ) + dan (ζ)/dn ∼ an (ζ) + [|an (0)|eiφn (0) /3ρ3n ]iπ/6

×{−ρn ζ[e(−ρn ζe−iπ/2+e(−ρn ζe−iπ/2)+iπ/6)−iπ/6− e(ρn ζe−iπ/6)]},(19)

The field evolution per pass can also be obtained by differentiation of Eq. (12) with respect to the pass number nunder the assumption that ρ n is independent of ζ as follows:-2dan(ζ)dn10an(ζ)+

10

10

Eq. (18) with ρn=1
numerical calculation
Eq. (12) with ρn=1
Eq. (12) with ρn=1.28

-3

-4

a)
-5

10
4
dan(ζ)
dn(solid line) by only 10% to −20% where |ζ| < 5, and thephase is different from the numerical calculation by only
±0.17 rad. These results suggest that the input field for thethird pass can be approximated by Eq. (12) with ρ 3 = 1.28.
In a similar way, one can obtain ρ n of the input field forpass numbers greater than n = 3 as well. For exampleρ 4 =1.52, ρ5 = 1.73, ρ6 = 1.90, and ρ7 = 2.05.
As ρn increases, ρ3n − 2 ∼ ρ3n and Eq. (18) asymptotically approaches

3arg an(ζ)+

MOPPH032

2

Eq. (18) with ρn=1
numerical calculation
Eq. (12) with ρn=1
Eq. (12) with ρn=1.28

1

b)

0
-5

-4

-3

ζ

-2

-1

0

dan (ζ)/dn = (|an (0)|eiφn (0) /3)(dρn /dn)iπ/6

×{−ζ[e(−ρn ζe−iπ/2+e(−ρn ζe+iπ/6)−iπ/2)−iπ/6− e(ρn ζe]}.

−iπ/6)(20)

Equation (20) should be equal to Eq. (19) subtracted byan (ζ) as long as the gain is much higher than the opticalcavity loss and ρn is large enough for Eq. (19) to hold.
This yields(21)dρn /dn = 1/ρ2n .
When we assume that Eq. (19) holds when ρ n > 2, Eq.
(21) gives(22)ρn ≈ (3n − 12)1/3
for n ≥ 7. Substitution of Eq. (22) into Eq. (20) yields√(1/|an (ζ)|)(d|an (ζ)|/dn) ≈ −( 3/2)ζ(3n − 12)−2/3 ,(23)√
1. Equation (23) shows thatwhen exp(− 3ρn ζ/2)
the gain per pass decreases with increasing pass number n.
Please see Ref. [13] for further discussions.

ACKNOWLEDGEMENTS
The author would like to acknowledge valuable discussions with T. Shizuma at JAERI, S. Hiramatsu at KEK, and
H. Hama at Tohoku University.

Figure 1: The amplitude (a) and phase (b) of the outputn (ζ)
as a function of ζ. The solid circles
field an (ζ) + dadζ
stand for the output field of the second pass given by Eq.
(18) with ρn = 1, and the solid line is that obtained from anumerical calculation where Eq. (12) with ρ n = 1, whichis represented by the dotted line, is used as an input fieldenvelope. The dash-dotted line expresses an approximatedoutput field of the second pass given by Eq. (12) with ρ n =1.28. The amplitude of the front edge |a n (0)| = 3.7×10−5
is used.
[5] W.B. Colson, in Laser Handbook, edited by W.B. Colson,
C. Pellegrini, and A. Renieri (North Holland, Amsterdam,
1990), Vol.6, pp. 115–193.
[6] Nicola Piovella, PRE 51, 5147 (1995).
[7] N. Nishimori et al., PRL 86, 5707 (2001); NIM A 483, 134(2002).
[8] R. Nagai et al., NIM A 483, 129 (2002).
[9] R. Hajima et al., NIM A 475, 270 (2001); ibid. 483, 113(2002).
[10] Z.-W. Dong et al., NIM A 483, 553 (2002).
[11] Ryoichi Hajima and Ryoji Nagai, PRL 91, 024801 (2003).
[12] Nobuyuki Nishimori, PRST AB 8, 100701 (2005).
[13] Nobuyuki Nishimori, accepted for publication in PRE.

REFERENCES[14] Norman M. Kroll and Wayne A. McMullin, PRA 17, 300(1978).

[1] G. Dattoli and A. Renieri, in Laser Handbook, editedby M.L. Stitch and M. Bass (North Holland, Amsterdam,
1985), Vol.4, p.75.

[15] W. B. Colson et al., PRA 34, 4875 (1986).

[2] N. Piovella et al., PRE 52, 5470 (1995); P. Chaix et al., PRE
59, 1136 (1999).

[17] W.B. Colson and S.K. Ride, Phys. Lett. 76A, 379 (1980).

[3] G. Dattoli and A. Renieri, Nuovo Cimento B 59, 1 (1980);
G. Dattoli et al., Opt. Comm. 35, 407 (1980).
[4] H. Al-Abawi et al., Opt. Comm. 30, 235 (1979); J. G. Kuper
et al., Opt. Comm. 34, 117 (1980).

110[16] R. Bonifacio et al., Riv. Nuovo Cimento 13, 9 (1990).
[18] Kwang-Je Kim, PRL 57, 1871 (1986); NIM A 250, 396(1986).
[19] N. Nishimori, R. Hajima, R. Nagai and E.J. Minehara, NIM
A 507, 79 (2003).

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH033

TWO-STREAM SMITH-PURCELL FREE-ELECTRON LASER USING A
DUAL-GRATING: LINEAR ANALYSIS*
1

Wenxin Liu1#, Zheng Liang 1, Ziqiang Yang1, D. Li2, K. Imasaki2
Institute of High Energy Electronics, University of Electronic Science and Technology ofChina, Sichuan Chengdu, 610054, P. R. China
2
Institute for Laser Technology, 2-6 yamada-oka, suita, Osaka 565-0871, Japan

Abstract
A linear theory of two-stream Smith-Purcell FreeElectron Laser (SP-FEL) using a dual-grating has been
given in this paper. A rectangular dual-grating is
considered to be driven by two admixed electron beams
with velocity separation. The linear dispersion equations
for even and odd modes are derived with the help of fluid
theory and the beam-wave interaction is analyzed throughthe numerical solutions. The considerable enhancement ofgrowth rate is demonstrated due to the presence of twostream instability. An example of THz-band two-stream
SP-FEL is discussed.

above the rectangular grating, which drift in the z
direction at a constant velocity v1 and v2, respectively.
The quantities D, H, d, a denote the rectangular grating
period, groove depth, slot width, the distance between z
axial and grating surface, respectively. For convenience,
the operation area is divided into five regions:− a ≤ x < −b is regionb < x ≤ a is region− b ≤ x ≤ b is region
Regionandis thelower groove − a − h ≤ x < −a and upper groovea < x ≤ a + h . In the following analyses, we focus on
the TM waves.

Ⅰ,
Ⅲ,

,

Ⅳ

Ⅴ

Ⅱ

INTROUCTION
It is well known that Smith-Purcell (SP) radiation isemitted when an electron passes near the surface ofgrating [1].At present, an intense interest has been raisedin SP radiation since J.Urata et al observed the superradiance in the THz regime from the experiment at
Dartmouth college [2,3]. The superradiance is regarded as
the result of periodic electron bunching, which is
produced by the interaction between the electron beamand the fields above the grating. Some theories [4,5] havebeen proposed to understand the physical mechanism ofbeam-wave interaction. Recently, D.Li and Z.Yang [6,7],
J.T.Donohue and J.Gardelle[8] have performed thesimulations of SP-FEL in the THz regime with PIC code.
The THz sources, a currently flourish research area,
are of importance in varieties of applications in farinfrared spectroscopy, imaging, ranging and biomedical[9]. In order to improve the performance of such kind of
device, it is necessary to find an efficient mechanism forthe beam-wave interaction. The two-stream instability is
an important physical mechanism, which has beensuccessfully applied to some high power microwave
sources [10-12].
In this paper, we present a two-stream Smith-Purcell
Free-Electron Laser using a dual-grating, as shown in
Fig.1. The two admixed electron beams are symmetric
about z axial and guided by an infinite magnetic field.
For simplicity, we assume that the system is uniform in
the y direction which is parallel to the slots of grating.

DISPERSION EQUATIONThe system of beam-wave interaction is illustrated in
Fig.1. Two admixed beams with thickness 2b are located____________________________________________*Work supported by National Nature Science Foundation of
P. R. China (60571020),#liuwenxin76@163.com

FEL Theory

Fig.1 Schematic illustration of two admixed beams propagatingover the dual-grating

We assume that (i)the externally applied magnetic
field is so strong that perturbed electron motions are)the effect of beams self
restricted in the z direction;
static fields are negligible; and ( )the perturbations are
uniform along the y direction. Maxwell’s equations andrelativistic hydrodynamic equations for two cold electron
beams are employed to describe this system as follows:

(ⅱ

(1)

ⅲ

r
r 1 ∂B∇× E +=0c ∂tr
r 1 ∂E 4π 2∇× B +=∑ Jic ∂tc i =1

(2)

(

∂
∂
e
+ vi 0 )δvi1 = − 3 E z∂t∂z
γ i m0

(3)

∂
∂
∂
(4)
+ vi 0 )δni1 = − ni 0 δvi1∂t∂z∂zHere, subscript i = 1,2 represents the first and secondrrelectron beam, respectively. E and B are the electric and(111

MOPPH033

Proceedings of FEL 2006, BESSY, Berlin, Germany

magnetic field vectors.

γ i = 1 + eVi / m0 c 2 istherelativistic mass factor, c is the speed of light ,Vi is the ith
beam voltage, the voltage ratio of two electron beams
is v r = V2 / V1 ,and vi 0 = c ⋅ [(γ i2 − 1) 2 / γ i2 ]1 2 is theunperturbed velocity of ith beam. -e, m0, ni 0 , δni1 , δvi1
are the electron charge, the electron rest mass , theunperturbed density , perturbed density and perturbed
velocity of ith beam, respectively. Ji = −e(ni0δvi1 +δni1vi0 )is perturbed current density. The relative density factor
α is n20 / n10 .To obtain the dispersion equation, werr
expand ni = ni 0 + δni1 , vi = v i 0 + δvi1 , E = δE z ,rr
B = δB y and solve for the perturbed variables. Using

Floquet’s theorem, all the fields and beam parameters canbe written as a sum of space harmonics which have theperiodicity of the grating [13],∞f ( x, z ) = ∑ f n ( x) exp( jk n z − jωt )(5)n = −∞

where k n = k 0 + 2πn / D , k 0 is wave number, ω is theangular frequency, n is an integer.
From Eqs.1, 2, 3, 4 and expression (5), the wave
equation for the nth space harmonic of axial electric fieldis given and the transverse components of electric andmagnetic fields can be expressed in terms of the axial
electric field as follows[14]:ω∂+ ε l , n ( 2 − k n2 )]δEˆ z ,n ,l ( x) = 0
2
∂x
c
2

2

δEˆ x,n ,l =jk n ∂ ˆ
δE z ,n ,lκ n2 ∂x[， l=1,2,3

(6)

(7)

jω ∂
δBˆ y ,n ,l = 2 δEˆ z ,n ,lcκ n ∂x

Employed the wave Eq.6 and expressions (7) and (8),the components of electromagnetic fields in the three
regions can be treated as follows:
The fields in Region Ⅰ − a ≤ x < −b and Ⅱ
b < x ≤ a can be expressed in terms of two coefficients,
respectively:δEˆ z , n,l = Anl sin κ n x + Bnl cos κ n x
0

0

0

(10)

δEˆ x,n ,l =0(11)

δBˆ y ,n,l =
0

jk n

κn

( Anl0 cos κ n x − Bnl0 sin κ n x)jω
( Anl0 cos κ n x − Bnl0 sin κ n x)
cκ n

(12)
where superscript l0 = 1,2 respects the region Ⅰ andregionⅡ, respectively.
Region Ⅲ( − b ≤ x ≤ b )δEˆ z , n,3 = C n sin β n x + Dn cos β n x(13)δBˆ y ,n ,3 =jωβ n
(C n cos β n x − Dn sin β n x)
cκ n2

(14)
where β n =ε 3, n κ n .

Ⅳ and Ⅴis the lower groove− a − h ≤ x < −a and upper groove a < x ≤ a + h ,respectively. As the grating period is less than the freespace wavelength, we represent the fields inside the 1thgroove using the form of TEM standing wave modes asfollows:
RegionωδEˆ z = S± a sin[ ( x m (a + h)] exp(ik0 D)(15)ωδBˆ y = jS± a cos[ ( x m (a + h)] exp(ik0 D)

(16)

c

c

(8)

ω pi2

2

ε 3, n = 1 − ∑i =1

γ i3 (ω − k n vi ) 2,

ε 1,n = ε 2,n = 1(9)where the “ m ” denotes the upper interface x=a and thelllower face x=-a, respectively. The A n0 , Bn0 , C n , Dn ,S± a mean unknown coefficients, which are depended onω pi = (e ni 0 / m0ε 0 ) is the beam-plasma
angular frequency, ε l,n is the dielectric function,

the boundary conditions.

isthetransversewave
κn =[(ω / c) −k ]number. l = 1,2,3 represents the region Ⅰ , Ⅱ , Ⅲ ,Applying the boundary conditions at the grating
surfaces x = ± a ,the beam surfaces x = ±b ,solving
simultaneously Eqs.10-16 and then eliminating the

2

where

2

1/ 2

2 12
n

respectively.

Components of electromagnetic fields in eachregion [13]112

Dispersion equationllcoefficients of A n0 , Bn0 , C n , Dn , S ± a ,the odd modeand even modes dispersion equation is obtained asfollows, respectively.

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany∞
k d Qn − Rn / ε3,nD ωhωcot( ) + ∑sinc2 ( n ) 1/ 2=0dc n=−∞ cκn2
ε3,n + Tn

NUMERICAL SOLUTIONS

1/ 2

(17)
is the dispersion equation for the odd modes, and∞1+ Tnε31,/n2D ωhω
2 kn dcot( ) − ∑sinc ( )=02 Qn / ε31,/n2 − Rndc n=−∞ cκn(18)
is the dispersion equation of the even modes, where

Qn = ε 31,/n2 cot[κ n (a − b)] , Rn = ε 31,/n2 ⋅ tan β n b ,Tn = tan β n b ⋅ cot[κ n (a − b)] .The Eqs.17and 18 is
the similar to Ref.[13] when the voltages of two electron
beams are the same. In the absence of beams, thedispersion equations of odd modes and even modes canbe reduced to:
∞
kd
D
ωh
ω
cot( ) + ∑sinc 2 ( n ) cotκ n a = 0dc2n=−∞ cκ n(19)is the dispersion equation for the odd modes, and
∞
kd
D
ωh
ω
cot( ) − ∑sinc 2 ( n ) tanκ n a = 0dc n=−∞ cκ n2

1.6

Similarly, the dispersion curves without beams forthe odd modes are obtained by the solutions of Eq.19,
which are shown in Fig.2 (b). The band gap is evident
extending from 0.46THz to 0.6THz. Obviously, the band
gap of even modes and the frequency of operation point(solid dot) which is the intersection point of beam-wave
are greater than that of the lowest odd mode.
The two admixed beams are turned into a single
beam when the beam voltages are the same. The
dispersion curves of single beam for the even mode foundby the solution of Eq.18 are shown in Fig.3, where the left
600

1.4
1.2

12

Frequency|Imf|
500 v /v =1.0
2 1

10

400

8

300

6

200

4

100

2

|Imf|(GHz)(a)

Frequency(THz)

In this section, we focus on the characteristics ofdispersion equation through the numerical solutions.
The dispersion curves without beams for the evenmodes are found by the solutions of Eq.20, which are
shown in Fig.2 (a). The beam line with voltage 40kv isplotted for reference. It is observed that the lowest ordermode has a cutoff frequency of 0.345THz and has amaximum frequency 0.475THz. There is a stop band
between the two lowest order modes extending from
0.475THz to 0.8THz.

Frequency(GHz)(20)
is the dispersion equation for the even modes.

MOPPH033

1.0
0.8

e
lin
ht
lig

0.6
0.4
0.2
0.0
0.0

0
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

line
beam

0.2

0.4

0.6

2πk/D

operation
point
0.8

1.0

2πk/D

Fig3. Dispersion curves showing the real and imaginary
components of the frequency for the lowest-order evenmode, the parameters of grating are the same as that of in
Fig.2. The beam voltage is 40kv, electron beam density is
n0=5.97 1018 m-3

×

1.6
(b)

600

1.2

500
Frequency(GHz)

e
lin
ht
il g

1.0
0.8
0.6
0.4

line
beam

0.2
0.0
0.0

0.2

0.4

operation
point
0.6

0.8

1.0

2πk/D

12

Frequency|Imf|
v2/v1=1.0

10

400

8

300

6

200

4

100

2

|Imf|(GHz)

Frequency(THz)

1.4

0
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
2πk/D

Fig2. Dispersion curves of (a) even mode and (b) odd
mode. The parameters are period D=0.2mm, slot width
d=0.1mm, slot depth h=0.1mm and the distance of twogratings 2a=0.3mm

FEL Theory

Fig4. Dispersion curves showing the real and imaginary
components of frequency for the lowest-order odd mode, theparameters are the same as in Fig.3

113

MOPPH033

Proceedings of FEL 2006, BESSY, Berlin, Germany

axis is the real component of frequency and the right axis
is the growth rate. Seen from Fig.3, the growth rate isfound at the vicinity where the slow-wave and electron
beam are synchronous, which occurs at a frequency near
0.41 THz. The peak growth about 4.5GHz is found at afrequency of 0.403THz. Similarly, the dispersion curvesof single beam for the odd modes are shown in Fig.4. The
peak growth rate about 3.24GHz is found at thenormalized wave number of 0.68, which occurs at afrequency of 0.371THz.Obviously, the peak growth rateof the lowest order even mode are greater than that of odd
mode.
600
500

(a)
10

400

8

300

6

200

4

100

2

0
0.0

|Imf|(GHz)

Frequency(GHz)12

Frequency|Imf|
v2/v1=1.12

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

2πk/D

×

600

10

400

8

300

6

200

4

100

2

0.1

0.2

0.3

0.4

0.5 0.6
2πk/D

0.7

0.8

0.9

|Imf|(GHz)

Frequency(GHz)

12

(a)

Frequency|Imf|
500 v2/v1=1.12

1.0

Fig6. Dispersion curves showing the real and imaginary
components of the frequency for the lowest-order odd mode.
The parameters of grating are the same as that of in Fig.2. The
beam voltage is 40kv, electron beam density is n0=5.97 1018
m-3, and the voltage ratio is vr=1.12

×

The dispersion curves of two-stream for the lowestorder even mode obtained by the solution of Eq.18 areshown in Fig.5. Obviously, the growth rate is remarkably
different from that of single beam, the cambered growthrate is produced by the TSI, and the growth rate isremarkably enhanced when the TSI wave is synchronouswith the slow-wave. The peak growth rate about 6.91GHz
is found at the frequency of 0.412THz, which is enhanced
by a factor of 2 than that of single beam. Outside thesynchronous range of TSI and electro-magnetic wave, thegrowth rate is still existed, which is thought to be yieldedby the TSI
Similarly, the dispersion curves of two-stream forthe lowest-order odd mode solved the Eq.29 are shown in
Fig.6. The peak growth rate about 6.04GHz is found at
the frequency of 0.375THz, which is enhanced by a factor
2. We may note from Figs.3, 4, 5and 6 that the even mode

114

CONCLUSIONSIn this paper, we have studied the two-stream SmithPurcell Free-Electron Laser with a dual-grating. The
linear dispersion equations for the even modes and odd
modes are derived by making use of fluid theory, andthose of characteristics are analyzed through thenumerical solutions. We find that the peak growth rate isenhanced by a factor of 2 than that of single beam when
the TSI wave is synchronous with the electromagnetic
wave. The nonlinear effect is under consideration, which
will be reported in the future.

ACKNOWLEDGEMENT
This work is supported by National Natural Science
Foundation of P. R. China (60571020, 60178011).

REFERENCES
0.1

Fig5. Dispersion curves showing the real and imaginary
components of the frequency for the lowest-order evenmode, the parameters of grating are the same as that of in
Fig.2. The beam voltage is 40kv, electron beam density is
n0=5.97 1018 m-3,the voltage ratio is vr=1.120
0.0

could be an operation mode for which the growth rate is
greater than that of odd mode. To obtain the higher
operation frequency, we should make the even mode as
an operation mode.

[1]S.J.Smith, E.M.Purcell, “Visual light from localized
surface charges moving across a grating”, Phys. Rev.
92,1069,1953[2]J.Urata,M.Goldstein,M.F.Kimmitt,A.Naumov,C.Platt.
andJ.E.Walsh,“Superradiant
SmithPurcell
Radiation”, Phys.Rev.Lett.80,(1998)516[3]A.Bakhtyari,J.E.Walsh,andJ.H.Brownell,“Amplifiedspontaneous-emission power oscillation in a beamwave interaction”Phys.Rev.E.65,066503(2002)[4]K.J.Kim,and S.B.Song, “Self-amplified spontaneous in
Smith-Purcell
freeelectronlasers”,
Nucl.
Instrum.,Methods Phys. Res., Sect. A 475,158 (2001)[5]H.L.Andrews and C.A.Brau. “Gain of a Smith-Purcell
free-electron laser”,PRSTAB 7, 070701 (2004)[6]D.Li, K. Imasaki, Z.Yang and Gun-Sik Park, “Threedimensional simulation of super-radiant Smith-Purcell
radiation”, Appl.Phys.Lett. 88 (201501), 2006
[7]D.Li and Z.Yang, K. Imasaki,and Gun-Sik Park
“Particle-in-cell simulation of coherent and superradiant Smith-Purcell radiation”,Phys Rev. ST. Accel.
Beams, 9, (2006)040701,[8]J.T.Donohue and J.Gardelle “Simulation of SmithPurcell terahertz radiation using a particle-in-cellcode” Phys Rev.ST.Accel.Beams,9,060701,2006[9]P.H Siegel, “Terahertz technology”, IEEE Trans,
Microwave and Tech., 50, (2002)910,[10]J. R. Pierce, et al “A new type of high frequency
amplifier,” Bell Syst.Tech ,J.28. (1949) 33[11]V.V. Kulish, A.V. Lysenko, V.I. Savchenko. Twostream free electron lasers. General properties. Int. J.
Infrared Millim. Waves, vol. 24, (2003)129[12]H.P. Freund, et al., “Multiple-beam free-electron
laser”, Nucl. Inst. Method A507, (2003)373[13]H.P. Freund and T.M.Abu-Elfadl.,“Linearized Field
Theory of a Smith-Purcell Traveling Wave Tube”,
IEEE, Plasma Science 32,1015,2004[14]K. Mehrany and B. Rshidaian, “Dispersion and Gain
Investigation of a Cerenkov Grating Amplifier”, IEEE
Trans. On Electron Devices, 50,1562, 2003.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH034

PRODUCTION OF ‘GIANT’ PULSES OF SCATTERED RADIATION FROM
PUMP WAVE SPOT RUNING OVER THE ELECTRON BEAM*
V. Baryshev, N. Ginzburg#, A. Sergeev, I. Zotova IAP RAS, Nizhny Novgorod, Russia.
Abstract
To generate ultrashort electromagnetic pulses it issuggested to scan a spot formed by pump wave along anelectron beam. When pump spot velocity is equal to thegroup velocity of scattered radiation the short ‘giant’pulse of scattered radiation with amplitude increasing
proportional to interaction distance will be produced. The
running spot of pump wave can be realized afterreflection of frequency chirped laser beam from echelettegrating.

INTRODUCTION
In [1] the generation of millimetre wave superradiance(SR) pulses have been observed in the process ofstimulated backscattering of relatively long pump wave
pulse by extended electron bunch with the length
restricted by cooperative length (the distance of thescattered wave propagation during the time of instability
growth up). Under such conditions the scattered radiation
represented a single pulse with peak power strongly
exceeding the level of spontaneous emission.
In this paper we study the alternative method ofgeneration superradiance type pulses in the process ofstimulated scattering when the relatively short spot
illuminated by pump wave runs over the quasi-continuous
electron beam. Obviously scattering and beam modulation
take place only in area illuminated by pump wave. In thecase when the pump spot moves with group velocity of
scattered radiation the pulse of scattered radiation
propagating along electron beam will be amplified
continually by fresh (unmodulated) electrons due todifference between signal wave group velocity c andelectron translational velocity v|| . As a result the peak
amplitude of scattered pulse increases proportionally toshifting distance. The running spot of pump wave can berealized after passing (reflection) of frequency chirped
laser pulse from frequency depended refraction system
like prism or echelette grating (see Fig. 1). It should be
noted that the shifting direction and velocity of the pumpwave spot are not correlated with the phase and groupvelocities of this wave. For our purpose to obtain the large
frequency conversion the direction of spot shifting should
be approximately opposite to the group velocity vector.
In the case of scattering of laser radiation by amoderately relativistic electron beam with energy ~13 MeV above process can be used to produce intense SR
pulses either at UV band (up frequency conversion), at
terahertz band (down frequency conversion) or bands
depending on direction of scattered wave propagation
with respect to electron beam. Correspondingly at the firstcase illuminated spot should run together with scatteredwave in the direction of electron motion while in thesecond case this spot together with scattered wave should
run at opposite direction.

shift direction
relativistic
electron
beam

t=t1

t=t2

t=t3

chirpedlaser pulse

echelette grating
Figure 1: Echelette scheme of scanning of pump field spot using frequency chirped laser pulse.
*Work supported by … Russian Fund for Fundamental Researches,
grant 05-02-17553#
ginzburg@appl.sci-nnov.ru

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Proceedings of FEL 2006, BESSY, Berlin, Germany

MODEL AND BASIC EQUATIONS
Let us consider the process of stimulated scattering insituation when the spot illuminated by a pump wave runs
along electron beam with velocity u in the direction ofelectron motion. In this case due to the Doppler effect thefrequency of scattered radiation Zs essentially exceeds
the frequency of pump wave Zi . Neglecting pump wave
exhaustion the generation of pulses of scattered radiationin the above process can be described by the system of
equations including the nonstationary equation for
scattering signal amplitude and the averaged electron
motion equations [2]:§w 1 w·¨ ¸as© wz c wt ¹

iF t  z u kc ai I

. (1)

2

§w
·
¨  1 w¸ T
¨ wz v|| wt ¸©
¹

Here ai ,s

1 2 S  iT
³ e dT 0
S 0^

Pkc2 F t  z u Im a s a*i e iT`

F W, Z

Zc t  k c z

dimensionless parameter which is proportional to thebeam current. Function F t  z u describes the profile ofthe spot illuminated by pump filed. Introducing the new
independent variables
Zc c t  z v||
Z(2)
Z C c z, W Cc
1 c  1 v||
and assuming that the velocity of pump spot is equal to
the group velocity of scattered signal (u=c) Eqs. (2) canbe presented in the form
2S
wa wa
i

 F W  Z ³ e  iT dT0
wZ wW
S
0
,
(4)
2
w T
 iT
F W  Z Im aewZ 2^

where aeAi ,s m0 J 0 c 2 is the dimensionless amplitudeof scattered and pump waves, T

electron phase respect to the combination wave,
Zc Z s  Zi , kc Zc c  Zi c , P J 02E||3 , I is theis thePa s a*i C 2 , C

Z2p ai`2 1/ 3is the gain (Pierce)parameter. Under assumption that the development of
instability starts from the small perturbation of electron
beam density the initial and boundary conditions can beaFigure 2: Production of the SASE signal in the case of standing pump field spot.

F W, Za

Figure 3: Production of ‘giant’ single pulse in the case of moving pump field spot.

116

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Proceedings of FEL 2006, BESSY, Berlin, Germany

written in the form
T Z 0 T0  r cos T0  M W , T0  >0,2S@, r  1

wTwZ Z 00, a Z 0(5)0

MOPPH0341.0

a2

where M W is the random function.

0.5

1
SIMULATION RESULTS
Let’s consider at first the traditional situation with theunmovable u 0 bell-shaped pump spot: (see Fig. 2a). In
this case, due to the slippage, radiation escapes frompump spot. As a result the well-known multi-spikes
regime of SASE [3,4] is realized (Fig. 2b) when different
parts of beam radiate practically independently.
The totally different situation takes place when thepump spot moves along the electron beam together with
scattered signal: u c (Fig. 3a). But because electron
velocity v|| is slightly less than c. the interaction(scattering) spot slips along beam and the pulse of
scattered radiation formed at initially stage of interaction
propagates through the unmodulated electrons being
effectively amplified (see Fig. 3b). As a result the
scattered radiation represents the single short pulse withamplitude essentially exceeding the amplitude of spikes in
the SASE regime (compare with Fig. 2b). In the ideal
situation the amplitude of above ‘giant’ pulse growths
proportionally to the interaction distance L (see Fig. 4).
It is important to note that due to short lifetime ofindividual electrons in the interaction spot above process
is less sensitive to the spread of beam parameters incomparison with traditional steady state regime (seeFig. 5).

10.0

'

0.0
0.0

1.0

2.0

3.0

4.0

Figure 5: Dependence of radiation peak amplitude onelectron velocity spread ' for steady state regime (1) and‘giant’ pulse regime (2).

CONCLUSION
In conclusion lets make preliminary estimations ofpossible experiments on backscattering of 10 P CO2 laser
radiation by high current () relativistic electron beam. For
electron energy 3 MeV scattered wavelength ~200 nm
will belong to UV bands. For laser pump pulse withduration 1 ns the shift of pump spot will be about 30 cm.
For power density of pump wave ~150 GW/cm2 andcurrent density 30 kA/cm2 the gain parameter is
C | 6.3  10 5 . As a result for initial perturbation
r 0.001 the maximal power density of scatteredradiation can achieved ~1 GW/cm.

REFERENCES[1] A. Reutova, M. Ulmaskulov, A. Sharypov, V. Shpak,S. Shunailov, M. Yalandin, V. Belousov, G. Denisov,
N. Ginzburg, A. Sergeev and I. Zotova JETP Lett.
82(5) 295.

a max

[2] V. Bratman, N. Ginzburg, M. Petelin JETP 76(3)(1979) 930.

5.0

L

0.0
0

10

20

30

[3] R.H. Bonifacio, N. Piovella and B.W.J. McNeil,
Phys. Rev. A, 44, (1991) 3441.
[4] C.Pelegrini “High power femtosecond pulses from an
X-ray SASE-FEL”, FEL’1999, Hamburg, Germany
August 1999, p.124.

Figure 4: Dependence of pulse peak amplitude on theshifting distance.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

INFLUENCE OF LINER FLUCTUATIONS ON LOW- AND HIGH-GAIN
CHERENKOV FELS
I. de la Fuente∗ , P.J.M. van der Slot, K.-J. Boller
Laser Physics and Non-Linear Optics Group, University of Twente
PO Box 217, 7500 AE Enschede, The Netherlands.
Abstract
Imperfections in the dielectric liner of a Cherenkov FreeElectron Laser (CFEL) result in fluctuations in the phasevelocity of a radiation wave when it propagates through thelined waveguide. Random fluctuations in the phase velocity reduce the bunching of the electrons and consequently
lower the gain of CFELs. Here we theoretically investigate the influence of these liner-induced phase fluctuationsin the radiation field on the saturated power of low to highgain CFELs. To obtain different gain regimes, we keep theelectron beam radius constant and vary the current density.
As an example, we study a 50 GHz CFEL and quantify
the reduction in the single-pass saturated power for different rms liner fluctuations when the CFEL is driven by anelectron beam with current densities varying from 1 A/cm 2(average gain of 0.43 dB/cm) to 25 A/cm 2 (average gain of
1.39 dB/cm).

INTRODUCTION
The increasing number of microwave applications inboth research and industry [1, 2] has increased the interest in tuneable high-power microwave sources. The
Cherenkov Free-Electron Laser (CFEL) is a promising candidate as a compact high-power microwave source for various applications. CFELs have been operated at 100 kW
peak power level at 1 mm wavelengths, at 200 MW peak
power level at 8 cm wavelengths and at wavelengths asshort as in the far infrared [3]. The simplicity of its construction, the high efficiency and an affordable compact design have made the CFEL attractive for applications wherehigh microwave frequencies and high powers are needed.
However, simple imperfections in either the electron beamor the lined waveguide section, that are used to generate thelaser gain, can seriously degrade the performance of the device [4].
In a CFEL, accelerated electrons are injected througha wave-guiding structure that slows the phase velocity ofthe electromagnetic wave to a sub-luminous value. An example is a metallic, cylindrical tube lined with a dielectricmaterial, e.g., quartz. By choosing appropriate dimensions
for the waveguide, i.e., the inner diameter for the tube, thethickness and dielectric constant of the liner, the phase velocity of EM waves can be matched to the velocity of theinjected electron beam for a desired wave frequency [5]. A
transversely magnetic (T M ) wave can decelerate or accelerate co-propagating electrons. A net deceleration of elec∗ i.delafuentevalentin@utwente.nl

118

trons in the pump beam and, correspondingly, a net amplification of the wave, occurs only if the electrons are forming
bunches, if these bunches travel with the phase velocity of
the radiation wave, and if the bunches are located within acertain phase range of the radiation wave (when seen fromthe frame of that wave). A fluctuating phase velocity of the
wave in the waveguide would appear as a fluctuating relative phase of the bunches; it could bring bunches out of the
optimum driving phase, and this would reduce the amplification. Likewise, a spread in longitudinal electron velocities results in a spread in relative phases between wave andthe electrons. This results in a reduced bunching within theelectron beam and consequently in a lower amplification of
the wave [3].
Although the variations in the phase velocity can havedifferent origins, we will model only one type of imperfection, namely, fluctuations in the inner radius of the liner.
Other types of fluctuations, such as a spatial inhomogeneityof the liner’s dielectric constant, are not treated separately
because we expect widely analogous results. In a previous study we have shown that in a low current CFEL, atypical manufacturing tolerance in the inner radius of theliner of 5 % can reduce the saturated power by a factorof 2 [4]. In this paper, we investigate the sensitivity of
the CFEL to small random liner imperfections for different
gain regimes. We therefore consider a 50 GHz CFEL witha fixed liner geometry, electron beam energy, and electron
beam radius. The different gain regimes are obtained byvarying the electron beam current density from 1 A/cm 2 to
25 A/cm2 .
In the remainder of this paper we first present a summaryof the theoretical model that describes the dynamics of the
CFEL in the presence of radii fluctuations. Next, we willshow the numerical results for a CFEL system operating
in different gain regimes. We end with a discussion andconclusions.

THEORETICAL MODEL
The theoretical model describing the dynamics of a
CFEL in the presence of small and random fluctuations of
the liner inner radius is presented in previous work [4] andhere we present a summary.
The standard CFEL dynamical model [3, 6] assumes thatthe electromagnetic wave co-propagating with the electron
beam can be described by a superposition of empty (i.e.,
without the electron beam) waveguide eigenmodes withamplitudes that vary slowly with longitudinal distance z.
Using the power orthogonality property of the eigenmodes,

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany
and applying the slowly varying amplitude and phase approximation to Maxwell’s equations, the dynamical equation for the mode amplitudes are derived. The system isclosed by the Newton-Lorentz equations, that describe themotion of the electrons under influence of the electromagnetic wave.
The effect of a small random fluctuation in the inner radius rd (z) of the liner that varies slowly along its lengthis twofold. First, it varies the phase velocity of the wave.
Second, it modifies, in principle, the transverse mode profile. However, our analysis shows that the liner fluctuations
mainly affect the phase velocity of the wave and that thetransverse mode profile remains approximately unchanged[4]. In our model, we allow the wave number to vary slowly
along the length of the liner, and write for the longitudinalcomponent of the electric field E z,n for mode T M 0n:
Ez,n (r, z, t) =  z
fn (r)

a0n (z) kn (z )dz − ωt , (1)exp i
kn (z)
0where fn (r) is the transverse mode profile of an empty
lined waveguide [7], a 0n (z) the slowly varying mode amplitude, and the slowly varying longitudinal wave numberkn (z) is given by:
  z
 z
∂kn dkn drd kn (z) = k0n +dz ≈ k0n +dz ,∂rd rd0 0 dz 
0 dz
(2)
where, for convenience, the inner radius of the liner at z =0 is taken equal to the mean radius r d0 and k0n is the wave
number corresponding to a homogeneous waveguide withrd = rd0 . The evolution of the normalized field amplitudeea0n (z) = mc
a0n (z) for the T M0n modes is:ωp2 βz0κ2 ∂a
kn (z)(1 − 2n ) 0n = −4 2
2 ×
k0n ∂zc0 An rd0
 rd0
βr iαnκn−iαne +drr iI1 (κn r)
I0 (κn r)e

|βz |
k0n
0
(3)
2

Here An is a normalization constant, ω p is the plasma
frequency, β is the electrons velocity normalized to the
speed of light in vacuum, I 0 and I1 are the Bessel functions of second kind, and κ n is the transverse wave number.
The symbol . . . represents an average over all electrons
within one radiation wavelength. Undefined symbols aredescribed in [4].

DESCRIPTION OF THE CFEL
This model has been applied to a particular design for
a Cherenkov free-electron laser that can be operated withboth low and high electron beam currents. In this analysis we choose Al2 O3 with a dielectric constant of =9.8 as
the liner material, and keep the geometry constant. Likewise, the outer radius of the cylindrically shaped electron

FEL Theory

MOPPH036

beam is fixed at rb =5 mm. However, to vary the singlepass gain and saturated power of this device, we consider
different total beam currents I b ranging from 0.8 A to 20 A.
The remaining geometrical parameters are: an average inner liner radius of r d0 =5.5 mm and an average liner thickness of d=0.57 mm. This system requires an electron beamenergy of 84.2 keV to operate at 50 GHz. We integrate
the dynamic CFEL equation (eq. 3) up to the point where
the laser saturates. Using a constant inner radius equal tord0 and an initial seed power of 10 mW, these electron currents produce a saturated power P 0 of about 200 W at a
distance z0 of 100 cm and 20.8 kW at a distance of 45 cm
for Ib =0.8 A and 20 A, respectively. The corresponding
average gain is 0.43 dB/cm and 1.39 dB/cm, respectively.
The variation in the inner liner radius is modeled usinga random fluctuation superimposed on the average radius
rd0 . A spatial low-pass filter with cut-off distance z c isused to remove fast fluctuations from the random distribution. Further, the fluctuations are scaled to obtain a certain
standard deviation σ rd of the distribution. For each particular realization of a fluctuating liner radius we numerically calculate the saturated power P sat and the position
zsat at which this power is obtained. To obtain also statistical information on the output as a function of the experimental parameters, we generate 100 different realizations of liner fluctuations for each combination of the rms
amplitude σrd and cut-off distance z c . For each combination we determine the ensemble average P sat and standard
variation σp and corresponding values for the distance tosaturation zsat .

RESULTS AND DISCUSSIONFirst, we numerically study the sensitivity of this particular CFEL to an increasing amplitude of the random fluctuations in the liner inner radius while the spatial filter is
kept constant at z c =10 cm, corresponding to approximately
16 times the free-space wavelength. The ensemble averageof the saturated power, P sat , normalized to the saturated
power in absence of fluctuations, P 0 , is shown in Figs. 1aand 1b as a function of the standard deviation of the fluctuations in the inner liner radius, σ rd , for the two beam currents of 0.8 A and 20 A, respectively. Corresponding values
for the distance to saturation z sat are shown in Fig. 2. Fig.
1 shows that for this particular CFEL and a beam currentof 0.8 A, a small rms liner fluctuation of 2.5 μm (=0.05 %of rd0 ) is sufficient to reduce the saturated power by a factor of 2 on average. The rms liner fluctuation increases to
25 μm (=0.5 % of r d0 ) to obtain a similar reduction when
the CFEL is driven by a beam current of 20 A. At the sametime we observe that the relative spread σ p /Psat is muchlarger for the 0.8 A beam current compared to the 20 A
beam current. The variation of the distance to saturation
with the rms liner amplitude (see Fig. 2) shows a different
behavior for the two beam currents. For the 0.8 A current, the distance increase quickly from 100 cm to close to150 cm and then remains approximately constant. The ob-

119MOPPH036

Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 1: Normalized saturated power (P sat /P0 ) and normalized standard deviation (σ p /Psat ) as a function of thestandard deviation of the liner fluctuations σ rd for a currentof 0.8 A (a) and 20 A (b).

served spread in z sat remains approximately constant. On
the other hand, for the 20 A current the distance to saturation increases approximately linearly with σ rd , while therelative spread is slightly reduced.
These findings indicate that this particular CFEL is far
more sensitive to fluctuations in the inner liner radius than
the system studied in our previous study [4]. In that study
we also considered a CFEL operating at 50 GHz. However,that system used a 0.8 A electron beam with a 1 mm radius(25 A/cm2 current density) to drive the CFEL. We foundthat an rms fluctuation of about 5 % was required to reduce
the saturated power by a factor of 2. For the device of thiswork, this is 0.5 % and 0.05 % for the same current density
and total beam current respectively. To allow the CFEL ofthis work to be driven by a higher total current, we haveincreased the beam radius. As a consequence, the transverse dimensions of the CFEL have increased and we havechosen a different liner material. This leads to a larger variation of kn with inner liner radius r d (see eq. 2): ∂kn /∂rdis -4.6 106 m−2 for the device in this work, while it equals-0.46 10 6 m−2 for the device in our previous study. It istherefore not surprising that the current system is more sensitive to liner imperfections than the system considered in
our previous study.
Second, we have investigated the influence of spatial
distribution of the liner imperfections by varying the cutoff distance z c of the low pass filter applied to the randomly generated liner fluctuations. The normalized ensemble average Psat /P0 and the normalized spread σ p /Psat
are shown in Fig. 3 for I b =0.8 A and 20 A, and the corre-

120

Figure 2: Normalized distance to saturation (z sat /z0 ) andnormalized standard deviation of z s at (σz /zsat ) as a function of the standard deviation of the liner fluctuations σ rdfor a current of 0.8 A (a) and 20 A (b).
sponding values for z sat are shown in Fig. 4. These figures
show that both the saturated power P sat and the distance tosaturation zsat vary only weakly with increasing z c if zc issufficiently large (z c >> λ = c/f ). Note, that the lattercondition is anyhow implicit in the approximations used inderiving the dynamical CFEL equation (eq. 3).
Last, we compare the sensitivity of this system to liner
imperfections as a function of the total beam current I b fora fixed σrd =15 μm and a fixed cut-off distance z c =10 cm.
Fig. 5a shows the normalized ensemble average P sat /P0
and spread σp /Psat as a function of I b and Fig. 5b shows
the corresponding values for z sat . These figures show thatIb must be larger than 30 A to keep the reduction in P sat
to less than 15 %. We also observe that the relative spread
σp /Psat reduces with increasing beam current, while thespread σz /zsat shows a slight increase.

CONCLUSION
We have studied the sensitivity to imperfections in theliner of a particular CFEL operating at 50 GHz as a function of total beam current. The system studied in this work
is based on a previously studied system with increasedtransverse dimensions and a different liner. The increased
dimensions allow a larger total current to pass through thelined waveguide and study the system in different gain
regimes. As a consequence, the variation of longitudinal
wave number with inner radius increased by a factor of 10
compared to the system we used in a previous study, that
also operated at 50 GHz. Taking this difference into ac-

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 3: Normalized saturated power (P sat /P0 ) and normalized standard deviation (σ p /Psat ) as a function of the
cut-off distance z c for a current of 0.8 A (a) and 20 A (b).

MOPPH036

Figure 5: Normalized saturated power (P sat /P0 ) and normalized standard deviation ( σ p /Psat ) (a) and corresponding values for z sat (b) as a function of the electron beam
current for σ rd = 15 μm and zc =10 cm.
rms liner fluctuation reduces P sat to less than 20 % of P0
for Ib <5 A. A high gain also reduces the relative spreadin Psat for an ensemble of similar imperfections, while atthe same time the relative spread in z sat increases slightly.
These findings show that systems with high gain are lesssensitive to liner imperfections compared to systems withlow gain. However, the actual allowable rms fluctuation
depends both on the gain and on the particular geometry of
the lined waveguide of the Cherenkov FEL.

REFERENCES[1] W.K. Gwarek, M. Celuch-Marcysiak, A review of microwave
power applications in industry and research, 15th International Conference on Microwaves, Radar and Wireless Communications, MIKON, p 843-848 (2004).
[2] D.A. Jones, T.P. Lelyveld, S.D. Mavrofidis, S.W. Kingman
and N.J. Miles, Microwave heating applications in environmental engineering–a review, Resources, Conservation andRecycling, 34, 2, 75-90 (2002).

Figure 4: Normalized distance to saturation (z sat /z0 ) andnormalized standard deviation of z s at (σz /zsat ) as a function of the cut-off distance z c for a current of 0.8 A (a) and
20 A (b).
count, we find that both systems show similar sensitivity toliner imperfections when the CFELs are driven by electron
beams having the same current density of 25 A/cm 2 . For
the current system we find that a total current of at least
30 A is required to keep the reduction in ensemble average
Psat to less than ∼15 % of P0 (for σrd =15 μm). The same

FEL Theory[3] H.P. Freund,‘Nonlinear Analysis of High-Power Cherenkov
Masers’,Phys. Rev. Lett., 65, p.2993 (1990).
[4] I. de la Fuente, P.J.M. van der Slot, and K.-J. Boller, ‘Phase
velocity fluctuations and gain in Cherenkov free-electron
lasers’, J. Appl. Phys. (accepted for publication).
[5] J.E. Walsh and J.B. Murphy, Tunable Cerenkov Lasers, IEEE
J. Quant. Electr., QE-18, 1259 (1982).
[6] H.P. Freund and A.K. Ganguly, Nonlinear analysis of the
Cerenkov maser, Phys. Fluids, B2, 2506 (1990).
[7] R.A. Waldron, Theory of guided electromagnetic waves, Van
Nostrand Reinhold Company, London (1970).

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THEORY OF RADIATION OF ELECTRONS IN THE FIELD OF A LINEAR
POLARIZED STATIONARY ELECTROMAGNETIC WAVE
Drebot I.V., Grigoryev Y.N., Zelinsky A.Y., NSC KPTI, Kharkov, Ukraine
In the paper the results of exact integration of Lorentz
equation for a free electron in the field of a linear
polarized standing electro-magnetic wave are presented.
Standing wave is considered as a sum of two running in
opposite directions linear polarized waves. Projections ofequations on coordinate axes can be integrated once. It
allows us to reduce the task to solution of nonlinear
equation of the second order for electron coordinate. The
axis of projection coincides with a wave line. For
approximate integration of the second order equation the
expansion on two small parameters are used. Velocity andcoordinate of electron in parametric form are presented in
the paper. It is shown that under interaction of a
relativistic electron with stationary wave there is amotion, which has of beating character. The amplitude
and period of the beating were calculated.

is considered as a sum of two running in opposite
directions waves with the same polarizations.
Two projections of the Lorenz equation can be
integrated once [4]. It allows to reduce the task to thesolving of a second order nonlinear equation. For theapproximate solution the expanding on two small
parameters was used.
In the work the expressions for velocity and coordinatesof an electron were derived in a form of parametricalfunctions of time. Using [5] and with the help of derived
formulas one can calculate radiation spectrum of anelectron in the field of standing linear polarized
electromagnetic wave.
As one can see from the derived solutions, the electron
motion in the standing wave has beating character and canlead to electron grouping in the propagation direction.
The period and amplitude of the beatings were calculated.

INTRODUCTION

MOTION EQUATIONS

The theory of the electron interaction with a standing
light wave originates in description of the Kapiza-Diraceffect [1]. The physical sense of the effect is stipulated
radiation of electrons in the field of a stationary wave.
After that sufficiently large amount of papers weredevoted to the theoretical investigations of electron
radiation in the field of a light wave.
The interest to the subject has been revived lately due
to huge progress in intense laser technique. The latest
works use both quantum and classical electrodynamics
approach.
The main difficulty in using of classicalelectrodynamics approach is determination of solution ofequations of electron motions in the form which will be
convenient for analytical calculations of the radiation
spectrum and for estimations of the electron velocity andcoordinate evolutions. For example, in basic works [2,3]the solving of motion equations is reduced to the solvingof the equation system of the two first order equations.
But in this case one can find only approximate solution
and the solution can be formulate as a function of intrinsic
time of the electron. Such approach makes calculations of
the radiation spectrum and other characteristics quitedifficult. In the paper [4] an electron trajectory in the fieldof a standing linear polarized electromagnetic wave was
reduced to the solving of nonlinear differential equation
system with time dependent coefficients. After
linearization of the system the Hill equations has to besolved.
In the presented paper, the approximate solutions of theLorenz equation for an electron in the field of linear
polarized standing wave are presented. The standing wave

An electron motion in the field of standing wave can be
described with Lorenz equation:

Abstract

122

d
dt

r

m 0v

(1 − β )2r= cE +
1
2

[ ]

e rr
vH ,
c

(1)

where, β = v c , m0 the rest mass of the electron, с is therr ∂r
is thevelocity of light, е is the electron charge, v =
∂t
r
r
r
r
vector of an electron velocity, r = i x + j y + k z , t is time,r r

E , H are vectors electrical and magnetic field.
We will consider the standing wave as a sum of two
linear polarized running in opposite direction waves:.

r r r r r
r r
E=E1 +E2; E1 =kE1z; E2 =kE2z;

E1x =0; E1y =0; E2x =0; E2y =0;
r r r
r rr
r
H = H1 +H2; H1 =[i ; E1] = −jE1z ;r
rr r
H2 =[−i ; E1] = jE1z ;

(2)

(3)

H1z = 0; H1x = 0; H2z = 0; H2x = 0;
r

r

r

r

⎡

⎛

⎣

⎝

E1 = k E01 cos ⎢2πν 1 ⎜ t −⎤x⎞⎟ + δ 1 ⎥;
c⎠
⎦

⎡
⎤
x⎞
⎛
E 2 = k E02 cos ⎢2πν 2 ⎜ t + ⎟ + δ 2 ⎥;
c⎠
⎝
⎣
⎦

(4)

Substituting (4) in (2) and (3) one can get:

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany
r

r⎛

⎡

⎛

⎝

⎣

⎝

E = k ⎜⎜ E01 cos ⎢2πν 1 ⎜ t −rrdξ= e(v E ) ,dt⎤
x⎞⎟ + δ1 ⎥ +
c⎠
⎦

(5)

⎡
⎤⎞
x⎞
⎛
+ E02 cos ⎢2πν 2 ⎜ t + ⎟ + δ 2 ⎥ ⎟⎟;
c⎠
⎝
⎣
⎦⎠

r

r⎛

⎡

⎛

⎝

⎣

⎝

H = − j ⎜⎜ E 01 cos ⎢2πν 1 ⎜ t −

(

)

(

(

)

)

(

)

1 d
ξ βy = 0
c dt

(8)

⎛
⎡
⎤
x⎞
1 d
⎛
ξ β x = eβ z ⎜⎜ E 01 cos ⎢2πν 1 ⎜ t − ⎟ + δ 1 ⎥ −
c
c dt
⎝
⎠
⎣
⎦
⎝

βy / 1− β 2 = A

(11)

⎛

⎝

⎣

⎝

⎡

⎛

⎣

⎝

⎤⎞
x⎞
⎟ + δ2 ⎥ ⎟
⎟
c⎠
⎦⎠

d
1 d 2x.
βx =dt
c dt 2Integrating (18), we derive:
1 + β x 2eE0 tψln=(1 − β x )Cos[ϕ − ] −m0 c t∫ (1 + ψ 2 + A 2 )1 −β xwhere β& x =

{

(19)

0

}

− (1 + β x )Cos[ϕ + ] dt + C2

1 + β x (t 0 ).
1 − β x (t 0 )For standing wave we can set:
r

r

r

x⎞
x⎞
⎛
⎟; ϕ + = 2πν ⎜ t + ⎟ .
c
c
⎝
⎠
⎝
⎠
As it follows from (19):1 + β x 1 + β x (t 0 ) Φ ( t )=e
1 − β x 1 − β x (t 0 )where⎛Than ϕ − = 2πν ⎜ t −t

Φ (t ) =

(12)

(20)

2eE 0
ψ
(1 − β x )Cos [ϕ − ] − (1 + β x )Cos [ϕ + ] dt
m 0 c t (1 + ψ 2 + A 2 )

∫

{

}

0

⎤
⎡
⎤⎞
x⎞
x⎞
⎛
⎟ + δ1 ⎥ + Sin⎢2πν 2 ⎜ t + ⎟ + δ 2 ⎥ ⎟ −
⎟
c⎠
c⎠
⎝
⎦
⎣
⎦⎠

ξ z = γ (t 0 ) β z (t 0 );eE 0;mc ( 2πν ) A = γ (t 0 ) β y (t 0 )rrAssuming

P << 1, ξ z << 1, Φ(t ) << 1

Φ(t ) 22
one can get from (20):1
β x (t ) ≈ β x (t 0 ) + (1 − β x2 (t 0 ))Φ(t )2
Φ ( t ) ≈ P 2 Φ 1 + Pξ z Φ 2 + P 2 ξ z Φ 2
where

and

e −Φ (t ) ≈ 1 − Φ (t ) + O

(14)

r

t 0 is initial time; E0=E01=E02 .
With use of two integrals (10) and (11) one can
express, β z , β y , ξ through β x ,ψ , A

β z2 = ψ 2 (1 − β x2 ) /(1 + ψ 2 + A2 )(14)

β y2 = A 2 (1 − β x2 ) /( 1 + ψ 2 + A 2 )(15)

ξ = m0c 2 (1 + ψ 2 + A2 )1 / 2 /(1 − β x2 )1 / 2

APPROXIMATE SOLUTION

(13)

⎛
⎡
⎤
⎡
⎤⎞
x(t0 ) ⎞x(t0 ) ⎞⎛⎛⎜ Sin 2πν ⎜ t −⎟ + δ1 ⎥ + Sin⎢2πν 2 ⎜ t0 +⎟ + δ 2 ⎥ ⎟;
1 0
⎢
⎜
⎟
c ⎠
c ⎠
⎝
⎝
⎣
⎦
⎣
⎦⎠
⎝

P=

(18)

E0=E01=E02; δ 1=δ 2=0; ν 1=ν 2=ν .

(10)

⎡

⎝

⎤
x⎞
⎟ + δ1 ⎥ −c⎠⎦− (1 + β x )Cos ⎢2πν 2 ⎜ t +(9)β z / 1− β 2 =ψ⎛⎣C 2 = ln

1 dy .
where β x = 1 d x , β z = 1 d z , β y =
c dt
c dt
c dt
Equations (7,8) can be integrated once. As a results thefollowing expressions can be derived:

F = ⎜⎜ Sin⎢2πν1⎜ t −

⎛

⎡
⎤
x⎞
⎛
− (1 − β x )Cos ⎢ 2πν 1 ⎜ t − ⎟ + δ1 ⎥ −
c
⎠
⎝
⎣
⎦

⎡
⎤⎞
x⎞
⎛
− E 02 cos ⎢2πν 2 ⎜ t + ⎟ + δ 2 ⎥ ⎟⎟
c
⎝
⎠
⎣
⎦⎠

where ψ = PF + ξ z⎡

Cos ⎢2πν 1⎜ t −

1

)

(

one can derive the second order equation for electron
coordinate x .
β& x
ψ
eE
(1 − β x )= 02m0 c (1 + ψ 2 + A2 )1 −β x(6)2= ξ (where ξ - isUsing expression: mc 1 − βelectron energy), and expressions (5),(6) we projectequation (1) on coordinate axes:⎡⎤
1 d(ξ β z ) = e 1 − β x E 01 cos ⎢2πν 1 ⎛⎜ t − x ⎞⎟ + δ 1 ⎥ +
c
c dt
⎝
⎠
⎣
⎦
(7)
⎡
⎤
x⎞
⎛
+ e 1 + β x E 02 cos ⎢ 2πν 2 ⎜ t + ⎟ + δ 2 ⎥
c⎠
⎝
⎣
⎦
2

(17)

(

⎤
x⎞
⎟ + δ1 ⎥ −
c⎠
⎦

⎡
⎤⎞
x⎞
⎛
− E02 cos ⎢2πν 2 ⎜ t + ⎟ + δ 2 ⎥ ⎟⎟;
c⎠
⎝
⎣
⎦⎠

MOPPH037(16)

1
Φ1 ≈ Γ − 2 {(− )(Cos[2ϕ − ] − Cos[2ϕ + ]) − 2( Sin[ϕ − (t 0 )] +2
+ Sin[ϕ + (t 0 )])( Sin[ϕ − ] − Sin[ϕ + ])
−

(21)
(22)

(23)

1
(Cos[2ϕ − (t 0 )] − Cos[2ϕ + (t0 )])}
2

Substituting (14-16) to (9) and using expression:

FEL Theory

123

MOPPH037

Proceedings of FEL 2006, BESSY, Berlin, GermanyΦ 2 ≈ 2Γ −2 {( Sin[ϕ − ] − Sin[ϕ + ]) −− ( Sin[ϕ − (t 0 )] + Sin[ϕ + (t 0 )])}

t
⎧
x⎤
⎡
⎪
Φ 3 = 2(2πν )Γ − 2 ⎨ ∫ Sin ⎢4πν ⎥ dt −
c
⎣
⎦
⎪
⎩t0
t
⎫⎪
− ∫ β x (t ) Sin[4πνt ]dt ⎬
⎪⎭
t0

−2

x2
Sin ϕ~+ ⎤1 ⎧⎪ ⎡ Sin ϕ~−= (1 − β x2 (t0 ))Γ − 2
−
⎨⎢
⎥+
c
2πν ⎪⎩ ⎣ (1 − β x (t0 )) (1 + β x (t0 )) ⎦

(24)

+

(25)

and Γ = 1 + γ (t 0 )(β (t 0 ) − β x (t 0 )) .
The approximate solution of (21) we will find in the
form:
2

2

2

x
= β x (t 0 )(t − t 0 ) + α1m (α1 x1 + α 2 x 2 )cβ x = β x (t 0 ) + α 1m (α 1 x&1 + α 2 x& 2 )
x&1 =

(26)
(26)

dx1
dx
; x& 2 = 2 ; α 1 << 1; α 2 << 1;dt
dt

Substituting(26,27)

to

(21)

one

can

get

m = 1; α 1 = P; α 2 = ξ z ;
x&1 1
~
~
≈ (1 − β x2 (t 0 ))(Φ1 − Φ 3 )c2
x& 2 1~≈ (1 − β x2 (t 0 ))Φ 2
c 2

(28)

At β x ≈ 1 an electron motion, which has beating
character [7] with period T:
1
(34)
T =
2πν (1 − β x (t 0 ))

3

(35)

3

(30)

~

corresponding expressions for Φ 1 , Φ 2 by substitution ofchangeAmax =

8πν Γ 2(36)

β x2 (t 0 )Substituting expressions for β x and x from (30) to(14) and keeping items of the second order on p and ε z
one can derive approximate expression for β z
where

F0 = Sin[2πν (1 − β x (t ))t + η 0 ] +where η 0 = 2πνβ x (t 0 )t 0~
Φ 3 And after approximate integration (25) is equal to:⎧⎪⎛ 1 ⎞~⎟(1 − Cos [2πνβ x (t )t − 2η 0 ]) +
Φ 3 = Γ − 2 ⎨⎜⎜⎪⎩⎝ β x (t 0 ) ⎟⎠+ β x (t 0 )[Cos [2πνt ] − Cos[2πνt 0 ]]}p 2 c (1 − β x2 (t 0 )) (1 + β x (t 0 ) )β z = Γ −1 (1 − β x2 (t0 ))1 / 2 ( PF0 + ξ z ) + 0 P 3

ϕ~− = 2πν ((1 − β x (t 0 )) + η 0 )ϕ~+ = 2πν ((1 + β x (t 0 )) − η 0 )(31)

Integrating (28) and (29) one can get for x1 , x 2+ Cos[2πν (1 − β x (t0 ))t − η 0 ] + 2Sin[2πνt 0 ]In the same way, substituting expressions for β x andx from (30) to (15) and keeping items of the second
order on p and ε z we can produce approximate
expression for β y :A⎧⎛ 1 ⎞ ⎡ Sin 2ϕ~−x1 1
1 ⎪Sin 2ϕ~+ ⎤= (1 − β x2 (t0 ))Γ − 2−⎨⎜ − ⎟ ⎢
⎥
c 2
2πν ⎪
⎩⎝ 4 ⎠ ⎣ (1 − β x (t0 )) (1 + β x (t0 )) ⎦βy =⎡ Cos 2ϕ~−Cos 2ϕ~+ ⎤ 7+ 4 Sin[ 2πνt0 ]⎢−⎥ − Sin[ 4πνt0 ](32)⎣ (1 − β x (t0 )) (1 + β x (t0 )) ⎦ 2⎡ 1⎤
β (t )+⎢− β x (t0 )Cos[ 4πν t0 ]⎥ 2πν (t − t0 ) − x 0 Sin[ 4πν t0 ]
(
)
β
t
2
⎣ x 0
⎦
1 1
1
⎫
−
Sin[2πνβ x (t )t − 2η 0 ] + β x (t0 ) Sin[ 2πν t ]⎬2 β x2 (t0 )2⎭− Pξ z124

Amax maximum and Amin minimum beatingp 2 c (1 − β x2 (t 0 )) (1 − β x (t 0 ) )Amin =
8πν Γ 2β x2 (t 0 )Expressions for Φ 1 , Φ 2 one can produce from theandAs it is followed from expressions (2-3), at β x ≈ 1
running in the initial propagation direction wave exits
electron oscillations with larger amplitude than the wave
running in opposite direction.
Two last items in (32):
⎧ 1
1
1 ⎪
1
(1 − β x2 (t 0 )) Γ − 2
Sin [2πνβ x t − 2η 0 ] +
⎨−
2
2
2πν ⎪
⎩ 2 β x (t 0 )1⎫+ β x (t 0 ) Sin[ 2πν t ]⎬2⎭

amplitude can be described with following expressions(29)x= β x (t 0 )( t − t 0 ) + P 2 x1 + P ξ z x 2cϕ− ,ϕ+ ,x = cβ (t 0 )(t − t 0 ) ,to~~
ϕ − → ϕ − ,ϕ+ → ϕ+ .

⎫⎪β x (t0 )Cos[ 2πν t0 ]⎬⎪⎭1 − β x2 (t0 )The

β x = β x (t 0 ) + P 2 x&1 + Pξ z x& 2 ;

~

(33)

Γ

2

⎡

β x (t 0 )⎢⎣1 − β x2 (t 0 )(1 − β x2 (t 0 ))1 / 2 ⎢1 − P 2

β x (t 0 )1 − β x2 (t 0 )x& 2 −

P2
2Γ 2

F02 −

x&1 −

(38)

Pξ z

⎤
F02 ⎥ + 0 P 3
2Γ⎥⎦Integrating (37) and (38) we derive dependence
coordinates z and y on time t

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany⎧ P(−1)z = c Γ −1 (1 − β x2 (t0 ))1 / 2 ⎨*⎩ 2πν
⎡ Cos[2πν (1 − β x (t0 ))t + η0 ] Cos[2πν (1 − β x (t0 ))t − η 0 ]⎤+⎢⎥+(1 − β x (t0 ))(1 + β x (t0 ))⎣⎦P 2Cos[2πνt0 ]⎪⎫++ (ξ Z + 2Sin[2πνt0 ])(t − t0 )⎬ + z0 (t0 )2πν (1 − β x2 (t0 ))⎪⎭⎡A
β x (t0 )y = 2 (1 − β x2 (t0 ))1 / 2 ⎢(t − t0 ) − P 2x1 −Γ
1 − β x2 (t0 )
⎣⎢

(39)

beam during interaction is very actual task. It necessary tonote, that the largest increasing of the electron beamtransversal size is produced with the wave running in the
direction of electron beam propagation and not the wave
which generates the shirt wave radiation.

REFERENCES(40)[1] P.L. Kapitze and P.A.M. Dirac, Proc. Combridge Phys.
Sos, 29, 287 (1933).

∫[2] V.I Ritus, «Quantum effects of interactions elementary
particles with intense electro magnetic fields», Proceedings
Physics Institute of Lebedev. 5-151 ст. (1979).

CONCLUSION[3] A. Ts. Amatuni, Yerevan 375036 Republic of Armenia.
I.V. Pogorelsky, Brookhaven National Laboratory, 725 C,
Upton, New York 11973, (034001-034001-8) pp, (1998)⎤
β x (t 0 )PPξ− Pξ zx2 − 2 F02 dt − 2z F02 dt ⎥ + y0 (t0 )2Γ t0
1 − β x (t 0 )2Γ t 0
⎥
⎦
2

t

∫

t

The expressions derived above, describe the electron
motion in the field of standing linear polarized light wave
and allows to calculate spectrum of electron radiation
with use of methods described in [5,6].
Today, it is supposed to use interaction of relativistic
electron with intense laser beams accumulated in an
optical cavity for generation of shirt wave radiation. The
transversal sizes of the beams in the interaction point are
equal of about several tens of micrometers. For thisreason, the evaluation of transversal sizes of the electron

FEL Theory

MOPPH037[4]. A. F. Kurin, Letters JTP, 2005, vol 31. issue 13[5] Landau & Lifshic, «Theoru of field»[6] A.N. Krilov, «Proceedings of academian A.N. Krilov», vol.
3, mathematics, part two, Publishers of Academy USSR,
481p. (1949)

125

MOPPH040

Proceedings of FEL 2006, BESSY, Berlin, Germany

TRANSVERSE COHERENCE PROPERTIES OF
THE LCLS X-RAY BEAM∗
S. Reiche† , UCLA, Los Angeles, CA 90095, USA.

Abstract
Self-amplifying spontaneous radiation free-electron
lasers, such as the LCLS or the European X-FEL, rely on
the incoherent, spontaneous radiation as the seed for theamplifying process. Though this method overcomes theneed for an external seed source one drawback is the incoherence of the effective seed signal. The FEL process
allows for a natural growth of the coherence because theradiation phase information is spread out within the bunch
due to slippage and diffraction of the radiation field. However, at short wavelengths this spreading is not sufficient toachieve complete coherence. In this presentation we reporton the results of numerical simulations of the LCLS X-ray
FEL. From the obtained radiation field distribution the coherence properties are extracted to help to characterize the
FEL as a light source.

INTRODUCTION
Self-Amplified Spontaneous Emission Free-Electron
Lasers (SASE FEL) [1] allow to overcome the restriction
in wavelength imposed by existing seeding sources and to
explore new wavelength regimes. A particular interest is in
the Ångstrom wavelength regime which opens entire newclasses of experiments such the 3D imaging of individual
molecules or the analysis of chemical reaction on the femtosecond scale. Supported by the successful demonstrationof SASE FELs at wavelength down to 14 nm [2], several
X-ray FELs are currently under construction such as the
Linac Coherent Light Source (LCLS) [3] or the European
X-FEL [4].
The drawback of any SASE FEL is that it uses the spontaneous undulator radiation as its seed signal, which is intrinsically broadband and incoherent. Though the FEL process increases the longitudinal and transverse coherence byslippage and diffraction over the length of the undulator it
never reaches the coherence level of a seeded FEL amplifier. In particular at short wavelength diffraction – the main
method to the build-up transverse coherence – is ineffective
and under certain circumstances the FEL can reach saturation before obtaining transverse coherence [5].
For the design of the optical transport line and diagnostic as well as proposed experiments it is of importance tocharacterize the radiation properties of the SASE FEL asa light source in advance. For that simulations were con∗ Work supported by the U.S. Department of Energy contract DEAC02-76F00515† reiche@ucla.edu

126

Table 1: LCLS Design Parameters
Beam Energy
Beam Current
Undulator Period
Undulator Parameter
Undulator Length
Radiation Wavelength13.4 GeV
3.4 kV
3 cm
3.5
130 m
1.5 Å

ducted and the results are presented here. The work wasdone in context of the LCLS (Tab.1 list the main parametersof LCLS). The main radiation properties have been presented elsewhere [6] and this presentation focusses solely
on the fluctuation in the spot size at the detector locations(expressed by divergence and effective source location of
the FEL beam) and the degree of coherence of the FEL signal.

RADIATION SIZE AND DIVERGENCE
Because a SASE FEL has no well-defined input to be
amplified, the output is of stochastic nature and varies fromshot to shot. For the purpose of designing the X-ray beamline the evolution of the FEL pulse along the optical beamline is of importance to know. In particular the divergenceand beam size determine the design of apertures and target
sizes.
The easiest quantities to extract from the results of FEL
simulations are the rms sizes of the radiation pulse in thenear and far field. To these values the envelope equation ofa fundamental Gauss-Hermite mode [7]2z − z0(1)
w(z) = w0 1 +zr
is matched. Although Eq. 1 has three unknown parameter –the waist size w0 , the waist position z0 and Rayleigh length
zr – the system is fully deterministic because w0 and zr are
related to each other by the radiation wavelength, which isa fixed parameter for our calculation.
Higher mode content obscures the results because themode number becomes an additional unknown parameter.
Due to the similarity of the Gauss-Hermite modes to the solution of the two-dimensional harmonic oscillator in quantum mechanics [8] and the fact that the calculation of therms size is equivalent to the energy eigenvalue of the harmonic oscillator the waist size w0 has to be corrected to

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany
w0 → w0 (1+n+m), where n and m are the mode numbersof the Gauss-Hermite mode. In the far field zone (z  z0 )it can be also viewed as a reduction in the Rayleigh length
zr → zr /(1 + n + m) for a given and fixed waist size w0 .
The motivation for this work is to estimate the radiation
size of the FEL pulse at any detector position in the far
field zone. With that assumption we treat the entire highermode content as a single fundamental mode, defined by its
Rayleigh length and waist position. This will yield wrong
results at the source position by a mismatch in the actually
waist size and the assumed one, however that information
is irrelevant for the design process of the X-ray beam beamline and diagnostics.
50

40

MOPPH040

constant waist position. However in deep saturation electrons gain some energy back while the radiation field has
spread out by diffraction. This causes a disruption in thephase front at the electron location, coupling higher modeto the field distribution. As a result the diffraction is enhanced and the Rayleigh length becomes shorter.
SASE Simulations, using the LCLS design parameters,
yield a radiation pulse with about 200 spikes at the undulator exit. Each spike is analyzed and the effective source
position and Rayleigh length are extracted. To avoid thatthe analysis is obscured by the incoherent part of the radiation pulse (namely the area between spikes) only spikes are
considered which have a peak power of at least 20 % of the
maximum power in the pulse. Also we assume that over a
single spike the phase fronts are very similar and thus canbe treated as a single sample point.

zr [m]

30

20

10

0
0

20

40

60
z [m]

80

100

120

120
100

z0 [m]

80

Evaluation Point
Source Point

60

As it can be expected from the intrinsic stochastic natureof the SASE FEL process there is fluctuation in both waist
position and Rayleigh length. The distributions are shownin Fig. 2. The effective waist position is in average 38 m
within the undulator from the undulator exit and has a rms
fluctuation of 4.8 m. The average Rayleight length of 32 m
is actually larger than the steady-state case. The rms variation is 4 m. The reason for a longer Rayleigh length is thedeep saturation behavior of an SASE FEL, where the radiation further gains power in this super-radiant regime. The
phase fronts are not as disrupted as in the seeded FEL case(see above). No significant correlation between Rayleight
length and waist position has been observed.

40
20
0
0

20

40

60
z [m]

80

100

120

Figure 1: Effective Rayleigh length and waist position (topand bottom plot, respectively) along the undulator for an
FEL amplifier.
As the initial step we analyze zr and z0 for the case ofa seeded FEL with LCLS like parameters. The results areshown in Fig.1. The FEL is seeded with a radiation field(zr = 50 m) larger than the electron beam size but aftera few gain length the FEL-eigenmode is dominating. Because the mode size becomes smaller the Rayleigh length
is reduced to about 20 m. In the lethargy regime of the
FEL the radiation field remains almost unaffected and follows free-space diffraction as is seen by the almost constantwaist position over the first 10 m. The FEL eigenmode has
an intrinsic phase front curvature enhancing the diffraction
and putting the source point behind the point where thefield distribution is evaluated. At saturation gain-guiding
vanishes and the phase front curvature straightens out as
indicated by the growth in the Rayleigh length and a semi-

FEL Theory

Start-end simulations yield a different electron distribution than specified in the design case. Most notable is that
only the electron bunch as a whole is aligned and match
to the undulator axis while each slice has a certain degreeof mismatch and misalignment. In addition wakefields areincluded which alter the energy of the electron along theundulator and thus disrupt the FEL process. While thestatistic of the waist position remains almost unchanged(< z0 >= 37 m with an rms fluctuation of 5.7 m) theRayleigh length is significantly shorter with 7.8 m and arms variation of 2 m. Though some asymmetry in theelectron distribution and the mismatch of the beta-function
yield a coupling of higher modes to the emission the main
reason is the centroid motion of the electron slices. In thesaturation regime most electron slices undergo a turning
point of their betatron oscillation. The strong focusing lattice provides a rather sawtooth-like trajectory, typical forany alternating-gradient focusing system, and the electron
beam slice emits predominantly in two directions. Insteadof once central distribution in the far field there are twooverlapping distributions, left and right of the axis. The
resulting distribution is significantly broader than for thealigned case, which is reflected by the shorter Rayleighlength in the statistic.

127

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Proceedings of FEL 2006, BESSY, Berlin, Germany

25#Count20

time delay due to the path length difference from r1 and r2
falls within the temporal coherence of the signal and thus
the time dependence in the mutual coherence function canbe neglected. The mutual coherence function becomes thenthe mutual intensity J12 ≡ Γ12 (0). In analogy to the temporal coherence function, the mutual intensity function isnormalized as
J12(3)
μ12 = √J11 J22<zr> = 32 m
Szr = 4 m

15

10

5

0
20

25

30

35

40

45

zr [m]
20<z0> = -38 m
Sz0 = 4.8 m#Count

15

10

5

0
-55

-50

-45

-40
z0 - Lu [m]

-35

-30

-25

Figure 2: Histogram of Rayleigh length and waist position(top and bottom plot, respectively) for an SASE FEL pulse,
evaluated at the undulator exit.

COHERENCE
In the previous section we expressed the quality of the
SASE FEL radiation pulse by the fluctuation in the divergence and effected source position for all longitudinalmodes (spikes in the radiation power profile). With the extracted Rayleigh length the size of a corresponding fundamental Gauss-Hermite can be calculated and be comparedto the radiation size of the FEL mode as an indication forthe higher mode content. However higher modes are notnecessarily an indication for poor transverse coherence. In
the case that the phase relation between all modes remains
constant from shot to shot corresponds actually to a fullytransverse coherent pulse.
Coherence is a statistical property of a radiation source
and refers to how much you can extrapolate the radiation
phase information in time and space for any given measurement. Mathematically it is expressed by the mutual
coherence function [9]: r1 , t)E( r2 , t + τ )(2)
Γ12 (τ ) = E(While the temporal coherence function is easy to define (Γ11 (τ )) any experiment which relies on spatial coherence (e.g. diffraction on a grating) will always include
some temporal information due to the difference in the path
length to the detector. For sake of simplicity we assume
 r, t) is quasi-monochromatic so that thethat the signal E(128

to yield values between zero and one. It is referred to also
as the complex coherence factor. A zero value refers to
no correlation in phase between the observed field at thetwo postions r1 and r2 while a value of one means that thephase remains constant over time.
The complex coherence factor compares two fixed points
in the transverse plane. If we allow both points to be freeparameter μ12 would yield a four dimensional distribution.
For sake of simplicity we restrict one point to be on theundulator axis. In analogy to the temporal coherence time[10] the coherence area is defined asAc = μ12 dA(4)
and reflects the size of a usable target area for experiments,
relying on coherence, without the need to enforce coherence (e.g. with a pin hole). The optimum case would bewhen the coherence area is much larger than the actual spot
size. Note that for a fully coherent signal the coherence
area is infinite.

Figure 3: Complex coherence factor for LCLS design caseat the undulator exit.

The entire field information of a time-dependent simulation for the LCLS design case was saved and used toevaluate the mutual intensity function and complex coherence factor. The resulting distribution for μ12 is shown in
Fig. 3. The coherence area, as defined in Eq. 4, is 0.071
mm2 , about five times larger than the spot size Σ. This indicates sufficient transverse coherence over the entire spotsize and that the FEL pulse can be used for diffraction experiments without the requirement to enhance coherence
by a pin hole aperture. The growth in the transverse coherence can be seen in Fig. 4 which is a monotonically increasing function along the undulator. On the other hand

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany
the radiation diffracts faster than the build up in the coherence area within the first tens of meter. However, at around
70 m gain guiding is dominant and the spotsize remains
constant till saturation where the spot grows again due todiffraction. At around 60 m, the coherence area becomeslarger than the spot size though it does not necessarily indicate good transverse coherence. For that the ratio between
Ac and Σ must be much larger than one.
0.08

Ac, 3 [mm2]

0.06

0.04

0.02

0.00
0

20

40

60

80

100

120

140

z [m]

Figure 4: Evolution of the coherence area Ac and spotsizeΣ ( triangle and diamond shape, respectively) along the undulator.

For LCLS the FEL pulse has to propagate at least 115
m till it reaches the first user station. The coherence area isfurther increase and in the case of the LCLS design case thevalue becomes 0.32 mm2 while the spot size is 0.044 mm2 .
The reason is that noise consists typically of higher modes
which diffracts stronger than the FEL pulse itself, clearing
up the signal at the detector location. This becomes more
apparent in the case of the start-end simulation where theelectron beam slices are not aligned and matched to thefocusing lattice (see previous section). The complex coherence factor is shown in Fig. 5 and the resulting coherence
area is 0.27 mm2 while the spotsize is 0.057 mm2 . The
ratio indicates that the coherence is still sufficient.

MOPPH040

CONCLUSION
Simulations have been conducted to study the radiation
properties of the LCLS pulse, namely the variation in the
beam size at the detector location and the degree of coherence. A fundamental Gauss-Hermite has been matchedto each spike in the radiation profile to describe the divergence by an effective Rayleigh length and source position.
The average source position is about 35 m within the undulator before the undulator exit and fluctuate by about 5
m. The Rayleigh length depends strongly on the underlying model of the simulation and shows significantly smaller
values for start-end simulation. It is caused by centroid
misalignment of the individual electron slice of the LCLS
electron bunch. The build-up of transverse coherence during the FEL amplification process is sufficient to spreadthroughout the entire bunch. For the LCLS case The effective coherence area, within which the field amplitude andphase have a significant correlation to each other, is about
5 times larger than the spot size when evaluated at the firstexperimental location 115 m downstream the undulator.

REFERENCES[1] R. Bonofacio et al, Opt. Comm. 50 (1984) 373.
[2] A list can be found e.g. W.B. Colson, Proc. of the FEL 2004
Conference (2004) 706.
[3] LCLS CDR, SLAC Report No. SLAC-R-593, 2002.
[4] A.S. Schwarz, Proc. of the FEL2004Conference (2004) 85.
[5] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov,
Opt. Comm. 97 (1993) 272.
[6] S. Reiche et al, Nucl. Inst. & Meth. A483 (2002) 70.
[7] A.E. Siegman, Lasers (University Science Book, Mill Valley, CA, 1986).
[8] S. Reiche, /it Numerical Studies for Single Pass HighGain
Free-Electron Laser, Ph. D. Thesis, DESY report: DESYThesis-2000-012 (2000).
[9] J. Goodman, Statistical Optics (John Wiley and Sons, New
York, 1985).
[10] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov,
Nucl. Inst. & Meth. A407 (1998) 291.

Figure 5: Complex coherence factor for LCLS for the startend simulation, evaluated 115 m downstream of the undulator exit.

FEL Theory

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AN ANALYSIS OF SHOT NOISE PROPAGATION AND AMPLIFICATIONIN HARMONIC CASCADE FELs
Zhirong Huang∗
Stanford Linear Accelerator Center, Stanford, CA 94309, USA.
Abstract
The harmonic generation process in a harmonic cascade(HC) FEL is subject to noise degradation which is proportional to the square of the total harmonic order [1]. In
this paper, we study the shot noise evolution in the firststage modulator and radiator of a HC FEL that produces thedominant noise contributions. We derive the effective input
noise for a modulator operating in the low-gain regime, andanalyze the radiator noise for a density-modulated beam.
The significance of these noise sources in different harmonic cascade designs is also discussed.

INTRODUCTION
Harmonic cascade (HC) FELs are envisioned to generate
fully coherent x-ray pulses [2] and are currently under active development for several VUV and soft x-ray projects(see, e.g., Refs. [3, 4]). It was pointed out in Ref. [1] thatelectron shot noise can be amplified by at least the squareof the total harmonic order in this process, much like a frequency multiplication chain in radar communications [5].
Thus, it is important to understand the shot noise contributions in the harmonic generation process which may be thelimiting factors in determining the temporal coherence or
the final wavelength reach of these seeded FELs.
In a self-amplified spontaneous emission (SASE) FEL,
the one-dimensional (1D) shot noise power spectrum isργmc2 /(2π) [6], where ρ is the FEL Pierce parameter [7] and γmc 2 is the electron energy. The shot noise
power spectrum can be identified to be about the forwarddirection spontaneous undulator radiation in the first two
power gain lengths [8]. The three-dimensional (3D) correction to this simple 1D result including effects of energy
spread and emittance is given in Refs. [9, 10]. If the first
undulator of a HC FEL operates in the high-gain regime(i.e., much longer than the gain length), the SASE noise
power (integrated over the gain bandwidth) may be used
to estimate its noise contribution to a HC FEL. However,
due to the availability of high-power seed laser, the typical design of the first undulator of a HC FEL is a short(energy) modulator that operates in the low-gain (or evenno-gain) regime [3, 4, 11]. Thus, the shot noise content of
this modulator can be different from a high-gain undulator.
After the dispersion section, the density-modulated electron beam entering the radiator generates additional shotnoise. In this paper, we analyze the shot noise evolution
in the first-stage modulator and radiator of a HC FEL that
produces the dominant noise contributions. We also dis∗ zrh@slac.stanford.edu

130cuss the significance of these noise sources in different harmonic cascade designs.

ANALYSIS
To illustrate this noise degradation process, we consider
a seed signal at the fundamental wavelength λ 1 = 2π/k1 =2πc/ω1 :E1 = (E0 +ΔE)eiθ+iΔθ ≈ (E0 +ΔE)eiθ (1+iΔθ) . (1)Here E0 and θ = −ω1 t are the amplitude and the phaseof the signal, ΔE and Δθ represent any small amplitude
and phase noises (such as caused by the electron shot noise
and/or any noise carried by the seed laser). After a total of
Nh = h1 h2 ... frequency multiplication, the electric field at
the output harmonic is
ENh =G(E0 + ΔE) exp (iNh θ + iNh Δθ)≈G(E0 + ΔE)eiNh θ (1 + iNh Δθ) ,(2)

where we have assumed that N h Δθ  1 (otherwise theeffect is rather large), and G is an arbitrary function of the
field amplitude (such as the Bessel function bunching factor). Thus, the noise-to-signal ratio at the final harmonic
radiation is [1, 5]
 
 
Pn
Pn
2
= Nh
.
(3)
Ps Nh
Ps 1
Nh can be a very large number (a few hundred to a few
thousand when harmonic cascading a UV laser to an x-ray
FEL). (Pn )1 is the initial noise power which includes boththe intrinsic laser noise and the electron shot noise. Suppose that the seed laser noise is controlled to a tolerable
level, the shot noise fluctuations of the electron beam provide the essential contributions, which will be studied here.
We focus our analysis on the first-stage of a harmonic
cascade that includes a modulator, a dispersion section anda radiator (tuned to the h th harmonic of the seed wavelength) as shown in Fig. 1. This first stage has the largest
total harmonic conversion factor and hence produces thedominate noise sources. The initial longitudinal phasespace distribution function isN

F (θ0 , η0 ) =e
k1 δ(θ0 − θj )δ(η0 − ηj ) ,
χ j=1

(4)

where θ0 = −ck1 t0 describes the electron phase relative tothe EM wave (i.e., input laser field), η 0 describe the initial
relative energy deviation, and χ = N e /lb is the line density of the electron bunch with N e electrons and l b bunch

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany
seed
laser

Modulator

electrons
……...

λ1

D

Radiatorλh=λ1/hto next
stage

Figure 1: Schematic of the first-stage HC FEL.

length. The normalization in Eq. (4) is chosen so that theensemble average
F (θ0 , η0 )dη0 = 1

In typical HC FEL designs [3, 4, 11], the first undulator
is relatively short and is mainly an energy modulator, thenwe have(6)

where ηs is the energy modulation amplitude induced by
the seed laser field, and η n is the energy modulation induced by the noisy spontaneous undulator radiation.
A dispersion section immediately after the modulator
can convert the beam energy modulation into a density
modulation. This is accompanied by a magnetic chicanethat changes the phase of the electron according to its energy deviation:
θ1 = θ0 + k1 R56 η1 = θ0 + Dη1 .

(7)

Here R56 is the net momentum compaction of the chicane together with the first undulator (modulator), andD = k1 R56 . The harmonic bunching near the h th harmonic (when ν ∼ h) can be found asdθ1dη1 e−iνθ1 F (θ1 , η1 )
k1 lb

dθ0
dη0 e−iν[θ0 +D(η0 +ηs sin θ0 +ηn )] F (θ0 , η0 ) .
=
k1 lb
(8)

bν =

Here we have assumed the laser pulse length is at least
as long as the electron bunch length. If the laser pulse
only overlaps a fraction of the electron bunch, l b should
be taken to be the laser pulse length instead of the electron pulse length, then N e represents number of electrons
within lb . Let us also assume that the modulated part of theelectron bunch is long compared to the laser wavelength(i.e., k1 lb  1), and that the electron energy distribution
is Gaussian with a slice rms energy spread σ η , we expand
Eq. (8) in Bessel series of ηs and to the first-order in η n (asFEL Theory|hDηn |  1) to obtain


∞

dθ0
dη0
Jp (−hDηs )ei(p−ν)θ0 e−iνDη0
bν =
k1 lb
p=−∞
×(1 − ihDηn )F (θ0 , η0 )

Ne
∞

1 
Jp (−hDηs )ei(p−ν)θj e−iνDηj
=
N
e
p=−∞
j=1
h2 D2 ση2−ihD exp −
2



(5)

for a constant current profile.

η1 =η0 + ηs sin θ0 + ηn (θ0 ) ,MOPPH042dθ0 i(p−ν)θ0eηn (θ0 ) ,
k1 lb
(9)

where we have applied the smooth distribution function in
the second term of the bracket as η n is treated as a small
perturbation.
When ν = p = h, the first term in the bracket produces
the desired harmonic bunching signal asNeJh (−hDηs ) bh =e−ihDηjNe
j=1=Jh (−hDηs ) exp −h2 D2 ση2
2

.

(10)

When ν = h, the first term produces the noise bunching in
the radiator as the ensemble average|brν |2  =

∞
1  2
1
J (−hDηs ) =.
Ne p=−∞ pNe(11)Thus, the modulated bunch generates the same amount of
the shot noise bunching in the radiator as a fresh electron
bunch.
The second term in the bracket of Eq. (9) is the noisebunching originated from the modulator. As η n is nearly asinusoidal function of θ 0 , it can be written ash2 D2 ση2m
− ihDJh+1 (−hDηs )ηn+ (Δν)
bν = exp −2− ihDJh−1 (−hDηs )ηn− (Δν) ,where Δν = ν − h anddθ0 i(±1−Δν)θ0±eηn (θ0 )ηn (Δν) =
k1 lb

(12)

(13)

is the Fourier component of η n near the first undulator(modulator) resonant frequency ck 1 .
If x = hDηs  1, we can expand J h (x) ∼ (x/2)h /h!;If the dispersion strength is optimized to yield the maximum |bh | at hDηs ∼ h or D ∼ 1/ηs , then Jh ∼ Jh±1 ∼0.3. In either case, we can approximate the bunching ratioas2bm|η ± (Δν)|2ν≈ 4h2 n 2
.
bh
ηs

(14)

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Proceedings of FEL 2006, BESSY, Berlin, Germany

The power spectrum dP/dω in the radiator is proportional
to |b|2 . Integrating over their respective bandwidths in theradiator, we obtain the modulator noise-to-signal power ratio as
 mΔωnm |ηn± (Δν)|2 
Pn
= 4h2
,
(15)
Ps h
Δωs ηs2

laser spot (i.e., σx ≈ σL ), we havewhere Δωs = 2πc/lb is the Fourier transform limited
bandwidth for the signal, and Δω nm is the bandwidth ofthe modulator noise. For simplicity, we assume that thefull modulator bandwidth is much smaller than the full radiator bandwidth centered around a much higher frequency(i.e., Δωm = Δνm ω1 < Δωr = Δνr ωh ), then we haveΔωnm = Δωm = Δνm ω1 without convoluting the bandwidths of the modulator and the radiator.
The laser-induced energy modulation amplitude can be
estimated as

Equation (21) can be shown to be the spontaneous undulator radiation in the forward direction (within a solid angle
λ21 /(2πσx2 ) and a full bandwidth ω 1 /Nu1 ). Equation (22)holds for K 12  1 and can be used for a quick estimationof modulator noise power. If the modulator length is much
shorter than two power gain lengths, then the modulator
noise power is much smaller than the usual SASE noise
power as discussed in the introduction.
As shown in Eq. (11), the density-modulated beam generates the same shot noise bunching. The additional radiator noise-to-signal ratio can be estimated asηs2 = K12 [JJ]2

L2u1 PL2 P ,γ 4 σL0(16)

where P0 = IA mc2 /e ≈ 8.7 GW. Using the onedimensional FEL theory, we find that the Fourier component of the shot-noise-induced energy modulation is
ηn± (Δν) =1 I
8γ 3 IA

λu1 K1 [JJ]
σx

2

2
Nu1
f (ν̄)N×e
1 ei(±1+Δν)θj ,Ne j=1(17)

where ν̄ = πΔνNu1 is the scaled detune in the first undulator with Nu1 period, andf (ν̄) =e−iν̄ sin(ν̄)/ν̄ − 1
iν̄


(18)

describes the energy modulation bandwidth due to the shotnoise with a relative bandwidth given by Δν m = 1/Nu1
for Nu1  1. Inserting Eq. (16) and (17) into Eq. (15), we
obtain finally
 2 
 m
2
2
2
mc /e IPn
2 λu1 Nu1 re σL K1 [JJ]
=h
Ps h
8σx4
1 + K12 /2
PL
 m
Pn
=h2
.
(19)
PL 1
Thus, the effective modulator noise isPnm =2
λu Nu1 re σL
K12 [JJ]2 mc2
I.
8σx4
1 + K12 /2 e

(20)

For efficient laser-beam interaction in the modulator,
 the laser spot size is usually chosen to be σ L =λ1 λu1 Nu1 /8π (i.e., the Rayleigh length is one half theundulator length with the laser waist located at the middle of the undulator). When the electron beam matches the132

λu1 Nu1 re K12 [JJ]2 mc2
I
8σx2
1 + K12 /2 e
πre mc2
I.
≈
λ1 e

Pnm ≈



Pnr
Ps

(21)
(22)



Δωnr |brν |2 Δωnr /Ne=
2 2 2 ,22Δωs bhΔωs Jh (hDηs )e−h D σηh(23)
where Δωnr = Δωr = Δνr ωh is the noise bandwidth in
the radiator. If the radiator is also a low-gain device, thenΔνr ≈ 1/Nu2 . If the radiator is a high-gain device, thenΔνr ≈ 2ρ. In either case we can write
 r
1/Nlc
1/Nlc
Pn
=
= 2
(24)
2 2 2 ,
2
Ps hbh
Jh (hDηs )e−h D ση=where Nlc = Ne lc /lb is the number of electrons within
the radiator coherence length l c = λh /(Δνr ). Note thatthe radiator noise-to-signal ratio is independent of the signal laser power PL , but depends strongly on the harmonicbunching strength. This has implications on different designs of HC FELs to be discussed below.

NUMERICAL EXAMPLES ANDDISCUSSIONS
Equations (20), (22), and (24) are the main results ofthis paper and may be used to estimate the shot-noise-tosignal ratio of a HC FEL using a high-power seed laser
in a short modulator. Let us take some numerical examples to illustrate the significance of various noise contributions. Consider the BESSY HC FEL design at the final
radiation wavelength λ f = 1.24 nm [3]. For I = 1.75 kA
and λ1 = 297.50 nm, the modulator noise power according
to Eq. (22) is 26 W. If the laser power is 100 MW, then themodulator noise-to-signal ratio at the final wavelength after
the total harmonic number N h = 297.50/1.24 = 240 is


Pnm
Ps


Nh

= Nh2 ×26
≈ 1.5% .
100 × 106(25)

Thus, the modulator noise contribution is noticeable but
still small. In passing, we note the bandwidth of the modu-

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany
lator noise is about ω 1 /Nu1 , hence the final relative bandwidth of the first-stage modulator noise is
1
Δωnm
=
.
ωf
Nh Nu1(26)

This may still be a small relative bandwidth than a SASE
FEL at 1 nm. For example, , N h = 240, Nu1 = 18 in the
BESSY FEL, and Δωnm /ωf ∼ 2 × 10−4 . Thus, even when
the final noise level due to the first modulator is comparable to the signal strength, the temporal coherence of the
HC FEL is still improved as any noisy structure within theslippage length λ1 Nu1 of the first modulator is naturallysmoothed. This noise filtering effect was observed in the
LUX HC FEL simulations [11].
Let us now consider the radiator noise. First, we takeI = 1.75 kA, Nu2 = 40, and λh = 297.50/5 = 59.50 nm,
then we have N lc = Ne Nu2 λh /lb ∼ 108 in Eq. (24). The
BESSY FEL employs a fresh bunch approach that shifts
the output radiation to a fresh part of the bunch for the
next-stage interaction and hence allows for a large energy
modulation to be induced in the part of the electron bunchthat overlaps with a very short laser signal [12]. In thisapproach, the harmonic bunching is usually maximized bychoosing D ∼ 1/ηs . If hDση  1, we have b2h ∼ 0.1.
The increase of the energy spread due to the large energy
modulation is not an issue as the next stage interaction occurs at a fresh part of the bunch with the same initial energy
spread. In this case, the radiator noise-to-signal ratio given
by Eq. (24) is extremely small, at the 10 −7 level. Even after another harmonic conversion factor of 48 (from the radiator wavelength λ h = 59.50 nm to the final wavelength
λf = 1.24 nm), the contribution from the radiator noise isstill small.

MOPPH042

ACKNOWLEDGMENTS
The author wishes to thank W. Fawley, W. Graves, K.J. Kim, L.-H. Yu, and J. Wu for many useful discussions.
This work was supported by the U.S. Department of Energy
contract No. DE-AC02-76SF00515.

REFERENCES[1] E.L. Saldin, E.A. Schneidmiller, and M.Y. Yurkov, Opt.
Commun. 202, 169 (2002).
[2] L.-H. Yu and J.H. Wu, Nucl. Instrum. Methods Phys. Res.,
Sect. A 483, 493 (2002).
[3] BESSYFELTechnical
DesignReport,http://www.bessy.de/publicRelations/publications/files/TDR
WEB.pdf.
[4] C. J. Bocchetta et al, In Proceedings of the 2005 Free Electron Laser Conference, Stanford, CA, USA, 2005.
[5] W. Robins, Phase noise in signal sources. Peter Peregrinus
Ltd., London, 1982.
[6] K.-J. Kim, Phys. Rev. Lett. 57, 1871 (1986).
[7] R. Bonifacio, C. Pellegrini, and L.M. Narducci, Opt. Commun. 50, 373 (1984).
[8] L.-H. Yu and S. Krinsky, Nucl. Instrum. Methods Phys. Res.,
Sect. A 285, 119 (1989).
[9] M. Xie, Nucl. Instrum. Methods Phys. Res., Sect. A 475, 51(2001).
[10] Z. Huang and K.-J. Kim, Nucl. Instrum. Methods Phys. Res.,
Sect. A 475, 59 (2001).
[11] W. Fawley, W. Barletta, J. Corlett, and A. Zholents, In 2003
Particle Accelerator Conference, Portland, OR, USA, 2003.
[12] I. Ben-Zvi, K. Yang, and L.-H. Yu, Nucl. Instrum. Methods
Phys. Res. Sec. A 318, 726 (1992).

Nevertheless, the fresh bunch technique requires a tighttiming control between the short laser pulse and the electron bunch. In addition, experiments demanding most photons in a narrow bandwidth may benefit from using a laser
pulse longer than the electron bunch length to seed thewhole bunch. In this case, the induced energy modulation must be controlled to a small level in order not to degrade the beam energy spread (i.e., η s < ση ). In viewof Eq. (10), the harmonic bunching cannot be maximized
as hDηs < hDση < 1, then the radiator noise-to-signal
ratio can increase dramatically. For example, in the wholebunch seeding example described in Ref. [1], the secondharmonic bunching at the radiation wavelength 130 nm isonly b22 ∼ 0.25 × 10−4 in order to avoid a significant increase in the energy spread. Thus, the radiator noise-tosignal ratio given by Eq. (24) can be much larger (∼ 10 −3 ).
An additional harmonic conversion factor of 16 (to the final wavelength at 8 nm) will amplify this radiator noise-tosignal ratio to 25%. Therefore, the shot noise contribution,
especially in the radiator section, may limit the temporal
coherence of such a harmonic cascade.

FEL Theory

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Proceedings of FEL 2006, BESSY, Berlin, Germany

OPTICAL BEAM QUALITY IN FREE-ELECTRON LASERS*
P.A. Sprangle#, Naval Research Laboratory, Washington, DC, 20375, U.S.A.
H.P. Freund, Science Applications International Corp., McLean, VA 22102, U.S.A.
J. Peñano, Naval Research Laboratory, Washington, DC, 20375, U.S.A.
B. Hafizi, Icarus Research Inc., P.O. Box 30780, Bethesda, MD 20824-0780, U.S.A.
Abstract
It is widely known that the mode quality of the output
of free-electron lasers (FELs) is near the diffraction limit.
In this paper, we analyze the optical mode quality in FELs
using the M2 parameter, which is an optical analogue ofthe emittance for particle beams and measures thedivergence of the optical mode. For a perfect Gaussian
beam M2 = 1 and increases as the mode quality
deteriorates (i.e., the divergence angle and the higher
order mode content increase). Thus, the optical mode isoften described as M2 times diffraction limited in the far
field. We show how M2 may be calculated in two ways:(1) by a direct integration over the transverse mode
structure, and (2) by allowing the mode to expand beyond
the wiggler and analyzing the divergence. We thensimulate a forthcoming experiment at Brookhaven
National Laboratory using the MEDUSA simulation codeand show that M2, as expected, is near unity at saturation.

INTRODUCTION
It widely known that the mode quality of the output of
free-electron lasers (FEL) is near the diffraction limit [13]. The question of mode quality is relevant toatmospheric propagation of high power FELs [4,5].
Numerical analysis has shown that the mode content inoscillators is predominantly in the TEM00 mode bysolution of the paraxial wave equation for a fixed electron
beam profile and the subsequent decomposition into
Gaussian optical modes [1]. The optical mode quality wasobserved in the Los Alamos FEL oscillator [2,3] where
the mode was shown to be near the diffraction limit. The
mode quality in this experiment was characterized by ameasurement of the Strehl ratio, which is defined as theratio of the on-axis intensity at the mode waist to theintensity of a pure Gaussian mode (TEM00) with the same
spot size at the lens plane. However, the Strehl ratio isdifficult to determine for optical modes that differ
appreciably from a Gaussian. Higher order mode content
is likely to be more important in single-pass FELs, such
as Master Oscillator Power Amplifiers (MOPA) or SelfAmplified Spontaneous Emission (SASE) configurations
that are operated past saturation. Hence, an alternate andless ambiguous measure of beam quality is desirable.
In this paper, we quantify beam quality by means of theM2 parameter, which is an optical analog of the emittancefor particle beams and provides a measure of the*Work supported by the JTO and ONR#
sprangle@ppd.nrl.navy.mil

134

divergence of the optical mode [6-8]. It is equal to unity
for a perfect Gaussian beam (pure TEM00) and increases
as the mode quality deteriorates (i.e., the divergence angleof the mode and the higher order mode content increase).
Thus, the optical mode is often described as M2 times
diffraction limited in the far field. The M2 parameter, as
well as optical mode distortion due to mirror heating wasmeasured in the FEL oscillator experiment at Thomas
Jefferson National Accelerator Facility [9]. This
experiment produced average powers in excess of 2 kW ata wavelength of 3.1 microns. Measurements indicatedbeam quality near the diffraction limit with M2 = 1.1 atthe output mirror for powers up to about 350 W. As thepower increased beyond 350 W, M2 increased andreached values of about 2 for powers of 500 W. However,much of the increase in M2 that occurred at higher powerincreased was attributed to mirror distortions and not thewave-particle interaction in the FEL. As a result, themode quality may be improved in high-power oscillators
using mirrors that compensate for distortions. Note thatthe mode quality in high-power amplifiers is governedsolely by the FEL interaction.
In this paper we determine M2 in two ways: (1) by adirect integration over the transverse mode structure, and(2) by allowing the mode to expand beyond the wiggler
and analyzing the mode divergence. This is discussed inSec. II. In Sec. III we study M2 in FEL amplifiers using
the MEDUSA simulation code [10,11] and then simulate
a forthcoming experiment at the Source Development
Laboratory at Brookhaven National Laboratory. A
summary and discussion is given in Sec. IV.

THE M2 PARAMETER
A perfect Gaussian beam experiences parabolic
expansion in which the spot size increases on either sideof the waist via [12]λ2z − z0 ,(1)
π w02
where w(z) is the spot size, w0 is the minimum spot size(i.e., at the waist), λ is the wavelength, and z0 is thelocation of the waist. Note that the Rayleigh range is
given by zR = πw02/λ so that w2(z0 ± zR) = 2w02 and theoptical mode area increases by a factor of two over thecourse of the Rayleigh range. The asymptotic diffraction
angle is given by tan θD = λ/πw0 = w0/zR. Since the waist
size is, typically, much less than the Rayleigh range, thismeans that θD ≈ λ/πw0.
w 2 z = w02 +2

2

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

A similar expression describing parabolic expansion
also holds for a more general optical beam that includes
higher order modes and can be written as [6-8]
W 2 z = W02 + M 4

λ22z − z0 ,2(2)πW
where the upper case W0 corresponds to the average waist
size for the overall optical beam, anddxdyr 2 I x,y,z2,(3)
W z =2
dxdyI x,y,z2
0denotes the spot size of the overall optical mode whereI(x,y,z) is the average (over a wave period) intensity.
Observe that in the limit of a purely Gaussian opticalbeam, W(z) = w(z) and M2 = 1. As such M2 (≥ 1) is ameasure of the optical beam quality and is the opticalanalogue of the emittance for particle beams. Note alsothat this definition of M2 can unambiguously deal with
optical modes that differ markedly from a pure Gaussian,unlike the definition of the Strehl ratio. This asymptotic
divergence angle θD is given bytan θ D = M 2

λ
,
πW0

(4)

so that θD ≈ M2λ/πW0 for small divergence angles. This isshown schematically in Fig. 1.

W(z)θD = M 2

√2W0
W0

λ
πW0

W2 z = w2 z
where

S2 = Σ 2
l,n

S2
.
S1

(6)

2
,
S 1 = Σ 2 l + nl!n!δ A l,nl,nl!n! l + n + 1 δ A

l+n

(7)

2
l,n

+ 2 l + 1 l + 2 δ A l,n1 δ A l1+ 2,n + δ A l,n2 δ A l2+ 2,n+ 2 n + 1 n + 2 δ A l,n1 δ A l,n1 + 2 + δ A l,n2 δ A l,n2 + 2 , (8)and δ A 2l,n = δ A l,n1 + δ A l,n2 . Observe that S1 = S2 for a pure
Gaussian Mode (TEM00) and we recover W(z) = w(z).
We now discuss the calculation of the M2 parameter. If
we express the overall field in the form δA(x,t) =A(x)êxcos[k0z – ωt +θ(x)], then it may be shown that
2

2

−1

M2=

dxdyI

×

1/2 2
∂θ 2
dxdy ∂Ι+I∂r∂r∂θ 2 1/2, (9)−dxdyrI

dxdyr 2 I∂rwhere the intensity is I = (ωk0/8π)A2. As a result, it can beshown thatW 2 z 2w 2 z
S 32 S 4 1/2
,
(10)
M2= 2
−
1
−
+
w z W2 z
S 22 S 2
where

S 3 = 2Σ 2 l + nl!n! l + 1 l + 2 δ A l,n2 δ A l1+ 2,n−δ A l,n1 δ A l2+ 2,nl,n+ n + 1 n + 2 δ A l,n2 + 2δ A l,n1 − δ A l,n2 δ A l,n1 + 2 , (11)S 4 = Σ Fl,l',n,n' δ A l,n1 δ A l'1,n' − δ A l,n2 δ A l'2,n' ,
l,l',n,n'z0

z0 + zRzπ

Figure 1: Schematic illustration of parabolic mode
expansion
In general, the optical mode may be expressed as asuperposition of Gauss-Hermite modes and we can write

δA x,t =e xΣ e l,n x,y δ A l,n1 cos ϕ x,t + δ A l,n2 sin ϕ x,t , (5)l,nwhere el,n(x,y) = exp[−r2/w(z)2]Hl[√2x/w(z)]Hn[√2y/w(z)],Hl is the Hermite polynomial of order l, ϕ(x,t) = k0z – ωt
+ α(z)r2/w(z)2 for wavenumber k0 (= ω/c) and angularfrequency ω, and α(z) describes the curvature of the phasefront. For propagation in vacuo, the amplitudes δA(1,2) areconstant, ϕ is the overall phase, and the spot size andcurvature vary as w(z) = w0[1 + (z – z0)2/zR2]1/2 and α(z) =(z – z0)/zR. However, the optical mode in an FEL is both
amplified and guided by the interaction with the electron
beam so that the amplitudes, spot size and curvature willvary in a more complex way along the length of the
wiggler. Nevertheless, it may be shown that the overall
spot size is given in terms of this representation by

(12)

and
Fl,l',n,n' = 1

FEL Theory

MOPPH044

2π
0

∞

dθ

d ρρexp −ρ20

× cosθ H l' ρ cosθ H n ρ sinθ+ sinθ H l ρ cosθ H n' ρ sinθ× cosθ H ' ρ cosθ H ρ sinθl'n'

+ sinθ H l ' ρ cosθ H n' ' ρ sinθ, (13)

is a coefficient that depends only on the mode indices. In
the limit of a purely Gaussian mode S1 = S2, W(z) = w(z),and S3 = S4 = 0 so that Eq. (10) yields M2 = 1 as expected.
In principle, if we know the modal decomposition at theexit from the wiggler in an FEL (including the mode
amplitudes, the spot size w and the curvature α), then M2
can be calculated for the output optical mode using theabove method. However, if there is significant higher
order mode content, then it can prove numericallyarduous to evaluate the Fl,l’,n,n’ coefficients. Therefore, it isuseful to have an alternate technique for obtaining M2.
One such technique makes use of the expansion of the
optical mode. If the spot size is known at three different
locations beyond the end of the wiggler, then the threeequations Wi2 = W02 + M4θ02(zi – z0)2 for i = 1−3 can besolved for M2 where θ0 = πW0/λ. Thus,

135

Proceedings of FEL 2006, BESSY, Berlin, GermanyM =λπ zi − z0

Wi2
−1 ,
W02

amplifier and can provide up to several tens of MW;
however, this is larger than needed for the experiment thatwill use about 10-100 kW of seed power for saturation to
be achieved within the length of the wiggler.

(14)

9

10

8

10

W0=

W + z1−z0

20.05

Power (W)

7

and
2
1

0.06

z3−z1 W22−W12 − z2−z1 W32−W12
z3 − z1 z3 − z2 z2 − z1

10

0.04

6

10

0.03

5

10

c

4

(16)

10

0.01
<y − y >c

3

10

NUMERICAL ANALYSIS
For simulation purposes, we use the 3-D FEL
simulation code MEDUSA [10,11] which can model
planar or helical wiggler geometry and treats theelectromagnetic field as a superposition of Gaussianmodes (Hermite or Laguerre) and uses an adaptive
eigenmode algorithm called the Source-Dependent
Expansion [13] to self-consistently describe the guidingof the optical mode through the wiggler and which
reproduces free-space diffraction in the absence of the
wiggler. The field equations are integrated simultaneouslywith the 3-D Lorentz force equations for an ensemble ofelectrons. No wiggler-average orbit approximation isused, and MEDUSA can propagate the electron beamthrough a complex wiggler/transport line including
multiple wiggler sections, quadrupole and dipole
corrector magnets, FODO lattices, and magnetic chicanes.
The example under consideration is that of a seeded
amplifier experiment to be conducted at the Source
Development Laboratory at Brookhaven National
Laboratory [14] that will operate at a wavelength of 0.8
microns using the VISA wiggler [15]. The electron beam
will have an energy of about 72.3 MeV and a peak currentof 300 A. The emittance and rms energy spread are 2.0
mm-mrad and 0.01% respectively. The VISA wiggler is a
Halbach design using NdFeB magnets and incorporates a
FODO lattice for stronger beam focusing. The wiggler
period is 1.8 cm and the maximum on-axis field strengthis 7.5 kG with a field error of 0.4% and a gap of 6.0 mm.
The FODO cells have a length of 24.75 cm and eachquadrupole has a length of 9.0 cm and a focusing gradientof 33.3 T/m. Hence, the separation between quadrupolesis 12.375 cm. The VISA wiggler was built in segments,
and the wiggler to be used in the experiment will have
110 periods of uniform field strength. The photo-cathodedrive laser is also used to provide the seed for the

136

0.0

0.5

1.0

1.5

2.0

0
2.5

z (m)

Figure 2: Evolution of the power, spot size and beamenvelopes in the x- and y-directions.
The first case we consider makes use of 34 GaussHermite modes and assumes a seed power of 10 kW. This
yields saturation at the end of the wiggler at a power levelof 115 MW. The evolution of the power, overall spot sizeof the optical mode, and the beam envelopes in the x- andy-directions is shown in Fig. 2. Observe that the beam is
not perfectly matched into the wiggler/FODO lattice since
the beam envelopes in the x- and y-directions vary in the
FODO lattice and that the overall mode spot size expands
and contracts with the beam envelope showing the opticalguiding of the radiation; however, the guiding is notstrong enough for the optical mode to follow all thevariations in the beam envelope.

1.2
1.0

Amplitude
Normalized Mode

This technique can be applied either in experiment or
simulation. When used in simulation (experiment), theoptical mode must be allowed to propagate into free space
and the overall spot size [(3) or (6)] must be calculated(measured) at three such points.

0.02<x − x >Spot Size (cm)for any choice of i, wherez + 2z1 + z2
z0 = 342222
z3 − z2 z3 − z1 W2 − W1 + z2 − z1 W3 − W1 , (15)+4z3 − z1 W22 − W12 − z2 − z1 W32 − W12

0.8
0.6
0.4
10

0.2

8
6

0.0

4
2
8

6

4

0
-2
2

0

y/w
0

0

2

x/ w

MOPPH044

-4
-2

-4

-6
-6

-8

-8

Figure 3: Transverse mode pattern at the wiggler exit fora seed power of 10 kW.
The use of 34 modes in the simulation means that very
high order modes are included. Because of this the

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

method for calculating M2 based on integration over thetransverse mode profile is numerically arduous, and wechoose rather to allow the mode to propagate beyond theend of the wiggler and use the three-point solution given
in Eq. (14). This can be accomplished easily insimulation simply by terminating the wiggler, after which
the Source-Dependent Expansion reproduces free-space
propagation when the resonant wave-particle interaction
ceases. The result of this calculation shows that M2 = 1.45
for the optical mode at the wiggler exit. This is close to
the diffraction limit as expected in FELs and corresponds
to a near-Gaussian mode pattern as shown in anormalized transverse mode pattern in Fig. 3.
1.5
1.4

SUMMARY AND DISCUSSIONIn summary, we have discussed the determination of M2
in FELs by two methods. One is a direct calculation based
upon the mode decomposition at any point within the
wiggler, and the other relies on a three-point fit to theoptical mode spot size as it propagates beyond the end of
the wiggler. These techniques have been applied to an
example that corresponds to an amplifier experiment at
Brookhaven National Laboratory. We found that thesimulation required a relatively large number of higher
order modes to achieve convergence in the determinationof M2. While MEDUSA employs a Gaussian modal
representation of the electromagnetic field, it is likely that
this implies that alternate techniques using a transverse
field solver will require a relatively fine mesh to achieve
the same result. Further, the results indicate that the beam
quality to be expected is near-diffraction limited when the
wiggler length is comparable to the saturation length.

M

2

1.3

MOPPH044

1.2

REFERENCES
1.1
1.0[1] D.C. Qiumby and J. Slater, IEEE J. Quantum
Electron. QE-19 (1983) 800.
0

5

10

15

20

25

30

35

Number of Modes

Figure 4: Variation in M2 versus the number of modes
included in the simulation showing convergence after
about 20 modes.
An important issue in modeling the beam quality in
FELs is the convergence of the simulation with respect tothe number of modes in the superposition. The number ofmodes required to obtain reasonable values for thesaturated power is generally smaller than that required toobtain an accurate determination of the optical mode
quality as measured by M2. For example, simulation
using 6 Gauss-Hermite modes also yields a saturated
power of 115 MW but the exponentiation length issomewhat shorter and M2 = 1.26. Hence, it is important todetermine the number of modes required to reachconvergence. This is shown in Fig. 4 for these parameters
where we plot M2 versus the number of Gauss-Hermite
modes in the superposition. It is clear from the figure thatconvergence is achieved using about 20-25 modes for M2= 1.45. It is important to bear in mind, however, that the
number of modes required for convergence will vary withthe specific parameters of interest. In particular, for
optical guiding to be effective the exponentiation lengthmust be shorter than the Rayleigh range. In general, thesmaller the ratio between the exponentiation length andthe Rayleigh range, the fewer the number of modes thatwill be needed to achieve convergence.

[2] B.E. Newnam et al., IEEE J. Quantum Electron. QE21 (1985) 867.
[3] B.E. Newnam et al., Nucl. Instrum. Meth. A237
(1985) 187.
[4] P.A. Sprangle, B. Hafizi, and J.R. Peñano, IEEE J.
Quantum Electron. 40 (2004) 1739.
[5] P.A. Sprangle, J.R. Peñano, and B. Hafizi, J. Directed
Energy (to appear 2006).
[6] A.E. Siegman, Proc. Soc. Photo-Opt. Instrum. Eng.
1224 (1990) 2.
[7] T.F. Johnson, Jr., Laser Focus World 26 (1990) 173.
[8] A.E. Siegman, IEEE J. Quantum Electron. 27 (1991)
1146.
[9] S.V. Benson, J. Gubeli, and M. Shinn, Nucl. Instrum.
Meth. A483 (2002) 434.
[10] H.P. Freund et al., IEEE J. Quantum Electron. 36(2000) 275.
[11] H.P. Freund, Phys. Rev. ST-AB 8 (2005) 110701.
[12] A.E. Siegman, Lasers (University Science Books,
Mill Valley, CA, 1986).
[13] P.A. Sprangle, A. Ting, and C.M. Tang, Phys. Rev.
A 36 (1987) 2773.
[14] T. Watanbe et al., “Design study of a compact
megawatt class FEL amplifier based on the VISA
undulator,” presented at the 27th Int’l. Free Electron
Laser Conference, Stanford, CA, 21-26 August 2005.
[15] R. Carr et al., Phys. Rev. ST-AB, 4 (2001) 122402.

FEL Theory

137

MOPPH046

Proceedings of FEL 2006, BESSY, Berlin, Germany

SEEDING THE FEL OF THE SCSS PROTOTYPE ACCELERATORWITH HARMONICS OF A TI: SA LASER PRODUCED IN GAS.
G. Lambert, M. Bougeard, W. Boutu, B. Carre, D. Garzella, M. Labat, CEA, Saclay, France
M.E. Couprie, O. Chubar, Synchrotron Soleil, Saint-Aubin, France
G. Lambert, T. Hara, H. Kitamura, T. Shintake SPring-8/RIKEN Harima Institute, Hyogo, Japan.
Abstract
A particular seeded configuration will be tested in 2006
on the SCSS prototype accelerator (SPring-8 Compact
Sase Source, Japan). This facility is based on a thermioniccathode electron gun (1 nC), a C-band LINAC (5712
MHz, 35 MV/m) and an in-vacuum undulator (15 mm ofperiod. 2 sections of 4.5 m length). The maximum
electron beam energy is 250 MeV and the SASE emission
from visible to 60 nm can be obtained. The externalsource, coming from the High order Harmonic Generation(HHG) process, can be tuned from the 3rd (266 nm) to the13th harmonic (60 nm) of a Ti: Sa laser generated in a gas
cell. The experiment contains a first chamber, dedicatedto harmonic generation and a second one for harmonic
beam diagnostics and adaptation of the harmonic waist in
the first undulator section. The tests have been performedin Saclay (15 mJ, 10 Hz, 50 fs). An energy of 2 µJ with ahigh stability for the 3rd harmonic and a good transversal
shape with an optimized energy level and a high stability
for the 13th harmonic have been obtained at the first
undulator center place. The performances using analyticalformulas, GENESIS and SRW have been updated. The
chambers will be installed on the SCSS prototype
accelerator in the beginning of October for the seeding
tests.

INTRODUCTION

the SCSS prototype accelerator FEL [7] has been observed
at 49 nm. The characteristics of the electron beam,
undulators, laser and harmonics come from ref. [8] and thebasic layout is given in Figure 1.

Figure 1: General layout of the seeding experiment withharmonics generated in a gas cell.

HHG SYSTEM
The harmonic generation in gas results from the strong
non linear polarization induced on the rare gases atoms,
such as Ar, Xe, Ne and He, by the focused intenseelectromagnetic field ELaser of a "pump" laser [9]. In ourcase, a 7 m focal length lens focuses a Ti: Sa laser in acell (Figure 2) filled with Xe or Ar gases, which are welladapted for the generation of 60 nm radiation. The laserpasses through the cell and is aligned by means of two
pinholes of 1 mm of diameter, made on Tantalus plates,
which create a constant leak of gas.

These last years, most of the new FEL sources werededicated to the so-called Self Amplified SpontaneousEmission (SASE) [1], which provides with a very highbrightness photon beam at short wavelength but withlimited temporal coherence. Consequently, a few FEL
facilities, like ARC-EN-CIEL (Accelerator Radiation
Complex for Enhanced Coherent Intense Extended Light) a
French proposal for a 4th generation light source [2], haveadopted a new configuration: a seeding configuration, in
which High order Harmonics of a laser Generated in gas(HHG) are injected into a FEL, giving its full coherence
property to the emitted radiation. It also reduces thesaturation lengths allowing a more compact source [3]. In
addition, other SASE projects have decided to implement iton their facility: SCSS prototype accelerator (SPring-8
Compact Sase Source) [4] and SPARC (Sorgente Pulsata e
Amplificata di Radiazione Coerente) [5]. Recently such a Figure 2: Gas cell system producing HHG light.
seeding experiment with high harmonics produced in gases
The general experiment is based on a system of two
was performed in an X-ray laser [6]. It is proposed here to chambers (Figure 3).
seed the FEL of the SCSS prototype accelerator at a 60 nm
radiation, corresponding to the 13th harmonic of a Ti: Sa
laser (H13) generated in a gas cell. June, the first lasing of138

Seeded FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH046

FIRST HHG TESTS IN SACLAY

Figure 3: General layout of the HHG system.
The first one is dedicated to the HHG production(Figure 4). The cell position is motorized for accuratealignment of the IR laser and optimization of theharmonic production rate.

The first tests have been performed in Saclay with
the LUCA laser beam (1 to 15 mJ, 20 Hz, 50 fs, 5 m longof focal lens). In the starting phase of tests, the seeding
wavelength was the 3rd harmonic (H3, 266 nm), which is amore intense and easily useable source (can bepropagated outside vacuum, and detected with a VUVphotomultiplier). The behavior of the harmonics (Figure 6
for the 3rd harmonic) in operation is mainly optimized
with the IR beam diameter (a), power, focusing positionin the cell and the gas pressure (b). The respective optimalvalues, in the test configuration, are 20.8 mm, 115 mW, 4
cm before the cell center and 5 10-3 mbar in the firstchamber.

a)Figure 4: HHG chamber with gas cell and motorization
system.
The second one (Figure 5) has been designed for
adjusting the harmonic beam at the focusing point in thefirst undulator section by means of two SiC sphericalmirrors. A periscope system is used to align the harmonic
beam with the e-beam.

Figure 5: Refocusing system and periscope.

Seeded FELsb)
Figure 6: Optimization of the 3rd harmonic flux, generated
in a 9 cm cell filled with Ar gas, with the Hamamatsu PM
R759, as function of the IR beam diameter (a) and of thegas pressure in the first chamber (b).
The transverse profiles (Figure 7) of the 3rd harmonic,
observed with a VUV CCD camera (COHU solid state
camera) are quit similar to a Gaussian fit.

Figure 7: Horizontal and vertical profiles of the 3rd
harmonic, at the theoretical focusing point in the first
undulator section.

139

MOPPH046

Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 8 shows the influence of the gas pressure on the
optimum of the flux on the two different harmonics.

IMPLANTATION ON THE SCSSPROTOTYPE ACCELERATOR
The harmonic generation experiment will be located in
the SCSS prototype accelerator tunnel, together with theaccelerator and the undulator sections, between the
chicane and the shielding wall (Figure 10). The focusingof an intense IR laser comes from the laser hutch, on the
opposite side of the shielding wall. The Ti: Sa laser isbased on a Tsunami mode-locked oscillator, a Spitfire
regenerative chirped-pulse amplifier and a Coherent
multipass amplifier and delivers more than 50 mJ at 100
fs. On an optical table, the IR beam is adapted forharmonic generation optimization and synchronized withthe e-beam.

Figure 8: Comparison between optimization of 3rd and13th harmonics (resp. H3 and H13) as function of thepressure inside the gas cell (proportional to the firstchamber pressure)
The shape of the 13th harmonic can be observed(Figures 9 a and b), 3 m after the cell corresponding to 8
m before the theoretical focusing point in the first
undulator section. A Micro-Channel Plate (MCP,
Hamamatsu F2221) was used with a phosphor screen(P43) associated to a CCD camera and placed after a Sn
filter (eliminating the IR laser and selecting especially the
13th harmonic). The beam section presents some lightaberrations particularly visible in the horizontal profile.
These latter must be really more important in the first
undulator section, where the interaction occurs with the ebeam (the overlapping can be decreased of 15%), but canbe compensated using a toroidal mirror.
a)Figure 10: Location for the HHG experiment on the SCSS
prototype accelerator.
The laser waist propagation in horizontal (x) andvertical (y) (Wox and Woy) has been calculated [10] toevaluate the geometrical aberrations caused by the two
spherical mirrors at the theoretical focusing point in thefirst part of the first undulator section. Correlated to the ebeam transverse sections, the filling factor (measuring theoverlapping of the two beams) can be calculated and isthen implemented in our simulation codes (see next
section). Figures 11 a and b present the focusing of the IR
beam and the 13th harmonic vertical and horizontal
propagations, which are quite similar until the focusing
part, where the geometrical aberrations lead to adifference of 35 cm in the focusing position between thevertical and horizontal propagations. (b) is a zoom of (a)with the implementation of the e-beam dimensions [8].

b)Figures 9 a and b: Transverse section (a) and profiles (b)of the 13th harmonic, 3 m after the cell but 8 m before thetheoretical focusing point in the first undulator.

140

a)

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Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH046

CONCLUSIONSb)
Figure 11: a) propagation of focused IR laser and the 13th
harmonic, b) focusing inside the first undulator section
and overlapping with the e-beam.

SIMULATIONS
New calculations (with ref. [8] characteristics) with
SRW [11], analytical expressions from G. Dattoli [12]and Genesis [13] (respectively Figures 12 a, b and c),have been performed for comparing the SASE and theseeding configuration, with 20 kW of seed (corresponding
to a slightly pessimistic value of what can be expected).
The different simulations converge very well to a similar
evolution. First, the saturation peak power levels are very
similar (108 W). Second, the saturation length for the
SASE case is about 10.5 m (107 W at 9 m) for all thesimulations but varies from 6m to 7.5 m in the seeding
case.

Using state-of-the-art High Order Harmonics in gas forseeding a FEL appears very interesting, because the seedradiation is fully coherent and tunable in the VUV-XUV
range. Moreover, it reduces the saturation lengths in amore compact source. From the HHG part, theexperiment has been perfectly designed and optimized for
producing harmonics and especially the 13th. New tests
will be performed in situ (near SCSS area in September)with a more performing vacuum system, a more powerfullaser system and with different optical characteristics,
allowing to still increase the harmonic production and tocompletely test remote control system before installing it
inside the accelerator tunnel for the seeding experiment(October).

REFERENCES[1] F. Ciocci et al, IEEE Jour. Quant. Elec. 31 (1995)
1242.
[2] G. Lambert et al., Proceedings SPIE 2005, San Diego,
USA, 31 July-4 August 2005.
[3] G. Lambert et al., Proceedings FEL 2004, 155-158,
Trieste, Italy, 29 August-3 September 2004.
[4] http:\\www-xfel.spring8.or.jp[5] L. Giannessi et al., Proceedings EPAC 2006, 95-98,
Edinburgh, 26-30 June 2006.
[6] Ph. Zeitoun et al., Nature 431, 426-429 (23 Sep
2004). Letters to nature.
[7] T. Shintake, Proceedings EPAC 2006, 2741-2743,
Edinburgh, 26-30 June 2006.
[8] G. Lambert et al., Proceedings EPAC 2006, 44-47,
Edinburgh, 26-30 June 2006.
[9] P. B. Corkum, Phys. Rev. Lett. 71 (1993) 1994.
[10] G. Lambert et al., Proceedings FEL 2005, San
Francisco, USA, 20 –26 August 2005.
[11] O. Chubar and P. Elleaume,yuyuyuyuyuyuyuyuyuyu
http://www.esrf.fr/Accelerators/Groups/InsertionDevi
ces/Software/SRW[12] G. Dattoli, P. L. Ottaviani and S. Pagnutti, J. Appl.
Phys. 97, 113102 (2005).
[13] Sven Reiche, http://pbpl.physics.ucla.edu/~reiche/

Figures 12 a, b and c: Comparison between SASE (black
plain line) and seeding configuration (red dash line) witha) SRW b) analytical expressions and c) Genesis.

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SEEDING THE SPARC TEST FACILITY WITH HARMONICGENERATION IN GASES: PRELIMINARY TESTS OF THE HARMONICGENERATION IN GAS CHAMBER
O. Tcherbakoff, M. Labat, G. Lambert, D. Garzella, M. Bougeard, P. Breger,
P. Monchicourt, H. Merdji, P. Salières, B. Carré, CEA, DSM/SPAM, 91191 Gif-sur-Yvette, France
M.E. Couprie, SOLEIL, 91192 Gif-sur-Yvette, France
A. Doria, L. Giannessi , ENEA C.R. Frascati, Italy.
Abstract
A coherent short wavelength source can be realised witha Free Electron Laser by using High Gain Harmonic Generation configuration. The injection of an external lightsource in the first part of an undulator results in a coherent
light emission in its second part. The SPARC FEL (Frascati, Italy), delivering an electron beam at 200 MeV passing through an undulator of 6 sections, can be configured
to test such schemes. We propose to use High order Harmonic Generation (HOHG) in gases process as the seed.
HOHG produces a coherent XUV source by focusing an
intense laser pulse into a gas medium. This beam, composed of odd harmonics of the fundamental laser, is thenshaped using a telescope of two spherical mirrors, allowing
the focusing at a given position, in the SPARC undulator.
Appropriate tuning of the undulator gaps will amplify the
3rd and 5th harmonics seeded, and non-linear harmonics
of those wavelengths, allowing the perspective of producing VUV coherent radiation. The chambers for harmonic
generation and shaping have been realised and tested at the
CEA (Saclay, France). We present these tests.

INTRODUCTION
Along the last few years, other Free Electron Laser(FEL) schemes than the common Self Amplified Spontaneous Emission (SASE) [1] have been proposed to generateintense and short pulse duration in XUV domain. In High
Gain Harmonic Generation (HGHG) configuration [2, 3],
an external seed, a laser source, induces energy modulationof the relativistic electrons in the modulator, leading to acoherent emission of the microbunched electron beam in
the radiator at the n th harmonics of the laser fundamental
wavelength. The harmonic radiated is selected tuning theundulator gap. The properties of the output radiation aredetermined by the seed laser and can thus inherit a highdegree of temporal coherence. Seeded FEL amplifier operation in combination with harmonic generation has been
demonstred experimentally in midinfrared and VUV domain [4, 5].
A way to reach shorter wavelengths is to use a seed laser
in VUV domain. Development in femtosecond laser technology have made possible to imagine new coherent shortwavelength sources. One of these sources, called High Order Harmonics Generation (HOHG), is based on the inter-

142

action between the laser beam and a gas target [6, 7]. Microjoule energies can be obtained at wavelengths down to
50 nm [8, 9]. It has been proposed to use HOHG as seed to
inject an undulator, either in the amplifier or in the HGHG
configuration [10]. HOHG seem to be a very good candidate to seed FEL cascade, to extend the operating wavelength of FELs down to sub nm. The SPARC configuration
will allow the study of the problems related to the injectionof an external radiation seed in a single pass FEL and theanalysis of the coupling efficiency of the electron-photon
beams in terms of the input parameters [11].

EXPERIMENTAL SETUP FOR THE
HARMONIC CHAMBERS
SPARC undulator is composed of 6 sections of 75 periods each. The e-beam energy may be varied up to 150-200
MeV. A Coherent femtosecond laser which delivers 120 fs,
2.5 mJ pulse with a central wavelength at 800 nm and amodified repetition rate of 10 Hz, generates HOHG in agas jet. The VUV radiation is then injected into the undulator by means of a magnetic chicane. Electron and photon
beams are then superposed at the entrance of the undulator (figure 1). SPARC undulator parameters allow to test
different configurations [12, 11, 13].

Figure 1: Experimental layout to seed harmonics generated
in gas into FEL.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH047

HIGH ORDER HARMONIC GENERATION
HOHG is obtained by focusing an intense laser pulse
into a rare gas medium. The atoms of the gas medium areirradiated and ionized by the strong laser field, releasing
free electrons with no kinetic energy. Those electrons arethen accelerated by the laser electric field. When the electric field sign changes, the electrons can be driven back inthe vicinity of the parent ions, and if a collision occurs,
the extra-energy of the ion-electron recombination is released by emitting a photon. New frequencies are created
and, after the gas medium, one can observe odd high orderharmonics of the fundamental frequency co-propagatingwith the fundamental laser beam. This VUV radiation
also exhibits an excellent spatial and temporal coherence[14, 15, 16]. The coherence properties of the harmonics
are similar to those of the fundamental laser beam whichmake them suitable for seeding experiment.
The setup for the production of the harmonics in gas ismainly composed of two chambers. The laser is focussed
by a plano-convex lens (f=2 m) and delivered through anantireflecting coated 790 nm window in the first chamberwhere HOHG occurs. Then, 1.5 meters downwards, thesecond chamber is used to adapt the waist, i.e. the harmonic beam mode in the middle of the first undulator for acorrect overlap with the e-beam. This shaping is performed
using two spherical mirrors reflecting nearly at normal incidence, both equipped with motorized mounts, and an additional translation stage under the second mirror, for theadaptation of the focusing point in the undulator. The distance between the gas jet and the middle of the first undulator is about 8 m. A scheme of the experimental setup is
given in Figure 2.

Figure 2: Experimental setup

CHARACTERISATION OF THE HHG
PRODUCED IN CEA-SACLAY
In order to prepare the seeding experiment on SPARC
facility, the chambers for harmonic generation have beentested during two months at the CEA-Saclay (see Figure3). The radiation generated in the chambers passes throughan interferometric filter centred at 266 nm (H3) eliminating

Seeded FELs

Figure 3: Picture of the chambers being tested at CEASaclay.
IR beam as well as other harmonics. The 266 nm radiationis then detected with a calibrated VUV photodiode blinded
for diffused IR light.
The femtosecond laser system (LUCA) of the Saclay
Laser-matter Interaction Center (SLIC) has been used as
fundamental source for the tests. The characteristics of thislaser based on 2 TW, 20 Hz CPA Titanium:Sapphire System [17] are given in Table . Both duration and energy ofthe laser pulse were tunable: several tests were performed
using a 2.5 mJ - 120 fs laser pulse in order to work in similar conditions as the one expected on SPARC facility.
Table 1: Characteristics of the laser system LUCA used forthe tests. The pulse duration was measured using autocorrelator, assuming a gaussian profile.
Laser characteristics Value Unit
Wavelength
800
nm
Spectral width20
nm
Pulse duration
56.8
fs
Energy50
mJ
Beam diameter
35mm
The initial configuration foreseen for harmonic generation, a simple gas jet with an aperture of 0.5 mm and no
additional nozzle, allowed a very small amount of UV photons to be produced. To reach a better conversion factor,
the geometry was improved through out the testing of four
different configurations: Jet and vertical guide, Jet and horizontal guide, Static Cell and finally Pulsed Cell. The increasing performances are summarized in Figure 4. In the
Pulsed Cell configuration, the gas is injected in a 1 cm
long-windowless cell by bursts of 1.3 µs through an electromagnetic valve synchronized with the incoming laser
pulses. A conversion factor of 10 −3 was obtained as regularly acheived in recent experiments. A good stability was
also reached, as well as a nearly perfectly gaussian harmonic beam.
The first step to optimize the harmonic yield was to con-143

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 4: Energy obtained on the third harmonic using different interaction medium configurations.

trol the laser aperture and the cell focus position[18, 19].
Closing an iris placed before the lens means decreasing theenergy laser and increasing the focal spot size, therefore
decreasing the focal intensity. As illustrated in Figure 5
with 2.5 mJ laser energy in Argon gas, a larger aperture isneeded in case of a long pulse duration: 14 mm (resp. 18mm) for 60 fs pulse (resp. 120 fs chirped laser pulse). Theenergy contained in each pulse remains unchanged, andfixed to 2.5 mJ. The optimum at 60 fs corresponds to a focal spot diameter of 340 µm, and at 120 fs of 279 µm; both
leading to an intensity of 2 × 10 14 W/cm2 . The reduced
spot diameter at 120 fs involves less medium in the lasermatter interaction, resulting into a lower energy emission(less photons are produced).

Figure 5: Aperture size dependence of H3 in Argon with
2.5 mJ laser energy for two pulse durations.

Figure 6 illustrates the third harmonic dependency in thecell position. The maximum efficiency has been reachedwhen the focusing point of the laser beam was 1.5 cm after
the cell.
Figure 7 illustrates the influence of the pressure on the
3rd harmonic signal. The amount of UV photons produced
increases with the backing pressure. No optimum could bereached, since the electromagnetic valve was limiting theavailable pressure in the cell.

144

Figure 6: Cell position dependence of H3 in Argon with
2.5 mJ laser energy, for two pulse durations.

Figure 7: Pressure dependence of H3 in Argon.

The number of 3rd harmonic photons generated in the
optimized conditions with 60 fs pulse is 1.3 × 10 13 (9,7µJ) and the corresponding conversion efficiency reaches
4 × 10−3 . In the same conditions, when 3rd harmonic is
generated by a chirped 120 fs pulse, the number of photons
decreases by factor 4.
We used a VUV spectrometer composed of a LiF prismand a photomultiplier to measure H3 and H5 with an entrance pinhole of 5 mm. Scanning on the prism angle being
manual, we only measured maximum signal at one position of the prism angle for H3 and H5 allowing the coarse
comparison of the relative contribution of each harmonic,
as illustrated in Figure 8.
The harmonic beam propagation has also been studied. It
is crucial for evaluating the overlap between the light wave
and the electron bunch in the undulator. The harmonic
beam is shaped using two concave mirrors optimized for
266 nm wavelength with respectively a focal length of 200
mm and 150 mm. The distance between the two mirrors
is about 38 cm. The incidence angle of 2 ◦ induces small
geometric aberrations. The total transmission for 3rd harmonic is 90 %. The spatial profile of the 3rd harmonics
has been measured using a CDD camera. Figure 9 showsthe evolution of H3 from the exit of the chambers throughout the undulator, and Figure10 shows the transverse pro-

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MOPPH047

CONCLUSION

Figure 8: 3rd and 5th harmonics in argon as function ofenergy laser for two pulse widths.

file of the harmonic at focusing point. The focal spot size
is about 940 µm. The theoretical fit with a quasi-gaussian
beam [20] gives a M 2 value of 1.6 and a 3rd harmonic sizeof 220 µm at generation point . With these measurements,
we will able to determine the filling factor which takes into
account the interaction between electrons and photons.

The results of the preliminary tests performed at CEASaclay on the chambers are encouraging. An efficient geometric configuration has been defined for the generating
medium. According to those first measures, the laser system foreseen at SPARC (120 fs, 2.5 mJ) should be adaptedfor generation of both 3rd and 5th harmonics with HOHG.
We expect more than 4µJ on the 3rd harmonic in Argon. The telescope system focuses the 3rd harmonic beam,
which is slightly astigmatic, at the estimated entrance ofthe first undulator with a focus waist size of 300 µm.
The peak power of this coherent VUV light was estimated to be 19 MW. Calculations with PERSEO andwith GENESIS 1.3 code have shown that saturation canbe reached with SPARC undulator, using a 266 and 160nm
wavelength seed with only a few kW power [11].
The harmonic chambers should be transported to SPARC
facility by the end of January 2007. After implementationon the linear accelerator modules, in spring 2007, first seeding experiments of SPARC FEL with this scheme should
start.

ACKNOWLEDGMENTS
This work was supported by the EU Commission in
the Sixth Framework Program, Contract No. 011935EUROFEL.

REFERENCES[1] S.V. Milton et al., Science 92, 2037 (2001).
[2] L.H. Yu, P.R.A. 44, 5178 (1991).
[3] I. Ben-Zvi et al., Nucl. Instrum. Methods Phys. Res. Sect. A
304, 181 (1991).
[4] L.H. Yu, Science. 289, 932 (2000).

Figure 9: Longitudinal evolution of the beam waist of the
3rd harmonic in vertical () and horizontal (◦) direction.
In solid line indicate the quasi-gaussian beam fit.

[5] L.H. Yu et al., P.R.L. 91, 074801 (2003).
[6] M. Ferray et al., J. Phys. B: At. Mol. Opt. Phys. 21, L31(1988).
[7] A. McPherson et al., J. Opt. Soc. Am. B 4, 595 (1987).
[8] J.F. Hergott et al., Phys. Rev. A 66, 21801 (2002).
[9] E. Takahashi, N. Y., and M. K., Opt. Lett. 27, 1920 (2002).
[10] D. Garzella et al., Nucl. Instrum. Methods Phys. Res. Sect.
A 528, 502 (2004).
[11] L. Poletto et al., FEL Conference, 63 (2005).
[12] L. Giannessi et al., www.sparc.it ref:SPARC-FEL-05/004.
[13] L. Poletto et al., proceedings EPAC 2006 (unpublished).
[14] T. Ditmire et al., Phys. Rev. Lett. 77, 4756 (1996).
[15] L. Le Déroff et al., Phys. Rev. A 61, 43802 (2000).
[16] L. Bellini et al., Phys. Rev. Lett. 81, 297 (1998).
[17] http://www-femtodrecam.cea.fr/slic/luca/luca1.htm.

Figure 10: Transverse profile of the 3rd harmonic at focusing point[18] P. Balcou et al., J. Phys. B 25, 4467 (1992).
[19] T. Ditmire et al., Phys. Rev. A 51, R902 (1995).
[20] A. E. Siegmann, ”Lasers”, University Science Books.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THE ARC-EN-CIEL FEL PROPOSAL
M. E. Couprie, C. Bruni, O. Chubar, J.M. Filhol, A. Loulergue, L. Nahon, Synchrotron SOLEIL,Saint-Aubin, France
B. Carré, D. Garzella, O. Gobert, P. Hollander, M. Labat, G. Lambert, P. Monot, O. Tcherbakoff,
CEA-DSM-DRECAM Service de Photons, Atomes et Molécules, Gif-sur-Yvette, France
G. Petite, CEA-DSM-DRECAM Service des Solides Irradiés, Gif-sur-Yvette, France
P. Bosland, G. Devanz, M. Jablonka, M. Luong, F. Méot, A. Mosnier, B. Visentin, CEA-DSMDAPNIA Service de Accélérateurs de la Cryogénie et du Magnétisme, Gif-sur-Yvette, France
J. R. Marquès, Lab. d’Utilisation des Lasers Intenses, École Polytechnique, Palaiseau, France
J. M. Ortega, H. Monard, Laboratoire de Chimie-Physique, Univ. Paris-Sud, Orsay, France
A. Rousse, Laboratoire d’Optique Appliquée, École Polytechnique, France.
Abstract
ARC-EN-CIEL (Accelerator-Radiation for Enhanced
Coherent Intense Extended Light) aims at providing theuser community with coherent femtosecond light pulses
covering from UV to soft X ray in France. It is based on a
CW 1.3 GHz superconducting linear accelerator
delivering high charge, subpicosecond, low emittanceelectron bunches at high repetition rate. Phase 1 exploits
the different sources of seeding with 220 MeV at 1 kHz,in particular High order Harmonic generation in Gas(HHG), to improve the longitudinal coherence andshorten the output radiation wavelength in a rather
compact device. Phase 2 is based on a CW 10 KHz 1
GeV superconducting linear accelerator for HHG seededHigh Gain Harmonic Generation (HGHG) extending to 1
nm. In phase 3, fs undulator sources in the IR, VUV and
X ray and a FEL oscillator in the 10 nm range will be
implemented on two ERL beam loops for beam current orenergy enhancement.

INTRODUCTION
France is now equipped with a third generationsynchrotron light source under commissioning [1] at
Saint-Aubin, close to Paris. The Storage Ring consists ina 357 m circumference ring, with 16 cells and 24 straightsections, out of which up to 21 will house insertion
devices (ID). High brilliance radiation, from the VUV up
to the hard X ray domain will be provided to external
users in 2007 with the low emittance (3.7 nm.rad) beam atthe 2.75 GeV. Innovative ID’s are under construction toprovide the best possible performances in a wide energy
range (5 eV to 50 keV) [2].
Prospects concerning the Fourth Generation Light
Source in France are based on the ARC-EN-CIEL project[3], following a long tradition in FEL in France, inparticular in storage ring based FELs (ACO [4], SuperACO [5]) and on infra-red LINAC based FELs (CLIO[6], ELSA [7]). After considering the installation of an
FEL in the VUV on SOLEIL in the oscillator or coherent
harmonic generation configurations, it was decided topropose an independent LINAC based dedicated facility
providing coherent radiation down to 1 nm, for easieraccess of the users. The possible implementation of the146

first and potentially second phase of ARC-EN-CIEL in
the former tunnel of the Accélérateur Linéaire de Saclay,
at l’Orme des Merisiers, next to SOLEIL, would make avery attractive acclerator based light source complex.
From the beginning, the project aims at developing astrong synergy between the FEL and the laser
communities, leading to couple the electron beam andlasers. The innovative choice of seeding the FEL withHigh order Harmonic produced in Gas, at a highrepetition rate leads to a significant shortening of the
wavelength of the seed, in addition to the advantages ofseeding with respect to SASE (pulse to pulse intensity
stability, reduction of jitter, compactness, enhanced
longitudinal coherence). Indeed, more than 70% of theusers intend to perform pump-probe experiments and ahigh stability is requested, confirming the choices ofseeding and High Gain Harmonic Generation, as
discussed in the frame of the user workshop“Applications of VUV X fs tunable sources combining
accelerators and laser: “slicing” at SOLEIL and the ARCEN-CIEL project” (Feb. 3-4 2004, Orsay). Besides,
propositions of plasma acceleration and Thomson
scattering emerged from the laser-electron beamcombination.
The request of high repetition rate (1-10 kHz) in order
to couple as efficiently as possible the electron beam withthe high harmonics produced in gas led to the choice of asuperconducting type of Linear Accelerator. Expertise
exits in DAPNIA in CEA and in SOLEIL with thesuperconducting RF cavity. A high repetition rate of thephoton source is also desirable for users. A 100 fs pulse
corresponds to the typical demand.
ARC-EN-CIEL is planned into three phases: a firstphase reaching an energy of 220 MeV for HGHG sourcesin the VUV, a phase 2 at 1 GeV with HGHG sources
down to 1 nm using High Harmonics produced in gas, anda phase 3 including two recirculation loops, for Energy
Recovery or energy enhancement where undulators (12 mlong, period 30 and 20 mm) are installed, providing
subpicosecond radiation in the VUV and X ray ranges(5.1012 phot/s/0.1%bw for 0.1 mA average current). In
addition, a 0.1-1 kW average power, 0.1-1 % bandwidth
FEL oscillator, installed in the first loop, could cover the120-10 nm, thanks to recent development of multilayer

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Proceedings of FEL 2006, BESSY, Berlin, Germany
mirrors for lithography, and SiC mirrors in normal
incidence. Harmonics can also be produced from the FEL
oscillator, with 500 MW at 4.5 nm and 10 MW at 2.7 nm.
The beam at 2 GeV from the loop will allow shortening
further the radiation wavelength down to 0.4 nm with anadditional undulator section. Expected radiation from
ARC-EN-CIEL is illustrated in figure 1, comparing
radiation of its three phases with respect to the insertion
devices of SOLEIL. THz radiation will also be provided.
The present work, part from the detailed analysis of thecomponents of the project, is concentrating on the
progress on several key elements.

MOPPH048

International Linear Collider. The design of thecryomodule may be revisited for a better cryogenic
efficiency accounting for the CW operation.
Studies concerning the compensation of the
microphonics are presently under way at CEA-DAPNIA
and BESSY [11]. The microphonics have been analysedwith appropriate techniques and different compensation
schemes are elaborated using active piezoelectric tuners.
However, the large number of the transverse mechanicaleigen-modes of the cavity represents a strong limitation
for the compensation. A passive damping of these modes
by a careful design and mounting of the cavity-tuner
system in the cryomodule would alleviate the complexityof the active compensation scheme and improve its
efficiency.

The electron beam dynamics

Figure 1 : Peak brilliance. Phase 1 :HGHG radiation +seeding wavelength, Pseed = 100 kW for HHG harmonics n°7-9,
600 kW for n°3-5. 1 kA, F= 0.1. Phase 2 :HGHG radiation 1.5
kA, 1.35 π mm.mrad, 0.0004% slice energy spread, 200 fs,
beta=2 m, F = 0.088. Phase 3 : spontaneous emission ofundulators of period 30 and 80 mm calculated with SRW.
Undulator period length in mm in ID name.

THE ACCELERATOR
The gun
The choice of the gun is not completely defined. It
should provide 1 nC for 2πmm.mrad total emittance ε. At
the beginning, we have considered a Zeuthen photoinjector [8], with a CsTe cathode, to be modified for
operation at 1 KHz. This requires a coupler modification
with respect to the present design. The active removal of
the power can be performed via a phase inversion during
falling time. A longer term system is based on asuperconducting gun, as presently developed byRossendorf [9], where emittance compensation andreliability can still be an issue. We also thought about theadaptation of the CeB6 thermo-ionic gun developed at
RIKEN for the SCCS project, and the recent very
spectacular results in terms of beam stability andemittance [10] bring us to go further in the analysis of thissolution for ARC-EN-CIEL. Besides, R&D is going on
the cathode materials in LSI (Polytechnique) with the useof Carbon nanotubes.

The cryomodules
ARC-EN-CIEL is based on TESLA type cavities at 1.3
GHz, to be operated in CW mode. The elliptical 9-cellcavities routinely provide 25 MV/m accelerating gradient,while recent advances in the cavity design and integration
procedures indicate the possibility of pushing the gradientto 35 MV/m, which is a target parameter for the

Seeded FELs

Calculations performed for ARC-EN-CIEL phase 1
accelerator consider an RF gun, a first cryomodule
bringing the energy to 100 MeV, a third harmonic cavity
compensating the non linearity of the longitudinal phasespace, a S-chicane compressor, and a second cryomodule
raising the energy to 220 MeV. 6 additional modules areincluded in phase 2. ASTRA [12] is used to simulate theRF gun and the cavity modules, and CSRTrack code [13]for the compression scheme, taking into account Coherent
Synchrotron Radiation in the chicane.
Figure 2a presents the evolution of the different
emittances along the bunch compressor. The total
emittance is raised to 2.7 πmm.mrad in the compression
process through the chicane (from 2.1 to 0.1 mm/ 300 fsrms). With an adequate electron beam optics [14], theslice emittances along the bunch remain almost
unchanged (ranging from 0.7 to 1.1) with a small
mismatch from slice to slice. The compressor creates acorrelated emittance that reaches 0.18 π mm.mrad,
betraying a spread of the slices in the transverse phasespace. It is the main contribution to the total emittanceincrease by strong mismatching.

Figure 2 : Evolution of the emittance along the chicane.
Chicane parameters: total length: 10 m, R56=0.15 m, dipole
length : 0.3 m. First dipole at s=23 m.

The influence of the laser pulse length on the
optimization of the different emittances while keeping a
constant space charge density was also investigated. A
longer laser pulse is favorable in the compressor, foravoiding emittance degradation due to coherent
synchrotron radiation, the longitudinal wake function
being proportional to σl −4/3, with σl the beam length.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Although the output bunch is also compressed down to
300 fs, its mean length through the chicane is longer andthe emittance is smaller. In order to avoid beam
degradation due to non linear part of the R566 coefficient,
the voltage of the harmonic cavity has to be increased togive an invert sign of the non linear component. For
longer laser pulse and longer electron beam length before
the chicane, the energy variation is more important andthe deformation of phase space is larger (see fig. 3).
Systematic simulations done for different pulse lengths(20-40 ps range) and harmonic cavity voltages (20-25
MV/m range), keeping the final bunch length constant at
0.1 mm bring to a minimum of the total emittance for
EH=22 MV/m. In Fig. 4, one finds at the end of the Schicane, a minimum total emitance at 2.1 π mm.mrad forthe laser pulse length σl=25 ps. The total emittanceglobally increases with the laser pulse length apart for
σl=20 ps, for which it is higher. The central slice
emittance decreases with the laser pulse length (radial
laser spot reduction). Further studies concern the preinjection in the case of the thermo-ionic gun (SCSS type)will be studied, calculations for the phase 2, including thesecond bunch compressor and for phase 3 with ERL
loops.
40

40

a)

b)

0

0

δΕ

20

δΕ

20

-20

-20
-3

-3

-40x10-40x10-6-400x10

-200

0

δs

200

400

-6

-400x10

-200

0

δs

200

400

Figure 3 : Longitudinal phase space representation for a laser
pulse length of a) 20ps, b) 40 ps for different voltages of theharmonic cavity. Black (resp. grey): EH=22 (resp. 20)MV/m.

(dimensions and shape) for preventing the electron beamemittance increase [15]. A laser amplifier delivering atleast 1 mJ in the IR (800 nm), followed by a regenerative
amplifier and single pass preamplifier, both pumped by a
15 W Q-switched solid state laser can be adopted. Veryhighly efficient third harmonic generation will be
performed with an ultra short pulse (~50 fs) on a
sufficiently thin nonlinear crystal (BBO), in order toreduce pulse distortion. A prism or gratings based UV
stretcher will bring the duarton up to 20 ps.. Transverseand longitudinal measurement as well as shaping of thelaser pulse call for a complete setup including a
DAZZLER system [16] in the IR, spectral interferometrictechniques (either self-referencing, like SPIDER [17] ornot), a beam transverse filter and deformable mirror withhigh dynamics. Such approaches are under study on the
CEA-SLIC servers LUCA (20 Hz) and PLFA (1 kHz)[18]. Recent promising developments by FASTLITE [19]of a Dazzler operating in the UV domain Dazzler, should
allow a direct shaping of the laser beam issued by THG
process. Otherwise, we intend to develop brand new
solutions for a dedicated UV regenerative amplifier, basedon the amplification and Kerr properties of crystals like
Ce3+:LiCaAlF6 [20].
The second one, a broadband system, includes nonlinear processes like Optical Parametric Amplification,
Third and Fourth Harmonic Generation (THG, FHG) and
HHG, for two color pump-probe based experiments. It isbased on Chirped Pulse Amplification (CPA) technique,on a basis of a 10 mJ, kHz or multi-kHz system, in which
a 4-pass amplifier is injected with the beam issued a firstregenerative amplifier. The first two systems will operate
at a multi-kHz rate, while the third will be limited to few
Hz (eventually few tens of Hz).
The third laser system will deliver high energy (1 J),
short duration pulses and will be mainly devoted toplasma acceleration and Thomson scattering.

The synchronisation

Figure 4 : Emittance evolution versus the laser pulse length.

THE LASER SYSTEM AND
SYNCHRONISATION
The laser system
One passive mode locked Ti:Sa based oscillator isforeseen, delivering 1 W at 76 MHz repetition rate(around 13 nJ /pulse). This will feed three independent
high power, multiple repetition rate, laser systems.
The first system, devoted to the photo-injector should
provide ~50-100 µJ pulse energy in the UV (266 nm),
producing a 1 nC electron beam following interaction
with a photocathode with 1 % quantum efficiency. Special
attention will be paid to the laser beam transverse features

148

The synchronisation of the RF and the master clock in
respect to the femtosecond time scale taking into accountthe natural pulse-to-pulse jitter for a Ti:Sa oscillator of a
few tens of fs lead to adopt a frequency-stabilized laser
oscillator. Care will be devoted to minimize the intrinsic
jitter encountered by the e- beam through its travel in theaccelerator to the wiggler. The jitter between the different
laser branches distributed on relatively long distance (~100 m) should also be reduced and environmental
contributions such as slow thermal drift should belowered. Moreover, unlike the accelerator beneficing of
the vacuum technique, inherent jitter sources along thecomplex laser system (stretcher /compressor pair,
regenerative /multipass amplifiers, thermal lensing…) is
under study in CEA-SPAM. Measurement of thesynchronisation between the laser pulse and the electron
is a key issue, the development of the electro-opticalmeasurement has been set-up on the ELYSE gun at LCI(Orsay). The first step of measurements leads to a
resolution of 250 fs.

Seeded FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

THE LIGHT SOURCES
The undulators
ARC-EN-CIEL phase 1 plans to use a 20 mm period
in-vacuum hybrid undulator as a modulator (50 periods),
and a 30 mm Apple-II undulator as a radiator (400periods). Identical sections of modulator and radiator will
be added for the second phase of ARC-EN-CIEL (4 to 8
m for the modulator, and 4 sections of 4 m for theradiator). Such undulators are currently developed for
SOLEIL third generation facility.
The choice of such radiator type undulators follows
estimations of magnetic performance of an Apple-II typeundulator with a small period based on magnetostatic
calculations performed using the Radia computer code[21]. The expected horizontal and vertical peak fields ofan Apple-II at 30 mm period and 6 mm vertical gap are
Bx = Bz ≈ 0.63 T; corresponding to the effective
deflection parameter K ≈ 2.5 (see fig. 5).

Figure 5. Peak magnetic fields (left) and deflection parameters(right) as functions of period of an Apple-II undulator in helicalmode at different vertical gaps. Calculations done for NdFeB
magnet blocks with remnant magnetization of 1.22 T andtransverse dimensions 30 mm x 30 mm, horizontal gap between
movable and fixed magnet arrays : 1 mm.

Seeding with High Harmonics generated in gas
Collaborations have been set up for demonstrating thefeasibility to seed a LINAC based FEL with HHG on
SCSS phase 1 in Japan [22] and on SPARC in Italy [23].
Tests of the chambers and of the optical transport havebeen performed this year with the Luca laser, and seeding
will be performed at SCSS on fall 2006 and in summer
2007 on SPARC. This will provide an experimental
demonstration of the concept for ARC-EN-CIEL. FEL
radiation based on analogous systems for ARC-EN-CIEL
is calculated using PERSEO 1D code [24] with a gain
reduction due to the filling factor [25] and recently

Figure 6: Steady-state GENESIS simulations for ArcEnCiel
phase 1, 1 – 1 HGHG scheme, 266 nm seed: a) gain inmodulator, b) gain in radiator (30 mm period helical mode).

Seeded FELs

MOPPH048

compared with GENESIS1.3 [26] integrated in a new test
version of SRW [27] allowing the wavefront to betransported in the beamline to the user sample (see fig. 6).
ACKNOWLEDGMENTS
The support given by EUROFEL contract No 011935
is acknowledged, and to ANR. The authors thank L.
Giannessi for fruitful discussions.
REFERENCES[1] J. M. Filhol et al, JACoW, EPAC’06, Edinburg, June
2006, p. 2723, http://www.jacow.org.
[2] F. Briquez et al, JACoW, EPAC’06, Edinburg, June
2006, p. 3556.
[3] M. E. Couprie et al, JACoW, FEL’05, Stanford,
August 2005; M.E. Couprie et al, Proceed. SRI 06,
Daegu, May 2006, M. E. Couprie et al, JACoW,EPAC’06, Glasgow, June 2006, p. 53, M.E. Couprie
et al, EPAC 04, 55.
[4] M. Billardon et al, Phys. Rev. Lett. 51, (1983) 1652.
[5] M. E. Couprie et al., Phys. Rev. A . 44(2), (1991)
1301.
[6] R.Prazeres et al Phys. Rev. Lett. 78(11), 2124-2127(1997).
[7] P. Guimbal et al, Nucl. Inst. Meth. A 341 (1994) 43.
[8] D. Dwersteg et al , NIM. A393, 93 (1997).
[9] R. Xiang et al, PAC 2005.
[10] T. Shintake et al, EPAC’06, Edinburg, p 2741 ;Togawa et al, APAC2004, Gyeongju, Koera, March
2004.
[11] M. Loung et al., JACoW, EPAC’06, Edinburg, June
2006, p. 3167, Kugeler et Neumann, EPAC06, p.
408, G. Devanz et al., EPAC’06, p. 378.
[12] K. Flottman, “ASTRA, a space charge tracking
algorithm”, http://www.desy.de/~mpyflo[13] M.
Dohlus,T.
Limberg,“CSRtrack”,
http://www.desy.de/xfel-beam/csrtrack/index.html[14] M. Dohlus and T. Limberg,. PAC 2005, p 1015.
[15] C. Limborg and P. Bolton, NIMA 557 (2006), pp
106-116.
[16] F. Verluise et al., JOSAB, n° 17 (2000), pp. 138-145).
[17] C. Iaconis and I.A. Walmsley, IEEE Jour. Quant.
Elec. 15 (4), April 1999 pp. 501-509.
[18] D. Garzella et al., this conference.
[19] N. Forget et al., “Direct Pulse shaping of ultraviolet
pulses by an AOPDF”, presented at CLEO/QELS
2006.
[20] Liu et al., Opt. Lett, Vol.26 n°5 (2001), pp. 301-303.
[21] P. Elleaume, O. Chubar, J. Chavanne, "Computing
3D Magnetic Field from Insertion Devices", PAC97
1997, 3509.
[22] G. Lambert, this conference.
[23] O. Tcherbakoff, this conference.
[24] Luca Giannessi, PERSEO, www.perseo.enea.it[25] W. Colson P. Elleaume Appl. Phys. B 29, (1982)10.
[26] GENESIS 1.3, http://pbpl.physics.ucla.edu/~reiche/[27] SRW, ESRF-SOLEIL collaboration http://wwwsources.synchrotron-soleil.fr:8002/mid.software

149

MOPPH050

Proceedings of FEL 2006, BESSY, Berlin, Germany

THE PROPERTIES OF THE FEL OUTPUT FOR SELF SEEDING
J. Bahrdt, BESSY, Berlin, Bart Faatz, Rolf Treusch, Deutsches Elektronen-Synchrotron (DESY),
Hamburg, Velizar Miltchev, Hamburg University (Uni HH) Institut fuer Experimentalphysik,
Ruben Reininger, ruben@sas-rr.com.
Abstract
Several seeding schemes, like self seeding for FLASHor seeded HGHG cascades for BESSY soft X-ray FEL,
are proposed for existing or planned free electron laser
facilities. The simulation of these schemes requires thedetailed knowledge of the properties of the seedingradiation and the implementation of these properties in
the codes. Time dependent simulations with the 3D code
GENESIS calculate the electric field distribution in andat the end of the undulator. The physical optics code
PHASE permits the propagation of wave fronts acrossgrazing incidence optics. Using the combination
GENESIS PHASE GENESIS, the properties of the FEL
output for different seeding schemes can be obtained.
For example, the radiation quality of a SASE FEL canbe improved in a self seeding scheme. Here, theradiation is monochromatized after a first undulator
section and seeded to the second undulator
modules. We present simulation studies for the self
seeding option of FLASH.

INTRODUCTION
Synchrotron radiation beamlines at 3rd generation
storage rings are generally optimized with ray tracing
codes which are based on geometrical optics. This isjustified as long as the radiation is incoherent. Coherent
radiation has to be propagated with physical optic codes
which describe the coherent properties of the light.
FELs, the 4th generation light sources, are built to
produce transversally and longitudinally coherent
radiation in the wavelength regime down to 1Å.
X-ray FEL facilities based on the SASE principle areunder construction at various places [1-3]. Since the
SASE is a random process the longitudinal distributionof the light pulse as well as the spectrum is spiky.
Using a coherent seed pulse the FEL output can hence
significantly be improved. The cascaded HGHG FEL
scheme uses the coherent properties of the seed laser andtransforms these properties through several stages to therequired wavelength regime where no seeding laser isavailable [4,5]. The radiation properties degrade with thenumber of stages involved. Therefore, it is advantageous
to start with a rather short seeding wavelength which canbe produced by high harmonic generation (HHG) [6] inorder to reduce the number of stages.
Self seeding is another approach to improve thespectral properties of the FEL [7]. The SASE radiation ispassed through a monochromator which filters out thecentral frequency. This radiation is used as a seed for thefollowing undulators.

150

It has also been shown that the output power of acascaded HGHG FEL can be enhanced if the radiation of
the first stage is monochromatized before transportation
to the next one [8].
These examples demonstrate that there is no strict
separation
between
FEL
undulators
andmonochromators. They have to be described in a closed
form, instead. In this paper we demonstrate for theexample of the self seeding option of FLASH thenecessity for a three dimensional and time dependent
description of the propagating coherent radiation within
the undulators and the monochromators.

THE PHYSICAL OPTICS CODE PHASE
The propagation of wavefronts in free space is usually
done using Fourier optics techniques [9]. Depending on
the geometry one of three propagators can be applied:i)
In the near field approximation the electricfield distribution is expanded in plane waves,the plane waves are propagated bymultiplication with a complex factor and theresult is back transformed to real space.
ii)
In the far field approximation the image
distribution is composed of the contributions
from individual point sources.
iii)
In the very far field the field distribution
equals the angle distribution in the source
plane (apart from a constant factor).
Optical elements can be introduced into thisformalism in the following way: The electric field is
propagated to the center of the optical element with
Fourier optics. Then, the wavefront is propagated over
the optical element using a ray tracing technique whichtakes into account the phase differences. Then, thewavefront is further propagated with Fourier optics
methods (ZEMAX, GLAD [10,11]).
The code PHASE, written at BESSY, is based onanother technique, the stationary phase approximation[12] which will be briefly explained.
The following equation correlates the electric fields inthe source and the image plane.

E (a ') = ∫ h(a', a) ⋅ E (a ) ⋅ d a

The integration is done over the source plane and therpropagator h has the form:
1
exp(ik (r + r ' ))h(a', a) = 2 ∫⋅ b( w, l ) ⋅ cos(α ) ⋅ dw ⋅ dl
λ Surfacerr 'r , r ' are the distances between the source / image
plane and the optical element, b is the obliquity factor

Seeded FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany
and the integration extends over the optical element
surface. Each point in the image plane requires theevaluation of a four dimensional integral. Each
additional optical element adds another two dimensions
in the integral and it is obvious that the expressions can
not be evaluated within reasonable time without certain
assumptions. The stationary phase approximation uses
the fact that the optical path length changes quadraticallywith the optical element coordinates in a region close to
the principle rays (extremum of the optical path). The
integration over the optical element coordinates can bedone analytically if the beam is not scraped at thatelement and hence, the dimensions of the integral can be
reduced from six to four.
All expressions (coordinates, path length, scaling
factors etc.) are expanded up to fourth order in thecoordinates and angles of the initial plane. Using these
expansions the transformation of cross products ofcoordinates and angles can be derived as well. Using
these cross terms the transformation over one element
can be expressed via a 70x70 matrix. The combinationof several optical elements is done simply by themultiplication of the individual matrices.
In principle the complete beamline can be describedwith one single matrix for each term as long as thephoton beam does not hit an aperture. In case of a
monochromator at least two runs are required: i)propagation from the initial plane to the exit slit and ii)
propagation from the exit slit to the image plane.
Monochromatic light is assumed during the
propagation. For time dependent simulations, the input
data have to be Fourier transformed and the individual
frequencies have to be propagated one after the other.
The results are again Fourier transformed yielding thetime dependent fields at the exit of the monochromator.
All equations have been derived with the algebraic
code REDUCE [13] and the basic code has been
produced automatically. For more details on thealgorithm we refer to [12].

THE SELF SEEDING OPTION OF FLASHThe basic setup of the self seeding option is
illustrated in Figure 1. It consists of two undulator stages
separated by a magnetic chicane and a monochromator.
The first undulator operates as a SASE FEL in the linear
regime. After it the electrons are separated from the
SASE radiation. The electron beam passes through themagnetic bypass that is used to remove the longitudinalcharge density modulation (micro bunching). The
radiation pulse is spectrally filtered in a high resolution
grating monochromator and afterwards is superimposedwith the electron beam at the entrance of the second
undulator. Thus the monochromatic photon beam serves
as a coherent radiation seed, which is amplified up to
saturation in the second undulator. The self seeding
technique increases the spectral brilliance significantly
i.e. the output power of the seeded FEL is concentrated
in a single line which is orders of magnitude narrower

Seeded FELs

MOPPH050

than the spectrum of the conventional SASE FEL. The
concept of the self seeding has the advantage that it isindependent of any external radiation source and theseed is naturally synchronized with the electron bunch.

Figure 1: Schematic layout of the self seeding setup.

THE MONCHROMATOR
The seeding requirements for energy resolution, unity
magnification, and only vertical deflections have beenaddressed [14] with a beamline (Figure 2) based on aspherical varied-line spacing grating (SVLSG).
The monochromator includes a plane mirror and three
SVLSG (in the same spherical substrate) covering theenergy range 6-64 nm. The plane mirror illuminates thegrating at the correct angle of incidence such that the
monochromator magnification is close to unity. In
addition, each grating is designed to perfectly focus thebeam along the dispersion (vertical) direction at the exit
slit at two energies in its range, and to zero the coma
aberration at one energy.

Figure 2: Seeding monochromator.
The pre and post focusing optics include four opticalelements. The first and last optical components are twosagittally focusing cylinders that provide the unity
magnification along the horizontal direction. The
demagnification along the dispersion direction onto theentrance slit is performed with a spherical mirror. A
spherical mirror after the exit slit magnifies the entrance
slit width such that the size and divergence at theentrance of the second undulator overlaps with theelectron beam for maximum amplification.

SIMULATIONSTime dependent simulations for the first undulator at a
carrier frequency of 60nm have been performed using
GENESIS [15]. The standard FLASH undulator
geometry has been assumed, where the electron beam iskicked in order to avoid saturation within the 15m
undulator length which is required for shorter

151

152

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

x50
x10
x5

0

500 1000 1500 2000

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

-0.001

0

0.001

ΔE/E

time / fs

Figure 3: Relative power versus time (left) andfrequency (right) for the initial pulse at the exit of thefirst undulator (black) and behind the monochromatorfor exit slits of 40μm (blue), 200μm (red) and 400μm(green). The monochromator transmission is not yet
included.
length simulated is about 4.3 m, after which maximum
peak brilliance has been reached.

RESULTS
The simulations for the three different slits show
similar results. The main difference is that the seed
power is different at the entrance of the second
undulator. However, in all cases it is well above
shotnoise and only influences the position at whichsaturation is achieved. In Figures 4 and 5, the results for
a 400 μm slit are shown.
Wider monochromator slits increase the total power
which is, however, not completely passed to the electron
beam because the transverse beam size acts as further
slit. The spectral power increases by a factor of 2.5
going from 40 to 200μm slit width and does not increase
further at 400μm.
6x10

6

5x10

6

7

10

SASE
SEEDED

6

10

5

10

4x10

6

4

10

3

10

P/λ

wavelengths [16]. The total length over which the SASE
interaction takes place is about 6.5 m, which is enoughto reach a power level of about 0.2 GW. This value iswell below saturation, but high enough to guarantee thatafter monochromatization the power is several orders ofmagnitude above shot noise. Electric fields for 560 slices(121x121 grid points) separated by 540nm provide thefull information of the radiation pulse. The frequency
resolution after Fourier transformation is determined by
the length of the total pulse to be transformed. For areasonable resolution the pulse length has been enlarged
to 4096 slices by adding slices with no intensity.
After Fourier transformation the frequency slice forthe central frequency (60nm) has been propagatedupstream to find the beam waist. For this specific casethe waist is located 1000mm upstream of the undulator
exit.
The PHASE propagation has been limited to 40
frequencies. The other frequencies are diffracted by thegrating to large angles such that they are blocked by theexit slit. The wavefronts corresponding to the 40
frequencies have been propagated to a plane close to thefirst element which is the initial plane for the subsequent
PHASE propagation. The PHASE simulations have been
done in two steps. First, the electric fields in the exit slit
plane have been evaluated on a grid with 51x51 data
points. The sizes of the slit aperture was chosen to be
2mm horizontally and 40μm, 200μm and 400mμvertically. These data have then been used in a second
PHASE run from the exit plane to the center of thesecond undulator (2500mm downstream of the undulator
entrance).
These 40 frequency slices plus the other 4096-40
frequency slices (the latter ones with no intensity) havebeen Fourier transformed to time space to be used infurther GENESIS simulations through the second
undulator. For this a modified version of GENESIS isused in order to include the full 6x6 matrix to describe
the electron bypass that debunches the electron beam.
The electric fields behind the monochromator have beenscaled such that the intensity at the central frequency has
dropped to 11 percent corresponding to the theoreticalbeamline transmission.
Figure 3 shows the temporal and spectral power of theinitial pulse and the pulses behind the monochromator.
Though the line width behind the monochromator
shrinks with the slit width, the pulse duration does notincrease.
The reason is the correlation between the wavelengthand the spot location in the dispersion plane of thegrating which is imaged to the center of the second
undulator. The bandwidth at a certain grid point does notscale with the slit width because only a small frequency
interval contributes to the intensity at that point.
For the simulation of the second undulator, theparticle distribution of the first undulator is taken, which
is debunched, using the full 6x6 matrix which has been
simulated with ELEGANT. The field used as a seed isthe one as calculated by PHASE. The total interaction

power / a.u.

Proceedings of FEL 2006, BESSY, Berlin, Germany
power / a.u.

MOPPH050

3x10

6

2x10

6

1x10

6

59

59

60

61

60

61

Wavelength/nm

Figure 4: Comparison of the power spectrum for SASE
(black curve) and a seeded pulse (red curve) for a slit of
400 μm. The small graph in the top left corner shows thesame spectrum on a logarithmic scale. Note that thecentral frequency of 60 nm for the seeded pulse is about
an order of magnitude higher compared to SASE,
whereas the other peaks are about a factor of 5 lower.

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Proceedings of FEL 2006, BESSY, Berlin, Germany
9

4.0x10SASE
SEEDED

9

3.5x109Power/GW

3.0x109

2.5x109

2.0x109

1.5x109

1.0x108

5.0x10

0.0
0

50

100

150

200

250

300

350

s/μm

Figure 5: Power along the bunch for a SASE pulse(black curve) and the seeded pulse (red curve). Note thatthe seeded pulse is much smoother. The remaining
spikes are at least partially due to the fact that thebunching is not fully suppressed in the simulation due tothe limited number of particles used.

[6]

CONCLUSION
We presented for the first time combined timedependent FEL simulations and physical optics
wavefront propagations using the codes GENESIS and
PHASE. The wavefronts generated in a time dependent
simulation of GENESIS have been propagated with thephysical optics code PHASE and the result has beenused as a seed for a further GENESIS run. It has been
demonstrated that the self seeding scheme significantly
improves the spectral performance of FLASH. The line
width becomes narrower, the power increases and thetemporal structure is smoother.

[7]
[8]

[9]

[10]

ACKNOWLEDGEMENT
We thank A. Meseck for adapting the code GENESIS
and for many fruitful discussions.

[11]

REFERENCES

[12]

[1]
[2]
[3]
[4]
[5]

TESLA-Technical Design Report, TESLA XFEL, Technical Design Report, 2002-9, 2002.
Linac Coherent Light Source (LCLS),
Conceptual Design Report, SLAC-R-593, 2002.
T. Shintake, Nucl. Instr. and Meth., A507
(2003) 382-397.
L. H. Yu, NIM A, 483 (2002) pp493-498.
X. J. Wang et al., DUV, Proceedings of the 26th
International FEL Conference, Trieste, Italy,
2004, pp 209-211.
C. Bochetta et al., FERMI, Proceedings of the27th International FEL Conference, Stanford,
CA, 2005, pp 632-685.
The BESSY Soft X-ray Free Electron Laser,
Technical Design Report March 2004, eds.: D.
Krämer, E. Jaeschke,
W. Eberhardt,
ISBN 3-9809534-08, BESSY, Berlin (2004).

Seeded FELs

[13]

[14]

[15]
[16]

MOPPH050

M.-E. Cuprie et al., ARC-EN-CIEL,
Proceedings of the 27th International FEL
Conference, Stanford, CA, 2005, pp.55-58.
A. Andersson et al., MAX IV, Proceedings ofthe 26th International FEL Conference, Trieste,
Italy, 2004, pp 190-192.
D. Wang et al., MIT, Proceedings of 2005
PAC, Knoxville, Tennessee, pp1961-1963.
J. Wu, Z. Huang, LCLS, Proceedings of the 27th
International FEL Conference, Stanford, CA,
2005.
Gullens et al., LBNL, Proceedings of the EPAC
2006, Edinburgh, Scotland, pp 142-144.
J. Qi-ka et al., SDUV, Proceedings of the 26th
International FEL Conference, Trieste, Italy,
2004, pp 494-497.
O. Tscherbakoff et al., Proceedings of the
EPAC 2006, SPARC, Edinburgh, Scotland, pp
47-49.
G. Lambert et al., SCSS, Proceedings of the
EPAC 2006, Edinburgh, Scotland, pp 44-46.
J. A. Clarke, 4GLS, Proceedings of the EPAC
2006, Edinburgh, Scotland, pp 181-183.
J. Feldhaus et.al., Opt. Commun., 140 (1997),
341.
K. Goldammer et al, Proceedings of the 27th
International FEL Conference, Stanford, CA,
2005, pp.23-26.
M. Abo-Bakr et al., Proceedings of the 27th
International FEL Conference, Stanford, CA,
2005, pp.19-22.
J. W. Goodman, “Introduction to Fourier
Optics”, McGraw-Hill Physical and Quantum
Electronics Series, New York, 1968.
GLAD, Theory Manual, Applied Optics
Research, 1087 Lewis River Road, 217
Woodland, WA, 2004.
ZEMAX, Optical Design Program, User’s
Manual, ZEMAX Development Corporation,
November 2005.
J. Bahrdt, Applied Optics, 34 (1995) 114-127.
J. Bahrdt, Applied Optics, 36 (1997) 43674381.
J. Bahrdt, Proceedings of the 27th International
FEL Conference, Stanford, CA, 2005, pp694701.
A. C. Hearn, “REDUCE 3.5, A General
Purpose Algebra System” [RAND, Santa
Monica, Calif. 90407-2138 (reduce@rand.org),
1993].
R. Reininger, J. Feldhaus, P. Gürtler, and J.
Bahrdt, Nucl. Instr. Methods A, 467, 38-41,
2001
S. Reiche, GENESIS 1.3, Nucl. Instr. Meth. A
429 (1999) 243.
V. Miltchev, “Simulation studies on the self
seeding option at FLASH”, presented at thisconference.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

DEVELOPMENT AND APPLICATION OF FIGURES OF MERIT TO
EVALUATE THE OUTPUT OF HGHG FEL CASCADES
B. Kuske Ý , R. Follath, A. Meseck, BESSY, Berlin, Germany
Abstract

INTRODUCTION
A growing number of proposals for FEL projects plan touse High Gain Harmonic Generation (HGHG) structuresin order to exploit the advantages that arise from seeding
the FEL process, at wavelengths much shorter than what isavailable today with conventional seed lasers [2]. As theefficiency in the generation of higher harmonics declines
rapidly with the harmonic number, a multi step harmonic
generation in cascaded structures can be used to extend thewavelength range of this concept down to a few nanometers. Cascaded structures require an overall bunch length ofthe electron beam in the order of some hundred femtoseconds, because for each stage an unspoiled part of the bunchmust be used (fresh-bunch technique). These long bunches
usually exhibit parameter profiles at the end of the linac thatare far from being constant. For example, an energy chirp
is needed for bunch compression, the current is not constant and the emittance and energy spread vary for different
slices. As a result, the temporal and spectral power functions are not as smooth as known from theoretical studies.
Fig. 1 shows the power spectra of three different simulations including errors of the BESSY low energy FEL. The
spectra are not Gaussian anymore, and they vary considerably for each set of errors. Although the peak power varies
by less than 20% the pulse energy differs significantly.
The result of start-to-end simulations including phaseand amplitude errors in the gun and in the linac and charge£ Funded by the Bundesministerium fr Bildung und Forschung(BMBF), the State of Berlin and the Zukunftsfond BerlinÝ Bettina.Kuske@bessy.de

154

6.0
5.0
4.0
power [GW]

In the design of Free Electron Lasers (FEL), parameters like the peak power and the spectral power were established as figures of merit to evaluate the FEL’s output quality. However, spectra obtained with studies using bunchesfrom start-to-end simulations including errors show that it
is not sufficient to optimise these simple parameters. To
establish a stable and reliable user facility, parameters likepulse reproducibility, stability of the source point or signal
to background ratio have to be considered and optimised.
This paper suggests different criteria and parameters to describe and compare the output of different FEL schemeswith respect to a regular user operation. As these criteria
are not readily available from common FEL codes a postprocessing IDL code has been written, that extracts the relevant information from a standard GENESIS output. The
code is used to reevaluate start-to-end simulations for the
BESSY low energy FEL [1].

3.0
2.0
1.0
0.0

0

5

10

15

20

25

s [μm]

Figure 1: Power emitted by the final amplifier of the
BESSY low energy FEL-line for three different sets of errors in the gun and the linac. The pulses are not Gaussian.
and timing errors of the photo cathode laser, for the twostage low energy FEL line have been published in [3].
Those 24 cases are reevaluated in the current paper incorporating aspects that are relevant for the users of the FEL
radiation.
The BESSY soft X-ray FEL is designed as a user facility and hence the quality of the radiation will be judged
at the position of the experiment. For the passage throughthe beam line, three radiation parameters are of major importance, namely the transverse and longitudinal positionof the source point and its size. Vertical offsets give rise
to energy fluctuations behind the monochromator. Horizontal offsets lead to intensity fluctuations behind horizontal slits. Both offsets should not exceed 20% of the radiation size. Variations in the size or the location of thesource point degrade the energy resolution. Location fluctuations should not exceed one Rayleigh length. The signal
to background ratio and the pulse energy within a selectedbandwidth are further figures of great interest to the experimenters and beam line designers. Most of these criteria
are indirectly supplied by FEL codes like GENESIS [5],but not easily accessible, especially when a larger numberof runs are considered, as in tolerance studies. Therefore, asmall evaluation program has been written using IDL [6] incombination with the original GENESIS output interpretation routines. The given figures of merit as well as the limits set for stability, result from discussions with the BESSY

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experimental group.

PULSE ENERGY AND BACKGROUND
In order to describe the FEL pulse, the FWHM of thepulse is determined as well as the width of the pulse at 10%of the peak power, called the 10%-width. For a Gaussian
pulse, the ratio of the two is  1.8. 75% of the 24 investigated cases have a ratio around 1.2, indicating a pulse shapewith steep flanks, only one case showed a wide profile witha ratio bigger than three.
The integral of the power inside the 10%-width is called
the 90% pulse energy. Fig. 2 shows the peak power versus
the 90% energy for the 24 runs. Especially around peak
powers of 4 GW, where most pulses lie, the spread in pulse
energy, which is the figure of interest for the experiment is
considerable, due to the different pulse shapes. Therefore
the peak power is not well suited as a figure of merit.
Any power outside the 10%-width is considered to be
background. The signal to background ratio is important
for the quality of the experiments. The background is computed in percent of the total pulse energy, see Fig. 3. It isbelow 2% in all cases.
It must be mentioned, that in order to reduce the computation time only short parts of the complete 700 fs bunch are
simulated in the studies. The calculation of the backgroundat this point includes power emitted outside the 10%-widthof the 100 fs long bunch part tracked through the final amplifier. Contributions of the two parts seeded in upstream
stages will approximately double the shown background,while the contribution of unseeded parts is negligible.

SOURCE POINT CHARACTERISATIONIn seeded devices, the determination of the radiation size
is not straightforward. At the beginning, the radiation isSeeded FELs

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Figure 3: The background signal of the lasing part of thebunch in percent of the total pulse energy.

dominated by the seed. While the seeding radiation diverges, bunching builds up in the seeded part of the electron bunch and power is emitted, increasing exponentially.
The radiation size calculated by FEL codes thus usually increases in the initial part of seeded FEL amplifiers due tothe diverging seed and only later decreases due to the build
up of coherent FEL radiation.
FEL codes usually calculate the radiation size for eachslice of the bunch. For seeded devices though, averaging
over all bunch slices will yield wrong results, as the radiation size at the location of the seed’s interaction is muchsmaller than in the rest of the bunch, where the little power
emitted is independent of the seeded process.
The radiation size and divergence of each slice provided
by GENESIS has to be weighted with the power emitted by
the slice. The result follows the behaviour described earlier.
The radiation size has a maximum inside the final amplifier, where the divergence slightly decreases. In order tocalculate the phase space volume, the radiation size and divergence at the end of the final amplifier are used. Note thatfrom [7] it is known, that the beam waist, when calculated
exactly by back tracking the radiation, lies a couple of meters upstream and is smaller than at the end of the device.
Thus, the data plotted in Fig. 4 is an upper limit, and thephase space volume is expected to be up to 50% smaller.
Still most points lie close to the line indicating twice thediffraction limit. As the waist location will jitter from shot
to shot, this conservative estimate seems adequate.

SOURCE POINT STABILITY
Transverse Stability
As mentioned earlier, transverse jitter of the source point
reduces the energy resolution of the beam line. It is desired
to reduce the transverse fluctuations to less than 20% of therms radiation size.
Rather than first locating the source point, and then com155

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paring the beam offsets at this point to the radiation size,
the ratio between the transverse offsets and the radiation
size is computed at each point in final amplifier. The maximum of each of the resulting curves for the 24 runs is depicted in Fig. 5. These results only show shot-to-shot fluctuations, that are due to phase and amplitude errors in the
gun and in the linac. The amplitudes at the beginning ofm rms in the horizontal andthe cascades amounted tom rms in the vertical plan.
The major source for beam steering, though, arequadrupole jitters, e.g. due to ground vibrations. All time
independent beam offsets will be corrected by the steering magnets. Start-to-end calculations assuming a Gaussian rms quadrupole jitter of 300 nm, resulted in rms beam
offsets at the beginning of the HGHG cascades as listed in
Tab. 1.
Table 1: Transverse jitter (rms) at the end of the linac, due
to random quadrupole vibrations with 300 nm offsets (rms).
offset [m]
27.5
10.0

angle [rad]
1.55
1.57

For an estimate of their effect, bunches where started on
the phase space ellipse described in Tab. 1 and tracked
through the final amplifier. The largest transverse offsets
in the undulator where reached for large initial horizontal
amplitudes, the maximum reached was 28m. The minimal radiation size of all investigated cases is 140m, Fig.
4, therefore the 20% criterion is fulfilled throughout the
final amplifier for all runs. Alternative optics, taking the

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max (Δx / σ) [%]Figure 4: The size and divergence of the radiation field at
the end of the final amplifier. The black line indicates twice
the diffraction limit. The beam waist will in reality lie a few
meters upstream the end of the undulator and will be up to
50% smaller, on the other hand jitter of the waist location
has to be taken into account.

horizontal
vertical0

Figure 5: The maximum of the vertical and horizontaltransverse offsets in the final amplifier in percent of theradiation size, when errors in the gun and the linac are included in the start-to-end calculations. To include effectsof quadrupole offsets, the data can be linearly scaled.
larger horizontal trajectory jitter into account, could even
improve on the results.

Longitudinal Stability
The longitudinal location of the source point is difficult
to determine. It does not coincide with the saturation point.
Furthermore, in start-to-end calculations including errors,each bunch is populated differently and is seeded at varying
locations due to timing jitter, so that the source point moves
from shot to shot.
In [7], an exact, but time consuming procedure is introduced to locate the position and size of the radiation waist.
It is pointed out that the waist lies over 5m upstream ofthe end of the undulator for the investigated cases. Furthermore, the horizontal and vertical waist position do notnecessarily coincide.
A shot-to-shot jitter in the location of the source point ora variation in its size, leads to a degradation of the energy
resolution. The criterion for longitudinal stability has been
set to fluctuations in the beam radius of less than a factor of, which for Gaussian beams corresponds to variations of
the source point location of less than one Rayleigh length.
It can be extracted from [7]that the distance, in which
the beam radius increases by  is  5m and thus muchlarger than the theoretical Rayleigh length. With a total
length of the final amplifier of 7.5 m, the longitudinal stability criteria is fulfilled as long as the beam waist location
lies well inside the final amplifier.

SPECTRUM
Due to the energy chirp on the electron bunch and thejitter between the arrival time of the bunch and the seedinglaser, the average energy of the electrons interacting withSeeded FELs

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Figure 6: Histogram over the percent of total pulse energy
in 0.1% bandwidth around the central frequency of eachpulse. High temporal resolution experiments usually workwithout monochromator.
the seeding radiation varies, which results in a fluctuationof the central wavelength of the HGHG spectrum.
In order to evaluate spectral properties, the routines supplied by the post processing IDL-code XGENESIS are usedon the Fairfield power on axis. The fraction of the energy
in 0.1% bandwidth is calculated and compared to the totalenergy in the spectrum. The bandwidth can be either taken
around a given frequency for all runs, or for the central frequency of the individual spectra.
Different experiments are interested in different spectral
qualities. Experiments depending on high temporal resolution will usually work without monochromator and dependon the energy in a certain bandwidth around the resonant
wavelength of each pulse. This case is depicted in Fig. 6,
where 75% of the runs hold more than half and up to 90%of their power in 0.1% of the bandwidth of their resonant
frequency, amounting to 50 J on average.
High energy resolution experiments need a large fractionof the total pulse energy close to the central frequency ofthe monochromator, Fig. 7. 70% of the runs would still
deliver above 40% of their total pulse energy within thegiven bandwidth. These experiments usually average overmany shots.

CONCLUSIONFEL codes deliver information about the development of
the radiation inside the amplifying devices during the interaction between the electrons and the electro magnetic
field. The quality of the produced radiation is judged muchfurther down the beam line at the experimental station. Figures of merit have been proposed to evaluate the FEL output in view of the beam line and experimental demands. All
quantities can be deduced from the output provided by, e.g.
GENESIS. A post processing code for GENESIS has been

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Figure 7: Histogram over the percent of total pulse energy
in 0.1% bandwidth of a given (monochromator) frequency.
The figure is important for high energy resolution experiments.
introduced. It has been used to evaluate the results of 24
complete start-to-end runs including errors in the gun andthe linac of the BESSY low energy FEL line. The given
criteria for the radiation quality could be met. Despite theimmense computing effort it would be desirable to improveon the statistics.

ACKNOWLEDGEMENT
I would like to thank my colleges Johannes Bahrdt andMichael Scheer of the BESSY experimental groups for thehelpful discussions.

REFERENCES[1] ”The BESSY Soft X-ray Free Electron Laser, Technical Design Report”, March 2004, eds.: D. Krmer, E. Jaeschke, W.
Eberhardt, ISBN 3-9809534-0-8, BESSY, BERLIN (2004)[2] ”VUV/Soft X-ray FELs on the Horizon”, Rene Bakker,
http://leg.web.psi.ch/public/publications/TOAB001 Talk.pdf[3] ”Start-To-End Simulations for the BESSY Low and Medium
Energy FEL Line Including Errors”, B. Kuske, M. AboBakr, K. Goldammer, A. Meseck, BESSY, Berlin, Germany,
FEL2005, proc.
[4] ”Impact of Realistic Bunch Profiles and Timing Jitter on the
Output of the BESSY Low Energy FEL Line”, B. Kuske, M.
Abo-Bakr, A. Meseck, BESSY, Berlin, Germany, FEL2005,
proc.
[5] ”GENESIS 1.3: A Full 3D Time Dependent FEL Simulation
Code”, S. Reiche, Nuclear Instruments and Methods A429
(1999) p. 243[6] Interactive Data Language, http://www.ittvis.com/idl/[7] ”Source Characterisation of the BESSY Soft X-Ray FEL ” A.
Meseck, M. Abo-Bakr, J. Bahrdt, B. Kuske, BESSY, Berlin,
Germany, FEL2005, proc.

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STUDY OF A DEFLECTING DISPERSIVE CHICANEFOR THE BESSY SOFT X-RAY FEL∗
A. Meseck† , G. Wüstefeld‡
BESSY GMbH, Albert-Einstein-Str.15, Berlin, Germany.
Abstract
High power, short pulse length and full coherence are
the main parameters of the second generation free electron
lasers like the BESSY Soft X-ray FEL. To provide radiation with these properties, BESSY proposed a seeded FEL
facility based on high-gain harmonic-generation (HGHG)
scheme [1]. This scheme uses cascaded stages each consisting of undulator/dispersive chicane/undulator section to
up-convert the seeding frequency.
The transverse separation of the seeding radiation andelectron beam after the first undulator is desirable, as not
only the output of the following undulators improves but
also the seeding radiation itself can be used for diagnostics.
Based on an exact linear model, a dispersive chicane isdesigned for the BESSY FEL, which deflects the electron
beam providing the separation without coupling and spoiling effects [2]. The linear model and the deflecting chicane
will be presented and the properties of the chicane will be
discussed by means of simulation results.

INTRODUCTION
The BESSY Soft X-Ray FEL is designed as a multi-user
facility consisting of three independent FEL lines. Eachline is seeded by a tunable laser covering the spectral rangeof 230 nm to 460 nm. The target wavelength ranges from
51 nm to 1.24 nm with peak powers up to a few GWs andpulse lengths less than 20 fs (rms). The polarization of the
fully coherent radiation will be variable.
Cascades of two to four HGHG stages are planned toreduce the existing laser wavelength to the target range of
the BESSY-FEL. In the first undulator of such an HGHG
stage, the modulator, an energy modulation is imprinted
on the electron beam by the seeding radiation. The following dispersive chicane converts this energy modulation
to a spatial modulation which is optimized for a particularharmonic. The second undulator, the radiator, is resonant
to this harmonic and generates radiation at the higher harmonic, which serves as seed for the next stage. The last
HGHG-stage is followed by the so-called final amplifier. It
is seeded at the desired wavelength and the amplification
process is brought to saturation.
The quality of the FEL output radiation depends strongly
on the quality of the frequency up-conversion procedure,
which again depends on the quality of the spatial modulation (bunching) and on the quality of the seeding radia∗ Work funded by the Bundesministerium für Bildung und Forschungand the Land Berlin† meseck@bessy.de‡ wuestefeld@bessy.de

158tion. Although in an HGHG stage, the radiator is resonant
to a harmonic of the seeding radiation, short interactions
between the seeding radiation and the electron beam arestill possible. During such an interaction the phase correlation between the seeding radiation and the electron beamis good enough to permit an energy exchange. These interactions are short as the resonance condition is not fulfilled for the seeding radiation, but due to the high intensity of the radiation, the electron beam quality degrades,
and thus the radiator output quality suffers. Separating theseeding radiation and the electron beam after the energy
modulation would avoid these undesired interactions. In
addition, the separation offers the possibility to use the radiation - seeding radiation as well as the spontaneous undulator radiation- for diagnostics.
In principle, the separation can take place before, insideor after the dispersive chicane, but it has not to affect the
spatial modulation. Also other effects like residual dispersion, coupling or increased beam size have to be avoided.
Each of the dispersive chicanes planned for the BESSY
FEL consist of four dipoles providing a closed bump. Generally, the dispersion strength, which is necessary to convert the energy modulation to the spatial modulation, is nothigh. Hence the bump amplitudes are not large enough toinstall mirrors or other optical elements to deflect the radiation. A separation of the radiation and electrons can only
take place by an additional bending of the electron beam. A
simple bending, with an additional dipole or due to a mismatch of the four bump dipoles, causes residual dispersion,
coupling between transverse and longitudinal motion andspoils the bunching. Thus it deteriorates the radiator output
strongly.
However, an exact linear model offers the possibility todesign an optimal dispersive section, which allows the separation of the electron beam and seeding radiation without any coupling and spoiling effect. In this paper we
present the dispersive section which is designed based on
this model. Comparisons of simulation results of an HGHG
stage using the four dipole chicane and the deflecting dispersive section respectively, demonstrate that the new dispersive section meets all demands.

THE DEFLECTING DISPERSIVE
CHICANE
The dispersive chicane, which converts the energy modulation of the bunch to a spatial density modulation is optimized for a particular harmonic of the seed. This spatial modulation results when the energy modulated beam
passes through a dispersive chicane, which is described bySeeded FELs

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Figure 1: Horizontal trajectory of the electron beam asa function of beam line position. The red line shows
the trajectory for the deflecting chicane (dipoles in red,quadrupoles in blue and undulators in yellow colours).

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This deflecting chicane consists of two dipole families andone quadrupole, tuned as an achromatic bend with variable
m56 value. The integrated dipole fields are kept constant todefine the deflection angle. One family is excited opposite
to the other one, the difference between the integrated fields
of both family yields the value of m 56 . The quadrupole
tunes the dispersion outside of the chicane to zero. At theentrance and exit side of the chicane an optical matching
section is required, consisting of one quadrupole doublet
on each side. For the full optical line m 56 =6.5 · 10−5 , thesame tuning as for the simple bump. Different settings ofthe dipoles leads to different orbits inside the quadrupole,
this steering has to be taken into account.
This optics is 10 m long and has the advantage of separating the electron and photon beams, and delivering thenecessary m56 . In addition it avoids the coupling between
different planes of the electron motion as described below.
The separation can be used for easier diagnostics purposesand eliminates further unwanted interaction of the photon
beam with the electrons.
The linear matrix theory can be used, to discuss the coupling of the horizontal (x, x  ) and longitudinal (z, z  ) particle oscillations [2]. Effects of the vertical plane have to
be treated similarly, but are presently not discussed. A general transfer matrix m ij describes the chicane plus matching sections. The longitudinal elements m 51 and m52 are
not independent. They are coupled to the horizontal plane,
described by

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and
m52 = m16 m22 − m12 m26 .

Figure 2: Horizontal (blue) and vertical (green) beta functions and dispersion (1000 times enhanced, red) of the deflecting chicane. The value of m 56 is tuned to 6.5 · 10−5(solid line) and 26 · 10 −5 (dots), colours of magnets as described in fig. 1.
a properly chosen matrix element m 56 . The energy modulated electrons must be shifted by λ/4 in the longitudinal
position within the dispersion section for the optimal radiator output. For BESSY FEL seeding wavelength, thistranslates to a distance of 60 nm to 120 nm. Note, the factor two in the distance tuning-range is given by the spectral
range of the seeding radiation.
The necessary density modulation is commonly
achieved by a simple four dipole bump of zero integrated
dipole field strength. By a scaled field strength change ofthe four dipoles, m 56 can be varied.
Instead of the simple 2 m long bump, we propose a moreelaborate optics, which deflects the beam by a fixed angleof 10 mrad, see Fig. 1 and 2. In addition, the value of m 56
can be varied by a factor of four, twice as much as required.

Seeded FELs

The coupling depends on the dispersive terms m 16 andm26 . If dispersion is produced and m 16 and m26 arenonzero, for example by a single dipole kick, one gets adependency of the longitudinal position z on the horizontal
plan (x, x ). Even a single dipole kick of 5 mrad generates
dispersion and in turn coupling. Using the BESSY FEL parameters of a horizontal beam emittance of 0.9·10 −9 m rad
one obtains a longitudinal spread of 280 nm as a result of
the final beam diameter. This can not be tolerated for aproper seeding process. With the presented chicane, thiscoupling is cancelled, i.e. the matrix elements m 51 andm52 are zero.
As the transverse beam amplitudes and the accumulated
spread in chromatic phase errors stay sufficiently small, thelayout of this section is done without any higher order correcting multi poles. The comparison between the simple
dipole bump and this deflecting chicane shows very good
agreement, as shown in the next section. For the comparison, the deflecting chicane has the same Twiss parameters
β and α as the four bump chicane at the start and end points.
Both sections have a m 56 value of 6.5 · 10−5 . In this casethe rms-beam dimensions are equal (within the numericaluncertainties due to limited number of macroparticle in the159

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Figure 3: The bunching at the entrance of the first radiatorof medium-energy FEL along the bunch for both dispersive sections. Both dispersive sections produces the optimal density modulation for the given energy modulation.

Figure 4: The radiator output power of the first stage of themedium-energy FEL for both dispersive sections. Thereexists a small difference between both cases, which is negligible concerning the seeding of the next section.

simulations) for both solutions, independent of the different phase advances obtained from the different approaches.
This chicane is similar to the optics of the NewSUBARU storage ring [3, 4]. It was recognized in this ring, thateven a very small power supply ripple of the dipole families
could limit the isochronous tuning of the optics [5]. However, this seems not to be a problem for our parameters. A
deflection error of 10 −3 in one of the dipole families leads
to a two times larger error of m 56 , which is negligible.

PERFORMANCE SIMULATION OF BOTHDISPERSIVE SECTIONSIn order to compare the performance of the new deflecting dispersive chicane with the simple four dipole chicane, the first stage of the medium-energy FEL-line of the
BESSY FEL [1] was simulated for both cases. The simulations were carried out using a modified version of thesimulation code GENESIS 1.3 [6] which includes a transfer matrix routine. This routine was used to model bothdispersive sections at the entrance of the radiator.
The bunching at the entrance of the radiator is shown in
Fig. 3 for both cases. For the given energy modulation, bothdispersive sections produce the optimal spatial modulation.
Fig. 4 displays the temporal power distribution at the exitof the first radiator. This radiation will be used as a seed
for the next section. The difference in maximum power
between both cases is negligible concerning the seeding.
The development of the horizontal and vertical electron
beam size (rms) along the first radiator is shown in Fig. 5
and 6 for both dispersive sections. Because of the limited
number of macroparticles that can be simulated, numericaldeviations of the rms beam size of order 0.5% are expected.
Therefore any deviation in beam sizes less than 0.5 % canbe neglected. Obviously, there exist a small difference in160

Figure 5: The development of the horizontal electron beam
size (rms) along the first radiator for both dispersive sections. The difference between the beam sizes is less than
0.5 % and can be neglected.
vertical divergence for both cases of about 0.4 μ rad. Thisdifference might also indicate small tuning differences of
the two chicanes.
The above simulations were done for constant averageenergy along the bunch. In order to exclude undesired effects due to the energy chirp of the electron beam needed
for the bunch compression [7], the simulations of bothdispersive sections were repeated with an energy chirped
beam. The bunching and radiator output are almost thesame for both dispersive sections. The spectral purity isconserved for both dispersive sections, see Fig. 7. Dueto the energy chirp, there is a shift in the wavelength [7],which is independent of the choice of the dispersive section.

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beam line,” BESSY (Berlin) Technical Report TB 227/05,
2005.
[3] A. Ando, S. Amano, S. Hashimoto, H. Kinosita, S.
Miyamoto, T. Mochizuki, M. Niibe, Y. Shoji, M. Terasawa,
T. Watanabe and N. Kumagai, “Isochronous storage ring of
the New SUBARU project,” J. Synchrotron Rad. (1998). 5,
342-344.
[4] A. Amiry, C. Pellegrini, E. Forest, D. Robin, “Study of magnetic lattice for a quasi-isochronous ring,” Particle Accelerators, Vol. 44, Num. 2, p.65, 1994.
[5] Y. Shoji, Y. Hisaoka, T. Matsubara, T. Mitsui, “Longitudinal
Coherent Oscillation Induced in Quasi-isochronous Ring,”
proceedings EPAC 2006, Edinburgh (UK).
[6] S. Reiche, GENESIS 1.3, Nucl. Instr. Meth. A 429 (1999)
243.

Figure 6: The development of the vertical electron beamsize(rms) along the first radiator for both dispersive sections.

[7] B. Kuske, M. Abo-Bakr, A. Meseck, “Impact of Realistic
Bunch Profiles and Timing Jitter on the Output of the BESSY
Low Energy FEL Line,” proceedings FEL 2005, Stanford
USA.

Figure 7: Spectrum of the output radiation for both dispersive sections. There is a shift in the wavelength due to theenergy chirp. This is independent of the dispersive section.

CONCLUSION
Using an exact linear model an optimized dispersive section is designed for the medium-energy FEL-line, which allows the separation of the electron beam and seeding radiation without any coupling and spoiling effect. Based on thelinear coupling matrix, a deflecting dispersive chicane is
introduced. The comparison of the simulation results of an
HGHG stage shows that the new dispersive section meetsall demands.

REFERENCES[1] The BESSY Soft X-ray Free Electron Laser, Technical Design Report March 2004, eds.: D.Krämer, E. Jaeschke, W.
Eberhardt, ISBN 3-9809534-08, BESSY, Berlin (2004).
[2] G. Wüstefeld, “Horizontal-longitudinal coupling in the FEL

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SIMULATION STUDIES ON THE SELF-SEEDING OPTION AT FLASH∗
V. Miltchev† , J. Rossbach, Hamburg University, 22761 Hamburg, Germany
B. Faatz, R. Treusch, DESY, 22603 Hamburg, Germany.
Abstract
In order to improve the temporal coherence of the radiation generated by the Free-electron LASer in Hamburg(FLASH), a two-stage seeding scheme [1] is presently under construction. It consists of two undulator stages separated by a magnetic chicane and a monochromator. In
this contribution we investigate various configurations of
the electron optics of the seeding set-up. The optimizationof the lattice in the first (seeding) stage and the parametersof the magnetic chicane will be discussed. Simulation results for the performance of the second (seeded) stage of
the FEL will be presented.

INTRODUCTION
The basic setup of the self-seeding option [1, 2] is illustrated in Fig.1. It consists of two undulator stages separated
by a magnetic chicane and a monochromator. The first undulator operates as a SASE FEL in the linear regime. Afterit, the electrons are separated from the SASE radiation. The

Figure 1: Schematic layout of the self-seeding setup.
electron beam passes through the magnetic bypass, that isused to remove the longitudinal charge density modulation(micro bunching). The radiation pulse is spectrally filteredin a high resolution grating monochromator [3] and afterwards is superimposed with the electron beam at the entrance of the second undulator. Thus the monochromatic
photon beam serves as a coherent radiation seed, which is
amplified up to saturation in the second undulator. The
seeding increases the spectral brilliance by about a factorof 100, i.e. the output power of the seeded FEL is concentrated in a single line which is about a hundred times narrower than the spectrum of the conventional SASE FEL.
The concept of the self-seeding has the advantage that it isindependent of any external radiation source and the seedis naturally synchronized with the electron bunch. An additional advantage is that the seeding wavelength is continuously tunable. The monochromator optics, to be installed∗ This work has been partially supported by the EU Commission in the
Sixth Framework Program, Contract No. 011935-EUROFEL† velizar.miltchev@desy.de

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at FLASH, is designed for operation in the 6-60 nm range[2]. It is important to note, that the gain in the first undulator section is essential for the effective operation of the selfseeded FEL. The output power level should be sufficiently
low (about two-three orders of magnitude below saturation)in order to preserve the energy spread and the emittance ofthe electron beam. On the other hand the power of the seed,obtained from the first stage, should be much higher thanthe power of the shot noise in the second undulator.

ELECTRON OPTICS
Undulator stages
The undulator stages for the self-seeding option are subdivided into segments of about 4.5 m length. The first andthe second undulator consist of three and six such segments
respectively. A separated focusing system for the undulator
stages is used at FLASH [4]. The focusing is accomplishedby quadrupole doublets placed in-between two neighbouring undulator segments. The main feature of such focusing
scheme, relevant to the implementation of the self-seeding,is the variable quadrupole strength. The total length of thefirst undulator (about 14.5 m) is optimized for operation ata wavelength in the order of 6 nm. The minimum average β-function for this case is about 4.5 m. As mentioned
above, the power gain in the first undulator is crucial for the
performance of the self-seeded FEL. Therefore, in order tocompensate the scaling of the gain with the wavelength,
one can vary the quadrupoles strength i.e. tune the average
β-function accordingly.

Electron bypass
The bypass has to meet various requirements in order toensure the proper operation of the self-seeding. The mostessential of them are summarized in the following:• Generation of an additional path length for the electrons, which is equal to the extra path length of thephotons in the monochromator.
• Reduction of the micro bunching generated by the
SASE process along the first undulator section. The
micro bunchingafter the
 bypass is reduced by a factor
2 2of exp − 12 σδ2 R56
kL [5]. Here σδ is the fractional
momentum spread, R 56 is the momentum compaction
factor of the bypass and k L the radiation wavenumber.
• Adjustment of the electron optics to the optics of thetwo undulator sections for radiation wavelengths in
the range 6-60 nm.

Seeded FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany• Correction of the first and second order dispersion,
minimization of the degradation of beam quality due
to coherent synchrotron radiation effects.

Figure 2: Final magnet layout of the electron bypass for the
Seeding Option (side view). black: steerer, blue: dipole,green: quadrupole, vertical focusing, red: quadrupole, horizontal focusing, yellow: sextupole.
In contrast to the simplified scheme shown in Fig. 1, thefinal design of the electron bypass optics [2], as sketchedin Fig. 2, consists of a total 37 magnets.

SIMULATION TECHNIQUESThe simulation studies presented in this paper divide into
two groups: studies on the performance of the self-seeded
FEL and investigations of the impact of the coherent synchrotron radiation (CSR), emitted in the electron bypass,on the output brilliance.

Performance of the self-seeded FEL
The performance of the self-seeded FEL has been simulated with the 3-D time dependent FEL-code GENESIS[6]. The simulation is split into two runs - the first undulator operating as a SASE FEL and then simulation of theelectron bypass together with the second undulator. The
complete particle distribution at the end of the first undulator is extracted and then is used in the next simulation step.
The electron bypass is implemented in GENESIS by themeans of a 6×6 transfer matrix. In the second step, the particle distribution extracted from the first part of the simulation is transformed with the help of the bypass matrix andthen tracked through the second undulator section. A certain wavelength λseed and average power P seed is assumed
for the external seed, which should be obtained at the output of the monochromator beamline. In the presented studies the two extreme cases λseed ≈ 6 nm and λseed ≈ 60 nm
are considered. It is helpful to remind that the seed powershould fulfill the requirement P seed  Pshot , where Pshot
is the effective shot noise power. Since P shot ≤100 W, aseed of Pseed ≈10 kW has been assumed in all cases. The
code ELEGANT [7] has been used for the calculations of
the electron optics, to find the electron beam matching conditions and for the calculation of the transfer matrix of the
bypass. The electron beam parameters, which have been
assumed in the simulations, are summarized in Table 1

Studies on CSR effects
These investigations follow a similar scheme as the one
described above. However, in order to include CSR ef-

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MOPPH053

Table 1: Nominal electron beam parameters for operation
at 6 nm
Energy, E0
Peak current, I0
rms energy spread
Normalized rms emittance,  n
rms bunch length, σ z1000 MeV
2500 A
0.2 MeV
2 mm mrad
50 μm

fects in the numerical calculations, the bypass has been
simulated together with the first undulator section with the
ELEGANT code. The program incorporates 1-D CSR algorithm [8] for dipoles and drift spaces. The produced
particle distribution file is afterwards analyzed and converted into averaged slice information, which is used by
GENESIS to simulate the interaction between the electrons and the radiation field along the second undulator
section. In order to quantify the influence of the emitted
synchrotron radiation, the described procedure has been repeated twice. Once including the CSR effects and second
time with the CSR algorithm switched off. The average
spectral flux has been considered as a figure of merit tocompare the radiation quality for the two cases.

SELF-SEEDING PERFORMANCE
As it is pointed out in [4], one of the main advantagesof the separate focusing is that the number of quadrupoles
in-between the undulator segments can be reduced, what

Figure 3: β-function (a) and dispersion (b) along the selfseeding electron beamline.
results however in an increase of the minimum average beta function β. For the case of electron energy
E0 =1000 MeV, corresponding to a wavelength λ ≈ 6 nm,
an average β-function of about 4.5 m is used. As shownin Fig.3, the design of the electron optics allows operation with the same β at the both sides of the magnetic
chicane. For such setup the first stage works in the linear
regime (see Fig. 4) with an average power of the output
radiation of about 5 MW. Again in Fig. 4 it is shown theevolution of the micro bunching along the undulator. The
kinks around Z=10 m and Z=5 m (less pronounced) are due

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Proceedings of FEL 2006, BESSY, Berlin, Germany

6.0
5.0

average power
micro bunching<P> (MW)

4.0
3.0
2.0
1.0
0.0
0

5

10

simulations, is to increase β in the first stage to a value inthe order of 25 m, corresponding to the desired low gain of
about three orders of magnitude below saturation.
|<exp(iT)>|

0.019
0.017
0.015
0.013
0.011
0.009
0.007
0.005
0.003
0.001
15

Z (m)

Variation of the seeding wavelength
The monochromator design gives the possibility for variation of the wavelength of the seed across the full bandwidth of the FEL amplifier. Therefore it is interesting toinvestigate the influence of the seeding wavelength on the
power and the spectrum of the output radiation. In Fig. 6
the spectral flux along the second undulator is presented
for various seeding wavelengths. The simulations show amaximum at Z ≈ 15.5 m for λ seed = 6.305 nm. One has to

Figure 4: Average radiation power and micro bunching(right axis) along the first undulator.

1.4

0.161

1.2

0.141

1.0

0.121
0.101

0.8

0.081

0.6

0.061

0.4

0.041

average power

0.2|<exp(iT)>|<P> (GW)

to debunching taking place in the quadrupole doublet intersections [4]. Figure 5 shows the radiation power and0.021

micro bunching

0.0

Figure 6: Spectral flux as a function of the undulator lengthfor different λ seed and constant seeding power.

0.001
0

10

20

30

Z (m)

Figure 5: Radiation power and micro bunching (right axis)
along the second undulator. Seeding wavelength λ seed ≈6.31 nm .
bunching as a function of the length of the second undulator. A comparison between the graphs in Fig.4 and Fig.5
demonstrates that the momentum compaction factor of the
bypass R56 ≈ 0.73 mm is sufficient for the reduction of
the micro bunching induced in the first undulator.
For operation at electron beam energy of 325 MeV, corresponding to a resonant wavelength of about 60 nm, one
has to consider modifications in the electron optics of thefirst undulator section and the chicane. These changes
are necessary because of the scaling of the FEL gain withthe wavelength. The electron optics designed for 6 nm,with β ≈ 4.5 m (see Fig.3), provides saturation length
in the order of 20 m for SASE mode. For the 60 nm case,however, the saturation length is only about 9 m, which issignificantly shorter than the first undulator (14.5 m) andtherefore not acceptable from the point of view of the selfseeding option. One possible solution, as confirmed by

164

Figure 7: Spectrum (a) and power along the radiation pulse(b) in the second (seeded) section at Z=15.5 m.
mention that the position of the maximum of the spectral
flux is related to the onset of the nonlinear regime (see Fig.
5). Further increase of the output power is coupled with aspectral broadening and in consequence with reduction of
the spectral flux. As studied in [9], the length of the second

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MOPPH053

undulator can be optimized in order to compensate the large
fluctuations of the seed intensity after the monochromator.
The simulation results plotted in Fig. 7 demonstrate the effect of the self-seeding on the spectrum and the power ofthe output radiation. The two graphs in Fig. 7 correspondto the maximum of the spectral flux.

CSR effects
The electron bunches entering the magnetic chicane areof rms length σz ≈ 50 μm and high peak current I 0 ≈2.5 kA. Therefore, despite the small bending angle θ = 3 ◦ ,Figure 9: Demonstration of the impact of CSR effects - thespectral flux as a function of the undulator length.

CONCLUSIONS AND OUTLOOK

Figure 8: Distortion of the longitudinal phase space due tosynchrotron radiation produced in the bypass dipoles.
the coherent component of synchrotron radiation, generated in the bypass dipoles, can be significant and might
dilute the electron beam quality. Simulations of the CSRinduced emittance dilution have been made using the ELEGANT code, which result in a projected emittance growthin the order of a percent. The slice emittance is, however,almost unchanged. A much more significant impact on
the longitudinal phase space is expected, as presented in
Fig.8. The total relative energy spread has increased from2 × 10−4 up to about 5 × 10 −4 . The growth of the energy
spread is due to the correlation in the longitudinal phasespace created by the synchrotron radiation, but on the other
hand the slice energy spread is practically unaltered. The
increased energy spread will drive more particles outsideof the amplifier bandwidth and as a result one anticipates a
reduction of the gain. Moreover the correlation in the phasespace produces side bands in the spectrum or in other words
spectral broadening. Fig. 9 shows that there is about a factor of two decrease in spectral flux due to CSR effects. It
is important to note that we have considered the worst casescenario i.e. the bypass optics and electron beam parameters have not been tuned to mitigate the impact of CSR.

Seeded FELs

The operation of the two stage FEL has been studied,taking into account all the details in the design of the electron optics. Simulation results demonstrate a feasible operation in a wide range of electron energies and wavelengths.
Investigated is also the possibility to fine tune the seeding wavelength, accomplished using the monochromator
beamline settings. The impact of the coherent synchrotron
radiation emitted in the bypass dipoles was studied. The
simulations predict about a factor of two reduction of thespectral flux due to CSR. Further studies including wave
front propagation through the monochromator beamline are
ongoing [10]. As a next step the tolerances of the electron
beam parameters, the accuracy of magnets alignment andthe impact of the magnetic field errors will be analyzed.

ACKNOWLEDGEMENTS
We thank A. Meseck for the modifications of the code
GENESIS and for many fruitful discussions.

REFERENCES[1] J. Feldhaus et. al., Opt. Commun., 140 (1997), 341.
[2] R. Treusch et. al. ”The Seeding Project for the FEL in TTF
Phase II”, HASYLAB Annual Report 2001.
[3] R. Reininger et. al., Nucl. Instr. and Meth. A (2001) 467468, 38.
[4] B. Faatz et. al., Nucl. Instr. and Meth. A 475 (2001), 603.
[5] E.L. Saldin et al., Nucl. Instr. and Meth. A 539 (2001), 499.
[6] S. Reiche, Nucl. Instr. and Meth. A 429 (1999), 243.
[7] M. Borland, ”elegant: A Flexible SDDS-Compliant Codefor Accelerator Simulation,” Advanced Photon Source LS287, September 2000.
[8] M. Borland, Phys. Rev. ST Accel. Beams 4, 070701 (2001).
[9] E.L. Saldin et al., Nucl. Instr. and Meth. A 445 (2000), 178.
[10] Johannes Bahrdt et.al., ”The Properties of the FEL Output
for Self Seeding”, these proceedings.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

FERMI@ELETTRA: A SEEDED FEL FACILITY FOR EUV AND SOFT XRAYS
E. Allaria, C.J. Bocchetta, D. Bulfone, F. Cargnello, D. Cocco, M. Cornacchia, P. Craievich,
G. D’Auria, M.B. Danailov, G. De Ninno, S. Di Mitri, B. Diviacco, M. Ferianis, A. Galimberti,
A. Gambitta, M. Giannini, F. Iazzourene, E. Karantzoulis, M. Lonza, F. Mazzolini, F. Parmigiani,
G. Penco, L. Rumiz, S. Spampinati, M. Stefanutti, G. Tromba, M. Trovo’, A. Vascotto,
M. Veronese, M. Zangrando, Sincrotrone Trieste, Trieste, Italy
J.N. Corlett, L.R. Doolittle, W.M. Fawley, S.M. Lidia, G. Penn, I.V. Pogorelov, J. Qiang, A. Ratti,
J.W. Staples, R.B. Wilcox, A. Zholents, LBNL, Berkeley, CA, USA
P. Emma, Z. Huang, J. Wu, SLAC, Stanford, CA, USA
W. Graves, F.X. Kaertner, D. Wang, MIT, Cambridge, MA, USA
Abstract
We describe the conceptual design and major
performance parameters for the FERMI@Elettra Free
Electron Laser (FEL) project funded for construction at
Sincrotrone Trieste, Italy. This user facility complements
the existing storage ring light source at Sincrotrone
Trieste, and will be the first facility to be based on seeded
harmonic cascade FELs. Seeded FELs provide high peak
power pulses, with controlled temporal duration of thecoherent output allowing tailored x-ray output for time
domain explorations with short pulses of 100 fs or less,and high resolution with output bandwidths of the orderof meV. The facility uses the existing 1.2 GeV S-band
linac, driven by electron beam from a new highbrightness RF photocathode gun, and will provide tunable
output over a range from ~100 nm to ~10 nm, and APPLE
undulator radiators allow control of x-ray polarization.
Initially, two FEL cascades are planned, a single-stage
harmonic generation to operate over ~100 nm to ~40 nm,
and a two-stage cascade operating from ~40 nm to ~10
nm or shorter wavelengh, each with spatially andtemporally coherent output, and peak power in the GW
range.

INTRODUCTION
The single-pass seeded FEL project FERMI@Elettra
will be a User facility providing quality photons in the
EUV to soft X-ray range. Photon production will be basedon harmonic generation. The concept design has beenstudied and optimised towards a detailed engineering
phase [1]. All major parameters and systems have beenstudied and an overview is presented here.
Comprehensive studies including collective effects fromspace charge, coherent synchrotron radiation andwakefields as well as nonlinear dynamics from RF
waveforms and bunch compressors have been performed
to determine the optimum electron beam parameters forthe facility. The studies have included error tolerancesand beam jitter sensitivities in start-to-end computations.
The project covers the lower energy region of the
XUV-X ray spectrum. With a peak brightness of morethan ten orders of magnitude greater than 3rd generation
sources, full transverse coherence, transform limited

166

bandwidth, choice of pulse lengths of the order of a ps orless, variable polarization and energy tuneability, the
FERMI source represents a powerful tool of scientificexploration in a large field of research. The coherence
properties will provide single-shot imaging, allowing thestudy of chemical reactions as they happen. The highpeak power will allow the study of non-linear multiphoton processes in a regime never explored before. The
short time properties will allow the visualisation of ultrashort nuclear and electronic dynamics. The facility will
enable the study of dilute samples of paramountimportanceinatmospheric,astrophysicalandenvironmental physics, as well as in the characterizationof nano-size materials. The applications extend fromchemical reaction dynamics to biological systems,
materials
andsurfaces,
nano-structuresandsuperconductors. The nature of harmonic generation
schemes, with an external laser driving the FEL process,is particularly suitable for pump/probe synchronization at
the ps time scale or less.
Figure 1 shows the layout of the facility. The
accelerator and FEL complex is housed below ground andis composed of the following parts: (a) A photo-injector
and two short linac sections, where a bright electron beam
is generated and accelerated to ~100 MeV. (b) The main
linear accelerator, where the electron beam is timecompressed and accelerated to a final energy of ~1.2
GeV. (c) A beam transport system to the undulators. (d)The undulator chains where the FEL radiation is
generated. (e) The undulator to experimental areatransport lines. (f) The experimental area. The new
constructions include pushing back by ~ 80 m the linac
tunnel and surface klystron gallery to make room for thephoto-injector, accelerating sections and the first bunch
compressor. At the downstream end, the klystron gallery
is extended by ~30 m to power more accelerating
sections. A FEL hall will be constructed below ground at
the exit of the linac with transverse dimensions for the
installation of up to four undulators side-by-side. Finally,an experimental hall, also below ground, will be
constructed to house the FEL radiation transport optics
and the experimental hutches. The facility will be
provided with new support laboratories and office spaces.

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MOPPH054

Figure 1: Schematic FERMI layout beside the ELETTRA storage ring building (g). See text for details.

THE PHOTO-INJECTOR
The photo-injector [2] is based on the proven 1.6 cellelectron gun developed at BNL/SLAC/UCLA andadopted by the Linac Coherent Light Source (LCLS). The
RF gun will provide a peak-accelerating gradient of 110
MV/m and an exit beam energy of around 5 MeV from a
10 MW peak input pulse (2.8 μsec). The injector willproduce a 10ps long pulse with 0.8-1 nC charge and a rms
normalized transverse emittance of 1.2 mm-mrad at 100
MeV. The initial repetition rate of 10 Hz will later be
increased to 50 Hz following a modified gun design. The
design includes a solenoid for emittance compensation, an
off-axis diagnostic line and acceleration to 100 MeV withtwo booster S-band rf sections. These sections, named
S0A and S0B, are part of the present Elettra injection
system. Their on-axis, iris coupled cells resonate at 2.998
GHz in the 2π/3 mode, and provide peak accelerating
gradients of ~18 MV/m, for a total energy gain of ~45
MeV (with operational 10% energy margin). The booster
modules include solenoid magnets to provide transverse
focusing, to assist with emittance compensation, and tomatch the optical functions at the input to the main linac.
A laser pulse provides temporal and spatial shaping of
the electron bunch. To compensate wakefield effects inthe main linac sections [3], the electron bunch should
ideally have a linear ramped peak current distribution at
the exit of the injector rather than a flat top [4]. Studies
have showed that such a profile at the start of acceleration
produces a more uniform energy and current profile at theentrance to the undulators. The FERMI photo-injector
addresses this novel concept by using a laser profile thathas a quadratic ramp. Space charge forces subsequently
transform this distribution to a linear ramped current
shape at the exit of the injector, i.e. a profile where thecurrent in the bunch increases approximately linearly withtime. The photo-injector laser system [5] includes two
amplifier stages, a regenerative one followed by amultipass, and reaches pulse energy of 20 mJ in the IR.

Seeded FELs

Pulse shaping is done partially in the IR, by an acoustic
optic dispersive filter (DAZZLER), and completed in UV
in a transmission grating based stretcher or Fouriersystem. Beam shaping is done either in the IR or in the
UV by an aspheric shaper. A small part ~400 μJ of the IR
beam is split away and transported for use by the laser
heater.
Beam dynamics in the injector system have been
extensively modelled from photocathode emission to theexit of the booster accelerator modules using 2D and 3D
space-charge tracking codes (GPT and ASTRA).
Simulations confirm that electron beam performance
objectives for injection into the main linac at ~ 100 MeV
are reachable. The timing and charge stability are bothchallenging, 0.5 ps and 1% respectively, but have beenshown to be within present state of the art techniques.

ACCELERATION, COMPRESSION AND
BEAM TRANSPORT
The accelerator is shown schematically in Figure 2 [6].
It consists of four linacs, two bunch compressors, a laser
heater and a beam transport system (spreader) to theundulators. The function of this system is to accelerate theelectron beam to the FEL energy of ~1.2 GeV and tocompress the ~10 ps long pulse from the photo-injector to
the final lengths and peak current. Two FEL layouts areenvisaged. FEL-1 will provide photons with wavelengths
in the range 100-40 nm. Depending on the experiments,
electron bunch lengths of 200 fs and a peak current of
800 A or higher can be provided (in this case with shorterbunch lengths). For those experiment where small time
jitter is important, and to account for a predicted jitter ofup to 400 fs, an electron bunch of 600 fs (“mediumbunch”) has been designed. Including the inevitableinefficiency of the compression system, the obtainablepeak current is ~800 A with 0.8 nC of charge from thephoto-injector. FEL-2 will cover the wavelength range
40-10 nm and will make use of a ~1 ps long pulse toprovide close to Fourier-transform-limited radiation and167

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Proceedings of FEL 2006, BESSY, Berlin, Germany

or a ~200 fs high brightness FEL radiation using the
fresh-bunch technique. In both cases a “long bunch” of
1.5 ps is required from the accelerator. With 1 nC charge
from the injector, the attainable peak current is ~ 500 A.
For both FELs the final energy and charge distributions
correlated with the distance along the electron bunchshould be as flat as possible in order not to broaden the
FEL bandwidth. The aim is to produce an energy
variation no greater than 1-2 x 10-4 along the useable partof the bunch and a peak current variation no greater than~100 A. In transverse space, the horizontal and verticalnormalized emittances at the end of the linac, 1.2 GeV,
will not be greater than 1.5 mm-mrad in order to meet thedesired photon throughput. This represents a ~30%
increase from the photo-injector simulation results andincludes a safety margin against emittance dilution
effects. The emittance value of 1.5 mm-mrad is acondition of the shortest wavelength and accelerator
performance is aimed at satisfying this most stringent
requirement. This specification may be relaxed for longer
photon wavelengths.

wakefields, momentum dispersion and coherent
synchrotron radiation in bending magnets. Exhuastive
computations with codes LiTRACK and “elegant” were
performed to optimise beam parameters and to simulate
expected jitter and parameter sensitivities. The computed
electron distributions were further used in the FEL
simulation studies.
The electron beam is transported from the end of thelinac to the FELs by a FODO spreader channel. It is
designed for diagnostics and parallel separation of the two
FELs. The spreader has been designed to preserve
electron beam emittance. This is done in two ways: byusing a lattice with a small “curly-H” function in themagnets and by employing a scheme of self emittancecompensation. Quadrupoles in the deflecting arcs, locatednear the positive and negative peaks of the dispersion
function, are separated by a unit transfer matrix and. This
allows simultaneous change of their gradients and the
production of a dispersion bump localized between thequadrupoles. Control of this bump regulates R56 within
the spreader allowing it to be exactly zero or any otherreasonable value. It is in fact kept slightly positive insome cases to disperse the electrons in the spikes of thepeak current.

THE UNDULATORS AND THE FEL
PROCESS

Figure 2: Schematic layout of the accelerator. The star
indicates the position of the laser heater, while the red
section the X-band accelerator.
At the exit of the photo-injector the electrons enter theL1 linac where they are accelerated to ~250 MeV.
Acceleration occurs off-crest to provide correlated energy
spread along the bunch that will compress it in the firstcompressor BC1. An RF structure tuned at the 4th
harmonic of the main s-band sections, ie at X-band
frequency, is placed half-way in L1. The function of the
X-band linac is to provide the non-linear quadratic and,
when operated off-crest, cubic corrections of thecorrelated momentum distribution along the bunch in thepresence of the non-linearities of the photo-injector, themagnetic compressors and the non-linear effects of thelongitudinal wakefields.
The linac structures L2 and L3 between the first andsecond bunch compressors accelerate the beam from ~250 MeV to ~650 MeV. They also provide the residual
momentum chirp for the second compressor, BC2. After
BC2 the beam is further accelerated to its final energy inthe L4 structure. The phases of the linac after BC1 arechosen to provide the necessary momentum spread forcompression and also to cancel the linear part of thelongitudinal wakefields. The non-linear correlated
momentum spread at the end of the linac is fine-tuned
with the amplitude and phase of the X-band structure. The
focusing structure of the linac is designed to minimize
transverse emittance dilution due to transverse

168

FEL configurations are based on harmonic generation
schemes seeded by an external laser. FEL-1 will utilise
one stage (modulator, dispersion section and radiator)
while for FEL-2 two stages will be used in a fresh part ofthe bunch seeding scheme. A whole bunch seeding
scheme was also studied for FEL-2 and requires a larger
number of undulators and a higher quality electron beam.
FEL-1 and FEL-2 are required to have continuously
tuneable output polarizations at all wavelengths, ranging
from linear-horizontal to circular to linear-vertical. For
this reason, the FEL-1 radiator and the final radiator in
FEL-2 have been chosen to have APPLE-II
configurations with pure permanent magnets. For themodulator a simple, linearly-polarized configuration, is
optimal both due to its simplicity and because the input
radiation seed can be linearly polarized. The tuning of the
wavelength will be done by changing the gap of theundulator while keeping the electron beam energy
constant. The magnetic lengths of the undulators
segments are 2.34 m (containing 36 periods) for the FEL1 and 1st FEL-2 radiators and 2.40 m (48 periods) for the
2nd FEL-2 radiator. FEL-1 and 2 consist of 6 and 10
segments respectively. The intra-segment spools containelectromagnetic quadrupoles, high quality beam position
monitors and quadrupole movers to steer the electron
trajectory.
Theoretical and computational studies led to a selectionof the accelerator and FEL parameters. An exhaustive
study through start-to-end simulations, that included theuse of FEL codes GENESIS and GINGER, wasperformed [7]. The simulations took into accountSeeded FELs

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perturbations in the accelerator and FEL parameters. In CW and pulsed transmission schemes. A central clockparticular parameter sensitivity and time dependent jitter system generating stable timing signals for the wholestudies were carried out for both FELs. Studies of the facility will be used. The signals will be distributed overvariation of mean energy, energy spread, peak current, distances exceeding 300 m by optical fibres in a staremittance and seed input power were done both for single configuration. Timing information is transmitted using
and multi-parameter variations. Methods, such as either RF modulated CW light mainly for the RF systems
undulator tapering, to reduce the sensitivity to variations, or pulsed light mainly for the laser systems.
were also examined. Table 1 gives the expected
The consequence of orbit displacements from the ideal
performance parameters for the two FELs.
trajectory in the undulators were simulated. The FEL
The seed laser will provide tuneable UV radiation in process at the shortest wavelength, 10 nm, requires thetwo pulse duration schemes: 100 fs and 1 ps. A dual pulse straightness of the electron orbit in the undulators to be
duration regenerative amplifier will be used. In the 100 fs within 10 μm (rms value over the undulators length).
case the amplifier directly pumps a travelling wave Although this is beyond state-of-the art mechanicalparametric amplifier (TOPAS) followed by harmonic alignment techniques, realistic simulations show that a
conversion stages. In the 1 ps case this output is further combination of the latter and of beam-based-alignment
amplified in a two pass stage to the 10 mJ level that then (tested at the Stanford Linear Collider and proposed forpumps a ps TOPAS. Timing and synchronization [8] of the LCLS) will achieve the desired performance.
RF, laser and diagnostic systems will be guaranteed to
sub 50 fs levels by an integrated system handling both
Table 1: Principal FEL output parameters
Parameter
Wavelength range [nm]Output pulse length (rms) [fs]Bandwidth (rms) [meV]Polarization
Repetition rate [Hz]Peak power [GW]
Harmonic peak power (% of fundamental)
Photons per pulse
Pulse-to-pulse stability
Pointing stability [µrad]
Virtual waist size [µm]Divergence (rms, intensity) [µrad]

PHOTON BEAM TRANSPORT AND
EXPERIMENTAL AREAS
After leaving the undulators the electron beam, carrying
an average power of 75 W (at 50 Hz) will be dumped intoa shielding block by a sequence of bending magnets,
while the FEL radiation will be transported to theexperimental areas. The transport optics is designed tohandle the high power density (up 10 GW) in a very short
temporal interval. In order to handle the high peak photon
energy density, the beam line optics operate at low
grazing incidence angles with low Z-materials and theradiation intensity can be controlled by a gas absorption
cell. The vacuum system is windowless with differential
pumping sections. Pulse length preservation, monochromatization, energy resolution, source shiftcompensation, focusing in the experimental chamber andbeam splitting are all included in the design of the FEL
radiation transport system.

REFERENCES[1] FERMI@Elettra Conceptual Design Report, 2006, tobe published.

Seeded FELs

FEL-1
100 to 40< 100
17 (at 40 nm)
variable50
1 to >5~21014 (at 40 nm)≤ 30 %< 20
250 (at 40 nm)
50 (at 40 nm)

FEL-2
40 to 10> 200
5 (at 10 nm)
Variable50
0.5 to 1~0.2 (at 10 nm)
1012 (at 10 nm)
~50 %
< 20
120
15 (at 10 nm)[2] M. Trovo’, et al., “Further Studies in the
FERMI@Elettra Photoinjector Optimisation”, thisconference.
[3] S. Di Mitri, “How to obtain high quality electron
bunches in the presence of normal conducting
wakefields”, this conference.
[4] G. Penco, et al., “Ramping longitudinal distribution
studies for the FERMI@Elettra injector”, thisconference.
[5] M. Danailov, et al., “Design of a two stage laser
pulse shaping system for FEL photoinjectors”, thisconference.
[6] G. D’Auria, “Linac design for the FERMi Project”,
LINAC conference, 2006, Knoxville, Tennessee,USA.
[7] G. De Ninno, et al., “Design and optimisation of the
FERMI@Elettra FEL” and “Start to end timedependent study of FEL output sensitivity to electron
beam jitters for the first stage of FERMI@Elettra
project”, this conference.
[8] M. Ferianis, “Timing and Synchronization in LargeScale Linear Accelerators”, LINAC conference,
2006, Knoxville, Tennessee, USA.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

COHERENT HARMONIC EMISSION OF THE ELETTRA STORAGE
RING FREE ELECTRON LASER IN SINGLE PASS CONFIGURATION:
A NUMERICAL STUDY FOR DIFFERENT UNDULATOR
POLARIZATIONS
F. Curbis∗ , University of Trieste & Elettra, Basovizza, Trieste, Italy,
H.P. Freund, Science Applications International Corporation (SAIC),
G. De Ninno, Elettra, Basovizza, Trieste, Italy.
Abstract
The optical klystron installed on the Elettra storage-ringis normally used as interaction region for an oscillator freeelectron laser, but, removing the optical cavity and using
an external seed laser, one obtains an effective scheme forsingle-pass harmonic generation. In this configuration thehigh-power external laser is synchronized with the electron
beam entering the first undulator of the optical klystron.
The laser-electron beam interaction produces a spatial partition of electrons in micro-bunches separated by the seedwavelength. The micro-bunching is then exploited in thesecond undulator to produce coherent light at the harmonics of the seed wavelength. The Elettra radiator is an APPLE type undulator and this allows to explore different
configurations of polarization. We present here numericalresults obtained using the code Medusa for both planar andhelical configurations. We also draw a comparison withpredictions of the numerical code Genesis.

INTRODUCTION
Coherent Harmonic Generation (CHG) can be implemented in a storage ring using two undulators as a cascade.
The first undulator (called modulator) is tuned at the wavelength of an external high-power laser and the second undulator (called radiator) at a higher harmonic of the seed.
Between the undulators there is a region, i.e., dispersive
section, with a strong magnetic field, which, in single-passconfiguration, converts the energy modulation, occurred in
the modulator, in spatial modulation (usually referred as“bunching”). The Elettra storage-ring FEL is presently operating in oscillator configuration [1, 2], but, with minor
modification, the optical klystron will be used as interaction region for CHG in single-pass configuration. In the
new configuration (see Figure 1) the optical cavity will be
removed and a conventional laser will be focused into themodulator and synchronized with the electron beam. The
main difference between conventional single-pass seeded
FEL and storage-ring harmonic generation is that in thelatter case the electron beam is re-circulated and not renewed each pass through the optical klystron. This peculiarity determines the maximum repetition rate for thisconfiguration, because the electrons need few synchrotron
damping times (order of ten of milliseconds) to cool down
after each interaction with the seed laser. Preliminary sim∗ francesca.curbis@elettra.trieste.it

170

seed laser

λmodulator

λ/ncoherent lightradiator

dispersive section

electron bunch

Figure 1: Layout of the Elettra storage-ring FEL after removing the optical cavity and using an external seed laser.
ulations [3] have been done using Genesis [4] for different
working points, i.e. different machine (electron-beam energy, Twiss parameters, emittance, strength of the dispersive section) and the seed laser (power and duration) parameters. The work reported in this paper characterizes theemission of the Elettra APPLE-type undulator, operated inboth linear and helical configurations. Numerical results
are obtained using Medusa and Genesis. Medusa provides
the possibility to calculate the harmonic power at the endof the radiator. This means that the radiator is tuned at
the third harmonic of the seed laser (i.e. the fundamental in the modulator) and Medusa is able to calculate any
desired harmonics besides the fundamental. This will allow to investigate if wavelengths shorter than the fundamental will be detectable. The external seed laser [5] isbe a titanium-sapphire (Ti:Sa) with a very high peak power(2.5 GW) and very short pulse duration (variable between
100 and 250 fs (RMS)). The repetition rate will be initially
10Hz. Using this frequency, the contribution from incoherent synchrotron emission, provided by electrons circulating in the storage ring but not interacting with the seedlaser, may spoil the signal-to-noise ratio. Possible strategies will be explored in the aim of increasing the repetition
rate, therefore improving the signal quality. The first undulator is tuned at the fundamental of the seed laser (240 nm),while the second undulator at the third harmonic (80 nm).

OPTIMIZATION FOR MEDUSASIMULATIONSIn this section we report some studies performed in timeindependent mode in order to optimize the parameters before the introduction of the slippage, e.g. time-dependent
simulation. The main run parameters used in Medusa simulations are reported in Table 1 [5, 6]. With respect to theSeeded FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH055

values used in Genesis simulations, there are some minor
differences: the pulse shape of the electron bunch and theseed laser is parabolic instead of Gaussian, the seed duration is 250 fs FWHM instead of 140 fs and the numberof periods for both undulators is 22 instead of 20, because
Medusa needs one period more at the entrance and exit of
the undulator to properly model the simulation. The variTable 1: Run parameters used in Medusa simulations
Electron beam
Energy0.9 GeVPeak current
77 A
x-Emittance2.46 mm-mrad
y-Emittance
0.246 mm-mrad
Energy-spread
0.12%
Bunch length
27 psBunch charge
1.38 nC
Bunch shapeparabolicTwiss parameters
αx = 0.24
βx = 8.986
αy = 0.89
βy = 4.695 m
Modulator
Magnitude
5.62kG
Period
10.0 cm
Length22 periods
Radiator
Magnitude
3.00kG
Period
10.0 cm
Length22 periods
Undulator-to-undulator gap
0.9 m
Seed laser
Wavelength
240 nmSeed power
2.5 GW
Seed duration
0.25 ps
Seed shapeparabolication of the radiator output power versus the dipole fieldstrength in the chicane is shown in Figure 2 for the case ofa planar radiator. We have found from Genesis simulationthat the energy spread induced by the seed laser is so highthat the beam needs only a drift to transform the energy
modulation in spatial modulation (bunching). In Medusa
simulation instead, the power level when the chicane field
vanishes is 1.06 MW (and this is very close to the timedependent result), but a little more power (about 1.36 MW)
could get using a chicane field of about 0.5 kG. However,in order to compare the results of these two codes, we havechosen to set to zero the chicane field also in this case.
The same power optimization with respect to the magnetic
field has been performed tuning the radiator at the third harmonic (see Figure 3). The output power at 80 nm is about
1.7 MW which is almost a factor two over the value found
for the planar undulator. The second harmonic (40 nm)
power is not very sensitive to the variation of the chicane

Seeded FELs

Figure 2: Output power versus dipole field strength at
80 nm for planar radiator.
field and is about 200 W when the chicane field is set tozero. These results have been confirmed by time dependent
simulations. The same behavior has been found for a heli-

Figure 3: Output power versus dipole field strength forhelical undulator tuned at at 80 nm and second harmonic(40 nm) power.
cal undulator tuned at the second harmonic (120 nm) of theseed laser. The result, shown in Figure 4, looks similar toprevious case: the highest power is found when the chicane
field is set to zero and the power is about 4.7 MW at 120 nm
and 5.7 kW at 60 nm. As before, while the power at thefundamental (120 nm) drops fast with increasing chicane
field, the harmonic power (60 nm) doesn’t drop so much.
An other important issue to be considered when using numerical codes is the number of simulated particles which isneeded in order to guarantee a correct modelization of theprocess. For the CHG in helical configuration, we foundthat a larger number of particles is needed with respect toplanar configuration. The case for zero energy-spread isreported in Figure 5. We can argue from the results that todo this kind of simulation about 60000 particles per slice
are needed without energy spread and, including the energy
spread, an order of magnitude more particles is required. In
the latter case, the power level will be of course smaller. To
conclude, in order to treat the energy spread and the additional harmonics, the following runs used 1210104 particles.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 4: Output power versus dipole field strength forhelical undulator tuned at 120 nm and second harmonic(60 nm) power.

Figure 6: Evolution of the 80 nm radiation and its first threeharmonics in planar configuration.

Figure 5: Output power versus number of simulated particles for helical undulator tuned at the second and the third
harmonic of 240 nm.

Figure 7: Power versus time of the 80 nm pulse at the endof the radiator in planar configuration.

MEDUSA PERFORMANCE
Planar undulator
In time-dependent mode, we firstly looked at the harmonics of the 80 nm wavelength, using 2.5 GW seed powerand zero magnetic field inside the dispersive section. The
evolution along the undulator of the fundamental (80 nm)
and the first three harmonics of that wavelength are shownin Figure 6. The second harmonic (40 nm) reaches a power
level of about 2 kW, the third harmonic (26.67 nm) a power
level of about 500 W and the fourth harmonic (20 nm) a
power of 2 W. While in the steady-state simulations welooked exclusively at the evolution of the power along theradiator, in time-dependent simulations the output temporal profile (see Figure 7) and the harmonic spectrum (seeFigure 8) can be displayed. The electron bunch is twoorder of magnitude longer than the seed laser (27 ps versus 250 fs) and the total slippage, considering 80 nm wavelength and 44-periods undulator, is much smaller than thebunch-length, thus the differences between steady-state andtime-dependent simulations are expected to be small. Indeed, the observed peak power is about 1MW in both cases.
The shortness of the laser pulse may lead to numericalproblems because one should increase the number of slices

172

in order to resolve the FEL pulse structure and an adequate
number of particles must be holden in each slice. In ourcase, the simulation includes 600 slices, with 17496 particles per slice, but only about 10 slices across the seed pulse.
This is the reason why the output spectrum in Figure 8 is
not smooth and displays a spiky behavior. If one believes
the problem is the lack of resolution, the envelope could beconsidered as the spectral shape. Considering the Fourier

Figure 8: Fourier transform of the output spectrum at 80 nm(planar configuration).

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Proceedings of FEL 2006, BESSY, Berlin, Germany

where c is the speed of light, Δt is the F W HM duration of the output pulse, Δλ is the F W HM of the output
spectrum and λ is the emission wavelength, the results presented here give a quantity that is 1.7 times above the limit.
This value indicates that the emitted light have an high levelof coherence.

10

10

10

6

5

5

4

time dependent simulation
3

3

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

10

3

10

10

2.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Power (W)

0.8

1.2

1.2

1.0

1.0

0.8

0.8

3

2.0

Planar undulator

0.2

time dependent

x10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

1.0
0.8

80nm

0.6

0.6

0.4

Helical undulator

0.4

0.2

0.2

time dependent

0.2

0.0

0.0

0.4

0.0

1.2

Power (W)

0.0
0.00

0.80

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

time (ps)time (ps)Figure 11: Temporal profile for planar undulator (at left)
and helical undulator (at right) obtained tuning the radiator
at 80 nm.

The Fourier transform of the output spectrum is reported
in Figure 12. Using the Equation 1, we found a value thatis 1.6 times above the limit. Also in this case, the radiation
emitted shows an high degree of coherence.

140

140

120

120

100

100

140

100
80 nm

80
60

80

80

60

60

40

40

20

20

0

0

Planar undulator
40
time dependent simulation

20
0
78.0

79.0

120

Spectrum

80 nm

80.0
81.0
wavelength (nm)80

Helical undulator

60
40

time dependent simulation

82.0

20
0
78.0

79.0

80.0
81.0
wavelength (nm)82.0

Figure 12: Harmonic spectrum for planar undulator (at left)
and helical undulator (at right) obtained tuning the radiator
at 80 nm.

CONCLUSION
The Medusa simulations confirmed in general the results
already obtained by Genesis, with a good agreement in bothplanar and helical configuration. Some differences should
be longer investigated, i.e., the higher power level found inplanar configuration when the dispersive section is 0.5 kG
and the factor two more power found in helical radiator.

REFERENCES[1] R. P. Walker, Proc. EPAC’99, 93.
[2] G. De Ninno et al., Nucl. Instrum. and Meth. A 483 (2002)
177.
[3] F. Curbis, G. De Ninno, Proc. FEL’05.
[4] S. Reiche, Nucl. Instrum. and Meth. A 429 (1999) 243.
[5] M. Danailov, Private Communication.
[6] F. Iazzourene, Private Communication.

173

6

0.4

Spectrum

Seeded FELs

4

x10

0.6

6

0.6

x10

6

80nm

100

The campaign of simulation has been completed exploring the helical polarization in Genesis. The power level
founded at 80 nm for each configuration is very close between Genesis and Medusa and between planar and helicalconfiguration the differences are lower than one order ofmagnitude. All Genesis simulation has been performed intime-dependent domain, but, to limit the computing time,
just a portion of the electron bunch around the seed pulse
has been simulated, with the implicit assumption that theslippage doesn’t not affect too much the emission.
The evolution of the output power along the radiator isshown in Figure 10 for both planar and helical configuration. In comparison with Medusa, Genesis results don’t
exhibit a big difference between planar and helical power.
The value found is about 1.1 MW in both cases, as shown
also in Figure 11, where the power is plotted as a functionof time at the end of the radiator.

5

Figure 10: Harmonic power for planar undulator (at left)
and helical undulator (at right) obtained tuning the radiator
at 80 nm.

120Comparison with Genesis simulation

6

z (m)

140

Figure 9: Evolution of the 80 nm radiation and its first two
harmonics in helical configuration.

10

80 nm

time dependent simulation

z (m)

1.0

As already reported before, the steady-state simulation
could give enough information about the power level of the
80 nm signal and the first two harmonics of that. For thisreason, the simulation of the helical configuration has beenobtained in time-independent mode. In Figure 9 the evolution of the signal power along the radiator is displayed. One
can observe that the 40 nm harmonic is still about 1 kW asin planar configuration, but the 26.67 nm harmonic has amuch lower power than for the planar undulator.

5

10

10

10
0.2

10

4

10

1.2

Helical undulator

10

10

80 nm
4

Planar undulator

6

10

6

(1)

Planar undulator

6x10c · Δt[F W HM ]Δλ[F W HM ]= 0.441λ2Power (W)10Power (W)limit, given by the equation:

MOPPH055

MOPPH057

Proceedings of FEL 2006, BESSY, Berlin, Germany

DESIGN AND PERFORMANCE OF THE FERMI AT ELETTRA FEL
G. De Ninno, E. Allaria, Sincrotrone Trieste, 34012 Trieste, Italy;
W. Fawley, G. Penn, LBNL, Berkeley, CA 94720-8211 USA.
Abstract
The FERMI at ELETTRA project will be comprised of
two FELs, each based on the principle of seeded
harmonic generation. The first undulator line, FEL-1, will
operate in the 40-100 nm wavelength range relying upon
one stage of harmonic up-conversion. The second
undulator line, FEL-2, extends the output spectral domain
to the 10-40 nm wavelength range and will use two
harmonic stages operating as a cascade. We review the
FEL studies that have led to the final design and present
results of numerical simulations with GENESIS and
GINGER codes including predicted output bandwidths
and the effects of shot-to-shot fluctuations in multiple
input parameters.

INTRODUCTION
The FERMI@ELETTRA project is based on theharmonic up-shifting of an initial radiation “seed” signal
in a single-pass FEL amplifier employing multiple
undulators. The basic principles which underlie thisapproach are: energy modulation of the electron beam via
the resonant interaction with an external laser seed in a
first undulator (modulator); use of a chromatic dispersive
section to then develop a strong density modulation withlarge harmonic overtones; production of coherent
radiation by the microbunched beam in a downstream
undulator (radiator). The first stage of the project, FEL-1,
aims at generating coherent output radiation in the 40-100
nm spectral range. For these wavelengths, users require
short (< 100 fs) pulses with adjustable polarization
together with high temporal and spatial reproducibility.
The project’s second stage, FEL-2, will extend thespectral range down to 10 nm. Present users’
requirements for FEL-2 point to long (narrow-bandwidth)
pulses with high peak brilliance and adjustable
polarization. FEL-1 relies upon a single-stage scheme(i.e., modulator-dispersive section-radiator), similar to theone already operational at Brookhaven [1]. As for FEL-2,
a two-stage harmonic cascade is necessary for reaching
short wavelengths. The selected configuration is based on
the so-called “fresh bunch” approach [2], in which theoutput radiation from the first radiator is used to energymodulate in a subsequent modulator a part of the electron
beam that did not interact in the first stage with theexternal seed.
In this paper we review the FEL studies that have led to
the final design of FEL-1 and FEL-2 and present resultsof both time-independent and time-dependent numericalsimulations with GENESIS and GINGER.

174

BASIC FEL OUTPUT REQUIREMENTS
AND RELATED ISSUES
Table 1 summarizes the basic FEL output requirements
for FEL-1 and FEL-2. At all wavelengths, both FEL-1
and FEL-2 are to have continuously tuneable output
polarizations ranging from linear-horizontal to circular tolinear-vertical. Consequently, the FEL-1 radiator and final
radiator in FEL-2 have an APPLE-type configuration.
Both FELs will operate at the accelerator repetition rate of
10-50 Hz.
At present it is believed that the major application for
FEL-1 will involve time-domain experiments such as
pump-probe interactions and possibly nonlinear
phenomena. Consequently, the requirements for FEL-1
are more related to total photon number per pulse (i.e., 0.4– 2 × 1014) and pulse duration (20-100 fs) than they are tospectral bandwidth. A critical parameter affecting theneeded electron beam duration is the timing jitter in the
beam relative to that of the seed laser. In order that there
be reasonably overlap between the seed and the electrons,
the duration of the electron beam must be bigger than the
duration of the seed pulse plus two times the RMS timing
jitter. The expected RMS timing jitter from theaccelerator is of order 130 fs [3], and therefore anelectron-beam pulse duration of at least 600 fs is neededfor 100-fs seed pulses. This timing jitter requirement may
be one of the more difficult to satisfy in terms of theinjector and accelerator subsystems.
Another important parameter associated with FEL-1
time domain experiments is shot-to-shot repeatability.
Ideally, for nonlinear phenomena experiments, shot-toshot RMS jitter in normalized photon number should be
5% or less. As reported in [3], we do not at present
believe that such a low value is obtainable with the
expected accelerator and injector parameters. Many FEL1 experiments will be able to deal (via recording
individual shot photon number for later post-processing)with values as high as 25% or greater.
In contrast to FEL-1 users, for whom timing andphoton number jitter are critical parameters, most FEL-2
users are (presently) interested in the frequency domain
experiments where longitudinal coherence and narrow
bandwidth are crucial. The most important output goal for
FEL-2 is ≥1012 photons/pulse/meV. Consequently, FEL-2
requirements favor long output pulses (≥ 200 fs) whose
spectral properties are as close as possible to thetransform limit. Although the total photon jitter is notcritical for most experiments in the frequency domain,
shot-to-shot central wavelength jitter is of concern.
Consequently, in order not to increase the effective time-

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Proceedings of FEL 2006, BESSY, Berlin, Germany
averaged, output bandwidth as seen by the user, thewavelength jitter needs to be less than the individual shot
bandwidth.

UNDULATOR DESIGNIn the FERMI case, wavelength tuning in the undulators
will be done by changing the gap (and thus aw) and not bychanging the electron beam energy.
The FEL-1 undulator layout is shown in Fig. 1.
Modulator

Dispersive
sectionRadiatorSeede-beamFig. 1: FEL-1 undulator layout
For the first modulator which must satisfy FEL
resonance over a nominal wavelength range of 240 to 360
nm, an undulator wavelength of 16 cm has been adopted.
The modulator will be a standard planar undulator about
3-m long. In order to reach saturation over the whole
spectral range, the necessary active radiator length for
FEL-1 is about 16 m. For many reasons (e.g., magnetic
forces, alignment, external focusing and diagnostic needs,
possible tapering), this is far too long to construct as one
continuous magnetic structure. Consequently, theradiators will be subdivided into six modules, eachconsisting of an active undulator segment (with a periodof 6.5 cm and a length of about 2.3 m) and a breaksegment (about 1 m long), with the latter containing a
number of items such as quadrupoles, a longitudinal
phase shifter, beam position monitors, dipole correctors,
and diagnostics. In order to produce light with variable
polarization, the radiator modules will be APPLE-type.
The FERMI design includes external quadrupole focusing
to produce an average value of 10 m for the Twiss beta
function in each plane.
Following the modulator is a break section (about 1 mlong) that contains a magnetic chicane whose chromatic
dispersion is used to develop a strong coherent
microbunching from the energy modulation impressed
upon the electron beam by the FEL interaction in themodulator. The undulator layout for FEL-2 is shown in
Fig. 2.

MOPPH057

radiation to a sufficient level to provide adequate coherent
energy modulation in the following undulator. The basic
parameters for the second stage modulator are the same as
for the first stage radiator (i.e., 6.5-cm period; 2.3-m
segment length). In general, the choice has been made tokeep the first stage as short as possible, both for costreasons and to minimize SASE growth which canincrease the incoherent energy spread of the “fresh”
portion of the e-beam to be used in the second stage
modulator and radiator. The second-stage radiator has ashorter period (5 cm) and is subdivided into 2-m longactive APPLE-type undulator segments separated by 1-m
breaks. These breaks contain a quadrupole singlet forfocusing, a phase shifter, dipole correctors, anddiagnostics. The length of the final radiator is somewhat
arbitrary; in general it has been presumed for the fresh
bunch approach one would want sufficient length for
power saturation, i.e., 6 segments at 10-nm wavelength.
However, one could certainly increase the output powerby adding more radiator segments and possibly also taper
the undulator strength.

FEL-1 PERFORMANCE
Figure 3 displays the growth of power at 40-, 60-, and100-nm wavelengths as predicted by the GENESIS and
GINGER codes (each operated in time-independentmode). Electron-beam and seed parameters are reported
in the figure caption.

Fig. 2: FEL-2 undulator layout

Fig. 3: Power growth as a function of radiator distance for
FEL-1 tuned at 100-, 60-, and 40 nm, as predicted byGenesis and Ginger. Electron-beam parameters utilized
for the simulation are: energy = 1.2 GeV; current = 800
A; incoherent energy spread (RMS) = 150 keV;
normalized emittance = 1.5 mm mrad; input seed power =100 MW; input seed wavelength = 240-300 nm.

The selected configuration is based on the so-called“fresh bunch” approach [2], in which the radiation fromthe first radiator is used to energy-modulate in a
subsequent modulator a “fresh” part of the electron beamthat did not interact with the external seed. The core
design for the first stage of fresh-bunch FEL-2 isextremely similar to that described earlier for FEL-1.
Where the design for FEL-2 fresh bunch layout begins todiffer significantly is that the first stage radiator isrelatively short (i.e., 2-3 segments) and only brings the

As can be seen in Fig. 3, at the longer wavelengths
power saturation is reached well before the end of thesixth section. The simulations show good basic agreement
between the GENESIS and GINGER predictions. A
factor of about two in output power can be gained byproperly tapering the six radiator segments.
In order to get an estimate of output power sensitivity
to electron beam and laser parameters, an extensive set of
GENESIS and GINGER simulations has been performed
varying single parameters at a time.

seed laser

λλ/n“fresh bunch” breakλ/nλ/(n×m)e-beamSeeded FELs

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Proceedings of FEL 2006, BESSY, Berlin, Germany
Parameter
Wavelength range [nm]Output pulse length (rms) [fs]Bandwidth (rms) [meV]Polarization
Repetition rate [Hz]Peak power [GW]
Harmonic peak power (% of fundamental)
Photons per pulse
Pulse-to-pulse stability
Pointing stability [µrad]
Virtual waist size [µ m]Divergence (rms, intensity) [µrad]

FEL-1
100 to 40≤ 100
17 (at 40 nm)
Variable50
1 to >5~21014 (at 40 nm)

FEL-2
40 to 10> 200
5 (at 10 nm)
Variable50
0.5 to 1~ 0.2 (at 10 nm)
1012 (at 10 nm)< 20
250 (at 40 nm)
50 (at 40 nm)

~50 %
< 20
120
15 (at 10 nm)≤ 30 %

Table1: FEL-1 and FEL-2 expected performance
We present here time-independent calculations inwhich the input laser seed power and various electron
beam quantities were allowed to vary independently
around their individual design values (see Table 1)
following Gaussian distributions characterized by thefollowing RMS values: mean electron energy: 0.1%;
current: 8%; emittance: 10%; energy spread: 10%; input
seed power: 5%. Expected output fluctuations are about
22 % (see Fig. 4). The most limiting factor to output
stability is represented by the 0.1% input energy
fluctuation.
Detailed
time-dependent
start-to-end
simulations, including the impact on output stability ofseed-bunch time jitter and beam distribution
homogeneity, are reported in [3].

Fig. 4: Power growth for different initial random
conditions (red curves, left vertical scale) and associatedpower fluctuation (blue curve, right vertical scale) vs.
radiator distance.
A campaign of time-dependent start-to-end simulations
has been performed making use of various electron-beam
distributions provided by the FERMI gun and linac
groups [4]. Figure 5 shows the GENESIS-predicted
output temporal and spectrum profiles at 40-nm
wavelength for an optimized (i.e., flat in both energy andcurrent) input electron-beam distribution. The input seed
was a 40-fs (RMS) Gaussian at a peak power of 100 MW.
Input Laser seed:
100 MW
40 fs rms30

fs

Fig. 5: FEL-1 temporal and spectrum profiles resulting
from a GENESIS simulation in time-dependent mode.

176

The output number of photons per pulse is about 9·1013
with ~80% in single transverse mode. The output pulse
length is 30 fs and the spectral bandwidth 17 meV, abouta factor of 2.5 above the transform limit

FEL-2 PERFORMANCE
Figure 6 displays the growth of power at 40-, 20-, and10-nm wavelengths as predicted by the GENESIS and
GINGER codes operated in time-independent mode. Fora final radiator of six modules (see Fig. 2) deep saturationis reached only at 40 and 20 nm. At 10 nm, the output
peak power is 1 GW for 800-A current and 0.35 GW for
500-A beam current (data not shown).

Fig. 6: GENESIS and GINGER time-independent
simulations for the FEL-2 radiation power at various
wavelengths versus radiator distance in the final radiator
for the fresh bunch approach. These runs were done with
800-A beam current and 200-keV initial incoherent
energy spread (for the other parameters see caption ofFig. 3).
FEL-2 is typically more sensitive to variations in input
parameters than is FEL-1. This is largely due to theshorter wavelengths targeted for FEL-2, which leads tosimilar displacement errors translating into larger
longitudinal phase errors, and there is the additional
complexity of having two rather than one stage ofharmonic conversion.
Furthermore, at shorter
wavelengths radiation diffraction is less important, which
renders the FEL more sensitive to deviations in theelectron orbit and to misalignments. However, it ispresently believed that most applications for FEL-2
output will be in the spectral domain where
reproducibility is less important and there is a premiumfor obtaining narrow bandwidth. Consequently, most of

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Proceedings of FEL 2006, BESSY, Berlin, Germany
our work on FEL-2 has concentrated utilizing a relatively
long (~1 ps) electron-beam pulse with a moderate (~500A) current. For the fresh bunch approach, such a longpulse is nearly essential given the practicalities of
temporal jitter between the electron beam and input
radiation seed. As discussed in [5], flatness of electronbeam phase space and homogeneity of current and energy
spread distributions at undulator entrance are essential for
obtaining the best output spectral resolution and shot-toshot stability. An example of output temporal andspectrum profiles at 10 nm based on an optimized input
electron-beam is shown in Fig. 7. The obtained number ofphotons per pulse is about 1013 (93% in single transversemode). The output pulse length is 110 fs (rms) and the
bandwidth 5 meV, about a factor of 1.5 above thetransform limit. The peak brightness is about 1032 photons/mm2/mrad2 /sec/ 0.1% bandwidth.
Laser seed:
100 MW
250 fs rms

110 fs rms

MOPPH057

is less sensitive to shot-to-shot fluctuations of the relative
timing between the e-beam and external seed laser. The
output temporal profile and spectrum obtained at 10 nm
using the whole bunch configuration are shown in fig. 8.
The initial electron beam distribution is the same as forthe fresh-bunch scheme (see Fig. 7).
Laser seed:
40 MW
450 fs rms

200 fs rms

Fig. 8: FEL-2 temporal and spectrum profiles for wholebunch scheme resulting from a GENESIS simulation intime-dependent mode.
In this case the obtained number of photons per pulse isabout 1013 (93% in single transverse mode). The output
pulse length is 200 fs (rms) and the bandwidth 4 meV.
This gives a result which is a factor about 2.5 above thetransform limit.

CONCLUSIONS
Fig. 7: FEL-2 temporal and spectrum profiles for freshbunch scheme resulting from a GENESIS simulation intime-dependent mode.
An alternative scheme we are considering for the FEL2 is based on the so-called “whole-bunch” approach.
Here, the entire electron beam pulse is energy-modulatedby the external laser seed and, following the first radiator,
there is neither a temporal delay section nor a second
modulator. Instead, the electron beam immediately entersa weak dispersive section followed by a second radiator
whose FEL resonant wavelength is tuned to an integer
harmonic of the first radiator. Due to the relatively small
harmonic microbunching at this new wavelength, thissecond radiator must operate deep in the exponential gain
regime. Thus, to keep the exponential gain length andpower saturation lengths acceptably small, the energy
modulation produced by the first (and only) modulator
must be relatively small compared to ρ2 γ where ρ2 is the
FEL parameter for the second radiator (generally ~ 1 ×
10-3). This small energy modulation means that at
entrance to the first radiator the e-beam will have asmaller microbunching level relative to that of the fresh
bunch scheme.
Consequently, the whole bunch approach canessentially fail (in terms of the needed second radiator
undulator length for saturation) if the initial energy spread
becomes too large. Moreover, because the microbunchinglevel is small at the beginnings of both the first andsecond radiator, the relative strength of the shot noise
microbunching is much higher and the final SASE
strength can be 2 or more orders of magnitude greater inthe whole bunch approach than in the fresh bunch
approach. The main advantage of such a scheme is that it

Seeded FELs

We have presented the current design configurations forboth FELs of the FERMI@Elettra project. Design
optimization has been driven by users’ requests (see table1), i.e. short pulse and low shot-to-shot power fluctuations
for FEL-1, and high energy resolution for FEL-2. We also
give results derived from both time-independent and timedependent simulations, using reference parameters andelectron-bunch distributions as provided by the FERMI
start-to-end group.

REFERENCES[1] L. H. Yu et al., Phys. Rev. Lett. 91, 074801 (2003).
[2] I. Ben-Zvi, K.M. Yang, and L.H. Yu, Nucl. Inst.
Meth. A 318, 726 (1992).
[3] E. Allaria, G. De Ninno, M. Trovo, these proceedings,
Paper MOPPH058.
[4] S. Dimitri et al.,these proceedings, Paper THBAU03.
[5] W. Fawley, G. Penn, and A. Zholents, theseproceedings, Paper THAAU01.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

START-TO-END TIME-DEPENDENT STUDY OF FEL OUTPUTSENSITIVITY TO ELECTRON-BEAM JITTERS
FOR THE FIRST STAGE OF THE FERMI@ELETTRA PROJECT
E. Allaria, G. De Ninno, M. Trovó, Sincrotrone Trieste, 34012 Trieste, Italy.
Abstract
Sensitivity of the output laser pulse to electron-beamjitters is one of the major issues affecting the expected
performance of both SASE and seeded FELs. Focusing on
the first stage of the FERMI@Elettra project, in this paper
we present results of time-dependent numericalsimulations in which the codes GENESIS and GINGER
have been used to run a large number of electron-beam
distributions generated at the gun by the code GPT andpropagated through the linac using the code ELEGANT.

INTRODUCTION
The FERMI@ELETTRA project is dedicated to thedevelopment of a FEL facility based on the principle ofharmonic up shifting of an initial “seed” signal in a single
pass [1]. The first stage of the project will be a single
harmonic cascade tuneable in the 40-100 nm range. At
present, it is believed that the major application for FEL-1
will involve time-domain experiments such as pumpprobe interactions and possibly nonlinear phenomena.
Consequently, the requirements for FEL-1 are more
related to total photon number per pulse (i.e., 0.4 – 2 ×1014) and pulse duration (20-100fs) than they are tospectral bandwidth. Another important parameterassociated with FEL-1 time-domain experiments is shotto-shot repeatability [1]. Time-independent simulations of
the FEL process based on the Fermi layout show a strong
sensitivity of the output power with respect to manyelectron-beam parameters [2]. Jitter studies performed
using jitter of input parameters as estimated by the linac
group of the Fermi project provided fluctuation on the
output power that can be greater that 20% for theradiation at 40nm. However, while time-independent
simulations can give just an indication of the FEL
performance, more accurate investigations should rely on“start-to-end” (S2E) simulations, that begin at theemitting cathode and end at the undulator exit.
In collaboration with the injector and linac groups of
the Fermi project, dedicated simulations have been
performed considering fluctuations on main machineparameters [3]. To examine the effects of injector andaccelerator jitters upon the shot-to-shot, time-resolved
properties of the output FEL-1 radiation, 100 individual
files of 1M macroparticles were propagated starting fromthe injector (GPT code) through the linac (Elegant code).
Nominal beam parameters are reported in the following
table [3,4].

Table1: Nominal electron-beam parameters for the firststage (FEL-1) of the FERMI projectParameter
Input Seed power
Electron Beam Energy
Peak current
Uncorrelated energy spread(“slice” value)
Norm. Transverse Emittance(“slice” value)
Electron Bunch Length(flat portion)

Value
100
1.2
800

Units
MW
GeV
A

150

KeV

1.5

mm-mrad0.6

ps

Each file included the effects of random jitter in theindividual injector and accelerator cell voltages. The jitter
follows Gaussian distributions with variances set by thebudget allowances allocated by the gun and linac groups.
GINGER and GENESIS time-dependent simulations
for the FEL-1 lattice tuned at 40 nm were performed overa large time window with high resolution. For eachjittered file, simulations where done using artificial
macroparticles created from the time-dependent envelope
quantities previously determined by the elegant2genesis
code and also using directly the ELEGANT particles.
It is important to note that we here only consider theeffect of the jitter on the electron bunches, without taking
into account any jitter source on the seed laser.

ANALYSIS OF ELEGANT JITTERED
FILES
The 100 jittered files have been produced starting from
100 GPT files that consider the possible jitter sources in
the gun. Those files have been propagated through thelinac with ELEGANT. Output distributions have been
pre-processed in order to evaluate the resulting jitter inbunch arrival times (Fig.1).

Figure 1: Arrival time jitter of the 100 elegant files withrespect to the arrival time of the nominal file.

178

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 2: Distribution of the arrival time jitter reported in
Fig.1; data can be fitted with a Gaussian distribution,
whose sigma is about 130fs.
The analysis shows a distribution with an rms jitter ofabout 130 fs, which is close to the one predicted by
LiTrack simulations [4]. These data can be fit with aGaussian distribution (Fig.2).
By plotting the electron energy and current profiles of
the 100 bunches taking into account of the arrival time
(figs.3-6) it is evident that it exists a time window of theorder of 400fs where the fluctuations of electron
parameters due to the jitter arrival time are small. This is
the “useful” part of the bunches to be used for the FEL
process. We also report the analysis of the electron beam
properties (electron energy, current, emittance, energy
spread) on that window.
The electron mean energy, γ, in the useful part of thebunch (from -200fs to 200fs, see fig. 3,4,5) presents a
distribution with an rms of 0.09%, in agreement with thevalues predicted by the linac group.

MOPPH058

Figure 5: Distribution of the average electron meanenergy of the useful part of the jittered bunches; data canbe fitted with a Gaussian distribution whose sigma is
0.09%.
Similar analysis have been performed for other electron
beam properties, (emittance, energy spread, ..). As foremittance, data show a distribution with an rms value
which is close to the one predicted (about 12%). Theenergy spread, instead, is slightly affected by the temporal
jitter of bunches and the rms distribution shows a larger
value (almost 20% instead of 10%). Calculated electronbeam average values and corresponding standard
deviations are reported in Table 2.

Figure 6: Temporal profile for current of the 100 jittered
files.
Table 2: Average values and corresponding standard
deviations for the main electron beam parameters
extracted from time-dependent simulations.
Quantity
Mean Value
Std. Dev.
Figure 3: Temporal profile of the electron beam meanenergy of the 100 jittered ELEGANT files.

Figure 4: Average of the electron mean energy of thejittered electron bunch calculated in the useful time window (-200fs; 200fs).
The current distribution shows an rms value (6.6%) thatis slightly lower than the one predicted by the linac group(8%).

Seeded FELs

Gamma
Current (A)Incoherent energy
spreadNormalized
emittance

2231.9
718
0.33

0.09%
6.6%
19.5%

1.35

12.4%

TIME-DEPENDENT FEL SIMULATIONSOF JITTERED FILES
For the FEL simulation we used the nominal setup of
FEL1 [1] that has been optimized in terms of aw and R56
in order to maximize the output power extracted from an

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 7: Average of the electron bunch current calculatedon the useful part of the jittered files (from -200fs to 200
fs).
ideal bunch, whose parameters are equal to the averagevalues reported in Table 2.
Time-dependent simulations using this optimized setup
for the jittered files show a quite high sensitivity to beamjitters (e.g., about 50% of fluctuation in the output
power), which is far from what it is predicted by timeindependent simulations [2].
A new optimization has been necessary in order to finda setup that minimizes the effect of the beam jitters. In
order to reduce the sensitivity of the FEL output power
we slightly changed the tuning of the radiator, setting asmaller value of aw.

in Fig.8,10 refers to the electron bunches reported in
Red, Green, Blue in Figs. 3-6.
The analysis of the FEL output power has been
performed by integrating the pulse profile in order tocalculate the number of photons of each FEL pulse.
Figure 9 report the number of photons of FEL output
pulses for each of the 100 jittered electrons bunches. The
statistical analysis of data shows a distribution which is
close to a Gaussian centered at 70e12 photons per pulse
with a standard deviation of about 23%.
By looking at the output spectra of the FEL pulses, one
can see that the jitter of the input electron-beam
parameters induces a fluctuation of the central
wavelength. However, such a fluctuation is about a factor
3 smaller than the average bandwidth and, as aconsequence, is not affecting too much the FEL
performance (see Fig.10 and Tab.3). Considering theequation for the undulator resonance λ = Lw ⋅(1 + aw )2γ 2

we can derive that, if the emission wavelength is definedby the resonance wavelength of the radiator, the jitter inwavelength, λ, should be two times that associated to thejitter in electron mean energy, γ. This is not true in aseeded FEL where the emission wavelength is defined by
the seeding laser and only partially by the undulator
resonance wavelength.

Figure 8: Temporal profiles for the FEL output radiation
at 40 nm obtained from GINGER simulations using thejittered ELEGANT files; Red, Green and Blue curve refer
to bunches reported with the same colors in figs. 3-6.
The setup utilized for simulations is the following: aseed laser of 100MW with a Gaussian temporal profile(100fs rms), the modulator tuned at 240nm, the dispersive
section set with a R56=19e-6 and the radiator tuned at 40
nm.
Figure 8 displays the output power profiles obtained
from the 100 jitter bunches, while Fig.10 shows thecorresponding output spectra. Red, Green and Blue traces

Figure 9: Number of photons per pulse obtained from the
FEL simulation at 40 nm. Data show an average numberof photons of the order of 70e12 with an rms fluctuationof about 23%.

180

Figure 10: Output power spectra obtained from the FEL
simulations of the jittered files.
Our results are in agreement with predictions and theobtained fluctuation for the wavelength is very lower
compared to the fluctuation of the mean energy of the
input jittered bunches.

Figure 11: Factor to the Fourier transform limit of the
FEL output pulses for the jittered ELEGANT files.

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Proceedings of FEL 2006, BESSY, Berlin, Germany
We also characterized the FEL output pulses in termsof how close they are to the Fourier limit. In Fig. 11 wereport the distance of each FEL output pulse with respect
to the Fourier limit for the 100 simulated jittered files.
The average Fourier factor for the simulated data is 2.2
and the standard deviation of the distribution is about
13%.
Table 3: Statistics of the 100 FEL pulses.
Quantity

Mean Value

Average pulse width(fs)
Average photon
numberAverage central
wavelength (nm)Average bandwidth

73.2

Fourier factor

MOPPH058

REFERENCES[1] C. Bocchetta et al., MOPPH054 proceedings of thisconference.
[2] W. Fawley et al., Sincrotrone Trieste tech. note,
ST/F-TN-06/16.
[3] P. Craievich, S. Dimitri, G. Penco, private
communication.
[4] M. Cornacchia et al., Sincrotrone Trieste tech. note,
ST/F-TN-06/15.

Std. Dev.

7.1e+1323.3%

40.00190.013%

0.033%
2.2

13%

In order to verify the prediction of time independent
simulations, which indicate the jitter in the mean electronenergy as the most limiting factor for achieving a good
output stability, in Fig. 12 we plot the number of photons
per pulse vs the average electron-beam energy.

Figure 12: Number of photons per pulse vs the average
electron mean energy of the corresponding electron
bunch.
The good correlation between the two quantities clearly
confirms the high sensitivity of the FEL output to theelectron mean energy.

CONCLUSIONS
An extensive campaign of start-to-end simulations forthe first stage of the FERMI@Elettra project has beenpresented. Results show a quite strong sensitivity of FEL
characteristics to shot-to-shot jitters of electron-beam
parameters.
The effect of the proposed strategies for the reductionof the output power fluctuation by means of sophisticatedradiator configuration (tapering) or linear chirping of theelectron bunches will be considered in a forthcoming
work.

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THE TEST FACILITY FOR HARMONIC GENERATION AT
THE MAX-LAB INJECTOR LINAC *Mathias Brandin, Tue Hansen, Sara Thorin, Sverker Werin, MAX-lab, Lund
Michael Abo-Bakr, Johannes Bahrdt, Kathrin Goldammer, BESSY GmbH, Berlin
Jörgen Larsson, Anne L’Huillier, Anders Persson, Claes-Göran Wahlström, Department of Physics,
Lund University.
Abstract
A test facility for harmonic generation is being built at
MAX-lab. The third and fifth harmonic, at 90 and 53 nm
respectively, will be created using a fs seed laser at 266
nm. The MAX-lab injector will be operated at 400+ MeV
with a photo RF gun and the optics will be retuned toachieve compression. An optical klystron will be installed
comprising of two undulators and a chicane.

OVERVIEW AND SCOPE
The BESSY FEL project [1] and the MAX IV proposal[2] are both focused on seeded FEL sources as part of the
facilities. In the aim of improving the designs a decision
was made to build a test facility for harmonic generation
at MAX-lab.
The MAX injector system [3] is a recirculated linac
with energy capabilities up to 500 MeV. Few otherlocations have this linac energy available for a test
facility. The joint effort includes simulations, a newelectron source, laser systems, an optical klystron andexperimental activities.
The test facility is intended to use an electron beam of
at least 400 MeV with an emittance of 3 μmRad and abunch length around 500 fs. It will be injected into an
optical klystron consisting of a modulator undulator, achicane and a radiator undulator. A fs seed laser at 266 nm
will be used and harmonic generation at 90 nm and later
53 nm will be studied.
Linac
RF gunRecirculator

wavelength and is modulated in energy. The particles thenpass through the magnetic chicane which serves as adispersive element. It consists of four dipole magnets andintroduces an energy-dependant longitudinal delay of theelectrons: the unmodulated particles are bent into a longer
trajectory than the higher energy particles so that thebeam is redistributed longitudinally. The process isreferred to as “(micro)bunching”. The bunching is tunable
to achieve a maximal Fourier component at either the
resonant frequency of the modulator or at higher
harmonics. In the MAX-lab FEL experiment, the third
harmonic will be used, thus efficiently shortening theoutput wavelength of the FEL to 88 nm. In the second
undulator, called radiator, the bunched beam will thenemit intense, coherent radiation at the shorter wavelengthwith an output power in the megawatt-range. Substantial
development of this method, HGHG, has been done at
BNL [4].

THE ACCELERATORS
While most of the accelerator systems are already athand at MAX-lab some additions and alterations arenecessary. These mainly regard a new photo cathode RF
gun [5] and finding a new optics [6] which createscompression and transports the bunch to the optical
klystron.

The Gun Pre Injector
In order to produce a transversely and energeticallycollimated electron beam, the electrons will be generated
in a low emittance photocathode gun. The gun is a 3 GHz
1.6-cell cavity, mounted slightly off axis, with a copper
cathode illuminated by a ten ps long laser pulse at 266
nm. This produces bunches with a total charge of 0.5 - 1
nC. The beam parameters at the exit from the gun can beseen in table 1.
Table 1: Beam parameters after the gun (simulated)

Fig 1. The MAX injector.

The FEL Principle
The FEL section consists of an Optical Klystron wherein the first undulator, called modulator, the electron beam
co-propagates with a strong seed laser of 266 nm* This work has been partially supported by the Swedish Research Council
and by the European Commission in the Sixth Framework Program, Contract
No. 011935 – EUROFEL.

182

EnergyEnergy spread
Normalized emittance εNChargePulse length
Peak current

3.7 MeV3%
3 mm mrad

0.5 nC
11 ps
45 A

The emittance compensation scheme adopted is similar
to the LCLS [7]. Results of the tracking are shown infig 2.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Emittance, norm (mm mRad)

12
X with 10 mRad bend
Y with 10 mRad bend
Gun to bend
X&Y no bend

4,2

10

4,0
3,8

8

36

6
4
2
0
0

2

4

6

8

Length (m)Figure 2: Emittance (normalised) (1 nC, 3.7 MeV, 10ps).
off axis compensation (10mR) at 0.75 m and linac from1m.

Linac and Recirculator
The linacs and recirculator system in the MAX-injector
have been in operation for several years. They routinely
deliver 380 MeV as injector for MAX I and II. They are
currently being conditioned above 400 MeV.

MOPPH061

electric field in the linac is given such a phase that anenergy chirp is induced in the electron pulses. Throughthe quadrupoles and dipoles in the recirculator block, thischirp can then be rotated time wise to result in a very
short pulse. Because of the sinusoidal shape of theaccelerating field, the energy spread will not becompletely linear but some second order effects will
occur. These second order effects can be compensated by
the use of sextupole magnets which introduce second
order corrections and straighten the energy chirp up to aline. In the MAX-injector sextupoles are incorporated insome of the quadrupoles in the recirculation blocks andare not separately tuneable. They can thus not be used tocompletely linearize the second order effects, but they docontribute a bit towards higher peak brilliances. With
separately tunable sextupoles linearization morecorresponding to that of a higher order cavity can be
done.
Approximately 25% of the bunch charge can be
confined within the usable part of the bunch. This way
bunch lengths shorter than 300 fs and peak currents of
300 A can be obtained. Table 2 and figure 3 show thebeam at the exit of the recirculator.
Table 2: Beam parameters after the recirculator
EnergyEnergy spread
Normalized emittance εNx, εNy
Bunch charge in peak
Pulse length
Peak current

400 MeV
0.1 %3 mm mrad, 8 mm mrad0.12 nC
400 fs300 A

Transport
The transport from the injector to the undulator section
is about 40 m and includes a vertical lift of the beam fromthe cellar to the ground floor. This lift is done with anachromatic dogleg [8] consisting of two 15 degree bends
with 5 quadrupoles in between. The middle quad is used
to control the beta-function while the two outer ones areused to close dispersion after the second bend. To avoid
space charge effects in the centre of the dogleg, where thebeta function can hit a very low minimum, the two quads
on either side of the middle are used for modification of
the beta function.

THE OPTICAL KLYSTRON

Figure 3: Electron bunch after the recirculator.

Since a high peak current is important for FEL
efficiency, the electron bunches have to be compressed
after the gun. Bunch compression is achieved using thelinacs and the magnetic optics in the recirculator. The

Seeded FELs

Existing magnet structures will be used to build theundulators. A pure permanent magnet (PPM) structure
has been loaned from the ESRF to be used in themodulator. The radiator will be equipped with the APPLE
structure of the BESSY UE56-1. The parameters are
summarized in table 3.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

For higher harmonics (shorter wavelengths) ΔL ≥ λ photon / 2
Table3: Parameters of the undulators and the chicane
Modulator
Period length
Number of periods
Minimum gap
Maximum K-parameter

48 mm
30
10 mm
4.3

Radiator
Period length
Number of periods
Minimum gap
Maximum K-parameter

56 mm
30
12 mm
4.3

ChicaneNumber of magnets
Type of magnet
Gap
Maximum field
Distance between magnets

4
H-frame, electromagnet
15 mm
0.2 T
400 mmcan be produced and overbunchig effects can be studied.

Mechanical Layout
The electron beam height at the HGHG-FEL is only
400 mm and conventional undulator carriages cannot be
used. Therefore, a new carriage has been developed
which can cope with this geometry (figure 4). The samestructure is used for both undulators.
The two undulators will be measured and shimmed at
the existing measurement bench at BESSY. For thispurpose the undulators have to be flipped into uprightorientation (figure 5). At MAX-lab the final magnetic
measurements will be performed in the operating position
using a pulsed wire system.

Both undulators will have a motorized gap drive. The
radiator provides also a motorized phase variation forpolarization control. The modulator is moved only in caseof an electron energy change whereas the radiator has tobe tuned also when the harmonic number of the radiationor the state of polarization is changed.

The Chicane
The magnetic chicane converts the energy modulationof the electron beam into a spatial modulation. Optimum
bunching is achieved if the energy modulation dominates
the energy spread times the harmonic number n :Δγ / γ ≥ n ⋅ σ γ

Figure 5: Radiator in measurement position.

LASER SYSTEMS
A combined laser system for the gun and the seeding of
the HG-FEL has recently been sent out with an invitation
to tender. We foresee a common system locked to the RFof the accelerators to better than 1 ps. The system shoulddeliver 500 μJ in a 10 ps pulse at 266 nm to the RF gun
and 100 μJ in a 300 fs pulse at 266 nm to the seeding. The
solution is up to the supplier while the basic thought is acentrally located oscillator locked to the accelerator RFsystem and an optical distribution to the amplifiers. (Dueto the commercial actions the information is minimized.
Please contact the authors for more information:
sverker.werin@maxlab.lu.se)

Figure 4: Modulator in operating position.
With a relative energy spread of σ γ = 5 ⋅ 10 −4 an energy
modulation of at least Δγ / γ = 1.5( 2.5) ⋅ 10 −3 is needed tooperate on the third (fifth) harmonic. This defines thelaser power.
The maximum bunching appears for a path length
difference of ΔL = λ photon / 4 between modulated and non
modulated electrons. The chicane is optimized such thatst
ΔL = λ1photon/ 4 = 67nm can be reached with 500MeV
electrons and an energy modulation of Δγ / γ = 1.0 ⋅ 10 −3 .

184

DIAGNOSTICS
The diagnostics have two main duties. The first is tocontrol the electron beam performance and the second toassure overlap in time and space of the laser andelectrons. Table 4 shows the intended methods to be used
to approach the different areas.
In a resent test set-up the uncompressed bunch length at
the MAX injector was measured to σ = 2.3 ps. The
technique used was detecting coherent transition radiation
with an interferometer [9]. This set up will now be
finalized to be able to diagnose sub ps pulses.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Table 4. Diagnostics
FeatureEnergy spread
Emittance
Bunch length
Current/charge
X and y positions
Alignment
Synchronization/time
Beam loss

MethodDispersive section
Q scans
CTR and interferometerBeamtransformers,
Faraday cage
YAG/OTR screens
Apertures for spontaneousand laser beams
Electro-optical methods
Energy spread,
Cherenkov fibre

THE FEL SIMULATION
For realistic simulation of the FEL, the particles weretracked all the way through gun, linac, beam transport andthe undulator section using ASTRA [10], elegant [11] andGENESIS [12]. In order to study time-dependant effectsof FEL interaction, the 6-dimensional phase space filefrom elegant was converted into a GENESIS input file bycutting out the seeded part of the beam +/-50fs and split itup into a collection of temporal slices. For each slice, therelevant beam parameters were calculated externally anddelivered to a GENESIS compatible input file.

Figure 6: Temporal and spectral power distributions of
FEL pulse at exit of radiator.

Simulation Results
Due to the fact that the simulation work is still ongoing,
the results for the FEL section presented in this section
were achieved without a formal start-to-end-transport ofthe original input bunch from ASTRA to GENESIS.
However, the beam parameters gained by the slice
analysis were used to perform fully time-dependantsimulations taking into acount the seed laser beam
temporal profile. A 95%-emittance of 3 mm mrad
(normalized) was assumed. The parameters used to model
the undulator section and the magnetic chicane are listed
in table 3.
Using a seed laser of 150 MW peak power and a
FWHM flat top length of 300 fs, the necessary energy
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MOPPH061

modulation can reliably be established within themodulator. When optimizing the magnetic chicane for
maximal bunching at the third harmonic, the radiator lases
at 88 nm with a power level in the range of 1-10 MW.
Figure 6 shows the temporal and spectral power
distribution at the end of the radiator.

SUMMARY
A test facility for FEL and HGHG is currently being
built at MAX-lab. The coming year will be spent on
installation of undulators, the new pre injector, build up of
the laser systems and finalizing the diagnostics. The aimof the facility is to test and develop the techniques, butalso to already at an early stage of the BESSY FEL andMAX IV projects practically address the processes.
Simulations and development of beam optics are alsopart of this process.
An important side effect of this project is to start theprocess of joining forces between the accelerator andlaser science. The future of accelerators lies in many ways
in starting to use lasers as natural parts of accelerator
installations.
The capabilities of this installation are also such thatnew ideas and a continuation after the initial generation of
the 3rd harmonic are a natural continuation.

REFERENCES[1] BESSY TDR, D. Kraemer et al., 2004.
[2] MAX IV Conceptual Design report, MAX-lab, 2006.
[3] S.Werin et al., Commissioning of the 500 MeV
Injector for MAX-lab, EPAC 2004
[4] L. H. Yu, J. Wu, Nucl. Instr. and Meth. in Nucl. Res.
A 483 (2002) 493.
[5] S. Werin et al, “Design of a New Preinjector for the
MAX Recirculator to be used in EUROFEL”, EPAC
2006
[6] S. Thorin et al, “Simulations for the FEL Test Facility
at MAX-lab within EUROFEL”, EPAC 2006
[7] R. Boyce, D.H. Dowell, J. Hodgson, J.F. Schmerge,
N. Yu, Design Considerations for the LCLS RF Gun,LCLS TN 04-4 (2004)[8] J. England et al., Sextupoles Correction of theLongitudinal Transport of Relativistic Beams in
Dispersionless translating sections, Phys. Rev. ST
Accel. Beams 8, 012801 (2005) .
[9] M. Brandin, B. Nelander, S. Werin, Measurement anddiagnostics on the MAX recirculaor, EPAC 2006[10] K. Flöttman “ASTRA User Manual”, September 18,
2000, www.desy.de/~mpyflo[11] M. Borland, "elegant: A Flexible SDDS-Compliant
Code for Accelerator Simulation" Advanced Photon
Source LS-287, September 2000.
[12] S. Reiche, “Numerical Studies for a Single Pass High
Gain Free-Electron Laser”, PhD Thesis, Uni
Hamburg, corona.physics.ucla.edu/~reiche/links.html

185

MOPPH063

Proceedings of FEL 2006, BESSY, Berlin, Germany

COHERENT X-RAY PRODUCTION BY CASCADING STAGES OF HIGH
GAIN HARMONIC GENERATION FREE ELECTRON LASERS SEEDEDBY IR LASER DRIVEN HIGH-ORDER HARMONIC GENERATION∗
Juhao Wu† and Paul R. Bolton, SLAC, Menlo Park, CA 94025, USA.
Abstract
Coherent x-ray production achieved by a seeded freeelectron laser (FEL) with cascaded high gain harmonic
generation (HGHG) is important for next generation development of synchrotron light sources. We examine thefeasibility and some features of FEL emission seeded bya high order harmonic of an intense infrared conventionallaser source (HHG). In addition to the intrinsic FEL chirp
phenomenon, the longitudinal profile and spectral bandwidth of the HHG seed are modified significantly by the
FEL interaction well before saturation occurs. This smearsout original attosecond pulselet structure. As an example,
we describe a cascaded HGHG scheme for coherent x-ray
FEL generation that is seeded by the twenty-seventh harmonic of an ultrashort 800 nm laser pulse with 10 fs rms
duration. By cascading two stages of HGHG, 15 GW peak
power FEL emission at 0.3 nm can be produced with 90
MW peak power radiation at 0.1 nm via the non-linear harmonic generation.

INTRODUCTION
Short-wavelength Free-electron Lasers (FELs) are perceived as the next generation synchrotron light sources.
Self-Amplified Spontaneous Emission (SASE) [1, 2, 3, 4],is the dominating approach to produce an x-ray FEL(XFEL). While it has good transverse coherence, the SASE
FEL pulses are composed of a series of ultrashort spikes
due to a short longitudinal coherent length. To improve thelongitudinal coherence, various approaches have been proposed. Among them, a cascaded high gain harmonic generation (HGHG) FEL [5, 6, 7, 8, 9, 10] looks promising by
invoking high order harmonic generation of an infrared (ir)laser (HHG) as the seed. In this paper, we study an HHG
seeded FEL. This is of particular interest [11], since HHG
can provide a uv to soft x-ray seed, making a coherent hard
XFEL feasible.

HHG SEEDED HGHG FELS AT LCLSHHG Seed: Attosecond Structure and Smearing
Effect
HHG generates an electric field comprised of multiple
harmonic orders, s and multiple time pulselets, n expressed∗ The work was supported by the US Department of Energy under contract DE-AC02-76SF00515.
† jhwu@SLAC.Stanford.EDU

186

as the following double summation [12, 13]:
2 2Es,0 ei(ks z−ωs t) e−iBs ωs t
EHHG (t, z) =
s
N


×

e

−

t2
n
4σ2
t,0

e−αs ωs [(t−tn )−z/c] , (1)
2

2

n=−N

where for each order, s we sum over the temporal sequenceof 2N + 1 pulselets for which n ∈ [−N, N ]. Becauseof temporal coherence of a group of harmonic orders, thepulselets can exhibit attosecond structure (with periodicityof τ /2), limited by the relative amplitudes and phases of thedifferent harmonic orders. The order dependent parameter,
Bs accounts for the small intrinsic chirp that characterizes
each harmonic order [14]. In Eq. (1), t n = nτ /2 with τ
being the period of the unchirped ir pulse (2.67 fs at 800nm); σt,0 is the ir pulse rms duration; k s and ωs are thewavenumber and angular frequency of the s th harmonic;
2and αs = (4σt,sωs2 )−1 with σt,s being the rms durationof each pulselet in the HHG pulse. Typically σ t,0 ≈ 10
fs and τ /20 ≤ σt,s ≤ τ /2 for a single pulselet, where
the lower limit assumes relative phase synchronization of aharmonics group [12, 15]. In this paper, we consider onlya single harmonic order, s as the carrier frequency and forsimplicity, we negelect the harmonic chirp (B s ≈ 0). The
HHG field expression then simplifies to:E(t, z) =NEs,0 ei(ks z−ωs t)

e

−

t2
n
4σ2
t,0

n=−N

×

e

−αs ωs2 [(t−tn )−z/c]2,(2)which represents an attosecond pulselet train (APT) derived from the amplitude modulation of carrier frequency,
ωs . We use σt,0 = 10 fs and σt,s = τ /8 ≈ 334 attosecond in the Fourier-transform limit. In this case, it
is important to note that, although the central carrier frequency of the seed is a single harmonic, the transform
limited seed spectrum also includes components from several neighboring harmonic orders [16]. A multi-pulselet
HHG seed is the sum of many single pulselets. We address the single pulselet at tn = 0 for n = 0 so thatEs (t, z = 0) = Es,0 exp(−iωs t − αs ωs2 t2 ), assuming forsimplicity that the single harmonic pulselet is transformlimited, i. e., σt,s σω,s = 1/2, so that the rms bandwidth√σω,s = αs ωs . Since each pulselet is ultra short, the spectral bandwidth is broad. The seeded FEL solution reads[17]√

EFEL (t, z) =E0,FEL eρ( 3+i)kw z(3)

Seeded FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH063

ei(ks z−ωs t) e−[αs,f (z)+iβs,f (z)]ωs (t−z/vg ) , initial pulselet is assumed to have σ t,s = τ /8. Assuming a Fourier-transform limited single harmonic pulselet,
where vg = ωs /(ks + 2/3kw ) is the group velocity of the we have σω,s = 1/(2σt,s ). The relative rms bandwidth is
FEL light,
σω,s /ωs ≈ 2.4 %. Due to the FEL interaction, accord1
αs,f (z) = 2,(4) ing to Eq. (7), the FEL bandwidth decreases. For the
4σt,s,f (z)ωs2
scheme shown in Fig. 1 with parameters in Table 1, we
have ρ = 0.54 % and λw = 0.2 m, we have z c ≈ 1.6
and2
m.
Considering that the first modulator is 25 m long andσω,s,f (z)
2
−
α
(z)
(5)
βs,f (z)2 = αs,f (z)
s,f
the
power
gain length is about 3 m, attosecond structure isωs2
smeared out within a short distance [16]. Consequently, thewith
HHG seed resembles a conventional harmonic seed gener⎧ated via wave-mixing in a solid such that we can ignore
3+6R(z)2 +4R(z)4⎨ σt,s,f (z) = σt,s3[1+R(z)2 ],(6) initial attosecond structure, at least as a good approxima⎩ σω,s,f (z) = √ σω,s 2
tion.
1+R(z)In Fig. 1, we show the generic configuration of an HHG
seededcascaded HGHG FEL. It has the following features.
with
σω,s
R(z) ≡,(7)σω,GF (z)
2

×

and

 √
3 3ρωs2.
σω,GF(z) ≡
kw z

2

(8)

Here σω,GF (z) is the rms bandwidth of the FEL Greenfunction for a coasting electron beam with ρ being the
Pierce parameter [1]. The transform limit also means that
αs,f (0) = αs , βs,f (0) = βs = 0, σt,s,f (0) = σt,s , andσω,s,f (0) = σω,s . The FEL-interaction intrinsically generates a chirped FEL waveform,
βs,f (z)R(z)2(t−t )(ω −ω ) =
= √
. (9)
2αs,f (z)2 3[1 + R(z)2 ]The emittance of the FEL light at any position, z, is conserved, ε ≡ {(t − t )2 (ω − ω )2 − (t − t )(ω −ω ) 2 }1/2 = 1/2, indicating that the FEL emission is fully
coherent longitudinally [17].
We introduce the critical location, z c , where the FEL
Green function bandwidth reduces to the pulselet initial) = 1. Recall that, the power√gain
bandwidth, i.e., R(z c√length LG = λw /(4 3πρ), hence, if σω,s /ωs > 3 2ρ,
1, thethen zc < LG . For large enough z, where R(z)FEL has⎧⎪
σt,s,f (z) → √3σ 1 (z)
⎨
ω,GF
(10)
σω,s,f (z) → σω,GF (z) ,⎪1⎩ (t − t )(ω − ω ) →√2 3i.e., the final characteristics are determined by the FEL interaction. In accordance with Eq. (6), the FEL interaction
rapidly reduces the seed pulselet bandwidth, extending its
duration [16].

HHG-HGHG FELs at LCLS
Considering the feasibility of an HHG seeded HGHG
XFEL, we use an ir laser at 800 nm with σ t,0 = 10 fs.
We choose the 27th harmonic as the seed to interact withan LCLS-type high brightness electron bunch [18]. The

Seeded FELs

Figure 1: Schematics of an HHG seeded cascaded HGHG
FEL. In this scheme an HHG seed of 30 nm is used. After
two stages of HGHG and a final amplifier, we obtain 15
GW at 0.3 nm, and 90 MW at 0.1 nm.
1. We need multiple stages. During each stage the nthharmonic of the seed laser will be produced at the end of theradiator, and then this harmonic will be used as the seed forthe next stage. In reality, n cannot be too large due to thatstability consideration [7, 9]. In our paper we use n = 10 toachieve stable performance, and we need only two stages.
2. Conceptually, the device is composed of two parts: aconverter [19] and an amplifier. The converter, consistingof several stages, converts the seed laser to the designed
wavelength step by step. Then at the end, an amplifier exponentially amplifies the radiation obtained from the laststage to saturation.
3. Except for the first modulator and the last amplifier,each stage only converts the light to its n th harmonic. Exponential growth is not required as long as the harmonic
power is high enough to be used as the seed for the nextstage.
4. The phase mixing induced by the emittance in thedispersion section is much smaller than that in an undulator. For an HGHG FEL, bunching is produced mainly inthe dispersion section; while for a SASE FEL, bunching is
produced in the undulator. Therefore, the emittance effectturns out to be less important in an HGHG FEL than in a
SASE FEL [10].

187MOPPH063

Proceedings of FEL 2006, BESSY, Berlin, Germany

5. Since we need to cascade several stages of HGHG,
we need some extra components. Each stage will consistof one modulator, a dispersion section (a small chicane),and one radiator. The physics process in each stage will be
the same as in Refs. [5, 6]. During the process, the output
radiation has disturbed the coincident part of the e-bunch.
Therefore, to achieve the best efficiency in the next stage of
HGHG, we need use a fresh region of the e-bunch. To dothis, the laser (i.e., the output radiation from the previous
HGHG stage) is shifted to the front part of the same ebunch, so that the laser will interact with a fresh part of thesame e-bunch. i.e., we use a magnetic shifter to relatively
delay the electron bunch.
As mentioned above, this conceptual design uses the27th harmonic of the 800 nm ir pulse with σ t,0 = 10 fs.
Assuming the input seed peak power of 5 MW, with twostages of HGHG and a final amplifier, we obtain a 15 GW
FEL at 0.3 nm, and 90 MW at 0.1 nm via nonlinear harmonic generation [20, 21]. In this example, the 27 th harmonic pulselet interacts with an LCLS-type electron beam
[18] (normalized emittance ε n = 1.2 π mm-mrad, relative
energy spread σ γ /γ0 = 1.13×10−4, energy E0 = 10 GeV,and peak current I pk = 3, 400 Amp). In the 25 m modulator of the first HGHG stage, the HHG seed is amplified,and simultaneously modulates the electron beam energy.
A small chicane then converts the energy modulation into
density microbunching at 30 nm. This microbunched electron beam then traverses the 8 m radiator which is resonant
at 3 nm (the 10th harmonic of the original 30 nm seed).
This microbunched electron beam first coherently radiates
at 3 nm and then exponentially amplifies this 3 nm radiation to a peak power of 5 GW, which is used to seed thenext HGHG stage. In the second stage, the 5 GW, 3 nm
seed energy modulates the electron beam in the 5 m modulator. The energy modulation is converted into density
microbunching at 3 nm via a second small chicane. Thisdensity modulated electron beam initially radiates coherently in the 5 m radiator, resonant at 0.3 nm (the 10 th harmonic of the 3 nm seed). At the end of the 5 m radiator, the0.3 nm radiation is amplified to 0.1 GW, which is further
amplified in the 22 m final amplifier, resonant at 0.3 nm.
At the amplifier exit, the FEL is well into saturation, andthe system finally produces 15 GW, 0.3 nm radiation. Dueto the microbunching at 0.3 nm, there are substantial harmonics. The third harmonic emission at 0.1 nm has a peak
power of 90 MW.
As shown in Fig. 1, we consider an HHG seed with awavelength of 30 nm, and a peak power of P in = 5 MW. As
we will discuss later, the corresponding start-up shot-noise
power is only about P noise ≈ 70 W. Thus the input seedlaser power dominates the shot-noise power. This dominance is necessary, because even though there is only negligible noise power in the initial stage, the signal-to-noise
ratio of the final radiation at 0.3 nm can be degraded [22].
A simple estimate shows that the noise-to-signal (NTS) ratio at the seed will be amplified by n 2tot times for the nthtotharmonic generation. In this case, the two stage approach

188

Table 1: Parameters for the undulator, the dispersive section and the electron bunch.
λr (nm)λw (cm)
dψ
dγ
σγ
γ0

Lw (m)LG (m)

1st stage
30
3
20
6
0.2
25
3

2nd stage
3
0.3
6
3
0.4
1.13 × 10−4
8 5
5
2 2
3

Amplifier
0.3
3

22
3

has an overall n tot = 100, hence, the NTS ratio will be
amplified by 10 4 times. Hence for the final radiation at 0.3
nm, the NTS ratio will be about 14 %.
After two HGHG stages, we have generated 0.3 nm radiation, and this 0.3 nm radiation is amplified to saturation
with a peak power near 15 GW in a final amplifier stage.
The parameters for the electron beam and the radiation are
given in Fig. 1. The number in the first row stands for the
output power and wavelength of the radiation of each stage.
The output power of one stage is the input power of the nextstage, though diffraction has been taken into considerationin the simulation. The e-beam parameters are printed below the schematic device. The relative local energy spreadσγ /γ0 given in Fig. 1 is the initial relative local energy
spread before the e-beam enters the first modulator. This isincreased by spontaneous radiation [23]. We take this into
account in the simulation [21].
In Table 1, the first row gives the radiation wavelength
λr ; the second row, the undulator period λ w , and the third
row the dispersion strength dψ/(dγ) with ψ being the ponderomotive phase in the radiator. The fourth row gives theinitial relative local energy spread σ γ /γ0 . In our simulation, quantum diffusion [23] has been taken into account[21]. The fifth row gives the length of the undulators (modulators, radiators, and the amplifier) L w . For example, thelast amplifier has a length of 22 m. The sixth row gives
the power gain length L G in each undulator without energy modulation. The table has three boxes; the first twoboxes are for the two convertor stages and the last one isfor the amplifier. For the two convertor stages, the left column gives the parameters for the modulator and the rightcolumn those for the radiator; the numbers in the middle
stand for the dispersion strength dψ/(dγ). For example,
the left column in the second box stands for the modulatorof the second stage. The table shows that in the modulator
the resonant radiation has a wavelength of 3 nm, the modulator has a period of 6 cm, the length of the modulator is
5 m, and the corresponding power e-folding length without
energy modulation is 2 m. The right column shows that theradiation in the radiator has a wavelength of 0.3 nm, theradiator has a period of 3 cm, the length of the radiator is
5 m, and the corresponding power e-folding length is 3 m.
In the middle, i.e. 0.4, stands for the dispersion strengthdψ/(dγ).

Seeded FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

Start-up Noise Issue
First, we need to compute the effective start-up noise
power for the fundamental SASE guiding mode [24, 9]
 √
2LG
3 3ρ
2λr
Start−up
= C1
π
(11)
PSASE
Lw
Lw
Nw
×

eZ0 Ipk 2 2
K2
Nw γ[JJ]2 ωr ,
2 2
4π
1+ K
2

where the coupling factor is found to be [24],
√

1
3
1
√
Cm (a) ≈
β
,
exp
−
+
β
m,0
m,1 2
πa2
a
a 1 + a2(12)
where, m is theindexreferringtoacertain
mode
being
√
excited; a = 4ρkw kr R0 is the scaled beam size withkw = 2π/λw , kr = 2π/λr , and R0 the hard edge of anelectron beam. The above formula is a good approximation, when a > 0.25. Within such range, β m,0 = 1.093,
and βm,1 = −0.02 for the fundamental guiding mode. In
Eq. (11), L G is the power gain length; L w the undulator
length; λr the radiation wavelength; N w the number of undulator period; Z 0 the vacuum impedance; I pk the peakcurrent; ωr (= c2π/λr ) the radiation angular frequency
with c the speed of light in vacuum. The Bessel factor
√
a2w
a2w
[JJ] = J0 2(1+a− J1 2(1+a2,
2 )2 ) , with aw = K/ww
and J0 and J1 are the zeroth order and first order Bessel
function, respectively. Approximately, K ≈ 93.4B w λw is
the undulator parameter with B w the peak field of the undulator in units of Tesla and λ w in units of meter.
In the above SASE calculation, the bandwidth of the fundamental guided mode is σ ω,GF for z = 2LG according to
Eq. (8). However, the seeded FEL has a different bandwidth of σω,s,f (z = 2LG ) according to Eq. (6). Hence,
the true start-up noise power in the seeded FEL bandwidthisStart−upStart−up σω,s,f (z = 2LG ).
PSeeded= PSASEσω,GF (z = 2LG)consider the accompanied noise power and electron beam
non-uniformity [10]. The true start-up noise power in theStart−upseeded FEL bandwidth, P Seededis only about 70 W.
Since the HHG seed has a power of P in = 5 MW, thenoise-to-signal ratio at the final radiation λ r = 0.3 nm
is still only about 14 %, even though it has n 2tot = 104(ntot = 100) times amplification, i.e., the effective noiselevel is increased from the initial 70 W to 0.7 MW.

REFERENCES[1] R. Bonifacio, C. Pellegrini, L.M. Narducci, Opt. Commun.,
50, 373 (1984).
[2] J.-M. Wang and L.-H. Yu, Nucl. Instr. and Meth., A 250,
484 (1986).
[3] K.-J. Kim, Nucl. Instr. and Meth., A 250, 396 (1986); Phys.
Rev. Lett. 57, 1871 (1986); Lawrence Berkeley National
Loboratory Report No. 40672 (1997).
[4] S. Krinsky and Z. Huang, Phys. Rev. ST Accel. Beams 6,050702 (2003); E.L. Saldin et al., Proc., 2005 Int. FEL
Conf., p.258.
[5] L.H. Yu, Phys. Rev. A 44, 5178(1991).
[6] L.-H. Yu, et al., Science, 289, 932(2000).
[7] J. Wu and L.H. Yu, Nucl. Instr. and Meth., A 475, 104(2001).
[8] L.H. Yu and J. Wu, Nucl. Instr. and Meth., A 483, 493(2002).
[9] J. Wu and L.H. Yu, Stanford Linear Acclerator Center Report No. SLAC-PUB-10494 (2004).
[10] J. Wu and L.H. Yu, Stanford Linear Acclerator Center Report No. SLAC-PUB-10495 (2004).
[11] M.-E. Couprie et al., Proc., 2005 Int. FEL Conf., p.55.
[12] R. López-Martens, Phys. Rev. Lett. 94, 033001 (2005).
[13] E.A. Gibson et al., IEEE J. of Selected Topics in Quant.
Elec. 10, 1339 (2004).
[14] J. Mauritsson et al., Phys. Rev. A 70, 021801(R) (2004).
[15] P.M. Paul et al., Science 292, 1689 (2001).

(13)

Considering the first modulator, the Pierce parameter isρ ≈ 5.4 × 10−3 ; the scaled beam size is a ≈ 0.8, which
gives the coupling coefficient to be C 1 ≈ 0.3. The SASE
effective start-up noise power in the fundamental guided
Start−up≈ 400 W; however, since σω,s,f (z =mode is PSASE
2LG ) ≈ 2.0 × 10−3 and σω,GF (z = 2LG ) ≈ 1.2 %, thetrue start-up noise power in the seeded FEL bandwidth isStart−up≈ 70 W.
only about P Seeded

DISCUSSION
In this paper, we explored the details of an HHG seeded
FEL. For simplicity, the HHG seed is modelled as an attosecond pulselet train (APT). Bandwidth reduction, intrinsic to the FEL interaction, smears out the initial attosecond structure of the seed within a very short distance,z < LG . The seeded FEL remains coherent, if we do not

Seeded FELs

MOPPH063[16] J. Wu, P.R. Bolton, J.B. Murphy, and X. Zhong, Stanford
Linear Acclerator Center Report No. SLAC-PUB-11891(2006).
[17] J.B. Murphy et al., Brookhaven National Laboratory Report
No. BNL-75807-2006-JA, and Stanford Linear Acclerator
Center Report No. SLAC-PUB-11852 (2006); J. Wu et al.,Stanford Linear Acclerator Center Report No. SLAC-PUB11985 (2006).
[18] J. Arthur et al., Stanford Linear Acclerator Center Report
No. SLAC-R-593 (2002).
[19] I. Boscolo and V. Stagno, Nuovo Cimento B 56, 219(1980).
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commun. 202, 169 (2002).
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[24] L.H. Yu, Phys. Rev. E 58, 4991(1998).

189

MOPPH065

Proceedings of FEL 2006, BESSY, Berlin, Germany

THE FIRST EXPERIMENTAL OBSERVATION OF FEL AMPLIFIEREFFICIENCY IMPROVEMENT USING ELECTRON BEAM ENERGY
DETUNING AT THE NSLS SDL
T. Watanabe∗ , J.B. Murphy, J. Rose, Y. Shen, T. Tsang, X.J. Wang, BNL, Upton, NY 11973, USA
H.P. Freund, Science Applications International Corporation, McLean, VA 22102, USA

Abstract
The first experimental observation of efficiency enhancement using electron energy detuning in a single-pass laser
seeded Free-Electron Laser (FEL) amplifier is reported.
Our experiments show that it is possible to double the FEL
efficiency by increasing the electron energy by +0.7 % relative to the resonance energy. The measurement of the laser
seeded FEL spectra versus energy detuning shows that thepeak wavelength of the FEL radiation is determined by theseed laser. The experimental results are discussed using
FEL theory and a three-dimensional simulation code GENESIS1.3 [1].

INTRODUCTION
One of the advantages of the FEL is the ability to produce high power laser light without the conventional thermal issues associated with other laser systems [2]. In addition, the operating wavelength of the FEL can be adjusted
according to the application. Because of the advantages,
the FEL has been regarded as one of the promising approaches to generate Megawatt (MW) average power laser
at 1 μm wavelength. Such an application is called directedenergy application [3, 4].
In order for the FEL to realize the MW average power
output, it is required to optimize the efficiency of the FEL
process. Supposed that the interaction between the electron beam and the radiation is strong enough in the undulator, the radiation power grows exponentially as the electron
beam goes through the undulator. According to the steadystate theory of a single-pass FEL, the radiation is saturated
at ρPe due to the deposition of the electron energy to theradiation. Here, ρ is the Pierce parameter and P e is the input electron power. After the saturation, the electrons withlower energy no more resonate with the radiation as it doesin the exponential gain regime. Instead, the mutual energy
deposition between electrons and radiation is repeated.
To overcome the saturation, several schemes have been
proposed and tested. One is to taper an undulator, in which
the field strength of the undulator is gradually decreased after the saturation so that the electrons with lower energy canmaintain the resonance with the radiation [5, 6]. Anotheris to detune the electron energy, in which the input elec∗ twatanabe@bnl.gov

190

trons with slightly higher energy can resonate with the radiation longer than the normal (resonant) case [3]. The detuning effect had been theoretically and numerically studied [7, 8, 9, 10]. The study indicates that the growth rateis deteriorated by the detuning, while the saturation power
can be enhanced by optimizing the detuning. It is an advantage of the detuning scheme that the scheme does not
require any modification of the experimental setup; only
the requirement is to change electron beam energy. As far
as authors know, however, the detuning effect in a singlepass FEL had not been experimentally verified.
In a self-amplified spontaneous emission (SASE) FEL,
in which no external seed laser is supplied, the radiation
wavelength is shifted when the electron energy is changed.
Thus, the wavelength of the output radiation is inevitably
resonated with the incident electron energy and no enhancement of FEL efficiency due to the detuning should
be expected. In a seeded FEL, where an external laser is
injected and then amplified via interaction with electrons,
the wavelength of the radiation may be affected by bothelectron energy and the seed laser. Eventually, it may enhance the efficiency of the amplification to detune electronenergy in terms of the wavelength of the seed laser.
In the paper, the experimental demonstrations of efficiency enhancement by the electron energy detuning is reported. The experimental results are compared with thenumerical simulation and interpreted by FEL theory.

DETUNING EXPERIMENTThe experiments were conducted at the Source Development Laboratory (SDL) of National Synchrotron Light
Source (NSLS), Brookhaven National Laboratory (BNL).
The picosecond (ps) electron pulse generated by a photoinjector is compressed to 1.5 ps by a chicane-type bunch
compressor. The compressed e-beam passes through a 10m long planar undulator, of which period is 3.89 cm and theundulator parameter is K=1.1. The seed laser generated bya Ti:Sapphire laser system is compressed to 6 ps, with thefrequency chirp being slightly negative. Passing througha bandpass filter, the seed laser has the central wavelengthof 795 nm and the bandwidth of 1.5 nm at Full Width atHalf Maximum (FWHM). The major experimental parameter are summarized in Table. 1.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

presented by the theory. Next, in a high gain regime, a cubic equation for time-dependent gain of FEL radiation in
the form exp(iλτ ) is written as,

Table 1: Major experimental parameters
Undulator parameter K
1.1
Undulator period
3.89 cm
Undulator length
10 m
Electron energy
98 - 102 MeVPeak current
380 A
Electron bunch duration (FWHM)
1.5 psEnergy spread (rms)
0.1 %Normalized emittance
2-4 mm.mrad
Seed laser wavelength
795 nmSeed laser bandwidth (FWHM)
1.5 nmSeed laser pulse duration (FWHM)
6 ps
Seed laser energy
4 kW

λ3 − δλ + 1 = 0,

Efficiency measurement
For a planar undulator, the wavelength of the FEL radiation, λr , is written as,λr =λu (1 + K 2 /2)
,
2γ 2

(1)

where λu is the undulator period and γ is the electronenergy normalized with its rest mass. In general seeded
FEL experiments, the electron energy is adjusted to satisfy
Eq.(1) for a given wavelength. In what follows, such anenergy is called the energy on resonance. In our experiment, the energy on resonance was determined by measuring SASE spectrum without the seed laser.
In Fig. 1, the energy gains in the undulator on resonanceand with two detuning cases are plotted; one is 0.7 % higher(+0.7 % detuning) and another is 0.5 % lower (-0.5 % detuning) relative to the energy on resonance. All the three
data are shown with root-mean-squared (rms) error bars,
but at most of points, the error bars are overlapped withthe dots. In -0.5 % detuning case, the seed laser energy isdominant until 7.8 m, because both transversely and longitudinally the seed laser size is larger than the electron
beam. The simulation results on resonance and with detuning were also presented in Fig. 1. The gain curve on
resonance is shown by the solid curve, and those with +0.5
and -0.5 % detuning are respectively shown by dotted anddashed curves.
It is obvious in both experiment and simulation that thegains with detuning are asymmetric between positive andnegative detuning; the negative detuning degrades the gain
by more than one order of magnitude, while the positive
detuning enhances it by factor of two. To interpret it, we recall one-dimensional steady-state theory [7, 8, 9, 10]. First,
at the early stage of amplification, small-signal gain theory
indicates that the direction of energy deposition between
electrons and radiation is opposite depending on the direction of detuning. In Fig. 1, the radiation energy with negative detuning is deposited to electrons once, while that withpositive detuning immediately gains energy from electrons.
On resonance, there is no energy deposition, which is also

Seeded FELs

MOPPH065(2)

where λ is an eigenvalue, of which negative imaginary partgives the growth rate, and δ is the normalized energy detun22)/2γR
ρ. In Eq.(2), the efficiency parameing δ = (γ 2 − γR
ter is assumed to be small, ρ ∼ 0. The preferable instability
exists only when the detuning is smaller than the threshold,i.e., δ < δth ∼ 1.89, where two of the three eigenvalues
in Eq.(2)√have imaginary part. The maximum growth rate,
Imλ = 3/2, occurs at no detuning, δ = 0. It has also
been shown with the aid of numerical simulation that as theelectron energy goes higher, the saturation energy becomes
higher until it reaches the threshold, δ ∼ δ th . Since theefficiency parameter ρ of the experiment is in the range of
0.003 through 0.004, the threshold corresponds to the electron energy detuning of +0.55 to +0.75 % (shown grey in
Fig.1). One can see in Fig. 1 that both experiment and numerical simulation represent the characteristics predictedby the theory and numerical simulation; the positive detuning in the range of threshold enhances the output energy,
whereas the same amount of detuning but in negative direction just degrades the gain due to the combination of energy deposition to the electrons in small-signal gain regime
and degraded gain in high gain regime.

Figure 1: Gain curves on resonance and with detuning.
To see the detuning effect more clearly, the output energyof FEL radiation was plotted as a function of the electronenergy in Fig. 2. The dots with peak-to-peak error bars
are experimental data and the solid line is evaluated by thetime-dependent simulation under the same condition as theexperiment. The output radiation energies are normalizedwith those on resonance in both experiment and simulation
results. The energy on resonance is 102 and 82 μJ respectively for the experimental and the numerical results. In

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Fig. 2, the asymmetry between positive and negative detuning is again clearly observed. The negative detuning of
0.5 % deteriorates the FEL gain by one order of magnitude,
while the positive detuning of 0.7 % enhances the gain by
70%. In addition, further detuning by a half percent in apositive direction, i.e., total detuning of +1.2 %, does nomore enhance the gain, but suppresses it. It is because thedetuning goes beyond the threshold δ th (grey in Fig. 2).
The experimental result agrees with the simulation result
except for two things in detail; the enhancement of the energy in the experiment is lower than that of by simulation,and the amount of the detuning that gives the enhancement
is +0.7 % in experiment and +0.5% in simulation. It is because there was an electron energy jitter in the experiment,so the energy enhancement at the detuning was smoothed
out by taking the average. In fact, the maximum energy
given at the +0.7 % detuning was 206 μJ, which is morethan 2 times higher than the average energy on resonance.

Figure 3: Spectra of laser seeded FEL on resonance (solidline) and with positive detuning at the threshold δ ∼ δ th(dashed). (a) experiment and (b) GENESIS calculation.

CONCLUSION

Figure 2: FEL output energy vs electron energy detuning.
Solid line is simulation and dots are experimental result.

Spectral measurement
The spectra of the seeded FEL pulse were also measured.
Figure 3 represents the example spectra of seeded FEL on
resonance (solid line) and with the positive detuning at thethreshold δ ∼ δth (dashed). The positive detuning in theexperiment (Fig. 3 (a)) is +0.7 %, and that in the numericalsimulation by GENESIS1.3 (Fig. 3 (b)) is +0.5 %.
It is both experimentally and numerically verified in Fig.
3 that the peak wavelength of output seeded FEL pulse is
not notably shifted by detuning electron energy. In bothcases, the difference of the peak wavelength between on
resonance and with the positive detuning is much less than
1 nm. It follows that the seeded FEL spectrum with detuning is dominated by the seed laser, so the detuning scheme
does not induce the undesirable frequency shift in the output pulse. Note that the detuning of +0.7 % in electron energy corresponds to the down-shift of SASE spectrum by
as much as 11 nm.

192

We experimentally observed the efficiency enhancementby the electron energy detuning. By applying the energy
detuning of +0.7 %, the efficiency was doubled. Both thefurther detuning and the opposite detuning significantly degrades the efficiency. The results were well consistent with
one-dimensional steady-state theory as well as the three dimensional numerical simulation.
The spectra of seeded FEL pulses on resonance and withdetuning were also measured. It was verified that the peakwavelength of seeded FEL with detuning was almost sameas that on resonance both by the experimental result and thenumerical simulation. It indicates that the detuning scheme
works without modifying the seeded FEL spectrum substantially.
The study gives fundamental knowledge for implementing seeded FEL experiments as well as designing the highpower FEL such as a directed energy application.

ACKNOWLEDGMENTS
We are grateful for support from the NSLS and BNL
director’s office and this work is supported by the Office of Naval Research and U.S. Department of Energy
under contract No. DE-AC02-98CH1-886. The authors
are pleased to acknowledge valuable technical contribution
from Boyzie Singh.

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MOPPH065

REFERENCES[1] S. Reiche, Nucl. Instrum. Methods Phys. Res. A 429, 243(1999).
[2] C.W. Roberson and P. Sprangle, A review of free-electron
lasers, Phys. Fluides, 429, 3, Jan. 1989.
[3] P. Sprangle et al., IEEE J. Quantum Electronics, 40, 1793
(2004).
[4] T. Watanabe et al., Proc. of FEL2005, p.320 (2005).
[5] T.J. Orzechowski et al., Phys. Rev. Lett. 57 2172 (1986).
[6] D.A. Jaroszynski et al., Phys. Rev. Lett. 74, 2224 (1995).
[7] P. Sprangle et al., Phys. Rev. A. 21, 302 (1980).
[8] R. Bonifacio et al., Opt. Commun. 50, 373 (1984).
[9] J.B. Murphy and C. Pellegrini, J. Opt. Soc. Am. B 2, 259(1985). J.B. Murphy and C. Pellegrini, NIM A 237, 159(1985).
[10] J.B. Murphy and C. Pellegrini, Laser Handbook Volume 6,(Elsevier Science Pub., North-Holland, 1990), Chap. 2.

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CHIRPED PULSE AMPLIFICATION EXPERIMENT AT 800 nm
L.H. Yu, T. Shaftan, D. Liu, T. Tsang, J. Rose, X.J. Wang, T. Watanabe
NSLS, BNL, Upton, NY 11973, USA.
Abstract
We report the chirped pulse amplification (CPA)
experiment carried out using 800 nm direct seeding and
NISUS undulator as free electron laser amplifier at SDLof BNL. The experiment indicated that due to saturationin the center part of the chirped electron bunch the output
pulse shape has a dip in the middle, as result the edge ofthe bunch has higher power than the center. Hence theoutput spectrum also showed a dip in the center, resulting
in a larger FWHM bandwidth than the seed. Aninteresting result is that the 800 nm chirped FEL output
was compressed down to a pulse length shorter than what
the seed pulse itself can be compressed to.

INTRODUCTION
Chirped pulse amplification (CPA) [1-4, 8] can be used
to generate short high intensity pulse in FEL, and it has
been shown theoretically possible to generate pulse
shorter than what the seed can be used to generate [2].
Initial CPA experiment has been carried out in HGHG
process at 266 nm but without the final compression of
the pulse [5]. The experiment showed that by matching
the electron bunch energy chirp with that of the seed pulse
properly we were able to maximize the bandwidth of theoutput pulse while maintaining coherence. First SPIDER
traces were measured and quadratic optical phasedependence along the pulse was obtained [7]. However,
due to limited beam time, we were unable to finish thecompression of the output pulse at 266 nm so far. In thispaper, we report our preliminary result on the CPA at 800
nm with direct seeding.

EXPERIMENT SETUP AND CPA
EXPERIMENT
A schematic diagram of the 788 nm experiment isshown in figure 1. The 788 nm seed pulse with pulse
length of 2.5 ps and bandwidth of about 6 nm is chirped
with the head of the pulse at longer wavelength. The 103
MeV electron bunch with charge of 500 pC is compressed
down to about 2.5 ps and chirped using the last section of
the linac to about 0.5% of projected energy spread withhead at lower energy. During the experiment the chirp isadjusted to maximize the output bandwidth. The seed andthe electron beam are sent into the FEL undulator NISUS
and aligned to overlap in the first section of the undulator.
The seed has a Rayleigh range of 1.95 m. We used firsttwo pop-in monitors inside the NISUS undulator to carryout the alignment. Since the seed table where the seed is
injected into the undulator beam line by a 45° mirror is 7
meters away from the entrance of the NISUS undulator,
the physical limitation of the system made it impossible tomatch the seed beam size to the electron beam size at thebeam waist of the seed, which is about 0.6 m inside of theentrance. As a result the laser beam size is much larger
than the electron beam. This is illustrated in figure 2

E-beam at pop23

Seed laser at pop23

Figure 2: Images of the beam (left) and seed laser (right)
where we show the images of the seed and electron beamat the first pop in monitor in the NISUS. Thus this FEL
amplifier setup is not very efficient. But it is sufficient to
be used for a demonstration of the CPA process. The
NISUS undulator has a period of 3.9cm with K=1.126.
The electron bunch length is measured by the zero-

FROG
λSpectrometer
λ
λ

t
FEL
t
undulator

Linac

N
E

N
E

t

t
Figure 1: Layout of the experimental set-up.

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+90º

-90º

Figure 3: Measurement of bunch length
The synchronization between the electron
Intensity (counts)
bunch and the seed laser pulse is realized
600
by observing the significant increase ofenergy spread when they temporally
overlap. The energy spread is measured
500
using the monitor after the beam passes
through the undulator and the last dipole.
This is shown in figure 4. The upper picture
400
shows that the energy spread is adjusted toabout 0.5% when the seed laser is turnedoff (the full screen corresponds to 1.5% ofenergy spread). When we turn on the seed300
laser and change the seed pulse time delayby an optical trombone so it overlaps withthe electron bunch, the energy spread is200
increased significantly and hence the imageof the electron beam occupies the fullscreen.
The seed laser pulse energy is 13.4 μJ
before sent into the NISUS undulator
during the CPA experiment. To ease the synchronization
procedure before we achieve the overlap between the seed
and the electron bunch, we remove the attenuation (which
is 10 when the pulse energy is 13.4 μJ) so the energy
spread increase will be more visible even when the tail of

Chirped bunch (no seed)

Chirped bunch (lasing)Due to energy and phase jitter and drift of the electron
bunch (energy jitter is about 0.2% rms, time jitter about
140 fs rms), during the scan for synchronization for each
trombone position we also scan energy within about 0.5%
range then move to next position about 100 μm apart.
Once the synchronization is found, we send the amplified
FEL output to the spectrometer to fine tune thesynchronization. Since the seed laser is chirped, and theoutput wavelength is determined by the seed, if the tail ofthe electron bunch overlaps with the head of the laser
pulse the output pulse wavelength is centered at longer
wavelength of around 795 nm. When the head of theelectron bunch overlaps with the tail of the seed, thewavelength moves to shorter wavelength of around 785
Masterseed-OD1-m250mu1.Master.Sample
seed-OD1-m500mu.Master.Sample
seed-OD1-m750mu.Master.Sample
seed-OD1-m1000mu.Master.Sample

780

790

800

Wavelength (nm)Figure 5: Measured FEL spectra
nm. This helps us to determine which direction and how
much we should move the trombone to maximize theoverlap. In figure 5 we show the measured FEL output
spectrum at different positions of the optical trombone
micrometer. The center of the spectrum is at 790 nm.
During the scan the FEL pulse central wavelength isCentral wavelength (nm)phasing method using the dipole right after the last linac
section as the energy spectrometer. The images of themeasurement at 90 and -90 degree of the RF phase areshown in figure 3.

MOPPH066

792

790

788

200

400

600

800

1000

delay (m)Figure 4: Electron beam energy spectra before (upperplot) and after (lower plot) interaction with electron beam
the electron bunch overlaps with the seed. This helps toincrease the step size that we used to move the opticaltrombone and complete the synchronization procedure
faster.

Seeded FELs

Figure 6 Central FEL wavelength for different delays
between seed and electron bunch
also measured and plotted against the micrometer
position, as shown in figure 6.
The figure 6 shows the wavelength has a linear
dependence on the delay of electron bunch relative to theseed laser, as determined by the micrometer position. The
slop of the curve (2.6 nm/ps) is the measured chirp of the

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Proceedings of FEL 2006, BESSY, Berlin, Germany

seed by FEL process. This is to be compared with thechirp setup by the seed laser compressor-stretcher system,
which is 6 nm/2.5 ps=2.4 nm/ps, providing with areasonable agreement.
The gain length of the FEL process is measured

SASE pulse energy (a.u.)

10

10

10

10

4

3

using SASE output pulse energy as function of distance in
the NISUS by kicking the electron beam away from axis
sequentially at different longitudinal locations inside the
NISUS undulator with the horizontal trajectory correctors.
The result is shown in figure 7. Considering the spacing
between the monitor is 0.62 m, the power gain length isobtained from this plot as 1m.
The normalized emittance was measured to be 6 mmmrad by fitting with the beam profile measurement in the
NISUS undulator. Once the synchronization is achieved,
we tune electron beam chirp by adjusting the last linac
section to vary the energy spread and observing the
bandwidth of the FEL output until we reach the maximum
bandwidth. When the chirp is optimized and when the2

January 19,2006. Compari son of Seed FEL(2 peak and si ngl e peak) seed at t enuat e by OD 1 and OD 1.5 (01)11900
seed attenuated by OD1
10

1700

0

2

4

6

8

10

12

14

16

18

Monitor number

seed attenuated by OD1.5

1500
1300

Figure 7: SASE gain length measurement
A.U

1100

D ec 22,2005 790 CP A, s eed FEL s pectrum ,Seed s pectrum ,Seednoatt01.m as ter.sam ple

700

290

10 nm

270

900

500

250
A.U

300
230

100

210

770
190

775

780

785

790

795

800

805

Wavel ength( nm)

170
770

775

780

785

790

795

800

805

W avelengt h(nm)Figure 9: Spectra of the seeded FEL output for two valuesof attenuation 10 (OD1) and 30 (OD1.5)

Jan 13,2006.Seed FEL spectrum .e-Beam no-chirp1000

OD1-seed-e-beam-no-chirp

900
800
700

A.U

600
500
400
300
200
100
775

780

785

790

795

800

805

Wavelength(nm)Dec 22,2005, 790 nm CPA Seed FEL
2500
520PC seed FEL
Seed spectrum
2000

A.U

1500

1000

500

0
770 772 774 776 778 780 782 784 786 788 790 792 794 796 798 800 802 804
Wavelength(nm)Figure 8: Measurements of seed (upper), unchirped FEL(middle) and FEL output with matched chirp (lower
plot)

196

seed laser is turned off, the image of the energy spread isshown in the top of the figure 4.
In the top plot of figure 8 we show the measurement of
the seed spectrum. The middle plot of the same figure is
the spectrum of the FEL output when the electron bunch
is not chirped (when energy spread is minimized with theseed laser turned off). Lower plot shows the FEL radiation
spectrum for the case when the chirp of the electron
bunch is optimized. To be able to compare the bandwidth,
we align the three plots vertically so that they use thesame horizontal scale. It is seen that when the electron
bunch is not chirped, the output bandwidth is narrower
than the seed, showing that only the part of the seed pulse
with the wavelength in resonance with the electron beamenergy is amplified, and the width of the line is clearly
determined by the bandwidth of the amplifier.
It is interesting to remark here that figure 8 shows whenthe energy chirped to match the seed chirp, the bandwidth
increases to about 10 nm, significantly larger than theseed bandwidth of about 6 nm. And in particular there is apronounced dip near the center of the FEL output
spectrum. This can be explained by deep saturation in the

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Proceedings of FEL 2006, BESSY, Berlin, Germany
central part of the electron bunch. If the current at thecentral part of the electron bunch is and since the central
part of the seed is also at peak, the FEL amplifier can beoversaturated so that power is lower than at the edge ofthe bunch where the FEL is just reaching saturation, thus
creating a dip in the spectrum because due to linear chirp,
the spectrum corresponds to time.
To further test this interpretation, we expect that when
the seed power is lowered properly so that the central partof the bunch just reach saturation, the dip in the central
part of the pulse will disappear, and hence the double
peaks in the spectrum should be replaced by a single peak.
And indeed, when we increase the attenuation from 10 to30, we did observe that the double peaks are replaced by asingle peak. This is shown in figure 9.
Because of the output bandwidth is larger than the seedbandwidth we expect that when compressed, the final
pulse width can have a smaller pulse length than thefourier-transform-limited seed pulse length. This has been
confirmed by our next step of the experiment, thecompression and measurement of the compressed pulse.

MEASUREMENT OF THE COMPRESSEDPULSE BY FROG
As shown in figure 1, the output FEL pulse is sent
through a compressor, compressed and sent to a FROG
(Frequency-Resolved Optical Gating) device [6]. This
device is designed to measure spectral and temporal
distribution of short laser pulse simultaneously, andgenerate the amplitude and phase as function of time forthe pulse. It is compact and, in particular, easy to align.
The schematic diagram of the arrangement of compressor,
spectrometer and FROG is shown in figure 10. In figure
11, we show the FROG result of compressed chirped FEL
output pulse. In the picture, the upper right one is themeasured FROG image while the upper left one is theretrieved image from the reconstructed pulse shape, theagreement between these two pictures testifies thecorrectness of the FROG result. The lower left is thereconstructed temporal pulse while the lower right one is
the reconstructed spectrum.

chirped FEL
pulsesTelescope

Spectrometer

Grating compressor
FROG

MOPPH066

Figure 11: FROG traces of the compressed FEL pulse.

The result shows that pulse length is 122 fs FWHM. We
remark that resolution of the spectrum obtained from the
FROG is not as good as that of the spectrometer we used,
so that in the reconstructed spectrum we could not see thedouble peaks feature as shown in figure 8 and 9.
This is to be compared with a fourier-transform-limited
compressed seed. With the seed bandwidth of 6 nm at 800
nm, assuming minimum wave packet of Gaussian shape,
the FWHM pulse length and FWHM bandwidth productis Log(2)/π*0.8 μm/(0.3 μm/fs) = 1.17. So the pulse
FWHM length should be 1.17*800 nm/6 nm =156 fs.
Hence even if the seed is fourier-transform-limited, it isstill significantly longer than the CPA result.
In conclusion, we carried compressed CPA from FEL
output at 800nm and obtained shorter pulse than what canbe obtained from compressed seed. The result can be
explained by the deep saturation of the FEL output. Thisillustrated the potential in the future to generate shortpulse using CPA process in an FEL device.

REFERENCES[1] G..T. Moore, Nucl. Instrum. Methods in Phys. Res. A
272, p. 302 (1988).
[2] L.H. Yu et al., Phys. Rev. E 49, 5, p. 4480 (1994).
[3] C. Pellegrini, Nucl. Instrum. Methods in Phys. Res. A
445, p. 124 (2000).
[4] G. Andonian et al., Phys. Rev. Lett. 95, 054801(2005).
[5] A. Doyuran et al., Nucl. Instrum. Methods in Phys.
Res. A 528, p. 467 (2004).
[6] R. Trebino et al., Lithuanian Journal of Physics, v. 33,
p. 247-252.
[7] Z. Wu et al., in Proc. of FEL-2004.
[8] E. Saldin et al., Phys. Rev. ST-SB, 9, 050702 (2006).

Figure 10: Time- and spectrum measurements set-up.

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ISSUES IN HIGH HARMONIC SEEDING OF THE 4GLS XUV-FEL
B. Sheehy, Sheehy Scientific Consulting, New York, USA; J.A. Clarke, D. J. Dunning, N.
R. Thompson, CCLRC, ASTeC, Daresbury Laboratory, Warrington, UK; B. W. J.
McNeil, SUPA, Department of Physics, University of Strathclyde, Glasgow, UK
Abstract
Using High Harmonics (HH) as a seed for free electron
lasers is currently under consideration in a number of
proposed facilities. An HH seed source is independent ofmachine dynamics, and allows for extensive manipulationof the seed pulse using well-established techniques ofultrafast laser physics. These allow for rapid tuning, andmay enable the extension of chirped pulse amplificationand even pulse shaping for coherent control to shortwavelengths. In addition, there are advantages in terms ofnoise and synchronization. There are a number of issues
involved in the implementation of HH seeding: energy,
tunability, coherence, temporal structure, etc. We discussthese issues and their application in the 4GLS XUV-FEL.
INTRODUCTION
The limitations of spontaneous sources have motivateda great deal of development in short-wavelength FEL
design.
For reasons of stability, coherence andbandwidth, SASE sources are disadvantageous relative tocoherent alternatives. A number of seeding methods havebeen proposed, including high-gain harmonic generation,
several self-seeding techniques, and using high harmonic
generation to produce sufficient radiation at thefundamental resonant wavelength of the radiator to
directly seed the FEL.
The attraction of seeding with high harmonics is that agreat deal of control over the seed radiation can be had byusing well-known ultrafast laser techniques to control thefundamental that drives the HH generation. Harmonic
pulses can be made extremely short, down to a few
femtoseconds, and tuning is relatively simple. Demands
on timing and synchronization with the electron bunch areless stringent than in other techniques. Also, the coherent
transfer of phase information from the HH pump to theharmonics opens the possibility of creating a chirped HH
seed and performing chirped pulse amplification [1] in the
FEL to achieve higher output energies, or even of
pursuing more elaborate pulse shaping.
The efficiency of HH generation is currently too low
for FEL seeding at soft X-ray energies. However, in the
wavelength range planned for the 4GLS XUV-FEL (8100 eV), available sources could provide sufficient energy
for seeding at kHz repetition rates, and the available
energy will increase with coming improvements inultrafast laser technology.
A number of other issues must also be addressed.
Tunability is required, and must be provided in a way thatminimizes downtime and perturbations to timing and198

synchronization. Other spectral and temporal properties
have also been raised as issues. We address these issues
and discuss the implementation of seeding in the 4GLSXUV-FEL.
ENERGY AND TUNABILITY
The 4GLS XUV-FEL will operate between 8-100 eV.
We have simulated the XUV-FEL [2], using GENESIS 1.3[3], using 100 kW peak seed power for output photon
energies below 30 eV, and 30 kW for energies between 30
eV and 100 eV. For 30 fsec pulses, this is equivalent to 3
nJ and 1 nJ pulse energies respectively. This is threeorders of magnitude above the spontaneous power
generated in the first gain length due to intrinsic density
fluctuations in the electron bunch, and, in simulations
produces an output pulse with good contrast [2].
A number of groups have measured harmonic yields
from Ti:Sapphire based systems, and we show a scaled
synopsis of recent results [4-6] in Fig. 1. The
experimental results represented here (unconnected points
on the plot) were obtained using fundamental pulse
energies from 3-50 mJ, and we have scaled the results toan energy of 14 mJ – the energy of the Ti:Sapphire systemdescribed below.
These scaled yields exceed ourrequirements by over three orders of magnitude at the low
energy end of the XUVFEL operating range, and by afactor of six at the high energy end.
The scaling energy of 14 millijoules was chosenbecause such a laser system has been demonstrated at kHz
repetition rates [7]. This is conservative, as ultrafast laser
technology is developing very rapidly, and extension tohigher powers is not constrained by a fundamental limit.
A number of recent developments, eg the use of opticalparametric chirped pulse amplification [8], high power
Yb:YAG lasers [9], and enhancement cavities [10-12],offer new opportunities for larger systems. Several 100Watt kilohertz system designs have been proposed [13],and are likely to be demonstrated soon.
There is also considerable effort in the community
focused on extending the wavelength range and yield ofharmonics. Recent experiments [6] using two-color fields
demonstrated an enhancement of over 2 orders ofmagnitude in the harmonic yield in Helium, producing
150 nanojoules in the 38th harmonic (59 eV), using only
2.8 mJ in the pump laser. Fig. 1 also shows the results ofthat experiment (scaled from the experimental energy of
2.8 mJ to 14 mJ). Since Helium is the least efficient of therare gas targets used, it is reasonable to expect that whenthese techniques are extended to other gases and longer

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Proceedings of FEL 2006, BESSY, Berlin, Germany

pump wavelengths, available seed energies over the XUVFEL operating range will increase substantially.
The simplest and most versatile way to tune between
the harmonic orders is through control of the amplitude
and phase of the fundamental. This can be as simple as a
chirp [14-16], but more general adaptive pulse shaping[17-20] allows greater tuning range and greater control
over the harmonic pulse width. This method presents
minimal impact on synchronization during tuning, and is
rapid once the system has been calibrated. The tuning
range is of the order of qΔν , where q is the harmonicorder and Δν is the bandwidth of the fundamental, so themethod does not work well at low harmonic orders.
Reitze et al [18] demonstrated complete tunability (i.e. atuning range exceeding the separation of adjacentharmonics) down to 40 eV in Argon using 28 fsec, 800
nm pulses, a tuning range of 2.2qΔν . At some energy
below 40 eV, complete tunability will be lost. For thisreason in the current design, a tunable fundamental isused for the low-energy end of the XUV-FEL energy
range.
Using a tunable fundamental entails a double loss, fromthe frequency conversion losses as well as the drop in
harmonic efficiency at longer wavelengths [21].
Conversion to wavelengths shorter then 800 nm, where
the harmonic efficiency is higher, is possible, but then theharmonic orders used to reach the very low end of thetuning range are smaller, and complete tunability cannot
be obtained there. For an infrared source tunable from1200 nm to 1475 nm, complete tunability would beobtained. Conversion efficiencies for commercial
noncollinear phase-matched optical parametric amplifier(NOPA) systems in this range, pumped by a Ti:Sapphiresystem, are typically ~10%, while laboratory systems
have reported efficiencies of 20% [22]. The harmonic
efficiency drops as λ−3 [21,23,24], so it is 15-30% of theharmonic efficiency at 800 nm. Harmonic efficiencies arehigh enough at these lower energies that sufficient seed
power can still be produced. Fig. 1 shows the projected
range of the tunable source’s harmonic yields in Xenon
using the expected wavelength scaling of the harmonic
efficiency, and assuming 15% conversion efficiency in the
NOPA. Above 40 eV, tuning is done using adaptive
control of the Ti:Sapphire fundamental
Developments in laser technology will probably makethis two-track system unnecessary in the near future, as
new high-power kilohertz ultrafast sources in the 1-2
micron wavelength range are developed [13]. Because
the high energy cutoff of harmonic production increases
with λ2 [25], at longer wavelength, gases with higher
harmonic efficiency can be used to generate higher photon
energies, offsetting some of the wavelength-dependent
drop in efficiency. A longer fundamental wavelength also
increases the wavelength range over which adaptive
tuning may be used, since the harmonic order q for agiven wavelength increases and the harmonic spacing
decreases. For example, assuming an adaptive tuning
range of 2qΔν , a source with a fixed wavelength of 1.8

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MOPPH067

Figure 1. Recent high harmonic generation
experimental results scaled by energy and wavelength.
The unconnected points were taken with an 800 nm
fundamental, and are scaled here to a pulse energy of
14 mJ. The solid Xe curves show the projected rangeof harmonic yields for the NOPA (2 mJ pulse energy),
tuning between 1200 and 1475 nm. The solid He
curve shows the results of a two-color experimentusing 800 and 400 nm fundamentals, scaled to a 14 mJpump energy. The minimum energy for seeding the
XUV-FEL with a 30 fs pulse is 1 nJ.
microns and 20 fsec pulse width could cover the entire
XUV-FEL energy range using only adaptive tuning.

COHERENCE, STRUCTURE AND CONTRAST
Other spectral and temporal qualities of the harmonics
must also be considered. Over the design range of the
XUV-FEL, the gain bandwidth of the FEL radiator is bothlarger than the bandwidth of individual harmonics, andmuch smaller than the separation between harmonics.
This allows for efficient seeding without requiring theseparation of harmonic orders in the seeding optics. The
transverse spatial coherence of harmonics depends
sensitively on the generation geometry, but very highcoherent flux has been measured [26]. This concerns
primarily the seeding efficiency, as the spatial coherence
increases dramatically as the pulse is amplified tosaturation.
Because harmonics are used to generate attosecond
pulses, there is some question whether subfemtosecond
temporal structure could affect seeding. There are,however, fundamental reasons for expecting little effectfrom this structure. Sub-femtosecond structure arises
from the coherent superposition of multiple harmonics; it

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is essentially an interference effect. Since the FEL
radiator’s bandwidth is restricted to a single harmonicorder (the harmonic separation is ~3 eV, while the FWHM
gain bandwidth of the radiator lies in the range of .04-.4eV) it effectively acts as a filter, and the time profile of anindividual harmonic, which is smooth [27], is the relevant
temporal shape. Furthermore, the period of any subfemtosecond structure is quite short – half of thefundamental optical cycle – so that, even if multiple
harmonics could be amplified, slippage would tend tosmooth out any short scale structure. We have considered
the attosecond structure issue in our simulations however,and it is discussed in greater detail in Ref. [28].
An issue in all seeding techniques is the achievable
contrast between the coherent output pulse and any
incoherent background. This is of particular concern inexperiments involving nonlinear interactions, as lowerorder interactions with the background pedestal
surrounding the main pulse can alter the target’s initialstate before the main pulse arrives or the product state
after the main pulse is over, so that both the height of the
background and the length of the window over which it
persists are important. Our simulations [2,28] show that,for the minimal seed power, we obtain, over the XUVFEL energy range, contrasts of 10-2 to 10-3 immediately
beneath the main pulse, dropping to 10-5 to 10-7 within apicosecond on either side of the pulse.
The background consists of SASE evolving in theunseeded part of the bunch, and so the context of thesenumbers should also be considered carefully. First, thecontrast improves with increasing seed power, as thelength to saturation decreases and the ratio of the coherent
seed power to spontaneous power in the wings of thepulse increases. The feasibility simulations were donewith minimal seed power but, depending on the energy
and tunability required, orders of magnitude more may beavailable. The simulations were also done with a Gaussianlongitudinal electron bunch distribution with a FWHM
pulse width of 625 fs; more sharply peaked distributions
would also improve contrast, as the gain in the wings
would drop accordingly. The full parameter space has not
yet been explored with respect to contrast, and these
aspects will be investigated further in future design work.
A more detailed discussion and simulation results may befound in Ref [2].

IMPLEMENTATIONThe current design for implementing HH seeding in the
4GLS XUV-FEL is shown schematically in Fig. 2. An
ultrafast Titanium Sapphire oscillator producing 30 fsec,
800 nm pulses is synchronized at a subharmonic of theaccelerator RF frequency. Pulses are selected at 1 kHz
and amplified to 14 mJ. Amplifier chains capable of thispower presently exist [7], and systems with higher output
are expected to appear soon.
After amplification, the pulse is switched into one oftwo paths, depending on the FEL photon energy. For low

200

Figure 2. Block diagram of high harmonic seeding forthe 4GLS XUV-FEL.
energies (8 to approximately 40 eV), a tunable pumppulse is generated using a noncollinear optical parametricamplifier (NOPA) operating between 1200-1475 nm. At
higher energies (40 - 100 eV), the 800 nm light is used for
HH generation, and adaptive tuning is used. Pulse
shaping for the adaptive tuning can be done either before
the amplifier, as shown here, or afterwards.
The geometry for the HH generation is still under study.
A loose focusing geometry in a variable length cell is thesimplest to implement over the entire range of the XUVFEL and is equivalent to waveguide geometries at
sufficiently high power [29]. Waveguide geometries [30]may be beneficial for the low photon energies, where thepump pulse energy is lower, Modulated waveguide
geometries [31] may provide greater efficiency, but it may
be difficult to implement multiple configurations to cover
the entire wavelength range. Efficient materials (eg SiC)
for grazing incidence optics are available for the optics
coupling the HH seed into the radiator.
SUMMARY
We have developed a design to establish the feasibilityof seeding the 4GLS XUV-FEL with high harmonics.
Currently available technology is capable of supplying
sufficient seed energy, and tuning may be accomplishedwith a tunable fundamental at the low-energy end of the
XUV-FEL operating range, and with pulse shaping of a
fixed-frequency fundamental at higher energies.
Technological improvements are expected to increase theavailable power and simplify the implementation.
Spectral and temporal properties of the harmonics appear
to be commensurate with the requirements for seeding.

REFERENCES[1] L. H. Yu et al., Physical Review E 49 (1994) 4480.
[2] 4GLS Conceptual Design Report. (Council for theCentral Laboratory of the Research Councils, UK,
http://www.4gls.ac.uk/, 2006)

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Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH067[3] S. Reiche, Nuclear Instruments and Methods A 429(1999) 243.
[4] E. J. Takahashi et al., IEEE Journal of Selected
Topics in Quantum Electronics 10 (2004) 1315.
[5] J. F. Hergott et al., Physical Review A 66 (2002)
021801.
[6] I. Jong Kim et al., Physical Review Letters 94 (2005)
243901.
[7] Y. Nabekawa et al., Optics Letters 23 (1998) 1384.
[8] A. Dubietis et al., Optics Communications 88 (1992)
437.
[9] D. J. Ripin et al., IEEE Journal of Quantum
Electronics 41 (2005) 1274.
[10] R. Jones and J. Ye, Optics Letters 27 (2002) 1848.
[11] R. Jones and J. Ye, Optics Letters 29 (2004) 2812.
[12] F. Ö. Ilday and F. X. Kärtner, "Cavity-Enhanced
Optical Parametric Chirped-Pulse Amplification,"
Joint Conference on Ultrafast Optics V andApplications of High Field and Short Wavelength
Sources XI, Nara, Japan, 2005,[13] F. X. Kärtner et al., "Experiments in Laser Seed
Generation," MIT Workshop on the Physics ofSeeded FELs, Boston, MA, June 2004,[14] J. Zhou et al., Physical Review Letters 76 (1996) 752.
[15] D. G. Lee et al., Physical Review Letters 87 (2001)
243902.
[16] H. T. Kim et al., Physical Review A 67 (2003)
051801.
[17] R. Bartels et al., Nature 406 (2000) 164.
[18] D. H. Reitze et al., Optics Letters 29 (2004) 86.
[19] T. Pfeifer et al., Optics Letters 30 (2005) 1497.
[20] T. Pfeifer et al., Appl Physical B 80 (2005) 277.
[21] M. Lewenstein et al., Physical Review A 49 (1994)
2117.
[22] V. Yakovlev, B. Kohler, and K. Wilson, Optics
Letters 19 (1994) 2000.
[23] B. Shan and Z. Chang, Physical Review A 65 (2002)
011804.
[24] A. Gordon and F. X. Kärtner, Optics Exp 13 (2005)
2941.
[25] J. L. Krause, K. J. Schafer, and K. C. Kulander,
Physical Review Letters, 68 (1992) 3535.
[26] L. Le Deroff et al., Physical Review A 61 (2000)
043802.
[27] I. P. Christov, M. M. Murnane, and H. C. Kapteyn,
Physical Review Letters 78 (1997), 1251.
[28] B. W. J. McNeil et al. “The Use of HHG at 4GLS”,
These proceedings MOCAU03[29] S. Kazamias et al., Physical Review Letters 90 (2003)
193901.
[30] C. G. Durfee III et al., Physical Review Letters 83(1999) 2187.
[31] A. Paul et al., Nature 421 (2003) 51.

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ATTOSECOND PULSES FROM X-RAY FEL WITH AN
ENERGY-CHIRPED ELECTRON BEAM AND A TAPERED UNDULATOR
E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov
Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany.
Abstract
0

10

-1

10

η

We present a new scheme for generation of attosecond
pulses in X-ray SASE FEL. A short slice in the electron
beam is strongly modulated in energy by a few-cycle laser
pulse in a short undulator, placed in front of the main
undulator. Gain degradation within this slice is compensated by an appropriate undulator taper while the rest of
the bunch suffers from this taper and does not lase. Threedimensional simulations with the code FAST predict thatshort (200 attoseconds) high-power (up to 100 GW) pulses
can be produced in Angstrom wavelength range with a highdegree of contrast. A possibility to reduce pulse duration
to sub-100 attosecond scale is discussed.

-2

10

-3

10

-4

10

-2

-1

0

α

1

2

INTRODUCTION
Generation of attosecond pulses would significantly increase scientific potential of future hard X-ray FELs suchas European XFEL [1] and Linac Coherent Light Source[2]. Up to now several schemes for generation of attosecond pulses from X-ray SASE FELs have been proposed[3, 4, 5, 6, 7, 8]. In this paper we study a new scheme making use of energy chirp in the electron beam and a tapered
undulator. The impact of energy chirp on SASE FEL performance was studied in details in [9]. It was found thatFEL gain degradation can be perfectly compensated by undulator tapering. An application of the compensation effect for generation of attosecond pulses from X-ray FELs
was conceptually proposed in [9]. In this paper we present
the results of numerical simulations demonstrating that thescheme works very well in a realistic situation. We also discuss a possible extension of this scheme that can allow to
generate high-power, high-contrast hard X-ray pulses witha duration in 10-100 attosecond range.

ENERGY CHIRP AND UNDULATORTAPERING
The energy chirp parameter [9]dγ
1(1)dt γ0 ω0 ρ2
is defined such that, for positive sign of α̂, particles in
the head of the bunch have larger energy than those in
the tail. Here ρ = λw Γ/(4π) is the efficiency parameter, Γ3 = πj0 K 2 A2JJ /(IA λw γ03 ), j0 is the beam current
density, IA = mc3 /e√  17 kA, γ0 is relativistic factor, K = eλw Hw /(2 2πmc2 ) is rms undulator parameter, AJJ = J0 (Q) − J1 (Q) is the Bessel function factor,
Q = K 2 /[2(1 + K 2 )], Relativistic factor γ0 and referenceα̂ = −

202

Figure 1: Normalized output power versus parameter α̂.
Solid: ẑ = ẑsat (α̂); dash: ẑ = ẑsat (0) = 13.
frequency ω 0 are connected by the FEL resonance condition: ω0 = 2ckw γ02 /(1 + K 2 ). It is also useful to define
normalized detuning [11]: Ĉ = [kw −ω(1+K 2)/2cγ02 ]/Γ.
A high-gain linear regime of a chirped SASE FEL operation was studied in [10, 9]. The main results of the simulations of the nonlinear regime [9] with 1-D version of
the code FAST [11, 12] are presented in Fig. 1. Saturation
length and power are functions of two parameters, α̂ and
Nc . For our simulations we have chosen N c = 3 × 107- a typical value for VUV SASE FELs. Note, however,that the results, presented in Fig. 1, very weakly depend on
Nc . In Fig. 1 the output power is plotted versus chirp parameter for two cases: when undulator length is equal to asaturation length for a given α̂ and when it is equal to thesaturation length for the unchirped beam case (ẑ = 13).
One can see sharp reduction of power for negative α̂ whilea mild positive chirp (α̂ < 0.5) is beneficial for SASE.
Let us consider now the case when there is no energy
chirp (α̂ = 0) and the detuning parameter changes linearly
along the undulator [11]: Ĉ(ẑ) = b̂1 ẑ. This change canbe due to variation of undulator parameters (K(ẑ) and/or
kw (ẑ)), or due to an energy change γ 0 (ẑ).1 We have foundfrom numerical simulations [9] that in such case the effecton FEL gain is exactly the same as in the case of energy
chirp and no taper if α̂ = 2 b̂1 for any value of α̂ (Figure 2
shows an example).
A symmetry between two considered effects (energy
chirp and undulator tapering) can be understood as follows.
1 An effect of undulator tapering (or energy change along the undulator) on FEL gain was studied in [13] in the limit b̂1  1.

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1

MOPPH068

Electronbeam

10

U ndulator(negative tapering)

200 attosecond
X-ray pulse-1

10Energym odulator

1
-3

10

Electronbeam dum pη

Ti:sapphire laser
5 fs pulse

-5

10

2

-9

10

0

5

10

15

z
Figure 2: Normalized power versus undulator length. Solidline 1: α̂ = 0, b̂1 = 0; triangles: α̂ = 4, b̂1 = −2; solidline 2: α̂ = 4, b̂1 = 0; circles: α̂ = 0, b̂1 = 2.
If we look at the radiation field acting on some test electronfrom an electron behind it, this field was emitted at a retarded time. In the first case a back electron has a detuning
due to an energy offset, in the second case it has the same
detuning because undulator parameters were different at aretarded time. The question arises: can these two effects
compensate each other? We give a positive answer basedon numerical simulations (see Fig. 2 as an example): bysetting b̂1 = −α̂/2 we get rid of gain degradation, andFEL power at any point along the undulator is the sameas in the case of unchirped beam and untapered undulator.
This holds for any value of α̂. For instance, if one linearlychanges magnetic field H w of the undulator, the compensation condition can be written as follows (nominal valuesof parameters are marked with subscript ’0’):
1 (1 + K02 )2 1 dγ
1 dHw=−
Hw0 dz2
K02
γ03 cdt(2)

Of course, in such a case we get frequency chirped SASE
pulse. Since compensation of gain degradation is possible
also for large values of α̂ (there is no theoretical limit on
the value of chirp parameter, except for above mentioned
condition ρα̂  1), one can, in principle, organize a regime
when a frequency chirp within an intensity spike is muchlarger than the natural FEL bandwidth (given by ρω 0 ).

GENERATION OF ATTOSECOND PULSESA new scheme looks similar to those considered in [5, 6]
making use of energy modulation of a short slice in theelectron bunch by a high-power few-cycle optical pulse ina two-period undulator. Due to energy modulation the frequency of SASE radiation in X-ray undulator is correlated
to the longitudinal position within the few-cycle-driven
slice of the electron beam. The largest frequency offset
corresponds to a single-spike pulse in time domain (about

The Angstrom Challenge

Figure 3: Schematic diagram of attosecond X-ray source.
Energy modulator performs slice energy modulation of theelectron bunch (see Fig. 5). Undulator tapering leads tocomplete suppression of the amplification process in themost fraction of the electron bunch, and output X-ray pulse
has 200 attosecond pulse duration.

Electric field strength [arb.units]-710

ϕ = π/2

ϕ=0

0

-5

0

5

10

t [fs]

Figure 4: Possible evolutions of the electric field in the 5fs pulse. carried at a wavelength 800 nm for two different
pulse phases (φ = 0, π/2)

300 attoseconds). The selection of single-spike pulses isachieved by using a crystal monochromator after the X-ray
undulator [5], or with the help of the other undulator tuned
to the offset frequency [6].
In this paper we consider a new scheme (see Fig. 3) thatmakes use of the compensation effect, described in the previous Section. Indeed, there is a strong energy chirp aroundzero-crossing of energy modulation. If one uses appropriate undulator taper then only a short slice around zerocrossing produces powerful FEL pulse. The main part ofthe bunch is unmodulated and suffers from strong negative
undulator tapering (see Fig. 1). One should also note thatfor large negative taper the SASE FEL gain is very sensitive
to longitudinal velocity spread. Therefore, a high-contrast
attosecond pulse is directly produced in the undulator.
Operation of attosecond SASE FEL is illustrated for theparameters close to those of the European XFEL operating at the wavelength 0.15 nm [1]. The parameters of theelectron beam are: energy 15 GeV, charge 1 nC, rms pulse

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Proceedings of FEL 2006, BESSY, Berlin, Germany

100

80

80
60

P [G W ]E-E 0 [M eV], P [G W ]

100

40
20

40

0

20

-20

0

-40
0

2

4

6
t [fs]

8

10

Figure 5: Energy modulation of the electron beam at theexit of the modulator undulator (dotted line) and a profileof the radiation pulse at the undulator length 100 m

length 25 μm, rms normalized emittance 1.4 mm-mrad,
rms energy spread 1 MeV. Undulator period is 3.65 cm,
and the rms K-value is 2.5.
The parameters of the seed laser are: wavelength 800
nm, energy in the laser pulse 3 mJ, and FWHM pulse duration 5 fs (see Fig. 4). The laser beam is focused onto theelectron beam in a short undulator resonant at the optical
wavelength of 800 nm. Optimal conditions of the focusing correspond to the positioning of the laser beam waist
in the center of the modulator undulator. It is assumed thatthe phase of laser field corresponds to ”sine” mode (dashedline with ϕ = π/2, see Fig. 4). Parameters of the modulator undulator are: period length 50 cm, peak field 1.6 T,
number of periods 2. The interaction with the laser light inthe undulator produces a time-dependent electron energy
modulation as it is shown in Fig. 5. This modulation corresponds to the energy chirp parameter α̂  2 at zero crossing (t = 5 fs in Fig. 5).
Optimization of the attosecond SASE FEL has been performed with the three-dimensional, time dependent code
FAST [12] taking into account all physical effects influencing the SASE FEL operation (diffraction effects, energy spread, emittance, slippage effect, etc.). Threedimensional simulations confirmed the predictions of the
one-dimensional model: the energy chirp and the undulator
tapering compensate each other, there is strong suppressionof the amplification in the case of uncompensated negative
taper.
Undulator tapering is performed by changing the gap ofundulator modules [1] such that magnetic field increases
linearly along the undulator length ( b̂1 < 0). We performed
the scan of tapering depth b̂1 in order to maximize thepower in the main peak on one hand, and to minimize contribution of the background, on the other hand. We ended
up with the value of taper which is about 20 % smaller thanthat required for a perfect compensation of chirp at t = 5

204

60

4.8

5.0

5.2

5.4 5.6t [fs]

5.8

6.0

Figure 6: Temporal structure of the radiation pulse (threedifferent shots) at the undulator length 100 m.
fs. Note that the chirp is not linear in the region of interest. In addition, a mild net positive chirp is beneficial for
SASE, as it was discussed above (see Fig. 1).
A typical radiation pulse at the undulator length 100 m isshown in Fig. 5. One can see a high-power spike in the region where the energy chirp is well compensated by the taper and two weak side peaks at t  2 fs and t  8 fs where
the net effect is negative taper. In the rest of the bunch alarge negative taper together with velocity spread and 3-D
effects completely suppresses amplification. In Fig. 6 we
present three different shots illustrating the properties ofthe main peak. Typical pulse duration is about 200 attoseconds (FWHM) and peak power ranges from several tens up
to hundred GW. To estimate the contrast (which we define
as the ratio of energy in the main peak to the total radiatedenergy at the experiment) we assume that an angular collimation is used in order to reduce spontaneous emission
background. A collimator with half-angle 3 μrad allows
the entire intensity in the main peak to be transmitted. The
contrast is influenced by SASE intensity in two side peaks
and by spontaneous emission in the first harmonic from therest of the bunch. For the charge of 1 nC, as in our numerical example, the contrast is about 95 %. Higher harmonics
of undulator radiation (if they disturb an experiment) can
be cut, for instance, by a multilayer monochromator with abandwidth of the order of 1 %.

BEYOND ”FUNDAMENTAL LIMIT”
It is generally accepted that the shortest pulse, that canbe obtained from a SASE FEL, is given by a duration of
intensity spike in time domain, i.e. it is defined by inverse
FEL bandwidth (ρω 0 )−1 . However, the fact that a SASE
FEL can operate with a strong chirp parameter (in combination with undulator tapering) without gain degradation,
opens up a possibility of a conceptual breakthrough: one
can get from SASE FEL a radiation pulse which is much

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MOPPH068

shorter than the inverse FEL bandwidth. Indeed, in the caseof α̂  1, the frequency chirp inside an intensity spike
is much larger than FEL bandwidth. Thus, one can use amonochromator to reduce pulse duration. By an appropriate choice of the monochromator bandwidth one√ can selectan X-ray pulse that is shorter by a factor of 2α̂ than the
inverse FEL bandwidth. The only theoretical limit in thiscase is given by the condition ρα̂  1. Note that for hard
X-ray FELs the parameter ρ is in the range 10 −4 − 10−3 .
To illustrate a possible technical realization of this idea,
we can suppose that the energy modulation by a few-cycle
optical pulse is increased by a factor 3 so that α̂  6. In
combination with undulator tapering and a monochromator, this would allow to obtain sub-100-GW coherent X-ray
pulses with a duration below 100 attoseconds and a contrast
above 90 %. Note that the contrast remains high because
the spectrum of spontaneous emission from the rest of thebunch gets broader due to the stronger taper.

REFERENCES[1] M. Altarelli et al. (Eds.): XFEL: The European X-Ray FreeElectron Laser. Technical Design Report, Preprint DESY
2006-097, DESY, Hamburg, 2006.
[2] J. Arthur et al.: Linac Cherent Light Source (LCLS). Conceptual Design Report, SLAC- R593, Stanford, 2002.
[3] E.L. Saldin and E.A. Schneidmiller and M.V. Yurkov, Opt.
Commun. 212(2002)377.
[4] A.A. Zholents and W.M. Fawley, Phys. Rev. Lett.
92(2004)224801.
[5] E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov, Opt. Comm.
237(2004)153.
[6] E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov, Opt. Comm.
239(2004)161.
[7] P. Emma, Z. Huang and M. Borland, Proc. of the 2004 FEL
Conference, p. 333.
[8] A.A. Zholents and G. Penn, Phys. Rev. ST Accel. Beams
8(2005)050704.
[9] E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov, Proc. of the2005 FEL Conference, p. 258.
[10] S. Krinsky, Z. Huang, Phys. Rev. ST Accel. Beams
8(2003)050702.
[11] E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov, The Physics
of Free Electron Lasers (Springer-Verlag, Berlin, 1999).
[12] E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov, Nucl. Instr.
and Methods A 429(1999)233.
[13] Z. Huang and G. Stupakov, Phys. Rev. ST Accel. Beams
8(2005)040702.

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TRANSVERSE AND LONGITUDINAL COHERENCE PROPERTIES OF
THE RADIATION FROM X-RAY SASE FELS
E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov
Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany

Abstract
We present a comprehensive analysis of coherence properties of the radiation from X-ray free electron laser(XFEL). We consider practically important case when
XFEL is optimized for maximum gain. Such an optimization allows to reduce significantly parameter space. Application of similarity techniques to the results of numerical simulations allows to present all output characteristics of the optimized XFEL as functions of the only parameter, ratio of the emittance to the radiation wavelength,ˆ = 2π/λ. our studies show that optimum performanceof the XFEL in terms of transverse coherence is achievedat the value of the parameter ˆ of about unity. At smaller
values of ˆ the degree of transverse coherence is reduced
due to strong influence of poor longitudinal coherence on
a transverse one. At large values of the emittance the degree of transverse coherence degrades due to poor mode
selection. Comparative analysis of existing XFEL projects,
European XFEL, LCLS, and SCSS is presented as well.

INTRODUCTION
In the X-ray FEL the radiation is produced by the electron beam during single-pass of the undulator [1]. The amplification process starts from the shot noise in the electron
beam. Any random fluctuations in the beam current correspond to an intensity modulation of the beam current at all
frequencies simultaneously. When the electron beam enters the undulator, the presence of the beam modulation at
frequencies close to the resonance frequency initiates theprocess of radiation. The FEL collective instability in theelectron beam produces an exponential growth (along theundulator) of the modulation of the electron density on thescale of undulator radiation wavelength. The fluctuationsof current density in the electron beam are uncorrelated not
only in time but in space, too. Thus, a large number oftransverse radiation modes are excited when the electron
beam enters the undulator. These radiation modes have different gain. As undulator length progresses, the high gain
modes start to predominate more and more. For enoughlong undulator, the emission will emerge in a high degreeof transverse coherence.
The first analysis of the problem of transverse coherence
has been performed in [2]. It has been found that even after finishing the transverse mode selection process the degree of transverse coherence of the radiation from SASE206

FEL visibly differs from the unity. This is consequenceof the interdependence of the longitudinal and transverse
coherence. First studies of the evolution of transverse coherence in the nonlinear regime of SASE FEL operation
have been performed in [3]. It has been found that thedegree of transverse coherence reaches maximum value inthe end of the linear regime. Further increase of the undulator length leads to its decrease. Despite output power of
the SASE FEL grows continuously in the nonlinear regime,
maximum brilliance of the radiation is achieved in the very
beginning of the nonlinear regime. Due to limited computing power available at that time we limited our study with a
specific numerical example just illustrating the general features of coherence properties of the radiation produced by
the SASE FEL operating in the nonlinear regime.
In this paper we present general analysis of the coherence properties (longitudinal and transverse) of the radiation from SASE FEL. The results have been obtained with
time-dependent, three-dimensional FEL simulation code
FAST [4] performing simulation of the FEL process withactual number of electrons in the beam. Using similarity techniques we present universal dependencies for themain characteristics of the SASE FEL covering all practical range of X-ray FELs.

BASIC RELATIONSDesign of the focusing system of XFEL assumes nearly
uniform focusing of the electron beam in the undulator, so
we consider axisymmetric model of the electron beam. It
is assumed that transverse distribution function of the electron beam is √Gaussian, so rms transverse size of matchedbeam is σ = β ,where  = n /γ is rms beam emittanceand β is focusing beta-function. In the case of negligibly
small effects of the space charge and energy spread, operation of the FEL amplifier is described by the diffraction
parameter B and the betatron motion parameter k̂β : [5]:B = 2Γσ 2 ω/c ,k̂β = 1/(βΓ) ,(1)
 2 2 2
1/2
where Γ = Iω θs AJJ /(IA c2 γz2 γ)
is the gain parameter. When describing shot noise in the electron beam, one
more parameter appears, the number of electrons in the volume of coherence: N c = I/(eωρ), where ρ = cγz2 Γ/ω isthe efiiciency parameter. The following notations are used
here: I is the beam current, ω = 2πc/λ is the frequency ofthe electromagnetic wave, θ s = Krms /γ, Krms is the rms

The Angstrom ChallengeProceedings of FEL 2006, BESSY, Berlin, Germany
undulator parameter, γ is relativistic factor, γ z−2 = γ −2 +θs2 , kw = 2π/λw is the undulator wavenumber, I A = 17
kA is the Alfven current, A JJ = 1 for helical undulator and2222/2(1 + Krms)) − J1 (Krms/2(1 + Krms))
AJJ = J0 (Krmsfor planar undulator. Here J 0 and J1 are the Bessel functions of the first kind.
Target value of interest for XFEL optimization is thefield gain length of the fundamental mode. For this practically important case the solution of the eigenvalue equation for the field gain length of the fundamental mode andoptimum beta function are rather accurately approximatedby [6]:

Lg

=

1.67

βopt



11.2



IA
I
IA
I

1/2
1/2

(n λw )5/6 (1 + K 2 )1/3
KAJJ
λ2/3
3/2 1/2

n λw
,
λKAJJ

(2)

Accuracy of this fit is better than 5% in the range of parameter ˆ = 2π/λ from 1 to 5. It follows from (1) and(2) that diffraction parameter B and parameter of betatronoscillations, k̂β are functions of the only parameter ˆ. FEL
equations written down in the dimensionless form involvean additional parameter N c defining the initial conditions
for the start-up from the shot noise. Note that the dependence of output characteristics of the SASE FEL operatingin saturation is slow, in fact logarithmic in terms of N c .

SIMULATION ALGORITHM
Rigorous studies of the nonlinear stage of amplificationis possible only with numerical simulation code. Typically
FEL codes use an artificial ensemble of macroparticles for
simulating of the FEL process when one macroparticle represents large number of real electrons. Thus, a natural question arises if macroparticle phase space distributions are
identical to those of actual electron beam at all stages ofamplification. Let us trace typical procedure for preparation of an artificial ensemble [7, 8]. The first step of particle loading consists in a quasi-uniform distribution of themacroparticles in the phase space. At this stage an ensemble of particles with random distribution is generated which
occupies a fraction of the phase space. Then this ensemble is copied on the other parts of the phase space to provide pseudo-uniform loading of the phase space. Pseudouniformity means that initial microbunching at the fundamental harmonic (or for several harmonics) is equal to zero.
Also, phase positions of the mirrored particles are correlated such that microbunching does not appear due to betatron oscillations, or due to the energy spread. Finally, artificial displacements of the macroparticles are applied to provide desired (in our case gaussian) statistics of microbunching at the undultor entrance. We note that it is not evident
that such an artificial ensemble reflects actual physical situation for a short wavelength SASE FEL. Let us consider an
example of the SASE FEL operating at the radiation wavelength of 0.1 nm. With the peak current of 5 kA we find

The Angstrom Challenge

MOPPH069

that the number of electrons per wavelength is about 10 4 .
On the other hand, it is well known that properties of an
artificial ensemble (even at the first step of pseudo-uniform
loading) converge very slowly to the model of continuous
media. In fact, even with the number of macroparticles
per radiation wavelength 6.4 × 10 4 the FEL gain still visibly deviates from the target value. Introducing of an artificial noise makes situation with the quality of an ensemble
preparation even more problematic. The only way to test
the quality of an artificial ensemble is to perform numericalsimulations with actual number of electrons in the beam.
We constructed such a version of three-dimensional, timedependent FEL simulation code FAST [4]. Comparison of
the results with direct simulations of the electron beam andwith an artificial distributions has shown that artificial ensembles are not adequate to the problem. Artificial effects
are pronouncing especially when calculating such fine features as transverse correlation functions. Thus, all the simulations presented in this paper have been performed withcode FAST using actual number of electrons in the beam.

GENERAL DEFINITIONS
The first-order transverse correlation function is definedasẼ(r⊥ , z, t)Ẽ ∗ (r⊥ , z, t)
γ1 (r⊥ , r⊥ , z, t) = 
1/2 ,
22
|Ẽ(r⊥ , z, t)| |Ẽ(r⊥ , z, t)| 
where Ẽ is the slowly varying amplitude of the amplified
wave. For a stationary random process γ 1 does not dependon time, and the degree of transverse is:ζ=|γ1 (r⊥ , r⊥ )|2 I(r⊥ )I(r⊥ ) d r⊥ d r⊥,[ I(r⊥ ) d r⊥ ]2(3)

where I(r⊥ ) = |Ẽ(r⊥ )|2 . The first order time correlation function, g 1 (t, t ), is calculated in accordance with thedefinition:
Ẽ(r, t)Ẽ ∗ (r, t )
g1 (r, t − t ) = 
1/2 ,2

2
| Ẽ(r, t) | | Ẽ(r, t ) | (4)For a stationary random process time correlation functions
are functions of the only argument, τ = t − t. The coherence time is defined as∞|g1 (τ )|2 d τ .

τc =

(5)

−∞

If one traces evolution of the brilliance of the radiation
along the undulator length there is always the point, which
we define as the saturation point, where the brilliancereaches maximum value [9]. In the following we presentcharacteristics of the radiation at the saturation point which207

are universal functions of the only parameter, ˆ. In fact,
the brilliance is proportional to the degeneracy parameter
δ, i.e. the number of photons in a single pulse which aretransversely and longitudinally coherent. We introduce a
notion of normalized degeneracy parameterδ̂ = η̂ζ τ̂c .
Here normalized FEL efficiency is defined as η̂ =P/(ρWb ) where P is radiation power, and W b = γmc2 I/e
is electron beam power. Normalized coherence time is defined as τ̂c = ρωτc . Parameter δ̂ and the degeneracy parameter δ are simply related as:δ=Wbδ̂ = 2.7 × 107 × λ[Å ] × I[kA] × E[GeV] × δ̂ .
ω 2

PROPERTIES OF THE RADIATION
Simulations of the FEL process have been performed forthe case of a long bunch with uniform axial profile of thebeam current. Such a model provides rather accurate predictions for the coherence properties of the XFEL, since
typical radiation pulse from the XFEL is much longer thanthe coherence time. Calculations has been performed with
FEL simulation code FAST using actual number of electrons in the beam. The value of parameter N c = 8 × 105
corresponds to the parameter range of XFEL operating at
the radiation wavelength about 0.1 nm.
A series of simulation runs have been performed in therange of the parameter ˆ = 0.25 . . . 4.5. Application ofsimilarity techniques described above allowed us to extract
universal parametric dependencies of the main characteristics of the optimized XFEL operating in the saturation (seeFigs. 1-3).
Figure 1 shows the dependence of the saturation lengthẑsat = Γzsat on parameter ˆ. Analysis of the curve showsthat the saturation length scales as ẑ sat ∝ ˆ5/6 . Such dependence directly follows from the optimization procedureof the gain length given by (2). The normalized coherence

Saturation length, Γzsat

150

100

50

0
0

1

2
3
2πε/λ

4

5

Figure 1: Saturation length Γz sat versus parameter ˆ.

208

sat
C oherence tim e, ^τcProceedings of FEL 2006, BESSY, Berlin, Germany

15

10

5

0

D egree oftrans.coherence, ζsat

MOPPH069

0

1

2
3
2πε/λ

4

5

0

1

2
3
2πε/λ

4

5

1.0
0.8
0.6
0.4
0.2
0.0

Figure 2: Degree of transverse coherence, ζ sat , and normal.
ized coherence time, τ̂ csat in saturation versus parameter ˆtime in the saturation, τ̂ csat is also proportional to ˆ5/6 (seeFig. 2).
The dependence of the degree of transverse coherencein the saturation on the parameter ˆ exhibits rather complicated behavior (see Fig. 2). It reaches maximum value
in the range of ˆ values about of unity, and drops at small
and large values of ˆ. Actually, the degree of transverse
coherence is formed due to two effects. The first effecttakes place due to interdependence of the poor longitudinal coherence and transverse coherence [2]. Due to thestart-up from shot noise every radiation mode is excited
within finite spectral bandwidth. Actually this means thatin the high gain linear regime the radiation of the SASE
FEL is formed by many fundamental TEM 00 modes withdifferent frequencies. The transverse distribution of the radiation field of the mode is also different for different frequencies. Smaller value of the diffraction parameter (i.e.
smaller value of ˆ) corresponds to larger deviation of the radiation mode from the plane wave. This explains a decreaseof the transverse coherence at small values of ˆ. When theparameter ˆ increases, the diffraction parameter increases
as well thus leading to the degeneration of the radiation
modes. Amplification process in the SASE FEL passes
limited number of the field gain lengths, and starting fromsome value of ˆ the linear stage of amplification becomes
too short to provide mode selection process. When amplification process enters nonlinear stage, the mode content of

The Angstrom ChallengeProceedings of FEL 2006, BESSY, Berlin, Germany

Table 1: Parameter space of XFEL projects
European XFEL LCLS SCSS
SASE1 SASE2
λ, nm
0.1
0.15
0.15
0.1
E, GeV
17.5
17.5
14.35 6.135
1.4
1.2
0.85
n , mm-mrad 1.4
ˆ
2.6
1.7
1.8
4.5
ζ
0.65
0.85
0.83
0.24

^
Saturation efficiency, η
sat

0.6

0.4

0.2

0.0

^
D egeneracy param eter, δsat

MOPPH069

0

1

2
3
2πε/λ

4

5

0

1

2
3
2πε/λ

4

5

1.0
0.8
0.6
0.4
0.2
0.0

Figure 3: Efficiency, η̂ sat , and normalized degeneracy parameter, δ̂sat , in the saturation versus parameter ˆ.

versely proportional to the parameter ˆ. Taking into account that the value of the coherence time τ̂ csat scales proportional to ˆ5/6 , we find that the normalized degeneracy
parameter of the radiation is nearly proportional to the degree of transverse coherence, δ̂ ∝ ζ/ˆ1/6 .
Finally, in Table 1 we present comparison of existing
XFEL projects, the European XFEL, LCLS and SCSS interms of degree of transverse coherence [10–12]. We seethat the European XFEL and LCLS are in the same rangeof parameter space. These projects assume conservativevalue of the emittance, and relatively high degree of transverse coherence is achieved by increasing the energy of thedriving accelerator. Project SCSS assumes much smaller
energy of the driving accelerator. However, despite muchsmaller value of the normalized emittance it falls in therange of parameters for the output radiation with poortransverse coherence.

REFERENCES
1.0[1] Ya.S. Derbenev, A.M. Kondratenko and E.L. Saldin, Nucl.
Instrum. and Methods 193(1982)415.

Σm P nm /P tot

0.8
0.6

[2] E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov, Opt.
Commun. 186(2000)185.

0.4[3] E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov, Nucl. Instrum. and Methods A 507(2003)106.

0.2[4] E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov, Nucl. Instrum. and Methods A 429(1999)233.

0.0
0

1

2
3
2πε/λ

4

5

Figure 4: Partial contributions of the modes with azimuthal
index m = 0 . . . 4 into the total power versus parameter ˆ.
SASE FEL operates in the saturation.

[5] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Nucl. Instrum. and Methods A475(2001)86.
[6] E.L. Saldin, E. A. Schneidmiller, and M.V. Yurkov, Opt.
Commun. 235(2004)415.
[7] W.M. Fawley, Phys. Rev. STAB 5(2002)070701.
[8] S. Reiche, Nucl. Instrum. and Methods A429(1999)243.
[9] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Preprint
DESY 06-137, Hamburg, 2006.

the radiation becomes even more rich due to independent
growth of the radiation modes in the nonlinear medium (seeFig. 4). Thus, at large values of ˆ the degree of transverse
coherence is limited by poor mode selection. Analyticalestimations presented in [9] show that in the limit of large
emittance, ˆ  1, the degree of transverse coherence scales
as 1/ˆ
2 .
We present in Fig. 3 the plots for normalized efficiency
and degeneracy parameter for optimized XFEL. Normalized efficiency in saturation has simple scaling, it falls in-

The Angstrom Challenge[10] M. Altarelli et al. (Eds.), XFEL: The European X-Ray
Free-Electron Laser. Technical Design Report, Preprint
DESY 2006-097, DESY, Hamburg, 2006 (see also
http://xfel.desy.de).
[11] J. Arthur et al., Linac Cherent Light Source (LCLS). Conceptual Design Report, SLAC- R593, Stanford, 2002 (seealso http://www-ssrl.slac.stanford.edu/lcls/cdr.
[12] SCSS X-FEL: Conceptual design report, RIKEN, Japan,
May 2005. (see also http://www-xfel.spring8.or.jp).

209

MOPPH071

Proceedings of FEL 2006, BESSY, Berlin, Germany

DESIGN STATUS OF PAL-XFEL∗
T.-Y. Lee† , Y. S. Bae, J. Choi J. Y. Huang, H. S. Kang, C. B. Kim, D. E. Kim, M. G. Kim,
Y. J. Kima , I. S. Ko, J. S. Oh, Y. W. Parc, and J. H. Park
Pohang Accelerator Laboratory, San 31, Hyoja-dong, Pohang, Kyungbuk 790-784, KOREAaFree Electron Laser Laboratory, Duke University, N.C. 27708-0319, USA
Abstract
Pohang Accelerator Laboratory has a plan to build an Xray FEL machine. This new machine will utilize the existing 2.5 GeV injection linac to the storage ring by upgrading
its energy up to 3.7 GeV or more. The target wavelength
will be 3-4.5 Å and its third harmonic 1-1.5 Å will also
be used. The project will proceed in two stages: In theﬁrst stage, a VUV SASE machine with 320 MeV will be
constructed and tested for the proof-of-principle. The full
X-ray machine will be constructed in the next stage.

INTRODUCTION
PAL-XFEL is the name of new project of Pohang Accelerator Laboratory (PAL) to build a new X-ray FEL machine based on SASE (self ampliﬁed spontaneous emission) scheme. This new machine will utilize the existing 2.5 GeV electron linac by increasing its energy to 3.7
GeV and upgrading the performance. The linac is currently
used for injection to the 2.5 GeV storage ring of PohangLight Source (PLS). The new linac energy will be 3.7 GeV.
The overview of the PAL-XFEL project was reported previously [1]. For readers unfamiliar with the project, fundamental parameters of PAL-XFEL are listed in Table 1
and the machine layout is displayed in Fig. 1. At the moment, detailed design study and machine R& D are goingon. In the ﬁgure, K2,...,K12 denote the currently used accelerating columns and X1,...,X9 denote the new accelerating columns that will be added to the existing linac. X3X
denotes the X-band high harmonic cavity. We are going tobuild the new part of PAL-XFEL while still running PLS.
However, there have been a few modiﬁcations in the
PAL-XFEL project. The ﬁrst important modiﬁcation is thetarget wavelength that will be used mainly. The X-ray community, which is the biggest synchrotron user community
in Korea, has demanded that the target wavelength be in
1-1.5 Å range, which put quite a challenge for the PALXFEL design. Since the available linac energy of PAL islimited, we decided to utilize the high harmonic radiationof SASE. It is well known that the high harmonic radiations
are also ampliﬁed to FEL by the so called nonlinear harmonic generation [2, 3]. The existence and usefulness of
SASE higher harmonic radiation was veriﬁed experimentally in VUV-FEL at DESY [4]. According to calculation
based on [5], the third harmonic radiation power is approximately 1% of the fundamental one.
∗ Work supported by Korean Ministry of Science and Technology† tylee@postech.ac.kr

210

The fundamental wavelength of PAL-XFEL was determined to be 3 Å in which case the third harmonic becomes 1 Å. These wavelengths are achieved by using an invacuum undulator of 4 mm gap. Recently, we are considering an alternative choice in which the fundamental wavelength is 4.5 Å and the third harmonic wavelength is 1.5 Å.
In this case, wider undulator period and gap (and thus outvacuum undulator) are allowed and the undulator wakeﬁeld
is smaller. Currently, we are estimating the two designs andthe ﬁnal decision is not made yet. Below, comparison of thetwo choices is given brieﬂy.
Another important modiﬁcation is the procedure of PALXFEL construction. The PAL-XFEL project will proceed
in two stages. In the ﬁrst stage, only a small 320 MeV
SASE machine will be constructed. The purpose of thismachine is to test and prove the design strategy of PALXFEL. Hence, this test machine (TM) will use the same
undulator as PAL-XFEL. Only in the second stage, the full
PAL-XFEL will be constructed. The design of TM is under active study. Brief introduction to the TM design will
be given below. This status report will describe major modiﬁcations of the PAL-XFEL design brieﬂy. The PAL-XFEL
photo-injector status has been prepared separately [6, 7].

ALTERNATIVE UNDULATOR DESIGN
The point of the alternative undulator design is to relax
the original design slightly and make the whole scheme
safer. For the purpose, the fundamental radiation wavelength is changed from 3 Å to 4.5 Å, which makes the third
harmonic wavelength 1.5 Å. This change makes some difference. The comparison of the two undulator designs isgiven in Table 2.
What advantages do we get from this alternative design
over the original one? First of all, the undulator gap is relaxed from 4 mm to 7.8 mm, which is wide enough to allow
an out-vacuum undulator. With out-vacuum undulator, thechamber inner gap would be 6.8 mm which gives wakeﬁeld 40 % smaller. The longitudinal wakeﬁeld induces relative energy spread in the bunch, which is inversely proportional to the electron energy E. The relatively low energy,
3.7 GeV, of PAL-XFEL as a hard X-ray FEL machine may
make the undulator wakeﬁeld particularly serious. Hence
40% reduction of wakeﬁeld is not negligible.
Another advantage is related to the transversal coherenceof the SASE radiation and explained by a number B=gain
length/Rayleigh length. B measures how fast the transversal higher modes diffract out of the electron beam. One of
the advantages of the SASE FEL radiation is the transver-

The Angstrom ChallengeProceedings of FEL 2006, BESSY, Berlin, Germany
εn= 0.96 μm, Q = 1 nC
σz = 875 μm (2.9 ps), Dx =0.4 mm, Dy = 0.6 mm
E = 135 MeV

432 MeV458 MeV

RF-GUNX3
X1 3 FODO X2
Cells
15.0
MV/m
(6.8-m length)-27.2°BC1
X3X
49.0 MV/m σδ ~ 1.76 %R56 = 40.8 mm
180°
θ = 3.55°°
0.6 m

633 MeV
X4

X5
15.2 MV/m-57.0°

σz : 875  168 μm
εnx= 1.0 μm, εny= 0.95 μm

E = 3.7 GeV(336 m)σδ ~ 0.032 % (1.2 MeV)
σx = 111 µm, σy = 87 µm

E = 1.2 GeV(168 m)

X6

X7

X8

18.0 MV/m-20°

X9

3 FODO
K2
Cells(12-m length)

K11

MOPPH071

BC2
σδ ~ 1.45 %R56 = 5.9 mm
θ = 1.76°°
σz : 101  25 μm
εnx= 1. 6 μm, εny= 0.95 μm

Undulator, 80 m

K1219.0 MV/m-20°

Dog-leg w/ energy filter
R56 = 0.133 mm
T566 = 6.3 mm

Δσδ = +0.0013% (added)
dN/N = 1 %Figure 1: Layout of the PAL-XFEL injector and linac. K2,...,K12 denote the currently used accelerating columns andX1,...,X9 denote the new accelerating columns that will be added.

Table 1: Parameters of PAL-XFEL
Beam Parameters
Value
Unit
Electron energy
3.7
GeV
Peak current
3
kA
Normalized slice emittance1
mm mrad
RMS slice energy spread
0.01 %
Full bunch length
270
fs
Undulator Parameters
Undulator period
1.5cm
Segment length
4.5m
Full undulator length
80mPeak undulator ﬁeld
1.19
T
Undulator parameter, K
1.49
Undulator gap
4mm
Average β-function
10m
FEL Parameters
Radiation wavelength
3Å
FEL parameter, ρ
5.7 × 10−4
Peak brightness
5 × 1031*
Peak coherent power
1
GW
Pulse repetition rate (Max.)60
Hz
1D gain length
1.2m
Saturation length, Lsat
45m2
2
* photon/(sec mm mrad 0.1%BW)

sal coherence. However, the transversal coherence is not an
intrinsic property of the undulator radiation but acquired by
the ampliﬁcation process in which all the transversal higher
modes diffract out oh the beam while only the fundamental
mode keeps growing. The bigger B is, the faster the higher
modes diffract. It is true that B values of both the original
design and the alternative design are not big enough compared with other machines such as LCLS. Figure 2 shows

The Angstrom Challenge

Table 2: Comparison of the two undulator designs
DesignOriginal
Alternative
Wavelength
3 Å
4.5 Å
Third harmonic
1 Å
1.5 Å
Undulator
in-vacuum out-vacuum
Undulator period
1.5 cm2.2 cmUndulator gap
4 mm
7.8 mmUndulator parameter, K
1.49
1.52
FEL parameter
5.8 × 10−4 6.6 × 10−4
1-D gain length
1.2 m
1.5 m
Gain Length/Rayligh length
0.04
0.07
Saturation length
45 m
48 m
Peak power
2 GW
4 GW

the power gain of the original design, while Fig. 3 showsthat of the alternative design.
It is hard but possible to see that the power gain in Fig.
2 is not in a straight line but slightly over it. This indicatesthat the transversal higher modes do not diffract out fastenough and thus a small portion of it might remain at theﬁnal stage. Figure 3 shows a better case.
The third advantage of the alternative design is that its
radiation power is bigger than that of the original design.
As shown in Figs. 2 and 3, the peak radiation power of theoriginal design is almost 2 GW while that of the alternative
design is almost 4 GW.
The disadvantage of the alternative design comparedwith the original design is that its third harmonic radiationis 1.5 Å not 1 Å that is preferred by scientists working onorganic samples. Those scientists include material scientists, biologists, organic chemists, and the number grows
rapidly. The alternative design can provide 0.9 Å radiation

211

MOPPH071

Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 2: Power gain of the original undulator design.

Figure 4: Radiation beam proﬁle obtained from start to end
simulation.

TEST MACHINE

Figure 3: Power gain of the alternative undulator design.
as a ﬁfth harmonic but its power is approximately 1/10 of
the third harmonic radiation.

BUNCH COMPRESSOR DESIGN
The bunch compressor design is not ﬁxed yet. There area few issues still to be examined. One of the issues is thespace charge in the bunch compressors. The ELEGANT
code that is used in the linac design does not include thespace charge effect and thus the space charge effect has notbeen checked seriously. It has been suggested that the second bunch compressor be in the higher energy region to
make the space charge effect unimportant. A simulation
study to estimate the space charge effect in the bunch compressors is going on.
Another important issue is the coherent synchrotron radiation (CSR). According to simulation, the electron distribution in the phase space is shifted slightly in the x, x
direction by CSR. This has to be ﬁxed for the successful
SASE FEL. A start to end simulation from the gun to theundulator was carried out. In case the CSR effect is off,the ﬁnal radiation proﬁle is very good as shown in Fig. 4,
which was obtained with the alternative undulator design.

212

The purpose of TM is to prove, in the low energy, that
PAL-XFEL is achievable. It will not be used as a user facility. The reason why we need TM is that PAL-XFEL ischallenging. It is challenging to generate hard X-ray (3 4.5 Å) SASE radiation with 3.7 GeV electron beam. The
validity of the PAL-XFEL scheme will be proved by TM.
TM will have a low energy of 320 Mev, lower than a tenthof PAL-XFEL energy, but the undulator will be the sameas in PAL-XFEL except the total length. It will still adopt
a pair of bunch compressors, but X-band higher harmonic
cavity is not planned to be used at the moment. Beam parameters are chosen to give comparable magnitude of energy spread to the PAL-XFEL case. The optimal average
β function of the undulator lattice is reduced from 10 m of
PAl-XFEL to 5 m. A few fundamental parameters of TM
are shown in Table 2.
Table 3: Parameters of the test machine
Parameters
Value
Unit
Electron energy
0.32
GeV
Peak current
0.7
kA
Normalized slice emittance
0.8
mm mrad
RMS slice energy spread
0.01 %
Full undulator length
8m
Average β-function
5mRadiation wavelength28
nm
FEL parameter, ρ
3.4 × 10−3
1D gain length
0.2m
Saturation length, Lsat
6m

Since the high harmonic cavity is not used, the compressed bunch has a different shape from the PAL-XFEL
case. The layout of TM is displayed in Fig. 5 and Fig. 6
shows the current distribution in a bunch at the test linac
end.

The Angstrom ChallengeProceedings of FEL 2006, BESSY, Berlin, Germany

RF Photoinjector
S1
S2

BC1

MOPPH071

BC2

S3

S4

S5

S6

S7

undulator

120 MV/m
19 / 24 / 19 MV/m
0.0 / 0.0 / ~ - 34 deg

16.8 MV/m-4.0 deg

E = 180 MeV

7.0 MV/m
0.0 deg

E = 280 MeV

E = 320 MeV

Figure 5: Layout of the test machine.
[5] E. L. Saldin, E. A. Schneidmiller, and M. V. Yurkov, Phys.
Rev. ST Accel. Beams, 9 (2006) 030702.
[6] Y. W. Parc et al., In this proceedings.
[7] J. H. Park et al., In this proceedings.

Figure 6: Current distribution in the linac end of the test
machine.

SUMMARY
The progress of the PAL-XFEL design since the previous
report [1] has been described. The bunch compressor design needs to be examined further with respect to the CSR
and space charge effect. As for the undulator design, an alternative design has been described in comparison with theoriginal design. The alternative design gives 4.5 Å fundamental radiation and 1.5 Å third harmonic, while the original design gives 3 Å fundamental and 1 Å third harmonic.
The ﬁnal decision for the undulator is not made yet. Also,
an important change of the PAL-XFEL construction plan
has been described. PAL-XFEL will be constructed in twostages. In the ﬁrst stage, 320 MeV test machine will be constructed and the full 3.7 GeV machine will be constructed
only in the second stage.

REFERENCES[1] I. S. Ko, Proceedings of the 27th International Free Electron
Laser Conference, SLAC, USA (2005) 216.
[2] R. Bonifacio, L. D. Salvo, and P. Pierini, Nucl. Instrum.
Methods Phys. Res. A 293 (1990) 627.
[3] Z. Huang and K.-J. Kim, Phys. Rev. E 62 (2000) 7295.
[4] S. Schreiber, Proceedings of the 27th International Free
Electron Laser Conference, SLAC, USA (2005) 12.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

ULTRA HIGH BRIGHTNESS ACCELERATOR DESIGN
R.J. Bakker, A. Adelmann, A. Anghel, M. Dehler, R. Ganter, S. Leemann, K. Li, M. Pedrozzi,
J-Y. Raguin, L. Rivkin, V. Schlott, F. Wei, A. Wrulich
Paul Scherrer Institut, Villigen CH 5232, Switzerland.
Abstract
The PSI FEL Project at the Paul Scherrer Institute in
Switzerland incorporates the development of a low
emittance gun as a driver for a cost-effective X-ray freeelectron laser user facility (λs ≥ 0.1 nm, ħωs ≤ 12.4 keV).
We investigate sources based on field-emitter technology
and photoemission, followed by high gradient (Γ ≥ 0.25
GV/m) acceleration up to 1 MeV. We present a concept topreserve the emittance in the acceleration process where
the first 250 MeV of acceleration is the most delicate.
Experimentally we intend to verify the validity of ultrahigh brightness acceleration over this energy range in the
period 2008-2011.

INTRODUCTION
In a free-electron laser (FEL) the resonant wavelength(λs) is given by:

λs =

(

)

λu
1+ K 222γ,(1)where λu is the undulator period, γ the Lorenz factor
corresponding to the beam energy (γ = E [Mev]/0.511),
and K the dimensionless undulator strength (K ≈ 0.66
λu·Bu [cm] [T]). It follows that the X-ray regime (0.1 nm)
is accessible with conventional undulator technology (λu≥ 0.8 cm) and a beam-energy as low as 4 GeV. Lasing at
such a wavelength is more restrictive, however, since it isfundamental to control the transverse emittance (ε), theenergy spread (σγ) and the current (I) of the electronbeam. An estimate for the critical wavelength limit λcr forsufficient gain in the FEL is [1]:λcr ≅ 18π ε n

σγ
γ

1 IA

γ I

,

(2)

where εn, σγ/γ, and IA are the normalized emittance, therelative energy-spread, and the Alfèn current (≈ 17 kA)
respectively. For typical electron beam parameters for
short wavelength operation (Q = 1 nC, εn ≈ 1 mm mrad)
λcr is then reduced by increasing beam-energy combinedwith an increased undulator period and length.
As a future alternative, the PSI-FEL project at the Paul
Scherrer Institute in Switzerland attempts to develop an
electron source with a significantly lower transverse
emittance as a basis to develop a cost-effective X-ray FEL
user facility [2] by pushing the beam-energy as low astechnological possible. That is, for the case with εn ≤ 0.1
mm mrad, parameter studies [2] suggest that the beamenergy and peak current may be limited to 6 GeV and 1.5
kA, respectively.

214

In this paper we present a concept for an ultra-highbrilliance 6-GeV accelerator. Starting point is theperformance expectations of the Low Emittance Gun(LEG) [3], which is under construction at PSI. The first
250 MeV deserves special attention since emittancepreservation proves to be most challenging in this part ofthe machine. It is our intention to test the concept ofemittance conservation in this part of the machine
experimentally. If successful, it should then serve as an
injector for a linac that feeds a cost-effective X-FEL. An
outlook follows at the end of this paper.
Table 1. Electron Source Parameters for the PSI FEL.
Peak current
Bunch charge
Bunch length (full width)
Bunch shape
Normalized emittance*
Repetition rate#

I
Q
τ
εn
f

≥5
0.2
≤ 40
uniform≤ 0.0510AnC
ps
mm mradHz* Slice parameter of a field-emitter at E=1 MeV and a slice-chargeof 1 pC, i.e., the charge in the FEL-corporation length [2].
#Limited by high-gradient pulser technology.

THE ELECTRON SOURCE
In a linac the emittance is limited by the intrinsic
emittance at the electron source, which can be expressedas [4]:ε n=R
2

2 Ekin3 mc 2(3)where R is the beam radius in the case of a uniform radial
distribution and Ekin is the mean kinetic energy of emitted
electrons. With Eq. (3) in mind two strategies are persued:laser assisted Field Emission and photo-emission. Bothtechnologies rely on laser-illumination to shape thetemporal profile of the pulse.
With field emission electrons are drawn from sharp tips
that are exposed to high gradient electric fields (Γ ≈ 6
GV/m). Normally the emitting radius is small (R ≤ 5 μm)
and the field-emission process keeps the kinetic energy ofthe emitted electrons low (Ekin ≈.0.15 eV), which suggests
a normalized emittance below 10-3 mm mrad. However,with increasing current the required electrical fieldstrength goes up followed by increased space-charge
forces. This makes the combination of high-current andlow-emittance challenging, both from technological andoperational point of view. To reach ultra-low emittance
two types of field emitters (FE) are under investigation:(i) a macroscopic single-tip FE and (ii) Field-Emitter
Arrays (FEA). Construction of the former istechnologically less demanding but the latter permits areduction of the current density and most likely a lower
The Angstrom ChallengeProceedings of FEL 2006, BESSY, Berlin, Germany

emittance. The status and performance are discussed indetail in [3]. Target specifications are summarized in
Tab. 1, where the emittance refers to the slice-value after
acceleration up to 1 MeV.
The transverse emittance of a photo-cathode for a 1 nC
electron bunch typically is εn ≈ 1 mm mrad. This value
may become smaller with a reduced bunch-charge, a
reduced peak-current, combined with an appropriate
choice of cathode material. Optimizations based on Eq.
(3) suggest that the slice emittance can reach εn ≤ 0.1 mm
mrad for a Cu cathode with beam parameters as quoted in
Tab. 1 and an initial transverse radius R = 0.25 mm.
Since the fabrication and operation of a photo-cathodeis less challenging then field emission, we anticipate
commencing with a photo-cathode. A second stage basedon field emission should then permit a lower initialemittance, which should permit a final value of 0.1 at theentrance of the undulator section of the FEL. Note that wehave chosen the beam parameters identical for both typesof cathodes such that the choice of cathode does not affectthe design of the following accelerator structure.
/energy:current:

/

/

z

z

250 MeV
off-crest
acceleration
0.35 kA
5.5 A

injectorlinac-1

BC1longitudinal
wakefield

MOPPH072

compressors BC1 and BC2 [7]. Hence, the difficulties
related to the emittance preservation are transferred to thedesign of the injector, which follows in the next section.
In terms of functionality the injector and BC1
accommodate most of the shaping of the longitudinal
phase-space (γ,z). Similar to the design of the LCLS [5],linac-1 and linac-2 serve to boost the energy and allow ofadiabatic damping of the emittance and relative energy
spread. Deformation of the longitudinal phase-space,caused by wakefields in the linac structures, is controlled
by off-crest acceleration in the injector and linac-1. In thepresent design both linac sections consist of 3-GHz room
temperature (RT) traveling wave structures. We did notconsider super-conducting technology because of the low
repetition rate of the injector. Higher frequency RT will
be considered later as an option to reduce the accelerator
length.

THE INJECTOR
Fig. 2 shows a schematic of the injector. Details of thelow-energy section are presented in Fig. 3.

/

Low Energy Accelerationzz

1.2 GeV

6.0 GeV

1.5 kA

1.5 kAlinac-2
BC2

Figure 1. Functional layout of a low-emittance linac for
an X-FEL. See text for details on the longitudinal shapingof the electron bunch.

ACCELERATOR CONCEPTThe performance parameters specified in Tab. 1 have,compared to more conventional RF photo-cathodedesigns, a low beam current and bunch charge at thecathode. This is beneficial to reduce the initial emittanceand its dilution due to space charge in the region where
the electron beam is sub-relativistic. The obvious
drawback is the increased bunch compression ratio, whichis required to obtain sufficient current for lasing. E.g., the
LCLS [5] and the European X-FEL at DESY [6] have a
total compression ratio of 70 and 100, respectively. The
PSI-FEL aims for a ratio of 270.
The concept shown in Fig. 1 enables the increased
compression ratio as it focuses on the control of thelongitudinal phase-space. This is possible because we do
not expect a significant emittance dilution in the bunch-

To minimize the initial blow-up of the emittance by
space-charge, the cathode is positioned in a high-gradient
field. The necessity of such a field is illustrated in Fig. 4,
which shows a CAPONE [9] simulation of the sliceemittance of an ideal uniform beam with parameters aspresented in Tab. 1. To obtain the gradient, the cathode isfollowed by a pulsed diode configuration as illustrated inFig. 3. A 500 kV pulser has been constructed, whichallows for initial tests with gradients up to 125 MV/m
(top curve in Fig. 4). After sufficient operational
experience the pulser will be upgraded to 1 MV to reach
gradients up to 250 MV/m.
1.5 GHz RF
anodepulsedfocusing coil

main
coil

cathodepulsedacceleration
Γ = 125 - 250 MV/mbuckingcoil

4.5 GHz RF

Figure 3. Layout of the high-gradient accelerating section
followed by the initial RF acceleration [8].

RF and ballistic compression
focussing
5.5 A
cathode1.5 cell(1.5 + 4.5 GHz)

injector linac(1.5 GHz)booster linac(3 GHz)

20 A

harmonic
cavity12 GHz
30 A

1MeV
4MeV
solenoids
high gradient acceleration solenoid(emittance compensation)

30 MeVsolenoids 285 MeV

250 MeVFigure 2. Schematic layout of the injector.
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215

MOPPH072

Proceedings of FEL 2006, BESSY, Berlin, Germany
0.25

0.12

0.06
0.04
0.02

0.6
σx,y, Δε nσx,y (mm), Δεn (mm mrad)

anode position

Δεn,slice (mm mrad)

0.20

0.08

0.00

250 MeV, 350 A

1.2 GeV, 350 A

280 MeV, 30 A
0.8
30 MeV, 30 A

125 MV/m
250 MV/m

0.10

4 MeV, 5.5 A

0.15εn,projected

0.10

σxy

0.4

εn

0.2

εn,slice

0.0
0.0

0.5

BC1

1.0

1.5

2.0

2.5

3.0

σxy (projected)

0.05

εn,slice (10 % of charge)
0

1

2

3

4

5

6

0.00

0

20

z (mm)

40

60
z (m)

80

100

Figure 4. CAPONE [9] simulation of the slice emittance
growth of a uniform electron bunch (Tab. 1) in a DC
accelerator field (1 pC slice with an initial radius of 0.25mm).

Figure 5. HOMDYN [10] simulation of the beamenvelope and emittance dilution for the PSI FEL linac up
to BC2, see Fig. 1. The inset is a zoom of the first 3 m.

For further acceleration we have chosen an initial RF
frequency of 1.5 GHz as a compromise between a highaccelerating gradient (≥ 40 MV/m) and a large acceptancewindow to collect sufficient charge in a single bunch. A
specially designed double-frequency 1.5-cell cavity [8]behind the diode further increases acceptance, see Fig. 3.
Additional advantages of the double-frequency are: (i) areduction of the emittance dilution caused by non-linear
RF fields [8] and (ii) optimized RF compression. The
latter is incorporated to reduce the bunch-length, see Fig.
2. We note that RF-compression is, in this part of themachine, the preferred choice as compared to magnetic
compression since it maintains the cylindrical symmetryof the beam. That is, it avoids a break-up of the horizontal
and vertical beam-optics in the space-charge dominatedregime. For the similar reasons there are no quadrupoles
included in the injector design.
During RF acceleration, it is important to control thetransverse beam size since non-linear off-axis fields in the
RF cavity may dilude the emittance otherwise. This isespecially true in the first RF-structures where the beamsize may be blown up by a strong defocusing field as thebeam passes the anode. For this reason, we plan to installa pulsed coil behind the anode to control the beam-size.
We note that the pulsed technology has the advantage thatthe eddy-currents in the anode naturally shield themagnetic field from the cathode area.

As a first step, the emittance dilution has been tracked
over the initial 1 GeV of acceleration (up to BC2) with
HOMDYN [10], see Fig. 5. Initial conditions were anelectron beam with the parameters presented in Tab. 1
with zero emittance at the cathode. It follows that a low
emittance can be maintained during compression andacceleration. Verification of these results with moresophisticated codes is still in progress. Here we use
MAFIA [11] to simulate the configuration presented inFig. 3. Calculations are complemented with PARMELA[12] and GPT [13] simulations for tracking of the electron
beam behind the diode. As a next step we will use
IMPACT [14] for more elaborate calculations andtolerance studies.

Performance

Energy Booster
The RF compression is finalized in a 3-m long 1.5 GHz
traveling wave structure. As soon as the electron bunches
are short enough they enter a 3-GHz structures. A 12GHz harmonic cavity at the end of the booster linearizes
the longitudinal phase-space before further compression.
All linac structures require additional focusing to control
the electron beam-size. The final energy is 250 MeV. At
this energy, the influence of space charge on the beamoptics is sufficiently reduced to permit the use of achicane to reduce the bunch length.
216

Figure 6. Installation of the 500-kV pulser in the testbunker OBLA.

STATUS AND OUTLOOKThe status of the field emitter development and theassociated test stands are reported in [3]. As a first step
towards the preservation of the emittance a 500 kV, 200-

The Angstrom ChallengeProceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH072

Figure 7. Layout of the 250 MeV test injector. The areas (a) and (b) mark the injector linac and booster linac as depicted
in Fig. 2. The designed tunnel is sufficiently long to house the first bunch compressor (BC1 in Fig. 1).
ns pulser has been installed in a bunker at the PSI. It
permits the operation of a diode configuration with avariable gap from 30 mm to 2 mm. A photo of the pulser
is shown in Fig. 6. In fall of 2006 the pulser will becomplemented with a diagnostic station for current andemittance measurements. First tests with pure fieldemitters (without laser illumination) are then foreseen for
the end of the same year. In 2007 the experimental setup
will be upgraded to permit laser assisted field emission
and photo-emission combined with 1.5 cell RF cavity as
depicted in Fig. 3. We note here the different laser
systems. Laser assisted field emission has a high quantum
efficiency (≈ 1) and requires a photon energy below the
work function (λ > 400 nm). This can be a sub-system of
the laser required for photo-emission, which typically has
to deal with a low quantum efficiency at a wavelength of
266 nm.
In parallel surface cleaning techniques are studied to
optimize the operation at high gradient and to minimize
the occurrence of breakdowns in the high-gradientaccelerator structure.
We plan to extend the experimental capabilities to a
250 MeV accelerator in the period 2008-2011. This linac
should demonstrate low-emittance acceleration and bunch
compression to reach a beam current of 350 A. In
addition, it should serve as a test environment for thedevelopment of diagnose for an X-FEL. A possible layout
is presented in Fig. 7. It includes the injector sketched
schematically in Fig. 2 as well as the first bunch
compressor, which is shown in Fig. 1.

REFERENCES[1] J. Rossbach, E.L. Saldin, E.A. Schneidmiller, M.V.
Yurkov, “Interdependence of parameters of an X-ray
FEL”, Nucl. Instr. Meth. In Physics Research, A374,
401 (1996)[2] http://leg.web.psi.ch/public/publications/2005/
ESFRI 20PSI-FEL.pdf[3] R. Ganter, R.J. Bakker, M. Dehler, J. Gobrecht, C.
Gough, E. Kirk, S.C. Leemann, K. Li, M. Paraliev,
M. Pedrozzi, F. Le Pimpec, J.-Y. Raguin, L. Rivkin,
V. Schlott, H. Sehr, S. Tsujino, “High Current

The Angstrom ChallengeElectron Emission from Microscopic Tips”,
THCAU04, this conference[4] S. Humphries, Charged Particle Beams (John Wiley& Sons, 1990).
[5] LCLS CDR, SLAC Report No. SLAC-R-593, 2002.
[6] TESLA TDR, DESY Report No. DESY-2001-011,
2001.
[7] K. Li, A. Adelmann, A. Anghel, R.J. Bakker, A.
Candel, M. Dehler, R. Ganter, G. Ingold, S.
Leemann, M. Pedrozzi, J-Y. Raguin, L. Rivkin, V.
Schlott, A. Streun, A. Wrulich, “Low Emittance XFEL Development”, Proc. of the 27th FEL Conf.,
Stanford (CA), USA , p. 483 (2005).
[8] J. -Y. Raguin, R. J. Bakker, K. Li, M. Pedrozzi, “A
Two-Frequency RF Cavity for the PSI Low
Emittance Gun”, Proc. of the 27th FEL Conf.,
Stanford (CA), USA , p. 324 (2005).
[9] A.E. Candel, M.M. Dehler, S.C. Leemann, “Electron
Beam Dynamics Simulations for the Low EmittanceGun”, Proc. of EPAC2004, Lucerne, Switzerland, p.
2505 (2004)[10] M. Ferrario, J.E. Clendenin, D.T. Palmer, J.B.
Rosenzweig, L. Serafini, “HOMDYN study for the
LCLS photoinjector”, SLAC-PUB-8400 (2000).
[11] CST GmbH, Bad Nauheimer Strasse 19, D-64289
Darmstadt, http://www.cst.com[12] L.Young, PARMELA, LA-UR-96-1835, LANL
(1996)[13] Pulsar Physics, De Bongerd 23, NL-3762 XA Soest,
http://www.pulsar.nl/[14] J. Qiang , S. Lidia, R. Ryne, C. Limborg, “A 3D
Parallel Beam Dynamics Code for Modeling High
Brightness Beams in Photoinjectors”, Proc. of the2005 Particle Accelerator Conference, Knoxville,
USA, p. 3316 (2005)

217

MOPPH073

Proceedings of FEL 2006, BESSY, Berlin, Germany

AN ENHANCED GINGER SIMULATION CODE WITH
HARMONIC EMISSION and HDF5 IO CAPABILITIES∗
William M. Fawley† , LBNL, Berkeley, CA 94720, USA
Abstract
GINGER [1] is an axisymmetric, polychromatic (r −z −t)
FEL simulation code originally developed in the mid1980’s to model the performance of single-pass amplifiers. Over the past 15 years GINGER ’s capabilities havebeen extended to include more complicated configurations
such as undulators with drift spaces, dispersive sections,and vacuum chamber wakefield effects; multi-pass oscillators; and multi-stage harmonic cascades. Its coding basehas been tuned to permit running effectively on platforms
ranging from desktop PC’s to massively parallel processors
such as the IBM-SP. Recently, we have made significant
changes to GINGER by replacing the original predictorcorrector field solver with a new direct implicit algorithm,
adding harmonic emission capability, and switching to the
HDF5 IO library [2] for output diagnostics. In this paper, we discuss some details regarding these changes andalso present simulation results for LCLS SASE emission at
λ =0.15 nm and higher harmonics.

terms of modularization and in the number of useful language features (e.g., array syntax and built-in operators,
type definitions, memory management). The code structure has proven very amenable to efficient multiprocessing
in which the different longitudinal slices are assigned todifferent processors with MPI [3] handling the necessaryinterprocessor communication. In the past year, we have
replaced the original predictor-corrector field solver by a
new implicit solver and also have extended the code to calculate radiation emission at multiple harmonics; the next
section gives details on these changes. We then present
results from a GINGER calculation for predicted harmonic
emission from the LCLS.
With the addition of calculations of harmonic emission,
typical GINGER output file sizes doubled or more. Basedupon file compactness, IO speed, and flexibility in data layout, the output file format was changed from simple ASCII
to HDF5[2]. In part because we believe that the FEL simulation community should become aware of the usefulness
of HDF5 IO, the last section of this paper gives details concerning its implementation into GINGER .

INTRODUCTION
Over the past 25 years, there has been a steady advancein the use of numerical simulation codes to explore FEL
physics, analyze experimental results, and to help design
elaborate and expensive projects such as the LCLS. As
the underlying computer hardware has grown both fasterand often more complex (i.e., massively parallel environments), FEL codes have similarly become more complex
both in terms of the underlying physical phenomena theymodel (e.g., wakefield losses) and the more realistic formsof simulation they attempt (e.g., importation of massive
macroparticle files for start-to-end tracking runs). Moreover, the amount of information the codes utilize and produce has increased by several orders of magnitude withmulti-GB output and/or particle restart files becoming necessary for full time-dependent simulations of x-ray FEL’sand multi-stage harmonic cascades.
This paper present recent changes to the GINGER simulation code[1] which originally was designed in the mid1980’s to study sideband growth in single-pass FEL amplifiers and which has steadily evolved since to study more
and more elaborate configurations such as SASE devices,
harmonic cascades and oscillators. The Fortran90 base currently underlying GINGER has proven very useful both in∗ Work performed in support of the LCLS project at SLAC under US
DOE Contract DE-AC02-76SF00515 (SLAC) and also supported underContract DE-AC02-05CH11231 (LBNL).
† WMFawley@lbl.gov

218

THE NEW FIELD SOLVER AND
IMPLEMENTATION OF HARMONICS
Adopting the slowly-varying envelope approximation(SVEA) with E(r, z, t) ≡ Ẽ(r, z, t) × exp i(ko z − ωo t),
the field equation becomes
2iks


ω
4πi
∂ Ẽ
0
= −∇2⊥ Ẽ − 2 − ko2 Ẽ − 2 ω0 J⊥
∂Z
c
c

(1)

where ∂/∂Z is the Lagrangian derivative in the forward(i.e., positive z) direction, and J ⊥ is the microbunchedtransverse current at angular frequency ω0 . The original GINGER field solver used a Gear predictor-corrector
scheme [4] which automatically controlled step size tomaximize computational speed for a given error allowance,
but had negative aspects regarding algorithmic complexity
and non-trivial coding difficulties with regards to adding
additional dimensions such as harmonics and (eventually)
non-axisymmetric modes. Consequently, we developed acompletely new field solver based upon a backward-biased,
implicit solution of the heat flow equation (“Case 5” in table 8.1 of [5]). This solution is always stable for arbitrary
step size ΔZ and the chosen default bias factor makes thescheme equivalent to the Crank and Nicholson algorithmwith errors scaling as Δr 2 and ΔZ 2 . Tests of simple vacuum Gaussian mode propagation over multiple Rayleighranges show normalized energy conservation to better than
10−3 for Δr/R0 ≤ 0.1 where R0 is the mode waist size.

The Angstrom ChallengeProceedings of FEL 2006, BESSY, Berlin, Germany

AN EXAMPLE LCLS HARMONICEMISSION CALCULATION
Nonlinear harmonic emission from the LCLS is potentially extremely useful, both for experimentalists and as adiagnostic of FEL performance. Adopting design parameters (3.4 kA, γ = 26693, 1.2 mm-mrad, Bw = 1.25 T,
σγ /γ = 10−4 ), and a quad FODO focusing lattice that
produces an average Twiss β-function of 28 m, we simulated a LCLS 9.2-fs segment at 6-attosecond temporal resolution with 32768 macroparticles per slice. The calculation was run on 128-POWER 5 (1.9 GHZ) processors of the“BASSI” IBM p575 system at NERSC and required ≈ 40

The Angstrom Challenge

1.E+11

1.E+001.E+10
1.E+09
1.E-01

Power (watts)

1.E+081.E+07
1.E+06
1.E-02

1.E+05
1.E+04
1.E+03

1.E-03

0

22

44

66

88

110

132

0

22

Z (m)

44

66

88

110

132

Z (m)

Figure 1: Time-averaged SASE power (left) and microbunching fraction (right) vs. z for an LCLS pulse at
the 0.15-nm fundamental (blue curve) and also the 3rd,
5th, and 7th harmonics (bunching only) (red, green, black
curves).
48

40

R-RMS (microns)

Sec. 8.5 of Ref. [5] gives an elegant (and simple tocode) solution method based upon a Gaussian elimination
procedure where one first sweeps outward in r and thenback to the axis Extension of the field solver to include
higher harmonics is simple with (k o , ω0 ) being replacedby (hko , hωo ) and use of the appropriate current source
term. For the latter, GINGER uses wiggler-period averaging and follows the standard formulation (see, e.g., [6])for odd harmonic emission that depends only upon the local harmonic microbunching amplitude (and ignores evenharmonic emission arising from transverse gradients inthe electron beam density). Tests by Z. Huang comparing the predicted 3rd harmonic power from nonlinear microbunching with that computed by GINGER for a simple
λ0 = 0.15 nm, steady-state amplifier with LCLS parameters show excellent agreement (e.g., 10% or better) for
sufficient macroparticle number (e.g., ≥ 65K per slice).
Use of smaller macroparticle number tends to lead to an
overestimation of the harmonic power, perhaps because thelonger Rayleigh length (and thus less radial smoothing inZ) at 0.05 nm makes the effective source term “grid noise”(i.e., in higher radial modes) much worse than that corresponding to the fundamental (for which 8K macroparticles
appear more to be than sufficient).
The original macroparticle longitudinal mover also useda Gear-scheme (which was extreme computational overkill
given the slow evolution of particle phase and energy)
and was replaced by a simple second-order Runge-Kutta
solver in which only the fundamental radiation field actsback upon the particles. Within this limitation one canstudy nonlinear harmonic generation (the dominant emission term for most SASE and harmonic cascade devices)
but not linear amplification. As shown in Ref. [7], ignoring
the harmonic emission feedback is an extremely good approximation for SASE x-ray FELs and essentially all FELs
in which gain at the fundamental wavelength is much larger
than that at the harmonics, as is the usual case.
In fall 2006 we expect to add the harmonic field feedback terms to the mover and also a fourth-order RungeKutta scheme as an option. Lastly, we note that Eq. (1) is
separable by azimuthal mode and thus the new field solver
can be easily extended (as is hopefully planned for 2007)
to solve for Ẽ(r, ϕ, z, t).

MOPPH073

32

24

16

8

0

0

22

44

66

88

110

132

Z (m)

Figure 2: RMS transverse size vs. z for SASE emission
from an LCLS pulse at the 0.15-nm fundamental wavelength (blue curve) and also the 3rd and 5th harmonics (redand green curves).

minutes of wall-clock time. Figure 1 plots the power at thefundamental wavelength of 0.15 nm and also the 3rd and5th harmonics as functions of z. One sees that the plateau
region (on this semi-log plot) for small z where spontaneous emission dominates the coherent FEL component
lasts much longer for the harmonics than the fundamental;
in reality the plateau region would extend even further because these calculation do not include non-axisymmetricspontaneous emission. While the third harmonic grows
more rapidly with z than the fundamental in the region
60 ≤ z ≤ 85 m, it saturates at a low (∼ 1%) relative power
level.
Comparing the behavior of the on-axis far-field power(not displayed) with the total near-field power (Fig. 1) reveals that the plateau region is much smaller for the fundamental but there is essentially no change for the harmonics.
This is likely related both to the short gain length for the219Proceedings of FEL 2006, BESSY, Berlin, Germany

.30

.30

.25

.25

Half Width Time (fs)Half Width Time (fs)

MOPPH073

.20

.15

.10

.05

.20

.15

.10

.05

.00

.00

0

22

44

66

88

110

132

0

22

Z (m)

44

66

88

110

132

Z (m)

Figure 3: Plots of C 1/2 (τ ) for the on-axis far field emission(left) and microbunching (right) for the fundamental andharmonics (same color scheme as Fig. 1).
4000

4.8E+06

4.0E+06

Power (Watts/bin)

Omega_o/(Delta Omega)3200

3.2E+06

2400

2.4E+061600

1.6E+06800

8.0E+0500.0E+00

0

22

44

66

Z (m)

88

110

132

.4984

.4992

.5000

.5008

.5016

.5024

Wavelength (Angstroms)

Figure 4: Plots of RMS spectral width for on-axis far fieldemission at the fundamental and harmonics (left) and the
3rd harmonic output (near-field) spectrum (smoothed witha 5-bin average) (right).
harmonics Lg,h ≈ Lg,1 /h and the smaller mode size (seeFig. 2) for the coherent harmonic emission which reducessome of the far-field contrast vis-a-vis the spontaneous harmonic emission. Near power saturation, the RMS transverse sizes of the 3rd and 5th harmonic emission are ∼20%
smaller than that of the fundamental (Fig. 2). However,after saturation, they also grow with z despite a greater
Rayleigh range, indicating perhaps that optical guiding effects are far more important for the fundamental.

Figure 5: Histogram of the probability distribution of
P (t)/ < P > at the fundamental and 3rd harmonic at theundulator exit.

220Standard SASE theory (e.g., Ref. [8]) predicts that theinverse spectral bandwidth ω/Δω and autocorrelation timeC1/2 (τ ) (the point at which the temporal autocorrelation
function drops to 0.5) for FEL radiation increase as z 1/2 .
Such behavior is demonstrated by radiation at the fundamental (blue curves in Fig. 3. For the harmonics, the coherent component of C 1/2 (τ ) suddenly dominates over the
spontaneous emission (for the radiation) and shot noise (forthe microbunching) at two-thirds of a saturation length,
reaches a maximum within a gain length, and then begins declining with z, in contrast to the fundamental whichreaches a maximum somewhat later in z (right plot in
Fig. 1) and only drops in the last 20-m or so. Presumably, debunching due to the development of a large energy
spread is responsible for the greater sensitivity of the harmonics.
An autocorrelation function and power spectrum canbe similarly calculated for microbunching by using thecomplex average computed over the macroparticles corresponding to each longitudinal electron beam slice. In contrast to the radiation quantities, the microbunching C 1/2 (τ )(right plot in Fig. 3) has a slow but steady linear decay
from its maximum which is perhaps associated with thetemporal variation of Ω syn over the individual microspikes.
Ideally, in a near time-steady situation with essentially novariation in radiation eikonal phase, C 1/2 (τ ) would be constant with harmonic. However, in the SASE regime, Saldin
et al. [7] have predicted from 1-D numerical studies that
fund.
h=3
C1/2
(τ )/C1/2(τ ) ≈ 0.65; the GINGER LCLS results
show a ratio 0.5, a reduction attributable perhaps to nonzero emittance effects not included in the 1-D study.
Figure 4 plots the inverse spectra width versus z together with the output spectrum at the third harmonic.
Another diagnostic of radiation field correlation, the ratio[ω/Δω]/[1.18ω C1/2 (τ )] (≡ 1 for a Gaussian power spectrum), is 0.76 for the fundamental and drops to to 0.69 and0.65 for the third and fifth harmonics at the position of maximum inverse bandwidth.
Another apparent difference with the Saldin et al. 1-D
results concerns the probability distribution for P (t). In
Fig. 5 we plot the normalized histogram for the fundamental and third harmonic ofthe output (near-field) radiation.
One sees that in accord with the earlier study, the third
harmonic emission is more peaked toward P = 0. However, the peak is more extreme and the first order moment ismuch smaller, evidently because of large temporal regionsof relatively low harmonic power. The probability distribution for the fundamental is also more peaked toward P = 0
whereas Ref. [7] found a peak near P =< P >. Because
our data is taken somewhat deeper in saturation than the z
point chosen by Saldin et al., it is possible (albeit unlikely)that the distribution function reverts back to a negative exponential corresponding to the exponential gain regime. orthat this particular SASE run does not have sufficient statistics in terms of slice number to clearly resolve the distribution shape. However, it may also be possible that inclusion of true transverse effects actually change the nature of

The Angstrom ChallengeProceedings of FEL 2006, BESSY, Berlin, Germany
the distribution function in the saturation regime. Consequently, this topic may warrant some additional study.

IMPLEMENTATION OF HDF5 IO
As is true for most large-scale simulation tools, an FEL
code must have numerous IO capabilities. On the input
side, the user must be able to specify a number of beamand run parameters. Depending upon the run complexity, additional input might be required, e.g., 6D macroparticle phase space information from a tracking particle output file or a “restart” file from a previous FEL code run (asmight be true for a harmonic cascade); a time-dependent input radiation field; an undulator “lattice” including a w (z),possible pole error field and dipole corrector information,and possible vacuum chamber longitudinal wake field input. Output information can be very extensive: spatiallyand temporally-resolved radiation field information including harmonics; 5D macroparticle phase space snapshots at
different z− and t− locations for later use in scatterplots;
z− and t− resolved “scalar” information such as total radiation power and macroparticle microbunching (at multiple
harmonics), energy spread, on-axis far field complex amplitude; and possible full 6D macroparticle and/or 2D (r, t)radiation field information for a subsequent downstream
undulator run. As the raw binary size of this information
can exceed 100 MB for fields and 1 GB for particles, simple ASCII formats are unattractive both due to their size(∼3X larger than pure binary) and slow IO transfer speed.
Moreover, unless one designs a very clever and robust selfdescribing data structure and/or divides the heterogeneous
output into many separate files per run, it is difficult to havean output file system that is reasonably easy to analyze (andwhich maintains good backward compatibility as the simulation code inevitably evolves in complexity).
In answer to the above requirements and problems,the HDF5[2] IO system offers a strong set of attractive
features: (1) self-describing data format, including optional dataset attributes (2) Unix-like directory trees including soft links (3) compact data storage with little additional overhead relative to binary (4) multiplatform data
file portability (e.g., little- to big-endian, 32- to 64-bit native) (5) a rich class of native data types range from simple
strings to 1-D integer arrays to many dimensional real arrays (6) user-definable data types (7) MPI-based parallel
IO on platforms such as the IBM-SP. The HDF5 development group also provides a set of useful tools for HDF5
file data visualization and data dumping of individual structures. Many projects in the high performance computing
community have embraced HDF5 as well as a number of
3rd party visualization tools venders (e.g., IDL). I note that
the GENESIS code [9] also has a growing HDF5 IO capability and would suggest that other FEL and tracking codedevelopers consider this option.
Currently, the GINGER HDF5 output file has 5 main
top directories: /base param to pass simulation run variables such as the central wavelength, number of slices, etc.;

The Angstrom Challenge

MOPPH073/grids which have the r- and z- locations of grid points; /input which has the complete ASCII input and template files
for the run; /radiation which contains all scalar and vector radiation field information; and /particles which has all
particle-derived information including scatterplot dumps,
if any. Separately, particle restart files can also be written in HDF5 format and the extension to radiation restart
files (as is needed for multistage harmonic cascades) will
be done in the near future. Knowledge of the exact “path”
of a given data set (e.g., /radiation/scalar data/...) is completely sufficient for a HDF5 utility (and GINGER postprocessor) to access the data set; the exact disk address
within the HDF5 file is not needed by external programs
but is provided by a low-level look-up table in the HDF5
file. This massively simplifies data access With the migration to HDF5 format, we believe it will be relatively
straight-forward and painless to extend the GINGER output file to handle fully “3D” field information (i.e., [r, z, t]→ [r, ϕ, z, t] ) and variable spatial resolution (e.g., relative
finely z-resolved scalar quantities such a radiation power
and microbunching but coarser resolution of vector quantities such as E(r, z, t)) as needed by future code upgrades.

ACKNOWLEDGEMENTS
I am pleased to acknowledge many useful discussions
with numerous individuals including A. Adelmann, E. Allaria, M. Borland, W. Graves, Z. Huang, H.-D. Nuhn, G.
Penn, E. Pourmal (HDF5 group/NCSA), and S. Reiche. I
also thank the LCLS project office at SLAC for financially
supporting much of the work presented here and also the
US DOE National Energy Supercomputer Center for providing Computational resources.

REFERENCES[1] W.M. Fawley, ”A User Manual for GINGER ...”,
LBNL-49625-Rev. 1 (2004);
see also http://wwwssrl.slac.stanford.edu/lcls/lcls tech notes.html/LCLS-TN04-3.pdf .
[2] National Center for Supercomputing Applications (U. Ill.),“HDF5 Home Page”, http://hdf.ncsa.uiuc.edu/HDF5/[3] Message Passing Interface Forum, “MPI: A Message-Passing
Interface standard”, Int. J. Supercomputer Applications andHigh Perf. Comp. 8 (1994); see also: http://www.mpiforum.org/docs/docs.html .
[4] C.W. Gear, Comm. ACM 14, 176 (1971).
[5] R.D. Richtmeyer and K.W, Morton, “Difference Methods for
Initial-Value Problems”, (Interscience, New York), 2nd. Ed.,1967.
[6] Z. Huang and K.-J. Kim, Phys. Rev. E 62, 7295 (2000).
[7] E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov, Proc. 27th
Int. FEL Conf. (2005, Stanford, CA), 51.
[8] K.-J. Kim, Phys. Rev. Lett. 57, 1871 (1986).
[9] S. Reiche, Nucl. Inst. Meth. Phys. Res. A 429, 243 (1999).

221

MOPPH075

Proceedings of FEL 2006, BESSY, Berlin, Germany

SIMULATIONS OF HIGH POWER -FEL AMPLIFIERS∗
J. Blau, D. Burggraff, T.Y. Voughs and W.B. Colson
Physics Department, Naval Postgraduate School
333 Dyer Road, Monterey, CA 93943.
Abstract
FEL amplifier simulations have been updated and parallelized, and system vibration effects have been added. The
simulations are used to study proposed high-power amplifier FELs at LANL and BNL. We look at the single-passgain and output power, including the effects of wiggler tapering, electron beam pinching, and shifting and tilting of
the electron beam.

INTRODUCTION
At the Naval Postgraduate School over the past several
years, we have made significant changes to our simulationsof FEL oscillators, including an improved light propagation method using expanding coordinates [1], cavity andelectron beam stability effects [2], better diagnostics suchas optical mode analysis [3], and parallelizing the codes torun on a cluster computer. These same improvements havenow been incorporated into our FEL amplifier simulations.
In this paper, we discuss the results of using these simulations to study several existing and proposed high-power
FEL amplifiers at Brookhaven and Los Alamos National
Labs. We look at the effects of tapering the undulator, as
well as shifting, tilting, and focusing of the electron beam.
We consider how each of these affect the single-pass gain,
energy extraction, and optical beam quality.

end of the undulator, the field is propagated to the first optical element using an expanding coordinate system [1] tohandle the large scale change due to diffraction.
In our simulations, we use dimensionless parameters,with longitudinal lengths normalized to the undulator
length L, transverse lengths normalized to Lλ/π, andtime normalized to L/c, where c is the speed of light.
Graphical output from the simulations shows the evolution of the optical field, bunching of the electrons in phasespace, and the structure of the optical wavefront at the endof the undulator and at the first optical element.

SIMULATION RESULTS
Brookhaven SDL FELAt the Source Development Lab (SDL) at Brookhaven
National Lab (BNL), they have an FEL amplifier basedon the NISUS undulator [4], with N = 256 periods, each
λ0 = 3.9 cm long, for a total length L = N λ0 ≈ 10 m.
The undulator parameter is Krms = 0.78. The electron
beam has an energy of 102 MeV, with a bunch length of 1
ps and a bunch charge of 0.35 nC. The optical wavelengthis λ = 0.79 μm, and the distance to the first optic is 20 m.
Figure 1 shows results from a simulation of this FEL. On
the top, a cross-section of the dimensionless optical field
amplitude |a(y)| is represented as it evolves from the be-

SIMULATION METHOD
We represent the optical field using a Cartesian coordinate system, following the amplitude and phase at each(x, y) grid point as it evolves through the undulator. The
initial field has a Gaussian transverse profile, focused at the
beginning of the undulator. The electron and optical pulse
lengths are assumed to be much longer than the slippage
distance N λ, where N is the number of undulator periodsand λ is the optical wavelength. We use a large number ofsample electrons, with an initial position and angular distribution determined by the transverse emittance, and an
initial energy spread determined by the longitudinal emittance. To study stability effects we can include an initial
shift or tilt in the electron beam, and we can also adjust thebeam focus position along the undulator.
At each time step within the undulator, the electrons
evolve according to the Lorentz force equation, including betatron focusing. The optical field evolves selfconsistently according to Maxwell’s wave equation. At the∗ Work supported by JTO, ONR, and NAVSEA.

222

Figure 1: Simulation results for the SDL FEL with no taper.
On the top is the evolution of the amplitude profile |a(y)|,as described in the text. On the bottom is the evolution of
the dimensionless optical power P (τ ) from the beginning(τ = 0) to the end (τ = 1) of the undulator. The maximum
value of the power is indicated in arbitrary units.

Seeded FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 2: Simulation results for the SDL FEL with a -5%
taper rate over the last 2.4 m of the undulator. On the top
is the evolution of the optical power, P (τ ). On the lower
left is the final electron phase space as described in the text,
with sample electrons shown in red. On the lower right isthe final optical wavefront, |a(x, y)|, at the output mirror.

Seeded FELs

Another factor of two improvement in extraction could
be achieved by starting the taper earlier at τs = 0.5, near
the onset of saturation for the untapered FEL. Figure 3
shows the results of many simulations, plotting extraction
η versus phase acceleration δ for this latter case. The phaseacceleration [5] is related to the undulator taper rate byδ = −4πNK 2 (ΔK/K).
1 + K 2 1 − τs

(1)

3
2.5
2
η (%)

ginning (dimensionless time τ = 0) to the end (τ = 1)of the undulator. The narrow yellow contour line marks the
1/e value of the field amplitude at each time step, while thebold yellow curves on the left and right plot the field profileat τ = 0 and τ = 1. A few sample electrons are shown inred. The simulation predicts high gain, G ≈ 1000, whichleads to optical mode distortion and guiding [5]. Without
the gain medium, the field would maintain a Gaussian profile and diffract out to a large radius, as shown in purple
on the right; the actual field profile shown in bold yellow
is much narrower and distorted. The simulation predicts an
extraction of η = 0.6% (extraction is defined as the ratio of
the output optical power to the input electron beam power).
In the actual experiment, an extraction of about 0.4% was
measured. The difference is likely due to pulse slippage
effects, which are not included in the simulation.
The lower half of Fig. 1 shows the power saturating
about halfway down the undulator, so we consider tapering the magnetic field to enhance the extraction. Figure 2 shows the simulation results with a linear taper rate
ΔK/K ≈ −5% over the last 2.4 m of the undulator.
Now the power continues growing, and the extraction isincreased to η = 1.2%. The final electron phase space on
the lower left shows about half of the electrons trapped inclosed orbits [5]. The electron phase ζ roughly corresponds
to the position of an electron within an optical wavelength,
while ν = dζ/dτ is the phase velocity. The induced spreadin phase velocities Δν translates to an electron beam energy spread ΔE/E = Δν/4πN = 3.7%, compared to2.5% for the untapered case. The final optical wavefront|a(x, y)| at the output mirror is shown in the lower right.

MOPPH075

1.5
1
0.5
0
0

50

100
δ/π

150

200

Figure 3: Extraction η versus phase acceleration δ for the
SDL FEL, with a linear taper over the last 5 m of the undulator. The maximum extraction η = 2.3% is achieved forδ = 60π, which corresponds to ΔK/K ≈ −7%.
Figure 4 shows the results of simulating the SDL FEL
with a taper rate of -7% over the last 5 m of the undulator, corresponding to the peak extraction value of 2.3%
in Fig. 3. The optical power P (τ ) grows significantly inthe second half of the undulator, and the phase space plotshows good bunching. The induced energy spread is 5%.

Figure 4: Simulation results for the SDL FEL, with a -7%
taper rate over the last 5 m of the undulator.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Brookhaven proposed FEL

1
0.8
η (%)

Another high-power amplifier FEL has been proposed
at BNL [6]. This system would use an 80 MeV electron
beam with a bunch length of 2.8 ps and a bunch charge of
1.4 nC. The undulator would have N = 120 periods, each
λ0 = 3.25 cm long, for a total length L = 390 cm, withKrms = 0.7. The optical wavelength would be λ = 1 μm,
with the first optic at a distance of 27 m.
Figure 5 shows simulation results for this FEL. Again we
see guiding of the optical field (top), and the power is nearsaturation at the end of the undulator (center). The simulation predicts gain G ≈ 800 and corresponding extractionη ≈ 1%; the design goal for this system is η = 0.25%.
In the lower left, the electron phase space shows bunching, and an induced electron beam energy spread of 3.5%.
In the lower right, the final optical wavefront has a nearly
top-hat shape.

0.6
0.4
Extraction goal
0.2
rb
0
0

0.5

1
yo (mm)1.5

2

Figure 6: Extraction η vs. electron beam shift y0 for the
proposed BNL FEL. The extraction goal is exceeded for all
values of y0 < 1.2 mm, well beyond a typical experimental
tolerance of ≈ 50 μm, and much greater than the electron
beam radius rb = 0.25 mm.

Figure 7: Optical field evolution for the proposed BNL
FEL. Initial conditions are chosen so that the electron beam(shown in red) is shifted off-axis by y0 = 1 mm at the center of the undulator. Betatron focusing bends the beam backtowards the axis at the ends of the undulator. The horizontal and vertical axis scales are quite different, as indicated.
Notice how guiding enables the optical mode (narrow contour line) to follow the electron beam as it shifts off axis.

Figure 5: Simulation results for the proposed BNL FEL.
We also studied electron beam stability effects for thissystem. Figure 6 shows the results of many simulations,with the electron beam shifted off-axis in the plane of theundulator magnetic field. The extraction drops as the beam
is shifted, but the design goal of η = 0.25% is still achievedfor y0 < 1.2 mm, about 5 times the electron beam radius(rb = 0.25 mm, indicated on the graph). Figure 7 shows
how guiding enables the optical mode to follow the shifted
electron beam over about half of a betatron oscillation, fora beam shift of y0 = 1 mm.
Figure 8 shows the effect of tilting the electron beam
about the center of the undulator. The simulations predictthat the system can tolerate a beam tilt of θy ≈ 0.9 mrad,
well beyond the beam angular spread of Δθ = 0.1 mrad.

224

Again, this is due to the guiding effect, as shown in Fig. 9.
Our simulations predict good extraction for electron beam
shifts x20 and tilts x100 greater than the experimental tolerance of existing FELs [7].

Los Alamos proposed FEL
At Los Alamos National Lab (LANL), they have proposed a somewhat different design for a high-power FEL
amplifier [8]. This system would use an 81 MeV electron
beam with a bunch length of 1 ps and a bunch charge of
1 nC. The undulator would have N = 110 periods, each
λ0 = 2.18 cm long, for a total length of L = 240 cm,
with Krms = 1.2. The optical wavelength would be
λ = 1.05 μm, with the first optic at a distance of 24 m.
Our simulations of this design predict that it would
achieve a gain of G ≈ 240, corresponding to extractionof η = 0.74%, with induced energy spread of about 5%.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

MOPPH075

the undulator exit, thus allowing it to rapidly diffract afterwards, which should reduce the intensity at the first optic.

1
0.8
η (%)

2
0.6
1.5
0.4
η (%)

Extraction goal
0.2
Δθ
0
0

0.5

θy (mrad)1

1.5

Figure 8: Extraction η vs. electron beam tilt θy for the
proposed BNL FEL. The extraction goal is obtained for all
values of θy < 0.9 mrad, well beyond a typical experimental tolerance of 10 μrad, and much greater than the electron
beam angular spread, Δθ = 0.1 mrad.

1
0.5
0
0

0.2

0.4

τ

0.6

0.8

1

β

Figure 10: Extraction η vs. electron beam focus position
τβ for the proposed LANL FEL. The inset plots show theevolution of the electron beam and the optical mode at τβ =0.4 (top) and τβ = 0.75 (bottom).

REFERENCES[1] R.L. Armstead, J. Blau, and W.B. Colson, ”Short Rayleighlength free electron laser simulations in expanding coordinates”, Proceedings of the 26th International Free Electron
Laser Conference (2004), p. 274. http://www.JACoW.org.

Figure 9: Optical field evolution for the proposed BNL
FEL. Initial conditions are chosen so that the electron beamis tilted by θy = 0.9 mrad at the center of the undulator.
The tilt appears exaggerated due to the different horizontal
and vertical scales. Notice that the optical mode (narrow
yellow contour line) follows the tilted electron beam (red).
However, the design goal for this system is η = 1.2%. We
find that by tapering the undulator, ΔK/K ≈ −18% overthe last 40 undulator periods, they could increase the gain
to G ≈ 500 and the extraction to η = 1.7%, while only
inducing an energy spread of about 6%.
We studied stability effects for the LANL amplifier design; our simulations predict that it will still achieve thedesired extraction with beam shifts up to 0.4 mm, or beamtilts up to 0.4 mrad. These results are again well beyond
the experimental tolerance of existing FELs.
We also tried varying the electron beam focus for thisFEL. Figure 10 is a plot of the extraction versus the beamfocus position, τβ . The peak extraction η ≈ 1.9% is atτβ = 0.15 or 0.75, rather than at τβ = 0.5 as one might
expect. This is due to the betatron motion of the electrons,
in both cases focusing the beam near the end of the undulator, where the tapering enhances the extraction. This
”scalloped” shape of the electron beam, as seen in the inset
plots in Fig. 10, leads to focusing of the optical wavefront at

Seeded FELs

[2] P.P. Crooker, J. Blau, and W.B. Colson, ”Stability of ashort-Rayleigh length laser resonator”, Phys. Rev. ST-AB, 8,040703 (2005).
[3] R. Vigil, ”Hermite-Gaussian modes and mirror distortionsin the free electron laser”, M.S. Thesis, Naval Postgraduate
School, June 2006.
[4] T. Watanabe, et. al., ”An experimental test of superradiancein a single pass seeded FEL”, Proceedings of the 27th International Free Electron Laser Conference (2005), p. 526,
http://www.JACoW.org.
[5] W.B. Colson, C. Pellegrini, A. Renieri (Eds.), Free Electron
Laser Handbook, North-Holland Physics, Elsevier Science
Publishing Co. Inc., The Netherlands, 1990 (Chapter 5).
[6] I. Ben-Zvi, D. Kayran and V. Litvinenko, ”High average
power optical FEL amplifiers”, Proceedings of the 27th International Free Electron Laser Conference (2005), p. 232,
http://www.JACoW.org.
[7] S. Benson, priv. comm.
[8] D. C. Nguyen, W. B. Colson and H. Freund, ”Scalloped electron beam FEL”, Proceedings of the 28th International Free Electron Laser Conference (2006), p. xxx,
http://www.JACoW.org.

225

MOCAU01

Proceedings of FEL 2006, BESSY, Berlin, Germany

THE BESSY SOFT X-RAY FEL: A SEEDED HGHG FEL ∗A. Meseck† for the BESSY FEL team
BESSY GmbH, Albert-Einstein-Str.15, Berlin, Germany.
Abstract
Reproducibility, high power and short pulse length combined with variable polarization and tunable wavelength
are required to open new frontiers for the soft X-ray users.
To provide radiation with such extraordinary properties,
BESSY has been designing a seeded FEL based on thehigh-gain harmonic-generation (HGHG) concept [1]. The
seeding with an external tunable laser ensures the reproducibility of the full-coherent radiation. The combinationof so-called HGHG stages, used to down-convert the seedwavelength, and a final amplifier provides for the highpower and superior spectral properties. Furthermore, the
HGHG concept and the fresh bunch technique planned for
the BESSY FEL mitigate the effects of parameter variation
along the bunch which are expected from realistic assumptions of the Gun and LINAC structure. The design conceptof the BESSY soft X-ray FEL will be presented and thestabilizing effect of HGHG stages and the benefits fromthe fresh bunch technique and the final amplifier will be
discussed.

INTRODUCTION
The BESSY Soft X-Ray FEL is designed as a multi-user
facility consisting of three independent FEL lines based on
HGHG-concept. Each line is seeded by a tunable laser covering the spectral range of 230 nm to 460 nm. The target
wavelength ranges from 51 nm to 1.24 nm with peak powers up to a few GWs and pulse lengths less than 20 fs (rms).
The polarization of the fully coherent radiation will be variable.
In the HGHG-FEL approach the light output is derived
from a coherent subharmonic seed field. Consequently
the optical properties of the HGHG-FEL output reflect thecharacteristics of the high-quality seed. The benefit is apulse with selectable short duration, a high degree of stability and control of the central wavelength and bandwidth.
Cascades of two to four HGHG stages are planned to reduce the existing laser wavelength to the target range of
the BESSY-FEL. The planned “fresh bunch” technique [2]prevents the final output from the electron beam heating effect of FEL interaction in the upstream stages, ensuring thehigh output power and the spectral quality.
The optimization of an HGHG-line includes the properchoice of the seeding radiation, the electron beam parameters, the harmonic cascade, the undulator parameters andthe strength of the dispersive section. In the following∗ Work funded by the Bundesministerium für Bildung und Forschungand the Land Berlin† meseck@bessy.de

226

the steps taken during the optimization process will be described.
All calculations have been performed with the timedependent 3D simulation code GENESIS [3].

THE HIGH-GAIN-HARMONICGENERATION
Several HGHG stages are necessary to reduce the seedlaser wavelengths availabel today to the desired spectral
range. Each stage consists of an undulator - dispersion - undulator structure. In the first undulator, the so called modulator, the interaction with a radiation field (e.g. provided by
an external laser) leads to an energy modulation of the electron beam with the period of the seeding wavelength. The
following dispersive section converts this energy modulation into a spatial modulation, or bunching, that includes
bunching on higher harmonics of the seeding frequency.
The fundamental of the second undulator, the so called radiator, is set in resonance with the chosen harmonic. The
prebunched beam then radiates at the harmonic wavelengthwith high efficiency. The radiator output is used as the seed
for the next stage. The last radiator is followed by the socalled final amplifier. It is seeded at the desired wavelengthand the amplification process is brought to saturation.
In a cascaded HGHG scheme the necessary seeding
power for each stage is produced by adjusting the output
power of the previous stage. The output power of the radiator is proportional to the square of the bunching factor,
bn , of the entering electron beam [4]:pout ∼ b2n .
The bunching factor for the n th harmonic of the seed laser
is given by:
bn = exp (i n θj )2 2  dθ−1 2 2 dθn σγ
Jn nΔγ
= exp
2
dγ
dγ

= exp

−1 2
σ
2 γ



dψ
dγ

2 



dψ
,
Jn Δγ
dγ

where θ is the ponderomotive phase of the electron beamin the modulator, ψ = nθ is the phase in the radiator, Δγ isthe maximum energy modulation generated in the moduladθis thetor, σγ is the energy spread of the electron beam, dγ
thstrength of the dispersive section and J n is the n order
Bessel function.

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Proceedings of FEL 2006, BESSY, Berlin, Germany
Large bunching factors can be achieved when the energy modulation impressed by the seed dominates the energy spread of the electron beam. Hence, for a reasonable
performance of an HGHG stage the energy modulation induced by the seed should fulfill the following inequality[4]:(1)
Δγ ≥ nσγ .
When the radiation size at the entrance of the modulator
and the transverse size of the electron beam are matched,
the energy modulation of the electron beam scales withthe seed power, p seed , seed wavelength, λ s , the modulator
length, Lmod , the electron beam energy, γ, and the undulator parameter, K, as [4]:

Δγ ∼

K
Lmod
γ



pseed
.
λs

(2)

The modulator length should not exceed twice its power
gain length in order to avoid an increase in energy spread
due to the spontaneous radiation. For given electron beamenergy and seed wavelength, and a fixed modulator length,
the energy modulation, Δγ, can be controlled by the undulator parameter, or the seeding power, p seed , both of whichhave their technical limits. The dispersive section has to be
adjusted according to the energy modulation, reached in themodulator, taking the effective dispersion in the modulator
and radiator into account. The total dispersive strength isgiven by [4, 5]: dψn 2πLmod4 πLrad
dψ
≈−
+
, (3)
−
dγ
λum γ
dγ dis.sec.
λur γ
where λum and λur are the modulator and radiator period
length, and L rad is the length of the radiator.
Due to the interaction of the electron beam with the seed,
the effective energy spread of the electron beam entering
the radiator is given by

(Δγ)2
.
(4)
σγef f = σγ2 +2An increased energy spread causes an enhanced gain lengthand therefore extends the necessary length of the radiator. The “fresh bunch” technique is employed to limit thegrowth of energy spread from stage to stage in a cascaded
HGHG FEL. In this approach the seeding pulse is significantly shorter than the electron bunch. As a result the harmonic generation process, and with it the enlargement of
the energy spread applies only to a fraction of the bunch.
After passing the first HGHG-stage the resulting radiationis shifted to a “fresh” part of the bunch which was not affected by the seed. A theoretical treatment of the HGHGscheme can be found in [4, 5].

SEEDING RADIATION AND ELECTRONBEAM PROPERTIES
Contrary to a continuous seed pulse as used for the DUVFEL [6, 7], in the case of a Gaussian-shaped pulse theSeeded FELs

MOCAU01

electrons do not experience the seed peak power during
the whole transition through the modulator. Since the integrated power experienced by electrons should be in thesame order of magnitude to induce the same amount ofbunching, the Gaussian-shaped seed pulse needs a higher
peak power. For example, the 30 M W continuous powerwith a wavelength of 800 nm used for the DUV-FEL where
the modulator has 10 periods, corresponds, according toequation 2, to a seed power of 90 M W for a seed wavelength of 266 nm, and the same number of modulator periods. A Gaussian-shaped seed with 266 nm wavelengthand 15 f s rms pulse duration would require a peak powerof 1.3 GW in a 10 periods modulator to induce the same
bunching. Since the modulator can be chosen longer forthe 266 nm seed radiation, using a proper modulator of
18 periods a peak power of 400 M W is sufficient. Note,
to suppress the noise degradation effects [8] a higher peak
power should be preferred.
The wavelength of the seed radiation within the range
provided by the laser is deduced from the desired final
wavelength and the harmonic cascade. Out of the several
combinations of harmonics that can be used to provide thedesired wavelength range in each particular HGHG-line,
the one requiring the minimal number of stages is chosen.
The accessible harmonic content in the bunching dropps off
with rising harmonic numbers and photon energies, limiting the usable harmonics to the first five. The fifth harmonic is used in the early stages, where, due to the longwavelength, enough power and thus bunching can be obtained with acceptably short radiator lengths. Later stages
use the third harmonics. The harmonic combination canchange when the gaps are moved and the resonant wavelengths vary.
The planned tunable seed laser covers the spectral rangeof 230 nm to 460 nm with a Gaussian profile, a peak powerof 500 M W and a pulse length of about 15 f s (rms), formore details see [1].
The energy of the electron beam has to fulfill the resonance condition, equation 5, for the whole HGHG-line withthe minimum possible gain length. The nominal values ofthe electron beam parameters, extracted from start-to-end
simulations, are listed in Table 1. The electron beam at theentrance of the HGHG-lines has a normalized transverse
emittance of 1.5 mm mrad, a relative energy spread lessthen 0.02%, and an average current of about 2 kA at the“flat top”. The duration of the flat top amounts to 730 f s.
For the presented calculation an electron bunch with transverse Gaussian distributions is assumed.

OPTIMIZATION OF UNDULATORPARAMETERS
The resulting resonant wavelength of the FEL, λ, depends on the undulator period length, λ U , the K-value andthe electron beam energy γ in units of the electron’s rest

227

MOCAU01

Parametern [mm mrad]
Ipeak [kA]
E [GeV]Δ E/E [%]
Δt [fs]Proceedings of FEL 2006, BESSY, Berlin, Germany

Highenergy
1.5
1.75
1.63-2.3
0.01-0.014
730Mediumenergy
1.5
1.75
2.3
0.01
730

Lowenergy
1.5
1.75
1.02
0.02
730

Table 1: The nominal electron beam parameters at the entrance of the first modulator used in the simulation studies.

2nd Stage
Mod.

Rad

3rd Stage

Rad

Mod.

Rad

Final Amplifier

2.3 GeV
Ephoton= 100eV - 600eV
L
i
n
a
c

1st StageLinac

2nd Stage

3rd Stage

4th Stage

Laser

Linac

Mod.

Rad

Mod.

Rad

Mod.

Rad

Mod.

Rad

Final Amplifier

1.625 GeV - 2.3 GeV
Ephoton= 500eV - 1000eV
Magnetic delayer

Dispersive section
1st Stage

2nd Stage

Ephoton= 24eV -120 eV

Mod.

Final Amplifier

Laser

1.02 GeV

Mod.

Rad

Rad

Figure 3: The BESSY HGHG multi user FEL-facility willconsist of three HGHG-lines to cover the target wavelength
range.
mass:
λ=Figure 1: Saturation length and power as functions of
the K-value for the final amplifier of the medium-energy
HGHG-FEL. The FEL performace deteriorates with decreasing K-value.

1st Stage
Mod.

Laser

Linac

1
λU (1 + K 2 ).
2 γ2

(5)

The maximum achievable K-value is limited by the permanent magnet undulator technology. The minimal gap is set
to 10.4 mm according to impedance considerations.
The minimum acceptable K-value is set to 0.8 as the interaction between the radiation field and the electron beam
suffers from too small K-values. Figure 1 shows the saturation length and power as functions of the K-value forthe final amplifier of the medium-energy HGHG-FEL. The
deterioration of the FEL performance with decreasing Kparameter is obvious.
The undulator period length is chosen such, that the desired wavelength range can be completely covered within
the given range of K-parameter. Figure 2 shows the tune
range for the medium-energy HGHG-FEL as an example.
With an undulator period of 5 cm the desired wavelength
range can be covered. Once the period length, λ U , is fixed,
the resonant wavelength can be altered by adjusting the gapof the undulator.

LAYOUT OF THE HGHG UNDULATORSECTION

Figure 2: The undulator period as function of K-value forthe final amplifier of the medium-energy HGHG-FEL. The
tune range is limited by the minimum acceptable and maximum achievable K-value. With an undulator period of 5 cm
the desired wavelength range can be covered by gap variation.

228

The BESSY HGHG multi user FEL-facility will consist of three undulator-lines to cover the target photon energy range from 24 eV to 1 keV (51 nm ≥ λ ≥ 1.2 nm).
The “low-energy” HGHG-FEL operates in two stages at abeam energy of 1.02 GeV delivering photons in a spectral
range of 24 eV to 120 eV . An energy of 2.30 GeV is chosen for the “medium-energy” HGHG-FEL. A cascade ofthree stages covers the energy range of 100 eV to 600 eV .
The “high-energy” HGHG-FEL operates at variable electron beam energies of 1.625 GeV to 2.30 GeV . It delivers in four stages photon energy ranges from to 500 eV to1000 eV . Figure 3 shows a schematic view of the BESSY
HGHG multi user FEL-facility. A description of the electron source, linac and compressor scheme providing electron beams with the required properties can be found in [1].
Each of the three HGHG-lines consist of several stages
and a final amplifier. In order to optimize an HGHG-stage

Seeded FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

Stage
1
2
3
4
Final

Stage
1
2
3
Final

Stage
1
2
Final

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Table 2: High Energy HGHG-FEL
MODULATORRADIATOR
λU
P
L
λU
P
L
[mm] #
[m]
[mm]
#
[m]
122
18 2.196
92
40
3.680
92
22 2.024
70
86
6.020
70
30 2.10050
180 9.000
50
69 3.450 28.5 225 6.413
28.5 630 17.955

Table 3: Medium Energy HGHG-FEL
MODULATORRADIATOR
λU
P
L
λU
P
L
[mm] #
[m]
[mm]
#
[m]
122
18 2.196
92
40
3.680
92
22 2.02470
104 7.280
70
30 2.10050
231 11.550
50.
393 19.650

Table 4: Low Energy HGHG-FEL
MODULATORRADIATOR
λU
P
L
λU
P
L
[mm] #
[m]
[mm]
#
[m]
80
20 1.600
62
56 3.472
62
26 1.612
50
69 3.45050
162 8.100

the lengths of the modulator und radiator as well as thestrength of the dispersion section has to be adjusted. The
modulator has to be long enough to imprint the necessary energy modulation according to the equation 1. The
strength of the dispersion has to be adjusted according to
the energy modulation with respect to the total dispersion
given in equation 3. The radiator length has to be chosen
suitable to deliver the required power for the next stage.
Note, that the effective energy spread generated in the modulator determines the efficient of the radiator according toequation 4. The main parameter of the modulators and radiators for each HGHG-line are listed in tables 2, 3 and 4.
Listed are undulator period length, λ u , number of periods,
P , and undulator length, L.
Magnetic delayers shift the electron bunch with respect
to the radiation field between the HGHG stages and ensurethat the radiation field interacts always with a undistrubed
part of the bunch in the modulator. Quadrupoles and phaseshifters are planned between the stages as well as between
the undulator segments of the radiators and the final amplifier to focus and match the electron beam.

Seeded FELs

Figure 4: Bunching on the fifth harmonic after the first dispersion section for the high energy HGHG

POWER AND SPECTRUM
OPTIMIZATION
For the optimization of the HGHG-FEL performance,
the adjustment of the bunching, by setting the modulator
length and the dispersion strength, is of major importance.
The laser seed interacts with electrons at the rear of thebunch. Due to the slippage effect only a part of the interacting electrons experience the full power of the Gaussian
shaped seed. Optimizing the modulator length and dispersive section to a somewhat reduced power level the outputof the following radiator can be maximised. In this casethe electrons at the center, which experience the full power
sufficiently long are somewhat overbunched.
Figure 4 shows the bunching after the first dispersion
section for the high energy HGHG. The overbunchingcauses a power dip in the radiation pulse provided by the
first radiator, as shown in figure 5a. Figure 5b shows thecorresponding radiation spectrum. The overbunched electrons fulfill synchrotron oscillations in the ponderomotive
bucket. The resulting modulation of the emitted radiation
frequency causes the side spikes (sidebands) [9].
The more electrons are overbunched the stronger is thegrowth of the sidebands. This effect is repeated in the following stages, where the slippage shifts the sidebands toone side. In this way the number of sidebands in the spectrum adds up from stage to stage. The higher the harmonic
numbers in the cascade the stronger are the sidebands. For
example in the case of the medium-energy HGHG-FEL
the sidebands for λ s = 2.07 nm with harmonic numbers
5×5×5, figure 7, are much stronger than for λ s = 12.4 nm
with harmonic numbers 3 × 3 × 3, see figure 6.
The side spikes can be avoided by optimizing the stages
for the seed peak power. In this case the output of the following radiator is reduced. The bunching is of more Gaussian shape. The resulting radiation power and pulse length
are reduced compared to the overbunched case. An example of such a spectrum purity optimized case is shown in229

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 5: Simulation results for the first radiator of thehigh-energy HGHG-FEL a)the time resolved power distribution (top) and b) the spectral power distribution (bottom).

Figure 6: Simulation results for the medium-energy
HGHG-FEL, λs = 12.4 nm the time resolved power distribution (top) and the spectral power distribution (bottom)
are calculated.

figure 8, where the power and spectral distribution of a purity optimized and a power optimized case are displayed in
the same graph for comparison.
The details of the cascades for the boundary wavelengthsof each HGHG-line are summarised in [1].

PERFORMANCE CALCULATIONS
For the performance calculations the seeding radiation
properties and electron beam parameters are chosen according to the considerations of the previous sections.
In order to obtain reliable results, the slippage effects
in the undulators and the radiation diffraction in the fresh
bunch sections have to be taken into account. The first effect lengthens the pulse, whereas the second one reduces
the power density on axis which is relevant for the energy modulation in the following modulator. The timedependent mode of GENESIS [3] used for the simulation
allows an adequate treatment of this effects.
In spite of the short lengths of the modulators and radiators, see Tables 2-4, the degradation of the unseededpart of the bunch due to the emission of incoherent radiation can not be neglected. The resulting increase of theenergy spread and decrease in the central energy from stage
to stage are shown in figure 9 for the high-energy case.
The relative increase of the energy spread at the entranceof the second modulator is only 0.2%, but it increases to230

Figure 7: Simulation results for the medium-energy
HGHG-FEL, λs = 2.07 nm the time resolved power distribution (top) and the spectral power distribution (bottom)
are calculated.

Seeded FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

MOCAU01

Figure 9: Degradation of the unseeded part of the bunch
for the high-energy HGHG-FEL, the relative changes inenergy spread (top) and the central energy (bottom) at theentrace of modulators, M1 to M4, are shown.
Figure 8: Simulation results for the low-energy HGHGFEL, the power and spectral distributions of a purityoptimized case and a power-optimized case.
Table 5: The performance of the three HGHG-line for theboundary wavelengths
λ[nm]
P ower[GW ]LE-FEL
10.33 51.00

ME-FEL
12.40 2.07

HE-FEL2.48 1.24

3.5

9.0

1.3

14.0

1.5

1.5

4% at the fourth modulator. The loss in the central energy at the entrance of the fourth modulator is about 0.45%
which is larger than the bandwidth of about 0.2% of the
fourth radiator and the final amplifier. This means that thefollowing radiator and amplifier have to be readjusted tomeet the resonance condition for the lower central energy.
This loss of the electron beam quality causes a reduction in the maximum bunching and a deterioration of thespectral properties of the radiation. Tracking the electrons
through all the previous undulators, this effect has beentaken into account. The performance of the three HGHGlines for the boundary wavelengths are summarised in the

Seeded FELs

Table 5.

S2E BUNCHS AND SELF-STABILIZINGStart-to-end simulations for the BESSY FEL show variation of the electron beam parameter along the bunch[10]. The possibility to adjust the undulator gaps and thestrengths of the dispersive sections independently, mitigates the effects of the parameter variations [11]. Eachstage can be optimized according to the particular parameters of the interacting part.
Furthermore, the concept of the final amplifier allows to
use the asymmetry of the detuning curve to reduce the output degradation due to the combination of the energy chirp
and the arrival-time jitter of the bunch [12]. The energy
chirp, induced for the bunch compression, combined withthe arrival-time jitter, due to gun and LINAC errors, causes
a mismatch between the central energy of the interacting
part of the bunch and the resonance energy. This leads toa fluctuation of the FEL output power. Adjusting the final amplifier to a somewhat reduced K-value, stabilizes theoutput power, as the average energy of the interacting electrons is somewhat higher then the resonance energy.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

CONCLUSIONBESSY has been designing a seeded FEL based on acascaded high-gain harmonic-generation concept. Simulations with start-to-end bunchs including all relavant effects
show that the BESSY FEL meets the user requirementswith respect to pulse duration, tunability, spectral purity
and power. Furthermore, simulation studies including errors in the gun and LINAC attest to the advantages of the
HGHG concept planned for the BESSY FEL.

REFERENCES[1] The BESSY Soft X-ray Free Electron Laser, Technical Design Report March 2004, eds.: D.Krämer, E. Jaeschke, W.
Eberhardt, ISBN 3-9809534-08, BESSY, Berlin (2004).
[2] L. Yu, ”High-gain harmonic generation of soft X-ray with the“fresh bunch” technique”, NIM A 393 (1997) 96.
[3] S. Reiche, GENESIS 1.3, NIM A 429(1999) 243.
[4] L. Yu, ”Theory of high gain harmonic generation: an analytical estimate”, NIM A 483 (2002) 493.
[5] J. Wu, ”Coherent X-ray production by cascading stages ofa high-gain harmonic generation free electron laser”, Thesis, May 2002.
[6] L.H. Yu, L. DiMauro, A.Doyuran,W. Graves, R. Heese, E.D.
Johnson, S. Krinsky, H. Loos, J.B. Murphy, G. Rakowsky, J.
Rose, T. Shaftan, B. Sheehy, Y. Shen, J. Skaritka, X.J. Wang,
Z. Wang, ”First Ultraviolet High-Gain Harmonic-Generation
Free-Electron Laser”, Phys. Rev. Lett. 91, 074801 (2003).
[7] A.Doyuran, L. DiMauro, W. Graves, R. Heese, E.D. Johnson,
S. Krinsky, H. Loos, J.B. Murphy, G.Rakowsky, J. Rose, T.
Shaftan, B. Sheehy, Y. Shen, J. Skaritka, X.J. Wang, Z. Wang,
L.H. Yu, ”Saturation of the NSLS DUV-FEL at BNL”, PAC
2003, Proceedings.
[8] E.L. Saldin et al.,”Study of a noise degradiation of amplification process in a mulistage HGHG FEL”, Opt. Commun. 202.
(2002) 169.
[9] E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov, The physics offree electron lasers, Springer-Verlag Berlin Heidelberg.
[10] M. Abo-Bakr et al., ”Start to end simulations the for BESSY
FEL", Proceeding of the FEL 2003 Conference, Japan, published in NIM-A, 258 (2004), 476.
[11] B. Kuske, M. Abo-Bakr, A. Meseck, ”Impact of Realistic
Bunch Profiles and Timing Jitter on the Output of the BESSY
Low Energy FEL Line”, Proceedings of the FEL 2005, Stanford, USA.
[12] B. Kuske, M. Abo-Bakr, A. Meseck, ”Start-to-End Simulations for the BESSY Low and Medium Energy FEL Line
Including Errors”, proceedings of the FEL 2005, Stanford,
USA.

232

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Proceedings of FEL 2006, BESSY, Berlin, Germany

MOCAU02

THE CHALLENGES OF SEEDED FELS
G. De Ninno, ELETTRA, Basovizza, Trieste

Abstract
Basic users’ expectations for the light produced by next
generation FELs are:• much higher peak brilliance than conventional synchrotron radiation and complete tunability in the VUV/Xray spectral range;• full transverse and longitudinal coherence of the radiation pulse;• possibility of controlling pulse duration and spectral
bandwidth;• high shot-to-shot reproducibility, i.e. low power fluctuations, good pointing stability and reduced temporal jitter.
Seeded schemes appear nowadays as a way to satisfy all
the above mentioned requirements. However, this achievement relies on the solution of several open technologicaland physical issues. In this paper we give a review of someof these challenges and discuss the expected performanceof future seed-based FELs.

PAPER NOTAVAILABLE

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THE USE OF HHG AT 4GLS
B.W.J. Mc Neil, SUPA, Department of Physics, University of Strathclyde, Glasgow, UK
D. Dunning and N.R. Thompson, ASTeC, CCLRC Daresbury Laboratory, UK
B. Sheehy, Sheehy Scientific Consulting, New York, USA.
Abstract
4GLS is a facility proposed for the Daresbury Laboratory in the UK which will offer users a suite of high brightness synchronised sources from THz frequencies into the
XUV [1]. In the current design, photon energies from 8100eV will be generated in a variable polarisation FEL
amplifier directly seeded by a High Harmonic Gain system. The reasoning behind this choice will be discussed
and characterisation of the sources based on the present design presented.

INTRODUCTION
The Conceptual Design Report for the 4GLS project
to be based at UK’s Daresbury Laboratory has been published [1]. A suite of synchronised coherent variably polarised radiation sources covering the spectrum from THz
frequencies to photons energies of ∼ 100 eV will provide
the scientific community with a tool that will enable new
windows of scientific exploration to be opened and thereafter exploited. Initially, the major themes of the 4GLS
science programme will lie in time-resolved measurements
and nanoscience. Details of the science case driving theneed for 4GLS were first published in [2] and more recently
updated in [1].
A major component of 4GLS will be the XUV-FEL. The
current design for this component is for a seeded FEL amplifier that operates in the 8-100 eV photon energy range
to provide peak powers between approximately 1-10 GW
allowing very high field intensities of up to 1017 W/cm2 tobe achieved. In order to tune over the spectral range boththe electron beam energy and the undulator magnetic field
are variable. Because the FEL acts as an amplifier the seed
sources also need to be continuously tunable.
There are several potential benefits in operating an FEL
as an amplifier of an injected seed as opposed to allowing
the FEL to self-seed from inherent noise to generate Self
Amplified Spontaneous Emission. An important benefit is
the potential improvement in the temporal coherence of the
FEL output over that of SASE. This increases the spectral brightness. Shot-to-shot reproducability and stability
are also improved. The amplified pulse width, being determined by that of the seed, may be significantly shorter thanthat of the electron pulse, and indeed there is the potential
to amplify more exotic pulses for post-amplification manipulation. Finally, the length of FEL interaction required
to achieve saturation may be shortened, thereby reducing
space requirements and ultimately costs. All of these bene-

234

fits require that the seed power be significantly greater than
the spontaneous power due to the inherent noise.

XUV-FEL OVERVIEW
The design of the 4GLS XUV-FEL has undergone several iterations [3]..[6]. The XUV-FEL branch of the 4GLS
conceptual design is shown in schematic form in Fig. 1.
Typical operating parameters and specification for the conceptual design are given in Table 1.
Table 1: XUV-FEL conceptual design parameters
General
FEL design
High Gain Amplifier
Seeding mechanism
HHG source
Photon output
Tuning Range∼ 8 - 100 eVPeak Power
∼ 8 - 2 GW
Repetition rate
∼ 1 kHz
Polarisation
Variable elliptical
Min Pulse length FWHM
< 50 fs
Typical Δf Δt∼ 0.6
Max pulse energy
400 μJ
Electron beam parameters
Energy750 - 950 MeV
Bunch Charge
1 nC
RMS bunch length
266 fsNormalised emittance2 π mm mrad
RMS energy spread
0.1%
Undulator parameters
Undulator TypePPM & APPLE-II
No of Modules
8&5
Module lengths∼2m
Period45 mm & 51 mm
Focusing
FODO
Minimum magnetic gap∼ 10 mm

The work of [6] describes some detail of the undulator
and focusing lattice choices based upon studies using thedesign formulae of Xie [7] and steady state 3-D simulations using Genesis [8]. Undulator module lengths of ≈2 m
were chosen with a simple FODO quadrupole focusing lattice inserted between modules along with BPMs and phasematching units. This solution requires a shorter total undulator length to achieve saturation than the longer module
options considered in [5], which require a more complex
quadrupole doublet or triplet focusing system. However,Seeded FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

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Figure 1: Schematic layout of the XUV-FEL conceptual design.

when gaps between modules are included, the total overall length of modules plus gaps is slightly longer for the
shorter module option. The ability to monitor and optimise
the electron beam transverse position at regular intervals toensure optimal radiation-electron beam coupling throughout the FEL and the relative simplicity of the design ensured the shorter 2 m module length with FODO focusing
was chosen.

vacuum vessel has therefore been proposed that gradually
decreases in aperture from module to module. The two advantages of this approach are that firstly resistive wall andsurface roughness wakefields are much reduced compared
to a constant minimum aperture, and secondly, as discussed
later, the tapered internal aperture allows optimal focusingof the seed pulse across the whole wavelength range.

A schematic for the undulator/focusing lattice is shownin Fig. 2. Also shown are the injected radiation seed fields
focused to the beginning of the first resonant undulator
module, for each of the cases. The undulator length istherefore controlled so that saturation always occurs in the
final variable undulator module VU5. In this way, variable
polarised photons may be generated across the full operational range of the FEL and it acts as a fixed source simplifying the optical transport system of the output to the finaluser experimental areas.

HIGH HARMONIC GENERATIONSOURCESIt can be seen from Fig. 2 that planar undulator module
PU1 is only required to ensure saturation at ∼ 100 eV andthat its magnetic gap will be at the operational maximumof ∼ 28 mm. This module will not be required to operate at gaps very much smaller than this, and therefore thevacuum vessel aperture containing both electron beam andradiation seed can be relatively large at this point. Similar considerations show that module PU2 will operate withminimum magnetic gap slightly smaller again, and so on
for the rest of the modules PU3..PU8. Use of a step-tapered

Seeded FELs

Peak pulse powers due to intrinsic noise at the beginningof the FEL interaction for the XUV-FEL parameters of Table 1 are typically 30..50 W across the photon energy range
10..100 eV. Any seed source for the XUV-FEL must therefore generate significantly greater power than this if it is todominate the evolution of the noise to saturation. In addition, these seed sources must be continuously tunable over
10-100 eV. Fortunately, High Harmonic Generation (HHG)
sources now exist that meet these seed requirements, or are
readily foreseeable within the very near future [1]. Indeed,
it can be expected that the rapid advances in this field will
be able to easily surpass present 4GLS design requirements
for seed sources over the next few years, so this is an area of
research that must be closely observed and the XUV-FEL
design modified accordingly. Here the method of HHG
generation is summarised and the properties of the HHG
seed fields described to enable simulation by the 3-D FEL

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Figure 2: Schematic of the modular undulator system andfocusing lattice of the XUV-FEL demonstrating the different modes of operation across the photon energy range 10100 eV. Electron beam transport is right to left. Undulator
modules marked in grey have large magnetic gaps āu ≈ 0
and are effectively absent for the purposes of the FEL interaction. The minimum required undulator gap (and vacuum
vessel internal aperture) decrease in gradual steps from 28
mm (25 mm) for PU1 down to 10 mm (7 mm) for PU8
and the variable polarisation modules VU1-VU5. Radiation beam waists of the seed and output are shown from100 eV (violet)..10 eV (red).
code Genesis [8]. Further detail and references regarding
the HHG sources systems may be obtained from [1, 9].
The HHG sources are based upon samples of Noble
gases driven by a high-energy drive laser [10]. A typicaldrive laser is a linearly polarised Ti:Sapphire system operating at ∼ 800 nm generating several to tens of mJ per
pulse of FWHM duration of a few tens of fs. For the 4GLS
conceptual design, 14 mJ pulses of width 30 fs FWHM are
assumed. The high fields generated by such lasers is the
key to harmonic generation. The process can be understoodsemiclassically at the atomic level in terms of ionization
and recombination steps occurring within an optical cycle,
with the energy gained by the electron from the laser field
between these steps going into the harmonics [11, 12], andthe phase of the harmonics being related to the trajectories
in the field between steps. By macroscopic phase matching,single trajectory lengths for each harmonic can be selected,
and a coherent output, with well-defined phases between
the harmonics obtained.
The experimentally observed shape of the HHG yield
curve is of a rapid decline of the lower order harmonics followed by a plateau-region, in which the harmonic
yield falls relatively slowly. An intensity dependent cutoff harmonic is then reached, beyond which the yield drops
quickly to zero [13]. This model is used to construct an
HHG field to simulate seed injection into the XUV-FEL in
the simulations of later sections - see Fig. 4.
Tuning of the HHG sources may be achieved by suitably
modifying the drive laser, for example by introducing achirp or more generally by adaptive pulse shaping. Contin-

236

uous tuning between adjacent harmonics is possible above
about the 25th harmonic or a photon energy of ∼ 40 eV(31 nm). Below this photon energy it is proposed to introduce an intermediate noncollinear phase-matched optical parametric amplifier (NOPA) between Ti:Sapphire laser
and the gas, which will give continuously tunable output
between 1200 nm to 1475 nm. For the 14 mJ specificationof the Ti:Sapphire laser this gives ∼ 2 mJ output from theNOPA. Although introducing this further efficiency loss,
the system will enable more than sufficient continuously
tunable power for XUV-FEL seeding for 8-40 eV operation.
Summarising, the powers available from HHG sources
exceed 4GLS requirements. In the XUV-FEL modellingthat follows, for 10 eV (100 eV) operation a Gaussian input seed of peak power Ppk = 100 kW (30 kW) in 30 fs
FWHM pulses are assumed. The repetition rate of ∼ 1 kHz
is well matched to the XUV-FEL seed requirements.

MODELLING SEEDING OF THE
XUV-FEL
Seed injection
For effective seeding, the seed pulse should be injected
coincident with the electron pulse at the start of the undulator and focused to a waist, w0 , of approximately the sametransverse dimensions as the electron pulse. (The waist
minimum w0 is defined as the radius at which the radiation
power is 1/e2 of its peak value.) Focusing should not be
so tight that the seed diffracts rapidly within a gain length
at the start of the FEL interaction (i.e. when the Rayleighlength ZR = πw02 /λ  Lg .) The relation for the radiation
waist size2z − z0,w(z) = w0 1 +ZR
where z0 is the position of the focus along the axis of theundulator lattice, restricts the minimum aperture size of thevacuum vessel that will allow transmission of the seed toits focus. As the focal size is determined by the electron
beam radius, which is nearly constant for all seed wavelengths, the vacuum vessel’s minimum transverse dimensions are determined by the longest wavelength seed (10 eV
photons) which must be focused furthest from the FEL entrance as shown in Fig. 2. As the minimum operational
undulator gap decreases with undulator module PU1..PU8,
as discussed for Fig. 2, the vacuum vessel may be tapered
to accommodate the focusing of the 10 eV photon energy
seed. This is demonstrated in Fig. 3, where the seed field
is injected at the entrance of undulator module PU1 andfocused to the optimal waist (as shown in following simulations) of w0 = 200 μm at the entrance of module VU1approximately 21 m downstream. It is seen that the vacuum vessel inner wall dimension at z = 0 is 25 mm toaccommodate wall thickness and clearance for the 28 mm
undulator magnetic gap. The walls are at least two beam

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Proceedings of FEL 2006, BESSY, Berlin, Germany
waists away from the peak power on axis at all positions up
to the start of the FEL interaction region at z ≈ 21 m. Thus
the tapered vacuum vessel should provide sufficient clearance for injection of this (worst case) 10 eV seed injection.

MOCAU03of investigating the effects a typical HHG radiation field
was generated for use with the 3-D code Genesis. The full
HHG spectral power is shown in Fig. 4. However, Gen0

Spectral power (arb. units)

10

−5

10

−10

10

−15

10

−20

10

−25

10

0

20

40
60
80
Photon energy (eV)

100

120

Figure 4: Simulated power spectrum from an HHG source.
Figure 3: Plot of the dimension of the inner vacuum vessel wall (blue) which has been step-tapered to enable theundulator module tuning ranges of Fig. 2. The waist size
w(z) (red) for a 10 eV seed is also shown, focused at theentrance to VU1 at z = 21 m.

Seed with full harmonic content
The method of seed generation and specification acrossthe XUV-FEL spectral range is summarised in the previous
section and described in more detail in [1, 9]. The HHG
seed has interesting spectral and temporal properties, being composed of a large number of narrow, phase-coherent
odd harmonics of a fundamental drive laser. This forms
a comb structure in frequency-space. Such a phase correlated comb in frequency space has a similar comb-likestructure in the temporal domain, resulting in a series of
atto-second pulse structures each separated by one half thedrive laser period. For a drive laser such as the Ti:Sapphirelaser with wavelength of ∼ 800 nm, the 65th harmoniccorresponds to the maximum XUV-FEL photon energy of
100eV. If the complete frequency content of a HHG pulse
were to be injected into the XUV-FEL it would be preferable if only one of the harmonics, say the nth harmonic,
interact resonantly with the electrons. The HWHM gain
bandwidth Δλ/λ ≈ ρ should then be less than the spacing between harmonics. This gives the condition ρ < 1/n.
A typical value of ρ ≈ 2 − 3 × 10−3 for 100 eV operation so that ρ < 1/65 ≈ 1.5 × 10−2 is easily satisfied.
Thus, it should be possible to inject all of the seed radiation,
including all non-resonant harmonics, into the XUV-FEL
without the need for band-pass pre-filtering of the seed,as all non-resonant harmonics will simply become negligible relative to the resonant harmonic as the FEL interaction proceeds through the undulator. For the purposes

Seeded FELs

esis is a time-averaged code with a minimum interval between sample points of the field of one radiation period so
the sampling rate is Δts = fr−1 , the inverse of the resonant frequency. The Nyquist frequency, fN = 1/2Δts
determines the bandwidth of frequencies that the field cancontain without the effects of aliasing. Hence the range of
frequencies that can be simulated by Genesis without aliasing effects is fr /2 < fr < 3fr /2. Thus from Fig. 4 it isseen that if simulating 100 eV photon energy generationin the XUV-FEL, only the 50-100 eV components of the
HHG spectrum should contribute to the Genesis input fileusing its ‘RADFILE’ option.
A Genesis simulation was performed for 100 eV operation with the limited spectral range HHG seed pulse as described above. A uniform current of 1.5 kA was assumed.
Due to the relatively short slippage experienced at thesephoton energies, this is very close to that experienced bya short pulse coincident with the Gaussian peak current of
the XUV-FEL. All 13 undulator modules were assumed tobe the planar type modules PU1..8. The seed at the beginning of the FEL interaction at z = 0, the entrance to PU1,is plotted in Fig. 5. Both the atto-second structure in thepulse power and the comb of odd-harmonic wavelengths(inset) are clearly visible. The peak power of the resonant
100 eV (∼ 12.3 nm) component is approximately 22 kW.
On propagating through the amplifier to z = 16.2 m,
Fig. 6 shows that the fine atto-second structure is beginningto be ‘washed out’ due to the selective amplification of theresonant wavelength at 12.3 nm (inset). All non-resonant
harmonics of the seed appear unaffected by the resonant
FEL interaction. This is further confirmed by Fig. 7 whichshows the output at saturation at z = 32.4m, the end of
the interaction region. The radiation pulse shows none of
the atto-second structure of the input seed and the spectral power density shows a single high power emission at

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 5: Radiation seed power at the beginning of the amplifier z = 0 m as a function of local distance, s. The
spectral power content of this pulse is shown as a functionof radiation wavelength in the inset.

Figure 7: Radiation power as a function of local distance, s,
at the end of the amplifier, z = 32.4 m. The spectral power
content of this pulse is shown as a function of radiation
wavelength in the inset.

which, for 100 eV operation, uses the full set of planar andvariable undulator modules with the FODO lattice incorporated between modules. The variable APPLE-II undulator
modules VU1..5 are set to helical mode so that circularly
polarised radiation is generated. The radiation power isplotted in a spatial window that travels along the undulator
axis at the speed of light. Fig. 8 plots the power distributionof the seed pulse of peak power Ppk = 30 kW and duration
30 fs FWHM at the entrance to the first undulator section,
PU1. The seed is assumed to have only the resonant har-Figure 6: Radiation power as a function of local distance,s, at z = 16.2 m through the amplifier. The spectral power
content of this pulse is shown as a function of radiation
wavelength in the inset.
the resonant wavelength 12.3 nm. It is concluded that, atleast for these three-dimensional simulations, the injectionof the (Nyquist limited) harmonic content of the HHG seedappears to have no adverse effects in the FEL evolution,or in the saturated emission. The same conclusion may be
drawn for lower photon energy XUV-FEL operation where
the condition to enable neglect of non-resonant HHG content, ρ < 1/n, is more easily satisfied. Thus in all subsequent simulations only the resonant harmonic of the HHG
seed content is used in the simulation input.

XUV-FEL 100eV simulations
A complete simulation of the design for the XUV-FEL
operating at 100 eV is now demonstrated, using the parameters as given in Table 1. Full details of all parameters may
be obtained in [1]. The system modelled is that of Fig. 2

238

Figure 8: Input radiation seed power (red) to PU1 as a function of local distance, s. The electron beam current profile(blue) is also shown against the same numerical scale.
monic component so that none of the atto-second structure
discussed above is present. Also plotted to scale is the electron beam current, here assumed Gaussian, of peak current
Ipk = 1.5 kA and duration 626 fs FWHM. At the exit of
the planar undulator modules, it can be seen from Fig. 9that the peak radiation power has increased to ≈ 70 MWwith little change in the pulse structure or width. This pulse

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 9: The radiation power at the exit of PU8 as a function of local distance, s.

MOCAU03

Figure 11: A log-plot of the radiation power at the exit of
VU5 as a function of local distance, s.

and the co-propagating electrons are then injected into theset of APPLE-II undulators, VU1 to VU5. By the end of
this set of undulator modules, it is seen from Fig. 10 that
the FEL interaction has saturated, achieving a peak powerof Ppk ≈ 2.5 GW and of duration Δt ≈ 60 fs FWHM.
Fourier analysis gives the bandwidth of the spectrum as

Figure 12: A Log-plot of the radiation power at the exit of
VU4 as a function of local distance, s.

Figure 10: The radiation power at the exit of VU5 as afunction of local distance, s.
Δν/ν ≈ 5.6×10−4 which gives a time-bandwidth productof Δf Δt ≈ 0.8 which compares favourably with that fora transform limited Gaussian pulse of Δf Δt ≈ 0.44. A
log-plot of the same data clearly shows in Fig. 11 the relatively clean central seeded region upon a noisier pedestal.
This pedestal is the amplified SASE radiation which remains well below saturation because of the smaller initialspontaneous noise radiation (typically a few tens of watts),
compared with the initial peak seed power of 30 kW. The
shape of the saturated pulse power envelope is not quite as
Gaussian as may be expected which suggests that the FEL
interaction may have progressed just past saturation. Taking the output power at the end of the previous undulator
module, VU4, and plotting it in a similar log plot in Fig. 12,
a cleaner Gaussian shape can be seen, with a slightly reduced peak power of Ppk ≈ 1.5 GW. The improved pulse

Seeded FELs

shape is confirmed from the pulse duration of Δt ≈ 43 fs
FWHM and spectral bandwidth of Δν/ν ≈ 6 × 10−4 giving an improved time-bandwidth product of Δf Δt ≈ 0.63.
An improved contrast between the peak power and that of
the SASE pedestal is also evident.

XUV-FEL 10eV simulations
Similar simulations to those at 100 eV were carried out
for the case of 10 eV operation of the XUV-FEL. Now
only the APPLE-II undulator modules VU1 to VU5 arerequired to achieve saturation as shown schematically in
Fig. 2. The input seed power is Gaussian with a peak power
Ppk = 100 kW and duration 30 fs FWHM. The electron
pulse current will have the same Gaussian distribution asthat for the 100 eV case of Fig. 8.
Radiation power output at the end of undulator module
VU5 is shown in Fig. 13 using a log scale. Pulse quality is very good with a peak power of ≈ 6 GW and pulse
time-bandwidth product very close to that of a transformlimited Gaussian (ΔtΔf ≈ 0.44). If the radiation is instead extracted at the end of undulator VU4, the radia-

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 13: Log-plot of the radiation power for 10 eV operation at the end of undulator module VU5, as a function of
local distance, s.

Figure 15: Radiation peak power for 10 eV operation at theend of undulator module VU5, as a function of seed beam
waist at the entrance to VU1.

tion power output is shown in Fig. 14. A better contrast

Figure 14: Log-plot of the radiation power for 10 eV operation at the end of undulator module VU4, as a function of
local distance, s.
between the peak power of Ppk ≈ 1 GW and the SASE
pedestal power is seen from the case of Fig. 13, indicatingthat the FEL had already saturated before the end of VU5.
The time-bandwidth product is approximately the same at
ΔtΔf ≈ 0.48.
Time dependent Genesis 1.3 simulations have also beenused to assess the sensitivity of the XUV-FEL output power
to the seeding geometry. It is assumed that the most difficult photon energy to achieve optimum geometry will be
10 eV because of the relatively long distance of ≈ 21 m between the seed injection point (before PU1) and the first operational undulator (VU1). The peak seed power of 100 kW
was focused to a waist at the beginning of VU1. Fig. 15
shows the effect of varying the size of the focal point waist.
An optimum waist of ≈ 200 μm yields a peak output powerof Ppk ≈ 7.5 GW. The corresponding Rayleigh length forthis focus is ≈ 1.0 m. The Xie formulae [7] estimate the240gain length at 10 eV for these parameters to be ≈ 0.5 m.
The optimum Rayleigh length for a seed focused at the undulator entrance is therefore found to be ZR opt ≈ 2Lg .
For this optimum focusing the seed beam waist at the injection point, z = 0 (beginning of PU1), is 4.1 mm. If it
is assumed that a full aperture at the injection point of six
times the beam radius is required to minimise diffraction
effects, then a vacuum vessel aperture of ≈ 25 mm (magnetic gap minus 3mm) is sufficient. This is achieved withthe step-tapered vacuum vessel design, as discussed above.
The above results show that the output power at the endof VU5 reduces as the seed waist size at the entrance to
VU1 increases. (Consequently the seed radius at the injection point also decreases.) The reduced coupling between radiation and electrons with increasing radiation
waist means that saturation is not achieved in the fixed undulator length. Nevertheless, it may be beneficial to use alarger seed waist size than the optimum value of 200 μm
and compensate for the increased saturation length by focusing the seed into the previous module PU8 for example.
(This will have no effect on the saturation power which is
independent of seed.) A larger waist size will reduce output power fluctuation due to seed source pointing stability. While this will be investigated further in future design
work, the current conclusion shows that the optimum seedfocusing geometry may be obtained with the use of the proposed step-tapered vacuum vessel.

Variable polarisation
As has been noted above, the HHG seed sources are linearly polarised. However, this should not present problems
in generating variable polarisation. When the HHG seedis injected into a planar undulator it causes the electrons
to bunch in the axial (ẑ) direction. The polarisation of
the radiation emitted is determined by the electron trajectory. Hence, if the electron bunching is initiated in a planar

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Proceedings of FEL 2006, BESSY, Berlin, Germany
undulator and subsequently transfered into an ellipticallypolarised undulator, the electrons will emit elliptically polarised radiation and progress via the FEL interaction tosaturation. If the linearly polarised HHG seed is injectedwith the electrons directly into an elliptically polarised undulator then coupling between seed and electrons will occur in the plane of the radiation electric field and will begin
to bunch the electrons. The bunching electrons will thenemit with the elliptical polarisation determined by the undulator. Optimal coupling will occur when the major axisof the elliptically polarised undulator is co-incident withthat of the electric field polarisation of the seed.

Timing
Detailed discussion of synchronisation and timing jitter effects between the seed and electron pulse at the entrance to the XUV-FEL are summarised here and presented
in more detail in [1, 14]. A relation between a timing offset Δt and the peak electron current has been used with
the Xie formulae [7] to estimate the effects of timing offset upon the saturation length and saturation power of the
XUV-FEL operating at 100 eV. From these estimates a 50 fs
offset increases the saturation length by ∼ 1.3%, and decreases the saturation power by ∼ 4%. A 100 fs offset
increases the saturation length by ∼ 5%, and decreases thesaturation power by ∼ 13%. Genesis simulations have also
been used to investigate the effect of timing offset and arein very good agreement. While timing jitters of ∼ 100 fs
should be readily achievable, it is projected that this figure
may be reduced to the low tens of femto-second level. It
may be possible to offset the effect of the increase in saturation length by allowing the amplifier sufficient length tooversaturate. In this way the saturated power will nearly
always be attained. This area is the subject of future design
and research effort.

MOCAU03

HHG sources have also been included in the 4GLS conceptual design as user sources in their own right. This
has not been discussed, but is of significant importance tothe overall concept of 4GLS as a facility providing multicolour synchronised sources to the user.
It has been demonstrated that the multi-harmonic content
of the HHG seed need not be filtered before injection as thegain-bandwidth of the FEL interaction ensures that only theresonant harmonic affects the FEL output.
The most critical aspect to ensuring the success of the
XUV-FEL design is in the spatio-temporal synchronisation
between electron pulses and HHG seed at the beginning of
the FEL interaction region. While initial study suggests thisis feasible, this and other aspects will now be the subject ofgreater scrutiny as the 4GLS project enters the technicaldesign phase.

REFERENCES[1] 4GLS Conceptual Design Report, Council for the Central
Laboratory of the Research Councils, UK (2006), available
from: http://www.4gls.ac.uk/documents.htm#CDR[2] The Science Case for 4GLS (2001), available from:http://www.4gls.ac.uk/Documents/EPSRCDec2001/Science Case.pdf[3] M.W. Poole and B.W.J. Mc Neil, Nucl. Inst. Meth. Phys.
Res. A 507, 489 (2003)[4] M.W. Poole and B.W.J. Mc Neil, Proceedings of the 25th International Free Electron Laser Conference, Tsukuba, Japan(2003)[5] B.W.J. Mc Neil, G.R.M. Robb, N.R. Thompson, J. Jones,
M.W. Poole and C.K.M. Gerth, Proceedings of the 27th International Free Electron Laser Conference, Stanford, JACoW / eConf C0508213 (2005)[6] B.W.J. Mc Neil, N.R. Thompson, and B. Sheehy, The Conceptual Design of the 4GLS XUV-FEL, ibid.
[7] Ming Xie, Proc. Of 1995 Part. Accel. Conf., 183 (1996)

CONCLUSIONS
The main use of HHG in 4GLS is to act as a seed source
for the XUV-FEL. These sources have enabled a robust
conceptual design for the XUV-FEL to be developed. Established theory and simulation codes predict this FEL will
generate photons of giga-watt power levels in pulses ofduration 40-60 fs FWHM. The design specification presented here is optimised for 10-100 eV operation but it
has been demonstrated [1] that extension to a revised photon energy range of 8-100 eV requires only small parameter changes. The quality and tunability of the HHG seed
ensures the FEL remains continuously tunable generating
pulses that will have very good temporal and spatial coherence with time-bandwidth products close to the Fouriertransform limit for a Gaussian pulse. The XUV-FEL interaction here is acting as a simple, bandwidth limited amplifier - so long as the radiation input seed pulses have sufficient spectral purity, the output radiation is very nearly asimple amplified version of the input.

Seeded FELs

[8] S. Reiche, Nucl. Inst. Meth. Phys. Res. A, 429, 243, (1999)[9] B. Sheehy, J.A. Clarke, D.J. Dunning, N.R. Thompson, and
B.W.J. Mc Neil, Proceedings of the 37th ICFA Advanced
Beam Dynamics Workshop on Future Light Sources, Hamburg, Germany (2006)[10] See e.g. Eiji J. Takahashi et al., IEEE Journal of Selected
Topics in Quantum Electronics 10, 1315 (2004)[11] K.J. Schafer, B. Yang, L.F. DiMauro, and K.C. Kulander,
Phys. Rev. Lett. 70, 1599 (1993)[12] P.B. Corkum, Phys. Rev. Lett. 71, 1994 (1993)[13] See e.g. Pascal Salieres, Anne LHuillier, Philippe Antoine
and Maciej Lewenstein, Adv. At. Mol. Opt. Phys. 41, 83(1999)[14] D. Dunning et al., First Tolerance Studies for the 4GLS FEL
Sources, ibid.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

FOCAL POINT LASER-FIELD AS OPTICAL SEEDER
Tsumoru Shintake, RIKEN/SPring-8, 679-5148 Japan.
Abstract
Focusing laser beam in wavelength size, passing
electron beam at focal point in normal direction to thelaser axis, we may apply periodic velocity modulation on
the electron beam at optical wavelength. With energy
chirp, the electron bunch is longitudinally compressed in
the magnetic chicane. With appropriate depth of opticalmodulation and energy chirp, we may obtain microbunching at compressed wavelength after the chicane. If
the slice energy spread of incoming electron beam is very
low, we may compress the optical modulation down to Xray wavelength, in principle. For example, using 2nd
harmonic YAG-laser at 532 nm (green), the resulting
optical modulation becomes 266 nm, then compressing
bunch length by 1/60 and 1/30 in two stage bunch
compressors, we may obtain 1 Å. The energy chirp will
be compensated due to single bunch wake field in thelinear accelerator. Sending the beam into undulator line,
the density modulation will provide seeding, which will
be strongly amplified and create single longitudinal modewith full coherence. If we use femto-second laser, such as
TiSa in the optical modulator, we can obtain atto-second
pulse of X-ray after the compression.

MOTIVATION
SASE-FEL: Self-amplified Spontaneous Emission Free
Electron Laser, as it was named the spontaneous radiation(noise power) is amplified along with long undulator line,
and reaches to saturation level. Since its power level isextremely higher than conventional X-ray sources, evenhigher than 3rd generation light sources, many new

scientific applications are expected. Also the short pulsefeature in femto-sec range is expected to be an importantfeature for analysing fast chemical and physical propertiesof condensed matter.
However, since SASE-FEL process starts from thespontaneous radiation at upstream undulator, the resulting
saturated radiation power varies by shot-to-shot. And
most importantly, there are many longitudinal modes,
same as ruby laser does, temporal profile has many spikes,
thus longitudinal coherence is quite limited.
If we seed a coherent signal from upstream undulator,
whose power level has to be higher than spontaneousradiation, only the seeding signal will be amplified andsaturated, thus it becomes (1) fully coherent, (2)temporally single-mode, and (3) stable energy in pulse-topulse. These features are favourable to all kind of
scientific applications. Therefore, various proposals havebeen made on seeding schemes, including HGHG, HHG
and wavelength shift [1, 2, 3]. They are promising
approach to generate coherent radiation at VUV and also
X-ray region. All of them use non-linear higher harmonic
generation in high gain FEL, which requests high density
electron beam.
In this paper, the author will propose a new approach:seeding density modulation at optical wavelength using
conventional laser, and compress the bunch length
together with wavelength of optical modulation down to
X-ray wavelength. It does not rely on higher harmonic
generation. Operational principle is simple. But there aremany technical difficulties. However, the author believes
that with extensive R&D efforts, in near future using thisscheme we will be able to reach the Xray wavelength with clean seeding signal
after compressing bunch by factor of1000 times. What we do is writing wave
or coding signal on the electron beam,and transfer to the X-ray world.

BASIC CONFIGURATION
Figure 1 shows the basic configurationof this seeding scheme. We apply energy
chirp on the incoming electron bunch,
and add energy modulation at optical
wavelength in the laser modulator, thencompress the bunch length in themagnetic chicane. At the same time thevelocity modulation is converted into
density modulation at compressed shortwavelength.
The compression factors for
t
he
bunch
lengthand the modulation
Fig. 1 Laser optical modulation and wavelength compression. Energy chirp
wavelength
areexactlysame. After
after the compressor can be corrected by single bunch wake field and off
accelerating
the
beam
up
to
higherenergy,crest acceleration in the linear accelerator.
andsending
intoundulator,
the
bunch
____________________________________________#
will radiate coherent signal. If the
shintake@spring8.or.jp
242

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Proceedings of FEL 2006, BESSY, Berlin, Germany

wavelength of undulator radiation meets with the density
modulation on the bunch, the undulator will radiate
coherent radiation at super radiant mode.
In case of SASE-FEL of X-ray wavelength, we need
1/1000 times compression. Any kind of non-linear effectin magnetic chicane or wake-field will smear the opticalmodulation. However, if the residual density modulation
exceeds the Schottky noise level, which is usually a few
kW level only, the density modulation will provide
coherent seeding signal to the SAS-FEL.
Similar approach was discussed independently by T.
Shaftan and experimentally demonstrated using DUV
FEL at BNL [3], where the tuning range that can beachieved is full range through a 10% tuning around eachharmonic and switching between different harmonics.

APPLYING LASER MODULATION ON
THE CATHODE
We may apply laser field directly on the cathode andcreate modulation on electron beam. If the electric field
intensity of the laser field is strong enough, theaccelerating field initially applied on the electron gun will
be controlled, thus the current flow can be switch ONOFF at the speed of the optical frequency. However, thethermal motion of electron erases the modulation at
optical wavelength during acceleration as discussed below.
Fig. 2 shows electron trajectory in a constantaccelerating field of E. The kinetic energy increases along
its trajectory as
Wk ( z ) = eEz ⋅ z + Wth(1)
Where Wth is the initial kinetic energy on the cathode,which is given by the thermal energy,

11
me vz2 = kT
2
2

(2)

Solving eq. (1) under initial condition of eq. (2), we cancompute thermal effect on the trajectory. Here wegraphically estimate the thermal effect, refer Fig. 2. Anelectron starts from the cathode with zero initial energy,
which follows curved line A, and reaches to the final
position zf at time tf, where the velocity is very close
to the speed of light. If the electron starts from thecathode with finite initial velocity, it follows
trajectory B, at time tf it runs more Δz, which smears
out the modulation. This effect can be graphicallyestimated as follows. In the trajectory A, near thecathode, electron reaches to the point (t1, z1) where
the kinetic energy becomes equal to the initialenergy of trajectory B:

ct1 =m0 c 2eEz

2WiW, z1 = i ,
2
m0 c
Ez

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As an example, we assume accelerating field of 10 MV/m,and thermionic cathode operating at 1800 K, thermalenergy in z-direction is 74 meV, and we find:t1 = 61 femto-sec.
z1 = 7.4 nm(5)ct1 = 19 μ m
Δz = 19 μ m
Δz is much longer than the optical wavelength, thus themodulation will be totally smeared out.
In case of RF-gun, the cathode temperature is room
temperature, and cathode field is much higher, thus
thermal diffusion becomes smaller. Assuming a very highacceleration field such as 100 MV/m, the diffusion
distance becomes Δz = 1.1 μ m . They are summarized inTable 1. If we use CO2 laser at 10 μm wavelength, themodulation will remain. Tuneable infrared radiation fromOPO (Optical Parametric Oscillator) will also be a
candidate.
Table 1: Thermal diffusion effect for electrons startingfrom the cathodePhysical Parameter

Thermionic
Gun

Photo-cathoderf-gunField Gradient: E

10 (MV/m)

100 (MV/m)

Temperature: T

1800 (K)300 (K)

Thermal energy: Wth

74 (meV)

12 (meV)

Equivalent point:t1
z1
ct1

61 fs
7.4 nm

3.8 fs0.12 nm19 μm

1.1 μmDiffusion length: Δz

19 μm

1.1 μmIn case of the photo-cathode rf-gun, the laser beam isintroduced on the cathode from normal direction, and theelectric field of the laser is oriented paralleled to thecathode surface, which takes minimum on the cathode(3)

Trajectory B is exactly same as A if we shift the
point (t1, z1) to origin (0, 0). Assuming the final
Fig. 2 The electron trajectory in the constant acceleration field.
energy is relativistic, the distance Δz is given by
Starting from the cathode (z = 0), reaches to final position zf at
Δz = ct1 − z1(4)
the time of tf. With initial energy, the electron runs more: Δz,which smears out the modulation.
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because the cathode is electric conductor, thus
the laser field does not directly modulate
velocity of emitting electron. However, in caseof pulsed laser, if it is not seeded with coherent
beam there are multi-modes in longitudinal
direction, resulting in temporal variation. If theperiod of this variation is longer than ΔZ, theproduced electron bunch from the rf-gun willcontain density modulation. This will be apossible source of CSR instability in themagnetic chicane. Tiny density fluctuation onelectron beam is amplified due to negative slopeof energy (energy loss at bunch head, opposite
to the wake-fields), which is amplified throughdispersion in the bunch compressor, results inhigher CSR radiation and positively feedbacks Fig. 3 Laser modulation, using focal point field in the standing wave
to the energy modulation on the electron bunch, of the laser beam. To make interaction area wider, the cylindricallens is employed rather than spherical lens. Polarization is chosen as
cause CSR instability.
to make the electric field being oriented to the electron path.

THRESHOLD ENERGY

1

Reason why such a small thermal energy causes
diffusion on accelerating electron in high gradient is thatthe electron remains near the cathode when the speed is
not high enough. It can be shown by the following
equations.

2eEz
⋅z
m0

(6)

1
1
dt = dz ∝
⋅ dz
v
z

(7)

v=

Near the cathode, z is small, thus it takes long time totravel. Once the electron departs from the cathode andincreases speed, the travelling time for unit distancebecomes shorter, and it becomes independent from initial
thermal energy.
The diffusion distance during acceleration between
point-1 and point-2 is given byΔzth =

Δγ th ⎛ 1 1 ⎞⎜ − ⎟γ ′ ⎝ β1 β 2 ⎠γ ′ = eEz / m0 c 2(8)For example, to accelerate beam up to 8 GeV (β2 = 1) on
20 MV/m field gradient ( γ ′ = 39.1/m), assuming
thermionic gun (74 meV, Δγ th = 1.4 x 10-7), to make thediffusion distance being lower than quarter wavelength of
4th harmonic of YAG: ΔZ<60 nm, we fined− 1 > 16.7

(9)

Thus, β1 > 0.056, or the beam energy has to be higher
than 810 eV. If we apply the laser modulation at thisenergy or at higher energy, the modulation will be kept up
to relativistic energy.
At high energy, eq. (8) becomes2
Δγ th 1 ⎡ ⎛ γ 1 ⎞ ⎤⎢1 − ⎜ ⎟ ⎥ .
Δzth =⋅
γ ′ 2γ 12 ⎢ ⎝ γ 2 ⎠ ⎥
⎣
⎦

(10)

For example, if we compress the bunch into 1 Å at 1 GeV
and accelerate to 10 GeV with 30 MV/m accelerating
gradient, the diffusion due to thermal energy becomes ΔZ= 0.3 femto-meter, this is much smaller than 1 Å, thus themodulation will be kept.
The betatron oscillation of each electron inside thebunch causes path difference and smearing effect.
Average path difference can be estimated byΔzβ =Δγ th = kT / 2m0 c 2

244

β1

2ε n

π γ
2

⋅

L

β

(11),

Assuming, ε n = 1×10−6 π mm ⋅ mrad , L = 300m, β = 30m, the path difference becomes 2 Å. Therefore, simple
betatron oscillation contributes to erase micro bunching.
But inside the bunch, near the core, betatron oscillation
amplitude is lower, thus the modulation pattern willremain. This is ideal case, there is only accelerating static
field, and no magnetic component which will create
dispersion and cause path length difference inside thebunch and will smear the modulation patter. Further
careful study is required.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

LASER MODULATION
When an electron beam passes through a laser beam in
free space, usually there is no energy transfer withrelativistic electron beam. This is because the laser field istransverse electro-magnetic field, and no longitudinal
electric field exists. “The laser acceleration” technology
uses dispersive media, such as gas or plasma, to obtain
longitudinal electric field propagating with speed ofelectron.
When we pass an electron in an undulator, the electrontransversely oscillates. We inject laser beam from behindof the electron, where longitudinal drift velocity ofelectron is slower than speed of light even in relativistic
case due to transverse velocity component, and theelectron delays from laser beam. With optimum tuning
condition, for each one period of undulation, the electron
delays one wavelength on laser field, thus recover phaseand continue to exchange energy through vt ⋅ Et coupling.

MOCAU04

This type of laser modulator is so called “inverse FEL”,
and experimentally demonstrated elsewhere. However thesystem becomes complicated.
Here we introduce new scheme, which uses transverse
electric field at focal point as illustrated in Fig. 3. This
scheme uses same configuration as the spot size monitor
tested at FFTB SLAC [4], but in this case we utilize theelectric field. Since two leaser beam overlap at the focal
point, the standing wave is created. By choosing
polarization of the laser beam as the electric field beingoriented to the electron beam path at the focal point, theelectron beam receives energy modulation through vz ⋅ Ez
coupling at each electric field maximum points with λ / 2apart as Fig.4 left. In between them, there are magnetic
field maximum points, where electron receives transverse
kick from the magnetic field as shown in Fig. 4 right. Thistransverse coupling provides Compton scattering of laser
photon, which causes increase of energy spread.
If the spot depth is much larger than laser wavelength,vz ⋅ Ez oscillates along its trajectory andintegration becomes zero, thus the electron does
not receive energy gain. If we focus the laser
beam into very small spot, the integral becomesnon zero.
Here we assume Gaussian laser beam, andfocus into a long elliptical spot using cylindricallens as shown in Fig. 3. Here we define thecoupling coefficient as follows.
+∞∫ E ( z, t = z / c) ⋅ dz
z

T=

−∞
+∞

= e −( kσ z ) / 4 . (12)2

∫ E ( z, t = 0) ⋅ dzzFig. 4 Overlapping two laser beams create standing wave. At theelectric field maximum location, electron receives velocity
modulation. In between these maximums, the magnetic field
deflects beam, which deteriorate beam emittance, also cause
Compton scattering with laser photon and generate gamma-ray,which contributes to energy spread.

−∞

Function T is plotted in Fig. 6. To obtain
substantial coupling, we need to focus the laser
spot very small close to the laser wavelength.
From Fig. 6 we find that in order to obtaincoupling of 0.1 or higher we have to focus the
spot size σ z < 0.5λ .
Can we focus the laser into such a small spot?
The answer is yes. The CD player uses photopickup, where a short focal lens is used to focus
laser beam into small spot in wavelength
dimension to fit with the micron-size pits, andread out the reflection from those. The relation
between the lens aperture, focal length andminimum spot size is given by

σz =

λ
πθ

NA = n ⋅ sin θf1
F= ≈D 2 NA(13),

Fig. 5 Standing wave laser beam adopts velocity modulation andgenerate density modulation pattern at double frequency.
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Proceedings of FEL 2006, BESSY, Berlin, Germany

Where NA is called “Numerical Aperture” and higher NA
provides smaller spot size, but it technically limited lessthan 1. One of the most advanced lens system is
employed in the lithography system in Si-process, forexample, NA of 0.85 has been realized in 157 nm F2-laser
lithography and 70-nm line width has been achieved[5].
From eq. (13), in order to obtain σ z < 0.5λ , we need

θ = 2 / π = 0.64 , and NA = 0.59. There are commerciallyavailable products of cylindrical lenses having NA value
0.5 or even higher.
Using pulsed laser of 2nd harmonic of YAG-laser at 532
nm, assuming 1 mJ pulse and 10 nsec duration, this issmall class laser oscillator in commercial production line,
we may obtain 170 MV/m of peak electric field at the
focal point, and 16 eV of modulation energy. This is quite
enough for our purpose.
Table-2: Example laser system and modulation energy.
YAG-Laser 2nd
wavelength
532 nmλ
Output power
100 kW, 10 nsec, 1 mJ
Focusing
Focusing length
Numerical aperture
Matched laser beam size
Focused spot size
Transverse widthField intensity
Modulation period
Coupling Constant
Modulation Energy

Cylindrical lens
f
5
NA
0.6
3
σ ~ 0.5D
266
σz0
3
σｘ0
Ez0
170
266
λmod
T
0.1
16

mm
mm
nm
mm
MV/m
nm
eV

REQUIRED ENERGY CHIRP AND
OPTIMUM MODULATIONIn the magnetic chicane, the bunch length iscompressed according to its initial energy chirp: bunchhead is lower energy and higher at tail, so that head partdelays and tail catches up, results in compressing bunch
length. If the optical modulation system is locatedupstream of the bunch compressor, the energy modulation
will overlap with the linear energy chirp. After bunching,Fig. 7 High-NA focusing optics.
246

Fig. 6. Coupling coefficient as a function of thelaser beam spot size.
the energy modulation will be converted into density
modulation with shorter wavelength. If the energy
modulation is too strong, the micro bunching will be overcompressed and modulation contrast becomes lower. Thus
there is certain relation between linear energy chirp andmicro energy modulation. As shown in Fig. 8 left, there
are three energy components: the initial energy chirp,
optical modulation and energy spread:

E = E0 − VI .RF ⋅ k RF z − Vmod sin(2π z / λmod ) + σ e ,(13)Where VI . RF , k RF is the RF cavity voltage to produce
energy chirp (off crest component), Vmod is the opticalλmod is modulation wavelength
before compression and σ e is the energy spread. In themodulation voltage,

chicane, the bunch length is compressed according
to z f = zi + R56δ i . Optimum bunching condition is
illustrated in Fig. 8 right, where the longitudinal spread ofbunched beam becomes minimum, which is given by thefollowing condition. Note the no space charge effect isconsidered in this discussion.

Fig. 8. Phase diagram of electron bunch before and after
the compression.
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Proceedings of FEL 2006, BESSY, Berlin, Germany

∂z2
= 0,
∂δ 2 z =0(14)

VI .RFVk RF + mod kmod = R56 −1 ,
E0
E0

(15)

The bunch compression factor ism = σ zf / σ zi = 1 −VI . RFk RF R56
E0(16)

At high compression ratio, i.e., we can approximate

VI .RF−1= ( k RF R56 )
E0

(17)

For the optical modulation the optimum condition is,Vmod−1= m ⋅ ( kmod R56 ) .
E0

(18)

For example, if we compress bunch length by 1000 times
at 3 GeV, m = 0.001, with R56 = 40 mm, and λmod = 266
nm, the required modulation becomes Vmod = 1× 10 −9 E0 ,that is optical velocity modulation becomes 3 eV. Thisvalue will be easily provided by the laser modulation asshown in Table 2.
If the energy spread is large, the modulation pattern
will be smeared out. The energy spread has to be smaller
than modulation energy. If the electron energy spread isstill as low as the thermal energy: 74 meV, the modulation
will be kept through the bunch compression process. The
wavelength of the micro-bunching after the compressor
becomes λ = m ⋅ λmod . If we use 532 nm wavelength, themodulation period becomes 266 nm, then, after thecompression with m = 0.001, the modulation wavelength
becomes 0.27 nm.

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MOCAU04

If we use femot-second laser, such as TiSa to opticalmodulator, we will be able to obtain atto-second pulse of
X-ray after the compression.

CONCLUSIONS
New optical modulation scheme has been proposed inthis paper. If we apply velocity modulation at optical
wavelength, and compress it with bunch length, we will
have density modulation at X-ray wavelength range. At
least in an ideal case, mathematics shows possible
parameter set. If we assume 1000 times compression ratio,
we will have direct seeding source at X-ray wavelength.
Further studies will be required on non-linear field inbunch compressor, non uniform velocity distribution inbunch, energy spread due to radiation excitation, etc.
In year of 2007, we will install a laser modulator in our
test accelerator to demonstrate velocity modulation, andcompress the wavelength by ten times in bunch
compression to seed FEL at 50 nm range.

REFERENCES[1] L.-H. Yu, Phys. Rev. A44 (1991) 5178.
[2] Timur Shaftan and Li Hua Yu, "High-gain harmonic
generation free-electron laser with variablewavelength", Phys. Rev. E 71, 046501 (2005).
[3] Timur Shaftan et al., "Experimental Demonstration of
Wavelength Tuning in High Gain Harmonic
Generation Free Electron Laser", Proc. FEL 2004, pp.
282-284, Trieste Italy.
[4] T. Shintake, “Proposal of nano-meter beam size
monitor for e+e- linear colliders”, NIM A311, (1992)
pp. 453-464.
[5] Toshiro Itani et al., "Effect of high numericalaperature lens on lighographic performance in 157
nm lithography", J. Vac. Sci. Technol. B 20(6),Nov/Dec 2002.

247

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Proceedings of FEL 2006, BESSY, Berlin, Germany

ANALYSIS OF THE PROCESS OF AMPLIFICATION IN A SINGLE PASSFEL OF HIGH ORDER HARMONICS GENERATED IN A GAS JET
L. Giannessi, M. Quattromini, ENEA C.R. Frascati, Frascati (Roma) Italy
P. Musumeci, INFN Sez. Roma I, Roma, Italy
G. Sansone, S. Stagira, M. Nisoli, S. De Silvestri, Politecnico di Milano, Milano, Italy.
Abstract
We have studied the amplification of high harmonics
generated by a short infrared pulse in a gas jet, injected ina free electron laser amplifier. The high-order harmonic
spectra have been simulated using a 3D non-adiabatic
model that includes both the single atom response and theeffect of the propagation of the XUV field inside the gas
jet. The response of a single atom to the IR field is
calculated in the framework of the Strong Field
Approximation (SFA); The nonlinear polarization
associated to this process is evaluated as the accelerationof the nonlinear dipole moment. This term is used assource term in the propagation of the harmonic field
inside the gas jet. The propagation effect are extremely
relevant for the temporal structure of the XUV field as thecoherent interference of the dipole emission of thedifferent atoms leads to the selection of only one XUVpulse for each semi-cycle of the driving IR field. The
amplification in the free electron laser has been simulatedwith GENESIS 1.3. The effects of filtering the seed
spectrum have been analyzed and the coherence
properties of the light are considered.

INTRODUCTION
The FEL amplification in the SASE regime [1] leads toa longitudinal pulse shape and amplitude governed by thestochastic properties of the electron beam shot noise. The
result is a reduced longitudinal coherence and intrinsic
pulse to pulse energy fluctuations [2]. A single pass FEL,
seeded with an external source, shows a number ofadvantages with respect to SASE, as the control over thepulse shape better coherence properties which are
determined by the seed [3,4]. Intense seed sources areavailable in the visible and UV region of the spectrum
based on reliable solid state laser technology. The FEL
operating range may be extended to shorter wavelengths
with cascaded schemes, i.e. taking advantage of theharmonic generation process in the FEL dynamics[5]. On
the other hand high harmonic multiplication factors in a
multi-stage cascade FEL are limited by the energy spreadinduced in each stage by the FEL process and these
configurations are affected by stability issues associatedto the fluctuation of one or more of the large number ofparameters defining the configuration [6,7]. Analternative to a multi-stage cascade with a high harmonic
multiplication factor is that of seeding the FEL amplifier
directly at short wavelengths with the high orderharmonics of an intense Ti:Sa laser pulse generated in a

248

Gas Jet [8].
Such a possibility is considered in thescheme of several proposed facilities [9,10,11] andexperiments are planned in the next future [12,13]. The
high frequency field produced in the interaction with thegas jet has some very peculiar features. The pulse has aspiky structure, with attosecond pulses separated by halfof the drive laser wavelength [14]. The spectrum contains
the odd harmonics of the Ti:Sa drive laser and extends toshort wavelengths with a cut-off depending on the natureof the gas used. The energy per pulse drops rapidly at the
shortest wavelengths, where the combination of this seed
source with an FEL amplifier would be more appealing.
We are the interested in understanding what is theminimum energy required by an FEL amplifier in order toovercome the electron beam shot noise and amplify the
harmonic pulse. A threshold intensity was obtained in thecase of a seed constituted by a uniform plane wave [15],but it is not clear whether that threshold remains valid
when the pulse has the time/spectral structure of theharmonics produced in gas and whether filtering the input
seed is required despite of the fact that the FEL has alimited bandwidth proportional to the FEL parameter ρ[1,2]. Start to end simulations of the electron beam
dynamics in a single pass FEL have been widely used tounderstand the dynamics of the coupled system ofelectrons and fields undergoing the FEL process. In orderto answer the previous questions we have implemented astart-to-end simulation from the radiation point of view,
starting with the process of harmonic generation in thegas jet and injecting the field distribution in a widespreadand reliable FEL simulation code as GENESIS 1.3 [16].
The paper is organized as follows: in the next section we
study the generation of the high harmonics field in the gas
jet. In the last section we select the field at the target
wavelength of 29.6 nm corresponding to the 27th
harmonic of the Ti:Sa and we analyse the results ofsimulations of the seeded FEL amplifier.

HIGH ORDER HARMONICS IN GAS
The high-order harmonic spectra have been simulatedusing a 3D non-adiabatic model that includes both thesingle atom response and the effect of the propagation of
the XUV field inside the gas jet. The response of a single
atom to the IR field is calculated in the framework of theStrong Field Approximation (SFA); in this model theatom is ionized via tunnelling by the IR field and thefreed electron is then accelerated by the electric field of
the driving pulse. For particular emission instant the

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Proceedings of FEL 2006, BESSY, Berlin, Germany

∫

(

(

⎛

t

[

)

) (

]

)}

(1)

⎞

* exp⎜ − ∫ w(t ' )dt ' ⎟
⎜
⎝

−∞

⎟
⎠

In this equation E (t ) and A(t ) are respectively theelectric field and the vector potential of the driving field;
pst (t , t ' ) is the stationary value of the momentum of thefreed electron, S st (t , t ' ) is the phase accumulated by theelectron wave packet, d ( p) and d * ( p) are the dipole
matrix element for transitions from the ground state to acontinuum state characterized by momentum p . The lastterm of equation (1) takes into account ground state
depletion through the term ionization rate w(t ) calculatedusing the ADK model. The nonlinear dipole moment isused as source term in the propagation of the harmonic
field inside the gas jet. The wave propagation equations
for the driving and the harmonic field are solved incylindrical symmetry in the framework of the paraxial
approximation. The harmonic power spectrum is obtained
integrating over the radial profile the harmonic electricfield at the output of the gas jet.
Propagation effects are extremely relevant for a correct
simulation of the time structure of the harmonic radiation.
Indeed usually the single atom response is characterized
by a complex time structure (usually two attosecond
pulses for each half optical cycle), whereas themacroscopic time structure of the XUV radiation ischaracterized by a single attosecond pulse for each semi
optical cycle. The origin of this difference is related to thephase matching mechanism operating during the
propagation of the XUV field inside the gas jet.
In the process of high order harmonic generation, theelectron can follow two different paths in order torecombine with the parent ion. These two paths areusually referred to as the “short” and the “long” path, as
they are characterized by different times spent by theelectron in the continuum of energy states. For the shortpath this time is usually less than half the optical period
T0 , while for the long paths this time is typically of theorder of the laser period. The coherent superposition of
the contributions of these two paths leads to thegeneration of two attosecond pulses for each half optical
cycle of the driving laser field. The coherent interferenceof the dipole emission of the different atoms inside thegas jet leads to different phase-matching conditions forthe two paths. The relative contribution of the two paths
Seeded FELs

27thintensity (a.u.)

3/ 2
⎫
⎧ t
⎧⎛
⎞
π
⎪
⎪
⎜
⎟
'
exp − iS st (t , t ' ) ⎪⎪
i
dt
⎨
⎪ −∞
⎜
⎟
ε + i t − t' / 2 ⎠d nl (t ) = 2 Re⎨
⎬
⎪
⎩⎝
⎪
⎪
*
⎪
⎭
⎩ E (t ' ) d p st (t , t ' ) − A(t ) d p st (t , t ' ) − A(t ' ) ⎪to the harmonic spectra can be enhanced or reducedchanging the relative position of the gas jet with respect
the laser focus. The phase-matching condition in the HHG
process are indeed determined by the geometric phase of
the driving pulse and by the phase accumulated by theelectron wave packet during his motion. In particularconditions, gas jet positioned few millimeters after thelaser focus, it is possible to efficiently select on thecontribution of the short path, leading to the selection of
only one XUV pulse for each semi cycle of the driving IR
field[17].
In other experimental condition (gas jet before or close
to the laser focus), the contribution of the long paths
increases and therefore also the time structure of thegenerated XUV radiation is more complex.
For our simulation we considered a Gaussian beamwith a beam waist of w0 = 50μm (in the focus), andfocused 3mm before a Neon gas jet with a thickness of
1mm. The pulse duration is FWHM=30 fs with a peakintensity in the focus of 1x1014W / cm 2 . The highfrequency portion of the spectrum, in the range 20 nm –60 nm of the on axis radiation is shown in Fig. 1. The
spectrum contains the odd harmonics of the Ti:Sa
resonant wavelength (800 nm).

20

25

30

35

40

45

50

55

60

wavelength (nm)Fig. 1 Short wavelength spectrum of the HHG seed field.
The slowly varying envelope approximation (SVEA)
has not been used in the model, but the FEL dynamics
studied with GENESIS 1.3 rely on this approximation.
1

Attenuation factor

electron can be driven back to the parent ion and canrecombine with the ground state emitting the exceedingenergy as a photon in the extreme ultraviolet region orsoft x ray region. The nonlinear polarizability associatedto this process is evaluated as the acceleration of thenonlinear dipole moment:

MOCAU05

Al 0.6 μm
10 nm
2 nm
0.1 nm
0.5

0

20

40

60

wavelength (nm)Fig. 2 Attenuation factor as a function of the wavelengthof the different filters used in the simulations. The redline correspond to 600 nm layer of Aluminium.
For this reason we have to limit the bandwidth of the
input signal by filtering the seed field and define the249MOCAU05

Proceedings of FEL 2006, BESSY, Berlin, Germany~
slowly varying field as E (z ) = E (z ) exp(−ik 0 z ) wherek 0 is the FEL central resonant wave vector. In our
example we consider filtering with different bandwidth asshown in Fig.2 centered at the resonant wavelength
λ 0 = 2π k 0 = 29.66nm corresponding to the 27th
harmonic of the Ti:Sa (Fig.1).

2

0

|E|2
phase

2

Al
0.6 μm0

Pulse shape (a.u.)

10 nm
2 nm
0.1 nm

200

400

r (μm)

600

Fig. 4 Transverse field at the undulator entrance averaged
over z.

1520

ζ (μm)

25

30

Fig. 3 Longitudinal pulse profile of the input seed after
filtering. The plot in the upper right corner is the pulse
shape filtered only with the Al broadband filter.

The radiation power as a function of the longitudinalcoordinate in the electron beam frame (horizontal) andposition along the undulator at the coordinate z (vertical)
is shown in Fig.5. The power is normalized at each z. The
plots have been obtained by different filtering of the seed.
The input seed energies, 2.5nJ@10nm, 1nJ@2nm and
0.5nJ@0.1nm have been chosen in order the energy in a
bandwidth 2ρ to be roughly the same (0.5nJ) in the threecases.

The effect of filtering on the seed temporal profile isshown in Fig. 3. The 10nm bandwidth is wide enough topreserve the attosecond structure of the input field. At
2nm the bandwidth preserves the pulse envelope, but
overrides the fine structure. The 0.1nm filter induces anincrease of the pulse length.

THE FEL SIMULATIONThe FEL configuration considered is based on theparameters shown in Tab. 1. The FEL parameter is ρ∼10-3
and an estimate of the seed intensity necessary to override
the e-beam shot noise as calculated in ref.[15] is about
I0 ≈0.3MW/cm2.
Table 1:FEL configuration parameters
Beam Energy (GeV)

1

Peak current (A)1000

Energy Spread (%)

0.06

Emittance (mm-mrad)

1

Average βT (m)6

Undulator period (cm)4.2

K (peak)

2.97

Periods per section

58

Sections

7

The field spot size and divergence have been matchedto the e-beam optical functions by propagation through adrift+lens+drift optical system. The field phase andamplitude at the undulator entrance are shown in Fig.4.
250

Fig. 5 Normalized longitudinal profile of the radiation
power as a function of the longitudinal coordinate in theelectron beam frame as it evolves along the undulator
with coordinate z. The seed has been filtered at different
bandwidths.
The fine structure present in the 10nm case is wiped out
by the finite bandwidth of the FEL. The different filtering
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Proceedings of FEL 2006, BESSY, Berlin, Germany

affects the pulse shape only before saturation, which
occurs at about 15m in all cases. Thereafter the pulse
enters the superradiant regime where the pulse length isrelated to the peak power and is the same in all cases. The
The input seed intensity is 15MW/cm2@10nm, 8.5
MW/cm2@2nm, and 4 MW/cm2@0.1nm averaged over z,
always much larger than I0. In Fig. 6, the simulation
corresponding to 0.1nm has been repeated with input
energies 0.05nJ and 0.01nJ, corresponding to intensities
slightly above and below the threshold I0 respectively. In
both cases SASE is clearly visible at the beginning. In thelatter case a structure in the pulse with loss of longitudinalcoherence is present and SASE spikes compete with theseeded signal until saturation.

Fig. 6 Same as in Fig.5, case with 0.1nm BW above (left)
and below (right) the threshold I0.
The input energy levels considered are however very
conservative. In fact recent results [18] havedemonstrated the feasibility of pulses with energies up to
several hundreds nanojoules at the considered photon
wavelength. In Fig. 7 the power vs. ζ and z as in Figs. 5
and 6 (left) and the spectrum (right) are shown for the
100nJ@10nm case. Saturation is reached after only 8m.
The splitting of the spectrum typical of the superradiantregime is clearly visible at the end of the undulator.

Fig. 7 Normalized longitudinal profile of the radiation
power as a function of the longitudinal coordinate in theelectron beam frame as it evolves along the undulator
with coordinate z (upper plot). Corresponding wavelength
spectrum as a function of z.

CONCLUSIONSIn this paper we have presented an analysis of the
dynamics of a FEL seeded with the high order harmonics
generated in gas. The minimum seed energy has been
estimated in a specific FEL configuration with theresonance at the 27th harmonic of the Ti:Sa drive laser.

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The results are in reasonable agreement with the threshold
estimation in [15]. Currently available sources in the
XUV appears to be sufficiently intense to implement sucha scheme. The analysis in the frequency domain, suggeststhat filtering the seed it is not necessary unless a linewidth smaller than the natural FEL line-width is required.
This work was partially supported by the EU
Commission in the Sixth Framework Programme,
Contract No. 011935-EUROFEL.

REFERENCES[1] R. Bonifacio, C. Pellegrini, and L. M. Narducci, Opt.
Commun. 50, 373 (1984)[2] E. L. Saldin, E. A. Schneidmiller, M. V. Yurkov,
Opt. Commun. 148, 383 (1998)[3] L. H. Yu et al., Science 289, 932 (2000)[4] L. H. Yu et al. Phys. Rev. Lett. 91, 074801 (2003)[5] G. Dattoli et al. Journal of Appl. Phys. 97, 113102(2005)[6] B. Kuske et al. Development of Figures of Merit to
Evaluate the Output of FEL HGHG Cascades,
MOPPH051, these proceedings[7] G. De Ninno et al. Start-to-end Time-Dependent
Study of FEL Output Sensitivity to Electron-beam
Jitters for the First Stage of the FERMI@Elettra
Project, MOPPH058, these proceedings[8] D. Garzella et al., Nucl. Instrum. Methods Phys. Res.
Sect. A 528, 502 (2004).
[9] C. Bruni, The Arc En Ciel FEL proposal,
MOPPH048, these proceedings[10] B. McNeil et al, The Conceptual Design of the 4GLSXUV-FEL, MOPPH012, these proceedings[11] C. Vaccarezza et al., Status of the SPARX FEL
project , MOPCH028 in procs. of the 2006 EPAC
conference (2006).
[12] G. Lambert, Seeding the FEL of the SCSS Phase I
Facility, MOPPH046 these proceedings[13] O. Tcherbakoff et al, MOPPH047 these proceedings,
see also L. Giannessi, Future seeding experiments at
SPARC, MOPPH028 these proceedings[14] P. Salieres, M. Lewenstein, Meas. Sci. Technol. 12,
1818 (2001)[15] L. Giannessi, Harmonic generation and linewidth
narrowing in seeded FEL, in Proc. of the 26th FEL
conference, Trieste 2004 JACoW (Joint Accelerator
Conference Website) at http://www.JACoW.org, p.
37 (2004)[16] S. Reiche, Nuclear Instrum. & Meth. A429, 243(1999)[17] P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G.
Paulus, H. Walther, R. Kopold, W. Becker, D. B.
Milosevic, A. Sanpera, M. Lewenstein, Science 292,902 (2001).
[18] E.J. Takahashi et al. IEEE J. of Sel. Topics in Q.Elec.
10, 1315 (2004)

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PERFORMANCE ACHIEVEMENTS AND CHALLENGES FOR FELSBASED ON ENERGY RECOVERED LINACS*
G. A. Krafft, Jefferson Lab, Newport News, VA 23060, U.S.A.
Abstract
During the past decade several groups have assembled
free electron lasers (FELs) based on energy recovered
linacs (ERLs). Such devices have been built to obtainhigh average power electron and photon beams, by using
high repetition rate beam pulses driving FEL oscillators.
In this paper the performance of many existing andseveral proposed facilities from around the world arereviewed. Going forward, many questions must be
addressed to achieve still better performance including:higher average current injectors, better optimized
accelerating cavities, higher energy acceptance and lower
loss beam recirculation systems, and better optical cavity
designs for dealing with the optical beam power
circulating in the ERL FELs. This paper presents some of
the current thinking on each of these issues.

INTRODUCTION
The basic idea in same cell beam energy recovery isfairly straightforward to understand and has been
discussed in great detail in recent reviews [1,2]. In a frontto-back recirculated linac the recirculation path length ischosen to be approximately an integer plus ½ RF
wavelengths, and if the beam current does not changemuch in the time it takes for a complete circuit of therecirculation loop to be made, then energy can betransferred directly from the decelerating higher-energy
beam to the accelerating first-pass beam, without the needfor power to be provided by the RF systems attached tothe cavities. This opportunity allows one to construct
recirculated linacs, particularly those consisting ofsuperconducting cavities, with energy transfer efficiencies
approaching those in storage rings. This fact, in turn,allows one to build linacs that can transport and acceleratebeam average currents approaching those in storage rings.
The energy transfer efficiency is nicely quantified by
the power multiplication factor

k = Pb,ave / PRF(1)

where Pb,ave is the average beam power and PRF is the RF
power needed to accelerate the beam. For normal
conducting recirculators k is much less than 1, for present
day ERL FELs k is of order 10, for advanced ERL lightsources k is of order 100, and for typical storage rings k isof order 1000. It is straightforward to show that in thelimit the optical cavity losses are small compared to theoutcoupled radiation power, the transfer efficiency fromRF power to photons is equal to ζk, where ζ is the fraction___________________________________________*Authored by Jefferson Science Associates, LLC under U.S. DOE
Contract No. DE-AC05-06OR23177.
c252

of beam energy converted to photons per pass in an
optical cavity oscillator FEL.
The first superconducting linac to demonstrate same
cell energy recovery was the Stanford University
Superconducting Accelerator as reported at thisconference twenty years ago [3]. In an experiment, therecirculation path length was set to allow energy recovery
to proceed. Nearly all of the beam energy was recovered
as indicated by the absence of RF power being needed todrive the beam load in the superconducting cavities of theaccelerator. However, in this early experiment there wasno optical cavity inside the recirculation loop.

PRESENT STATUS
Presently, there are three ERL-based free electron lasers
in existence and a fourth being rapidly assembled as aprototype project for an advanced fourth generation lightsource suite. Two of the existing FELs, at Jefferson Lab
and the Japan Atomic Energy Agency (JAEA), are basedon superconducting RF (SRF) cavities, and the third, at
the Budker Institute for Nuclear Physics (BINP), is based
on CW normal conducting RF cavities. In all the devices,
an optical cavity FEL is placed inside the beam
recirculation loop.

Jefferson Lab Free Electron Laser
A group at Jefferson Laboratory has spent the last
decade building and improving many increasingly capable
free electron lasers based on energy recovery, including
the first ERL to have an FEL inside the energy recovery
loop [4]. This demonstration device has been upgraded inorder to achieve higher average electron beam and opticalbeam powers. Some recent electron beam parameters are
summarized in Table 1. Beam starts from a DC
photocathode source, is accelerated to 10 MeV using two
standard CEBAF superconducting cavities, injected onto abeamline containing an energy recovered linac that canachieve up to 150 MeV. The beam is recirculated with two
Bates bend beam recirculation systems specially designed
to contain and transport the large energy spread generated
by the FEL in the electron beam.
Recent work at Jefferson Lab has concentrated on
extending high power CW operations at the 10 kW levelfrom 6 microns down in wavelength. Over the last year
the average power has increased from about 4 kW to 6.7
kW at 2.8 microns, from 1 kW to 5.4 kW at 1.6 microns,
and from 1 kW to 2.2 kW at 1 micron. The shortwavelength performance of the FEL has improved as low
absorption dielectric coatings have been developed for thehigh power optical systems. The group expects a
considerable improvement of the high power performance

Energy Recovery FELs

Proceedings of FEL 2006, BESSY, Berlin, Germanyof the FEL when cryogenically cooled optical cavity
mirrors are deployed to help deal with mirror distortion in
the optical cavities at high power.
Table 1: Electron Beam Parameters for ERL FELs
PROJECT

JLAB

JAEA

BINP

Frequency (MHz)

1500

500

180 NC

Energy (MeV)

130

17

13

Current (mA)

10

8

20

Bunch Charge (pC)

130

400

500

Rep. Rate (MHz)

75

83

11.2

Normalized
Emittance (mm
mrad)

8

20

30

A user program has developed at the FEL. Because of
the short bunch length at the FEL, copious amounts of
wideband THz radiation are produced in the bend magnetsof the chicanes surrounding the wiggler through thecoherent synchrotron radiation emission. The THz
radiation has been taken up to a user lab and is now
routinely used for electron beam diagnostic purposes.
Other experiments are performed with the FEL radiation
extending from studies in condensed matter physics, tostudies of fundamental optical physics using the FEL lightto make far off resonance traps, all the way tofundamental particle physics in dark matter candidate
searches.

JAEA Free Electron Laser
The JAEA FEL injector consists of a 230 keV
thermionic gun, and 83 MHz subharmonic buncher, andtwo single-cell 500 MHz superconducting cavities that
accelerate the beam to about 2.5 MeV. The injected beamis merged onto the axis of a linac that consists of two 5cell superconducting cavities that boost the beam energy
to 17 MeV. Beam is recirculated with three-bend
achromats, and the undulator and optical cavity of the
FEL are just upstream of the return achromat. As seen in
Table 1, the lower cavity frequency allows higher charge
per bunch in the beam to be accelerated efficiently.
Recent work has focused on doubling the electron
bunch repetition rate by upgrading the gun grid pulser andthe RF power for the non energy recovered 2.5 MeV
accelerating cavities, increasing the energy acceptance of
the achromats by reworking quad magnets and beam
pipes in the achromats, and investigating and optimizing
the achromat settings for increasing the FEL efficiency.
Recently, the FEL extraction efficiency has beenmeasured and the peak efficiency reaches 2.8%, and thegroup has achieved 0.7 kW output at 22 micron from an 8
mA beam during a 230 microsecond macropulse. A more
complete summary of recent work has been given by N.
Nishimori at this conference [5].

Energy Recovery FELs

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BINP THz FEL
The Budker Institute THz FEL is based on a normal
conducting CW linear accelerator. Beam originates in athermionic electron gun, is accelerated to 2 MeV throughtwo 180 MHz cavities, injected on the main linac axis andaccelerated up to 13 MeV by 16 180 MHz cavities. The
beam drives an FEL oscillator which produces radiation in
the THz band, and the beam energy is recovered in thesecond pass through the linac. This device is the highest
average power source of narrowband THz radiation.
Because of the low frequency and hence large aperture of
the accelerating cavities, this device is able to handle
much higher average current than the superconducting
ERL FELs, achieving 20 mA average current now andplanned to achieve 150 mA average current after an
injector upgrade. This device has energy recovered thehighest average beam current to date, and is unique in thatthe recirculation loop is oriented vertically.
There are plans to upgrade this device with two higher
energy FELs that will produce radiation at 20-100 μm and3-20 μm, in optical cavity oscillators. The 20-100 μm
optical klystron will sit after a second pass of beam
recirculated acceleration for a beam energy greater than
20 MeV, and the shorter wavelength optical klystron will
sit after four beam passes up to about 40 MeV. The
recirculation loops for this device will be oriented
horizontally to the existing linac, which does not need to
be upgraded substantially. When completed, the BINP
FELs will be unique among energy recovered FELs inthat a large number of passes will be accommodated, as
the other existing ERL FELs are two pass machines. The
multipass “energy recuperator” free electron lasers will beassembled throughout 2007 and commissioning is
anticipated to begin towards the end of 2007. A more
complete summary of recent work has been given by N.
Vinokurov at this conference [6].

4GLS
The British 4GLS project is to produce a suite of three
superconducting linac based free electron lasers in
addition to an energy recovered high average current
recirculated linac light source, to be located at Daresbury
Laboratory. The IR FEL and the XUV-FEL in this project
are not energy recovered, the IR FEL operating at a MHzscale repetition rate and the XUV-FEL operating at arepetition rate of 1 kHz, ambitious for a SASE or a seeded
source. The UV FEL source, based on a regenerative
amplifier, is located in the high average current energy
recovered recirculation loop. It is anticipated to operate
this FEL simultaneously with the high average current
ring.
In order to start the process of building the full 4GLS,
which is based on 1.3 GHz superconducting cavities, a 35
MeV energy recovered FEL, ERLP, is being built [7]. Justprior to the conference, beam was extracted from the DC
photocathode source of ERLP for the first time. The
accelerator consists of two two-cavity cryostats, one
inside and one outside the beam recirculation loop. These
have now been assembled, as well as the three bend

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Proceedings of FEL 2006, BESSY, Berlin, Germany

achromatrecirculation
opticssystems.
Coldcommissioning of the linac, in its planned location isscheduled for the month of October 2006, with themachine completely installed by the end of 2006.
Machine studies, including beam energy recovery, are to
be completed in the spring of 2007 and there should be a“first lasing” contribution by ERLP at the next FEL
conference. A more complete summary has been given by
J. Clarke at this conference [8].

High Average Power X-FELs
Perhaps the ultimate light source, i. e., one that could
produce both high peak power and high average power Xray beams, would consist of an energy recovered X-FEL.
A superconducting linac as a driver for such an FEL has
many inherent advantages: greater potential efficiency andthe possibility of high gradient CW operation, thepossibility to achieve repetition rates at the MHz or higher
level, and the ability to transport cleanly high bunchcharges because of the low transverse impedance of theaccelerating structures [9]. Such a scheme has beenstudied in detail as a follow on project for the TTF FEL[10]. A major concern is achieving a high repetition rate
injector. As discussed more thoroughly below, thisinjector would seem to require an SRF gun electron
source.

FUTURE DEVELOPMENTS
In order to achieve another order of magnitude inelectron and photon beam power many improvements
must be made to the existing devices. The present
photocathode injectors must be upgraded to produce
higher average current. The accelerator design optics must
be stable to the higher average recirculated beam current
in the more ambitious designs. The optical cavities must
be able to handle the increased recirculating beam power.
High order mode (HOM) cooling becomes more
problematic at higher average currents. Finally, noninvasive electron beam diagnostics should be developed
to help monitor the beam during CW operations.

Electron Photocathode Sources
In order to increase the average beam current in thenext generation FELs by an order of magnitude, it seems
that the easiest method is to increase the bunch repetition
rate until every accelerating (and decelerating!) phase in
the RF waves are filled. This can be done with littlechange to the bunch charge presently obtained. Thisapproach has been adopted by Cornell for the first energy
recovered recirculated linac light source, which mustachieve beam emittances much smaller than is typical forthe long wavelength ERL FELs. Because of the higher
average current in the non energy recovered portions ofsuch accelerators, it is expected that the injection energy
will be reduced and the number of superconducting
cavities increased in order to deal with the increased beam
power in the non-recovered portions of the accelerator[11]. Also, larger beam dumps may be needed to dissipate
the non-recovered beam energy.

254

In the further future, one anticipates that SRF
photocathode sources will be developed to produce
electron beams at high energy and high levels of average
current. The group at Rossendorf, who have been leaders
in developing SRF guns, hope to achieve 1 mA average
current from a 10 MV 3.5 cell gun in construction now,and Brookhaven National Laboratory have beendeveloping guns in the 100 mA-1 A class for electon
cooling applications [12]. The main benefit of marrying
the SRF and photocathode source technology is thepossibility to have high CW accelerating gradient on thephotocathodes, which may lead to superior emittance in
CW high repetition rate applications.

Drive Lasers
In the high average current applications ofphotocathode electron sources there is a need to develop
drive lasers of sufficient power to extract the needed
average current. Roughly an order of magnitude in laser
power is needed beyond present experience for the DC
photocathode sources presently used. In addition to thepower requirement, to get the best beam parameters out ofphotocathode guns laser pulse shaping is needed. Cornell
University is developing a fiber based system with 20 W
capabilities untilizing transverse shaping and longitudinalpulse stacking in order to obtain a uniform laser pulse
longitudinally. Jefferson Lab is also developing a systemthat should be able to deliver 32 W [13], about 5 times
more than the present drive laser for the Jefferson Lab
FEL.
Similar high average power lasers with high repetition
rate may be quite useful in seeding applications in highrepetition rate X-FELs.

Beam Breakup and Advanced Beam Optics
Recent work at Jefferson Lab has allowed direct
quantification of the multipass beam breakup instability,
as in some electron beam optical conditions the FEL beam
is unstable. A recent review of the subject has been
performed [14], including discussions of utilizing special
electron beam optics to suppress the instability. The
methods studied are likely sufficient for stabilizing the
instability in future FELs, but simulation evidence exists
indicating that some of the intended solutions may not
apply to larger scale accelerators [15]. Significantly, manyof the BBU simulation codes have now been properly
benchmarked against experimental instability data.
Driven by the desire to operate the ERL FELs at higher
energy extraction, advanced beamline designs for beam
recirculation with energy spreads of 10% or more havebeen developed [16]. These designs feature magnet shapes
and edges chosen to automatically yield nearly
isochronous beam recirculation due to the shape choices.
It is anticipated that such designs will become
increasingly important as higher average power ERL
FELs are built.

Energy Recovery FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

High Power Optical Cavities
In designing the next generation of optical cavities thefollowing aspects of the problem must be understood[13]:• One must minimize the absorptive loss which canquickly lead to mirror distortion and low output.
• Scatter loss should be minimized to control
subsequent absorption on components causingpressure rise and drift.
• Mirror coatings and substrates must be chosen to
mitigate the effects of any power loading from outof-band radiation which may be incident on the
mirrors.
Optical cavities and beam transport lines must be
designed with these effects in mind.

HOM Power
Superconducting RF cavities have been used in storage
ring applications for many years at beam average currentsof 100 mA and above. Because the power deposited into
HOMs can be substantially larger than the heat depositedin the cavity walls when the cavity is operated at gradient,
it is particularly important to couple the HOM power outof the cavity volume to be absorbed at locations withhigher temperature to reduce cooling requirements on the
He refrigerator. Recent storage ring HOM absorbers
consist of ferrite absorbers located upstream anddownstream of the SRF cavities mounted on the beam
pipe wall with a separate cooling loop to deal with the
HOM power.
Similar solutions will be needed to absorb the HOM
power in 100 mA-scale ERLs, and there is an additional
complication. The bunch durations in ERLs can be up to
two orders of magnitude smaller than in storage rings andnow there is bunch spectrum available to excite HOMs atmuch higher frequencies than in rings. Thus, the overall
power excited increases and the operational range of the
HOM absorber must be much broader in frequency tohandle the wider range of frequencies excited. This
problem afflicts advanced ERL light source designs, andalready a group has investigated material which is highly
absorbing at frequencies up to 40 GHz at a temperature of
80 K [17]. Also, it is anticipated that advanced HOM
absorbers will include several different materials
absorbing in different frequency bands [18].

Electron and Photon Beam Diagnostics
Because the average current of next-generation ERLs isapproaching that in storage rings, one would expect thatthe more standard electron beam diagnostics, e.g. beam
position monitors, beam profile monitors, and current
monitors, would follow the techniques previously
developed for storage ring applications. The beam
attributes unique to ERLs and ERL FEL sources are theneed to diagnose and control short bunches, the need todeal with low average power tune up beam diagnostic
modes, and the need to deal with high average beam
power. Many longitudinal techniques are being

Energy Recovery FELs

TUAAU01

investigated in X-FEL projects. Mainly they are highly
disruptive and might not be technically useful in thehigher average beam power regimes we are pushing into.
Real time measurements of bunch longitudinal
distribution and phase space based on electro-optic
methods or based on coherent synchrotron, edge, orundulater radiation, may provide correct approaches for
non-invasive monitors. Presently, there seems to be a lackof a universal method yet demonstrated that isunambiguous in the results it reports [19]. Achieving sucha universal longitudinal measurement will be at least as
important for future ERL development as the developmentof good profile monitoring was in storage rings.
For photon beams, the key near-term developments
need to occur in the shaping, both longitudinally andtransversely, of the higher average power drive laser
beams for electron production on the photocathodes. The
production methods will be need to be diagnosed to somelevel with techniques suitable for power levels of several
tens of W needed in the next generation electron sources.
In the further future it will perhaps be required by theusers of high average power FELs that the emerging highpower optical pulses display customized and controlledcharacteristics. Very little is known about this subject
now.

CONCLUSIONS• The field of ERL-based FELs continues to grow andthe performance of devices continues to improve.
• Upgrade paths for at least an order of magnitude inboth electron beam and photon beam power, though
not trivial, have been identified.
• Many new ideas are being explored, some inconjunction with recent work on Energy Recovered
Linac light sources.
• The field seems to be thriving and there is no
shortage of interesting problems to work on.

REFERENCES[1] L. Merminga, D. R. Douglas, and G. A. Krafft, Ann.
Rev. Nucl. Part. Sci., 53 (2003) 387.
[2] G. A. Krafft, “Recirculated and Energy Recovered
Linacs”, Joint Accelerator School 2002, Long Beach,
CA, USA, p. 301.
[3] T. I. Smith, H. A. Schwettman, R. Rohatgi, Y.
Lapierre, and J. Edighoffer, Nucl. Inst. and Methods
A 259 (1987) 1.
[4] G. Niel, et al., Phys. Rev. Lett. 84 (2000) 662.
[5] N. Vinokurov, these proceedings.
[6] N. Nishimori, these proceedings.
[7] D. J. Holder, et. al., “Status of the Daresbury Energy
RecoveryPrototype
Project”,
EPAC’06,
http://www.jacow.org[8] J. Clarke, these proceedings.
[9] G. A. Krafft, and J. J. Bisognano, “On Using a
Superconducting Linac to Drive a Short Wavelength
FEL”, PAC’89, Chicago, IL, USA, p. 1256,
http://www.jacow.org

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Proceedings of FEL 2006, BESSY, Berlin, Germany[10] J. Sekutowicz, et al., Phys. Rev. ST-AB 8 (2005)
010701.
[11] I. V. Bazarov and C. K. Sinclair, Phys. Rev. ST-AB
8 (2005) 034202.
[12] I. Ben-Zvi, private communication.
[13] M. Shinn, private communication.
[14] E. Pozdeyev, et al., “Multipass Beam Breakup in
Energy Recovery Linacs”, ERL 2005, Newport
News, VA, USA, Nucl. Inst. and Methods A 557(2005) 176.
[15] G. A. Krafft, and J. J. Bisognano, “Two Dimensional
Simulations of Multipass Beam Breakup”, PAC’87,
Washington,DC,USA, p. 1356, http://www.jacow.org[16] D. Douglas, private communication.
[17] V. Shemelin, M. Liepe, and H. Padamsee,“Measurements of Epsilon and Mu of Lossy
Materials for the Cryogenic HOM Load”, PAC’05,
Knoxville, TN, USA, p. 3452, http://www.jacow.org[18] M. Liepe and J. Knobloch, “Superconducting RF forenergy-recovery linacs”, ERL 2005, Newport News,
VA, USA, Nucl. Inst. and Methods A 557 (2005) 354.
[19] G. A. Krafft and J.-C. Denard, “Diagnostics for
Recirculated and Energy Recovered Linacs”,
BIW’02, Upton, NY, USA, AIP Conf. Proc. 648. p.
118.

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FUTURE LIGHT SOURCES: INTEGRATION OF LASERS, FELS AND
ACCELERATORS AT 4GLS
J. A. Clarke, CCLRC Daresbury Laboratory, Warrington, UK, on behalf of the 4GLS Design Team.
Abstract
4GLS is a novel next generation proposal for a UK
national light source to be sited at Daresbury Laboratory,
based on a superconducting energy recovery linac (ERL)with both high average flux photon sources (undulatorsand bending magnets) and three high peak brightness freeelectron lasers. Key features are a high gain, seeded FEL
amplifier to generate XUV radiation and the prospect ofadvanced research arising from unique combinations ofsources with femtosecond pulse structure. The conceptual
design is now completed and a CDR recently published[1]. The 4GLS concept will be summarised, highlighting
how the significant design challenges have beenaddressed, and the project status and plans explained.

INTRODUCTION
The 4GLS project design takes advantage of the verylatest advances in accelerator science and technology
incorporated in a unique scheme to provide state-of-theart research facilities. This will enable a broad range ofoutstanding science to be undertaken by the UK andinternational communities.
4GLS will enable the study of real time molecular
processes and reactions on timescales down to tens offemtoseconds in short-lived, nano-structured or ultradilute systems. The emphasis is on molecular and device
function, rather than the largely ‘static’ structural focus ofwork on 3rd generation synchrotron radiation sources and
X-ray FELs. Key areas where 4GLS will make uniquecontributions are in:• understanding
thefunctionofsinglebiomolecules in living systems and membranetransport;• determining reaction pathways in areas asdiverse as enzyme processes, reactions
contributing to atmospheric pollution orreactions occurring in the interstellar medium;• studies of electron motion in atoms/moleculesand developing ‘coherent control’ of reactions
and intense laser-matter interaction leading to
new physics;• developing new nano-scale devices throughunderstanding electron charge and spin transport;
and• development of new dynamic imaging
techniques to improve early diagnosis ofconditions such as cancer and prion based
diseases.
The major themes of the science case are time-resolved
measurements in the life sciences and nanoscience.
Particular areas of strength are high resolution pumpprobe spectroscopy of atoms, molecules and clusters,

Energy Recovery FELs

including high field dynamics, dynamics at surfaces andinterfaces, many-body problems in condensed matter, andstudies of the dynamics of biomolecules in ‘real’environments.
The science requirement is for an ultra-high brightness
facility that allows the use of short pulsed sources incombination, and where the energy range is optimised toallow the extraction of electronic and vibrational
information. The 4GLS suite of synchronised sources,
operating from the THz to the soft X-ray range isdesigned to meet this science need.
The 4GLS facility is planned from the outset to be amulti-source, multi-user facility. This is achieved bysuperconducting radio-frequency (SCRF) accelerator
technology, operating using energy recovery, to provide
short pulse spontaneous radiation with pulse lengthvariable from ps to < 100 fs. At long wavelengths thisallows the condition for coherent synchrotron radiation(CSR) production to be met, with the result that 4GLS
will provide enormously bright THz radiation. The highquality low emittance electron beam provided by thephotoinjectors additionally provides an ideal source withwhich to operate free electron lasers (FELs). In the 4GLS
conceptual design these are embedded within the facility,
delivering ultra-high brightness short-pulse radiation in
the IR, VUV and XUV energy ranges, with pulse lengths
as short as 50 fs FWHM. In world terms, this gives aunique suite of synchrotron radiation (SR) and FEL
sources covering the THz to the soft X-ray range. Manyof the light pulses originate from the same electron bunch,thus offering potential levels of internal synchronization
at the tens of femtoseconds level. All the 4GLS sources
are offered with variable polarization, while the flexibilityof SCRF technology allows the repetition rates of thesources to be varied. The peak brightness of the 4GLS
sources is given in Figure 1. There is a typicalenhancement of eight orders of magnitude whencompared with 3rd generation light sources.
The 4GLS accelerator design concept consists of threeinter-related accelerator systems [2, 3]. The high average
current loop uses energy recovery as an essential element
to deliver a 600 MeV electron beam of 77 pC bunches atrepetition rates of up to 1.3 GHz. Distributed bunch
compression allows for SR pulse lengths from a few ps toapproximately 100 fs (RMS) to be delivered according touser requirements. A low-Q cavity VUV-FEL device isincorporated at the end of this loop. The most challenging
area of accelerator design for 4GLS is in transporting andaccelerating an extremely high quality high-average
current (100 mA) beam to this loop, while simultaneously
providing extremely high peak current (1.5 kA) at 750 –950 MeV for the second accelerator system, the XUVFEL branch. This beam is derived from 1 nC bunches

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produced by a normal conducting RF photoinjector
operating at 1 kHz and it is dumped after traversing a
final spontaneous undulator source. The XUV-FEL uses
an HHG (high harmonic generation) seed, offering
considerable advantages in pulse quality over a SASE
(self-amplification of spontaneous emission) design. The
third accelerator system is required for the IR-FEL. SCRF
linac technology is used to accelerate electrons to 25 – 60
MeV to provide a fully integrated and synchronized IRFEL facility.
Significant aspects of the 4GLS design have been
informed by experience gained on the 4GLS Energy
Recovery Linac Prototype (ERLP) currently approachingcompletion at CCLRC Daresbury Laboratory [4, 5]. In
considering detailed 4GLS design decisions considerable
attention has been given to ensuring that future upgrade
options are not designed out at this early stage. Thesepossibilities include various routes to higher energy
operation, increased repetition rate for the XUV-FEL anddecreased photon pulse lengths.
4GLS is thus the leading energy recovery proposal in
Europe and the most comprehensive in terms ofutilisation of combined sources. In terms of multi-user
capability it is currently the most advanced energy

recovery linac (ERL) proposal in the world. 4GLS iscomplementary to XFEL, to table-top lasers and to 3rd
generation sources.
The unique advantages of 4GLS are:• Combinations of sources. The fully integrated
capability to utilize both short pulse SR(ERL)and the FEL sources for pump-probe and twocolour dynamics experiments. This results inboth experimental flexibility and cost effective
delivery.
• Intense, tuneable, variable polarisation FEL
sources optimized for spectroscopy and imaging
in the frequency ranges of XUV, VUV and IRTHz.
• Energy recovery linac spontaneous light sources
available from soft X-ray to THz. This gives
short pulse, high repetition rate operation, thecapability to ‘pulse tailor’, and low probabilityof sample damage.
• Europe’s most intense broadband source ofcoherent THz radiation.

Figure 1. Peak brightness for 4GLS FELs, undulators, wiggler, OPA and dipoles compared with EUFELE, XFEL,
Diamond and Max III undulators.

OVERVIEW
The 4GLS project design takes advantage of the verylatest advances in accelerator science and technology
incorporated in a unique scheme to provide state-of-theart facilities. This has been made possible by a number ofparalleldevelopments
atleading
international
laboratories, including successful demonstrations oftechnical solutions. The proposed design builds on current
world achievements and in some cases extrapolates
beyond them. In the most challenging areas an active
R&D programme is already underway world-wide and the258

4GLS team has augmented this, not least because to do soenhances the necessary skill base for detailed design,
construction and operations.
The provision of high intensity electron beams has been
revolutionised in the last decade by the successful
development of a new variant of accelerator: the Energy
Recovery Linac (ERL). Traditionally beam currents inlinear accelerators can have high instantaneous values but
are restricted to pulses with low repetition rates because
the average power dissipation must be kept to manageablelevels. For a light source high average flux emission ishighly desirable and this output has been possible so far
only by the widespread application of the electron storage

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Proceedings of FEL 2006, BESSY, Berlin, Germany
ring (e.g. Diamond and other 3rd generation sources) that
achieves average currents of hundreds of milliamperes byrecirculating the same electrons many times (and formany hours). This solution has serious drawbacks, inparticular the ring defines the beam properties and they
are dominated by the very emission of synchrotron
radiation that the ring is built to deliver. If long-term
storage of the electron beam can be avoided then greatly
superior properties can be provided and this is one of theprincipal features of the ERL.
The ERL delivers high average currents without beamstorage, since electrons are injected, accelerated andcirculated only once before the system recovers theirenergy, dumps them and replaces them with newelectrons. This means that if the beam is injected withsuperior brightness properties it maintains these during its
radiation emission phase. The 4GLS project has an ERL
at its heart in a generational leap from storage ringsources. Globally, pioneering work on ERLs has been
undertaken at the Jefferson Laboratory in the USA wherea low energy proof-of-principle ERL has beensuccessfully demonstrated.
4GLS is best thought of in terms of three inter-related
accelerator systems (see Figure 2). The first is the highaverage current loop. In this a 600 MeV beam of 77 pC

TUAAU02bunches is delivered at repetition rates of up to 1.3 GHz
and energy recovery is an essential element. Progressive
compression of the electron bunches in this loop allows
for photon pulse lengths from a few ps to approximately
100 fs (RMS). The VUV-FEL is placed towards the endof the high-average current loop.
The second major accelerator system is the XUV-FEL
branch. The XUV-FEL requires a peak current of ~1.5 kA at beam energies from 750 to 950 MeV. This
beam is derived from 1 nC bunches produced by a normal
conducting RF photo injector operating at 1 kHz. At thisrepetition rate the 1 kW of beam can be safely dumped
after traversing a final spontaneous undulator source.
Although the XUV-FEL beam and the high averagecurrent beam discussed above are derived from separate
electron sources after suitable low energy acceleration
they are merged and accelerated in a single
superconducting linac. The two beams are then separatedusing magnetic, energy dispersion for delivery to theirrespective devices.
The third accelerator system is that required for the IRFEL. The same linac technology is used to accelerate
electrons to between 25 and 60 MeV to provide a fully
integrated and synchronised IR-FEL facility. The mainelectron beam parameters for 4GLS are given in Table 1.

Figure 2. The conceptual layout of 4GLS.
Table 1. Main electron beam parameters of 4GLS
Bunch Parameter
Electron Energy
Normalised EmittanceRMS Projected Energy Spread
RMS Bunch Length
Bunch Charge
Bunch Repetition Rate
Electron Beam Average Power

Energy Recovery FELs

XUV-FEL

100 mA HACL
Operation
750 to 950 MeV
600 MeV
2 mm mrad
2 mm mrad
0.1 %
0.1 %
< 270 fs
100 to 900 fs
1 nC
77 pC
1 kHz
1.3 GHz
1 kW
60 MW

VUV-FEL HACL
Operation
600 MeV
2 mm mrad
0.1 %100 fs
77 pC
n x 4.33 MHz
n x 200 kW

IR-FEL
25 to 60 MeV
10 mm mrad
0.1 %1 to 10 ps
200 pC
13 MHz156 kW

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Proceedings of FEL 2006, BESSY, Berlin, Germany

SUPERCONDUCTING LINACS
The 4GLS design utilises superconducting linacs toaccelerate and manipulate the three beams required todrive the photon sources. The accelerating structures are
all based on a fundamental RF frequency of 1.3 GHz anda modified TESLA type cavity design operating at 2 K or
below [6, 7]. The chosen RF frequency takes advantage ofextensive development and operating experience of such
systems (including the fact that industrialisation of the
production and processing of such cavities is already wellunderway in preparation for the international linear
collider ILC and superconducting XFEL).
Importantly the 4GLS design team at Daresbury are
currently close to completing construction of an energy
recovery prototype, ERLP, based on commerciallyprocured linac modules incorporating TESLA 9-cellcavities which will provide a valuable test bed for thecritical cavity and module developments required to
produce linacs capable of operating in CW mode with thehigh-average beam currents.
For the high average current injector linac the major
challenge is the delivery of the beam power required toaccelerate a beam of up to 100 mA to 10 MeV without
energy recovery. A cavity and coupler scheme similar to
the two-cell geometry with symmetric couplers currently
being developed at Cornell for the Cornell ERL prototype
will be adopted for 4GLS. Two modules consisting offive of these two-cell cavities will suffice to provide therequirements of the ~ 10 MeV high average current
injector system.
The main linac will be made up of six cryomodules
each containing eight, seven-cell cavities which are
currently under development within an international
collaboration that includes CCLRC. This development isdesigned to meet the extreme demands of CW highaverage current operation. The choice of six accelerating
modules for the main linac is a balance between capitaland operating costs which also provides a reasonable
overhead in accelerating voltage. Another five similar
accelerating modules are required within the accelerator
system, two within the XUV-FEL injector system, two for
the XUV-FEL linac to take this beam from 750 MeV to950 MeV and one to give the 60 MeV requirement for the
IR-FEL. Development and verification of this challenging
module design will be a major activity during thetechnical design phase of 4GLS. A prototype 2 cavity
cryomodule is currently being developed at Daresbury
Laboratory [8].

INJECTORSFor linac-based light sources the injectors are an
essential element in the delivery of high performance,high quality beams. The requirements for the three
injectors proposed for 4GLS come directly from thechallenging demands of the FEL and spontaneous
sources. Unlike storage rings light sources where thebeam properties are essentially decoupled from the260

properties of the injector beam, the performance of ERLbased sources are directly dependent on the quality of theelectron beam as produced by the injector and preserved
during transport and acceleration.
The IR-FEL of 4GLS makes relatively modest demandsof the injector and the source envisaged requires 200 pC,
1 ps electron bunches with a normalised emittance ofaround 10 mm mrad. This can be delivered in a costeffective and reliable way by mature thermionic gun
technology. In contrast, the proposed injectors for boththe high-average current loop and the high brightness
XUV-FEL branch are based on developments of existing
injectors.
The XUV-FEL injector source is required to deliver
1.5 kA peak current at 1 kHz repetition rate, thenormalised emittance required to drive the device is
2 mm mrad. Normal conducting RF photoinjectors today
already exceed the bunch charge (1 nC) and emittancerequirements and are a proven mature technology but they
are typically low duty-cycle systems operating at a few
Hz and require development to meet the 4GLS target
repetition rate. Development of the PITZ gun is alreadyunderway that would increase the demonstrated 0.9 %duty cycle to 2.5 %, a slightly higher duty cycle than that
required for 1 kHz operation of the XUV-FEL.
Simulations using well developed particle codes haveshown that a normalised emittance of 1.7 mm mrad canstill be delivered whilst using relatively modest
accelerating gradients, producing acceptable thermalloads in a gun engineered to supply additional cooling.
This design is an effective starting point for the technicaldesign of the XUV-FEL gun-cavity.
The photoinjector chosen for the high average current
loop is required to deliver an unprecedented 100 mA
beam with an emittance of 2 mm mrad. With such a highcurrent demand an optimal choice of cathode material is ahigh quantum efficiency semiconductor which limits thelaser power required to reasonable levels. From theexperience of the JLAB DC photo-injector, that has beenutilised on the ERLP photo-injector, caesiated gallium
arsenide may provide a suitable option for the cathodematerial. To meet the 4GLS requirements this gun will be
driven by a simple stable 160 W, Yb-doped fibre laser
operating at 1.3 GHz. Whilst the TJNAF DC and ERLP
photo-injectors are already designed to achieve the 77 pC
bunch charge required, the emittance of these guns islimited to around 5 – 10 mm mrad and the maximum,
average current achieved at JLAB is only 9.1 mA. Further
development is clearly required to meet the requirementsof 4GLS and verification of such performance goesbeyond the scope and capability of the current ERLP.
Evolving from JLAB DC photoinjector developments,
Cornell University is currently building a prototype
injector which will produce a 100 mA beam of 77pC
bunches. Extensive simulations of this gun based on theuse of particle tracking codes predict that the emittancerequirements for 4GLS would be fully met by this design.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

BEAM DYNAMICS
The most challenging area of accelerator design for
4GLS is in meeting the requirements of extremely highpeak current, (1.5 kA) for the XUV-FEL branch whilst
simultaneously transporting and accelerating very highquality high-average current (100 mA) beam to theenergy recovery loop. The conceptual solutions to the
dynamics challenges for delivering the two mostchallenging beams are discussed below.
These two beams originate from separate photoinjectors, a high brightness RF photoinjector operating at
1 kHz delivering 2 mm mrad normalised emittance, 1 nC
bunches for the XUV-FEL and a low emittance 100 mA,
normal conducting DC injector. At relatively low injector
energies these high quality beams are susceptible tointense space charge effects. Within the RF gun, the 1 nC
beam undergoes rapid acceleration to a few MeV and isthen injected into a superconducting linac which quickly
boosts the energy to 220 MeV. Rapid acceleration of the
100 mA beam is achieved through the use of a high DC
voltage followed closely by two superconducting booster
modules delivering the ~1 MW power required toaccelerate the beam to 10 MeV.
The bunches within both of these beams have toundergo a significant amount of compression to deliver
the required peak currents to drive the XUV- and VUVFELs and to meet the requirements of the science casefor different pulse lengths from undulators in the highaverage current loop. An innovative, integrated
acceleration and compression scheme is proposed whichmeets the unique requirements for each of the two beams
whilst using the same main superconducting accelerator[9]. By defining appropriate accelerating phases within
the linacs, the high compression demands of the XUVFEL are met using a two-stage compression scheme
including a higher harmonic RF system for flexible nonlinear correction, whilst progressive compression throughthe undulator arc delivers the high peak current in the
77pC bunches required to drive the VUV-FEL. An
important part of this design is the optimisation of thescheme to maintain a high quality beam throughout thetransport. Wakefield effects in the accelerator are reducedby performing the final compression stage at full energy
so that the bunches around the arcs are kept relatively
long to control the disruptive effects of coherent
synchrotron radiation (CSR) emission which if
uncontrolled can produce unacceptable energy loss andemittance growth. Acceleration of a 100 mA beam is very
challenging; to accelerate and decelerate such a beamrequires that the linac transport design is tailored to give ahigh threshold for the disruptive beam break-up
instability. This is achieved through a combination oftechniques including substantial damping of HOMs in anadvanced design of RF cavity, tight control of beamfocussing throughout the linac and optimisation of
coupling and overall transport properties in the energy
recovery loop [10, 11].

Energy Recovery FELs

TUAAU02

For the 4GLS XUV- and VUV-FELs, very high peakcurrent is demanded simultaneously with narrow magnet
gaps. These high peak currents are vulnerable todisruption by associated strong wakefields in nearby
metallic chamber walls. This wakefield interaction and its
undesirable consequences will be controlled through theuse of appropriate vacuum materials and an optimisationof the FEL design which maintains vessel apertures thatare compatible with delivering the required high quality
beam.

FREE ELECTRON LASERS
The characteristics of 4GLS and its central ERL will be
optimally exploited by the inclusion of three FELs, eachcovering a distinct photon energy range matched to thescience needs of the UK and each offering excellent
performance levels. The three designs are all state-of-theart with key advantages over other designs being
proposed elsewhere.

XUV-FELA simple yet robust seeded design for the XUV-FEL is
proposed to ensure that ultra-high quality, reproducible,
tunable radiation is available in the 8 to 100 eV photon
range [12, 13].
A tunable laser seed pulse from a High Harmonic
Generation source, that covers the full photon energy
range, is amplified within the FEL. The FEL undulator
consists of a lattice of individual undulator modules
allowing electron beam focusing elements and diagnostics
to be placed in between. The final undulator modules of
the FEL will be of APPLE-II design that will enable thegeneration of variable elliptically polarised radiation.
Figure 3 shows a schematic layout for the undulator
modules and illustrates that for the low energy photons
only the APPLE-II modules are in use whilst at highenergy all of the modules are required.
100eV
90eV
80eV
70eV
60eV
50eV
40eV
30eV
20eV
10eV

VU5 VU4 VU3 VU2 VU1 PU8 PU7 PU6 PU5 PU4 PU3 PU2 PU1VU5 VU4 VU3 VU2 VU1 PU8 PU7 PU6 PU5 PU4 PU3 PU2VU5 VU4 VU3 VU2 VU1 PU8 PU7 PU6 PU5 PU4 PU3VU5 VU4 VU3 VU2 VU1 PU8 PU7 PU6 PU5 PU4VU5 VU4 VU3 VU2 VU1 PU8 PU7 PU6 PU5 PU4VU5 VU4 VU3 VU2 VU1 PU8 PU7 PU6 PU5VU5 VU4 VU3 VU2 VU1 PU8 PU7VU5 VU4 VU3 VU2 VU1 PU8 PU7VU5 VU4 VU3 VU2 VU1 PU8VU5 VU4 VU3 VU2 VU1Figure 3. Schematic of the modular undulator system of
the XUV-FEL demonstrating the different modes ofoperation across the photon energy range 10-100 eV.
Electron beam transport is right to left. The minimum
required undulator gap decreases in gradual steps from28 mm for PU1 down to 10 mm for PU8 and the variable
polarisation modules VU1-VU5.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

The output pulses will have selectable polarisation anda pulse repetition rate of 1 kHz is set by the seed laser andthe electron beam. Established FEL theory and state-ofthe-art simulation codes predict this FEL will generate
photon energies at multi giga-watt power levels in pulsesof duration 40 - 60 fs FWHM. The pulses will haveexcellent temporal and spatial coherence with timebandwidth products close to the Fourier transform limit
for a Gaussian pulse. Unlike the self amplified
spontaneous emission mode of operation, which
effectively self-starts from intrinsic noise, the FEL
interaction here is acting as a true amplifier. The highquality spectral properties of the radiation input seedpulses are maintained by the amplified output radiation
pulses, as illustrated in Figure 4. Recent advances in High
Harmonic Generation seed sources mean that the seedrequirements for the XUV-FEL already exist and clearly
future advances in conventional lasers can be readilyharnessed. Further details on the issues raised by the useof HHG seeding can be found in [14].
The 4GLS design also incorporates an undulator after
the XUV-FEL which enables the generation of
spontaneous SR light with natural synchronisation to the
XUV-FEL radiation
35

2000
HHG Seed Pulse PowerElectron Bunch Current

30

1800
1600
1400
1200

20

1000
15

800

Current (A)Power (kW)

25

600

10

400
5

200

0
0

100

200

300

0
500

400

µm)
Longitudinal Position (µ
1E+07
1E+06

Power (kW)

1E+05
1E+04
1E+03
1E+02
1E+01
1E+00
0

100

200

300

400

500

Longitudinal Position (µµm)

Figure 4. (a) Input HHG seed power (FWHM 30 fs) andelectron bunch current as a function of longitudinal
position (linear scale) and (b) radiation power (FWHM~50 fs) at the exit of the XUV-FEL (log scale).

262

VUV-FELThe VUV-FEL will be a Regenerative Amplifier FEL(RAFEL) which is a high gain system that is of
insufficient length to achieve saturation in SASE mode. A
small fraction of the radiation emitted by an electron
pulse at the end of the undulator is fed back to thebeginning of the undulator to act as a seed field to a
subsequent electron pulse. The radiation feedback may
readily be achieved by placing the undulator into a low-Q
cavity. This self-seeding process rapidly builds up andallows the RAFEL to achieve saturation after only a few
electron pulses have propagated through the undulator.
Figure 5 shows the intracavity pulse power for a cavity
length detuning of ~ 12 µm after the first and eighth pass.
After the first pass, the pulse power has a noisy profile
characteristic of SASE. However, after only eight passes
saturation occurs and the intracavity peak power is
290 MW, equivalent to an output power of 218 MW. The
corresponding spectrum, also shown in Figure 5, is seen
to be noisy after the first pass. On subsequent passes
however the spectrum narrows about a single wavelength.
At saturation the spectrum has FWHM bandwidth of
0.26% giving a time-bandwidth product of ~1.0. This isjust over a factor two greater than a Fourier transform
limited gaussian pulse and indicative of excellent
longitudinal coherence.
The FEL will offer high repetition rates (multiples of
4.33 MHz) with giga-watt peak power and > 100 W
average power [15]. Here advantage is taken of mirrors(with hole out-coupling) that are able to operate over thephoton energy range of 3 to 10 eV. Photon pulse lengthsof ~ 170 fs (FWHM) will be obtained in standard modeand simulations suggest that pulses as short as ~ 25 fs will
be generated in a super-radiant mode. The output pulses
will have selectable polarisation and be fully tunable.
By using a pair of mirrors to reflect light emitted by the
FEL back to the entrance of the device it becomes, in
effect, self-seeding and no external conventional laser
system is required. Hence high quality, stable light isensured through a rather simple optical feedback loop. A
particular feature of this FEL when compared with similar
designs covering the same wavelength range is thetolerance to low mirror reflectivity. Extensive simulations
have shown that mirror reflectivities in the range 40 to
60 % are acceptable for this design [16].
Detailed modelling has been used to study the effect oftiming jitter in the electron bunch arrival time [17]. Figure
6 shows the build up of saturation with no timing jitter
and with a jitter of ±80 fs, calculated using the 1D timedependent code FELO [18]. Statistical analysis of thepeak output power during saturation suggests that theRMS variation in the peak output power increases from
2.5% for the no jitter case to 8% for a jitter of ±80 fs.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

TUAAU028

4

2.5 10

Pass 1

1.5 10

Pass 8

8

P [W]

P [W]

2.0 104

1.0 108

1.5 108

1.0 103

5.0 107

5.0 10

0

150

200

250
s [µm]

0

300

150

200

250
s [µm]

300

0.12

0.08

P(λ) [a.u.]P(λ) [a.u.]

8000

Pass 1

0.10

0.06
0.04

Pass 8

6000
4000
2000

0.02
0.00
123

124

125
λ [nm]

126

127

123

124

125
λ [nm]

126

127

Figure 5. Genesis 1.3 [19] simulation of the radiation pulse power and the radiation spectrum after one and eight passes
through the VUV-FEL for a cavity detune of 12 m.
300

500

250

400

P [MW]

P [MW]

200
150
100

200
100

50

0
0

0
0

0.2

30

0.2

20

0.4

(a)

300

t [ps]

0.6

10
0

30

0.4

20

t [ps]

pass

(b)

0.6

10

pass

0

Figure 6. FELO simulation of the VUV-FEL at 10eV and cavity length detuning of 18 m with (a) zero electron bunch
arrival time jitter and (b) jitter of ±80 fs. The red points show the peak intensity of the pulse at each pass.

IR-FELThe IR-FEL has been designed to produce highintensity, spatially and temporally coherent radiation withvariable pulse lengths, flexible output pulse patterns andvariable polarisation over the wavelength range 2.5 200 µm. The high-Q cavity-based design employs two
undulators in parallel and hence can serve two user
experiments simultaneously. The provision of shortelectron bunches offers the potential to operate the FEL insuper-radiant mode to produce shorter FEL pulses withhigher peak intensities than available in normal operation:
simulations predict FWHM pulse lengths of only a few

Energy Recovery FELs

optical cycles can be produced in this way. The
implementation of a superconducting RF linac with the
IR-FEL will offer highly stable operation and also highaverage powers (> 100 W) though the option of runningin modes that reduce the average power for sensitive
samples will also be available.

SPONTANEOUS SOURCES
There are six insertion device straights in the highaverage current loop, one of which is allocated to the
VUV-FEL. The remaining five will be used to generatespontaneous radiation. To maximise the potential of the
spontaneous sources three different undulator straight

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Proceedings of FEL 2006, BESSY, Berlin, Germany

lengths have been chosen; two 14 m straights; two 10 m
straights and two 8 m straights. Thus the total space
available for undulators is ~ 64 m, which exceeds allother existing low energy 3rd generation light sources.
More than one insertion device can be placed in eachstraight with a small corrector magnet between them so as
to angularly separate the photon output. Distributed pulse
compression will be employed in the high average current
loop in order to deliver to users pulse lengths optimised
for their experiments ranging from a few ps down to 100
fs (RMS).
It is well known that electrons in a bunch radiate
coherently at wavelengths of the order of, and longer
than, the bunch length. Since 4GLS has very short bunch
lengths this so-called Coherent Synchrotron Radiation(CSR) is emitted over a broad wavelength range.
Calculations indicate that the onset of the CSR for 4GLS
is at around 40 m and hence it will be an extremely
intense source THz radiation.

TABLE TOP LASERS
In order to make full use of 4GLS it is important toallow integration of its sources with conventional lasers.
Continuous coverage of the visible and near-IR parts ofthe spectrum is provided by the spontaneous sources as
illustrated in Figure 1. However, there are currently noplans to provide FEL radiation in the spectral range from0.5 – 3 eV, as this is covered more cost-effectively bytabletop laser systems. These wavelengths will be madeavailable by using continuously tuneable mid-infraredlaser systems, such as mid-infrared Optical Parametric
Oscillator and Optical Parametric Amplifier systems,
Difference Frequency Generators and diode lasers.
Ability to synchronise the additional lasers to within thetemporal profile of the 4GLS sources is required. Current
synchronisation is achievable to within < 100 fs, and is
the subject of a vigorous worldwide research anddevelopment programme.

STATUS
The conceptual design of 4GLS is now complete andreported in [1]. The project is now entering the technicaldesign phase which includes a substantial R & D element.
The Energy Recovery Linac Prototype at Daresbury
Laboratory is presently being commissioned and theresults from this will be fed into the technical design of
4GLS. In addition to this a superconducting RF linac
module prototype is under construction that will becapable of operating CW at a high average beam currentof 100mA. It is intended that this will be installed into
ERLP at a later date for electron beam trials. In addition
to this a high current photoinjector project is being
initiated at Daresbury Laboratory to ensure that the target
current of 100 mA can be delivered with the required
electron beam parameters.

264

REFERENCES[1] 4GLS Conceptual Design Report 2006, available
from www.4gls.ac.uk[2] M. W. Poole and E. A. Seddon, '4GLS and theEnergy Recovery Linac Prototype Project at
Daresbury Laboratory', PAC 05, Knoxville, p431.
[3] J. A. Clarke, 'The Conceptual Design of 4GLS at
Daresbury Laboratory', EPAC 06, Edinburgh, p181.
[4] D. J. Holder et al, 'The Status of the Daresbury
Energy Recovery Prototype Project', EPAC 06,
Edinburgh, p187.
[5] S. L. Smith, 'A Review of ERL Prototype Experienceand Light Source Design Challenges', EPAC 06,
Edinburgh, p39.
[6] P. A. McIntosh et al, 'RF Requirements for the 4GLS
LINAC Systems', EPAC 06, Edinburgh, p439.
[7] S. Pattalwar et al, 'Key Cryogenics Challenges in theDevelopment of the 4GLS', EPAC 06, Edinburgh,p499.
[8] P. A. McIntosh et al, 'Development of a Prototype
Superconducting CW Cavity and Cryomodule forEnergy Recovery', EPAC 06, Edinburgh, p436.
[9] B. D. Muratori et al, 'Lattice Design for the Fourth
Generation Light Source at Daresbury Laboratory',
EPAC 06, Edinburgh, p184.
[10] E. Wooldridge and B. D. Muratori, 'Linac Focusing
and Beam Break Up for 4GLS', EPAC 06,
Edinburgh, p2871.
[11] E. Wooldridge, 'Alternate Cavity Designs to Reduce
BBU', EPAC 06, Edinburgh, p2874.
[12] B. W. J. McNeil et al, 'Design Considerations for the
4GLS XUV-FEL', FEL 2005, p506.
[13] B. W. J. McNeil et al, 'The Conceptual Design of the
4GLS XUV-FEL', these proc.
[14] B. Sheehy et al, 'Issues in High Harmonic Seeding of
the 4GLS XUV-FEL', these proc.
[15] N. Thompson et al, 'A VUV-FEL for 4GLS: Design
Concept and Simulation Results', FEL 2005, p79.
[16] N. R. Thompson et al, 'A 3D Model of the 4GLSVUV-FEL Conceptual Design Including Improved
Modelling of the Optical Feedback Cavity', theseproc.
[17] D. J. Dunning et al, 'First Tolerance Studies for the
4GLS FEL Sources', these proc.
[18] B. W. J. McNeil et al, 'FELO: A One-Dimensional
Time-Dependent FEL Oscillator Code', these proc.
[19] S Reiche, Nucl. Instrum. Methods, A 429 (1999)
p243.

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TUAAU03

FEL OSCILLATION WITH A HIGH EXTRACTION EFFICIENCY AT
JAEA ERL FEL
N. Nishimori∗ , R. Hajima, H. Iijima, N. Kikuzawa, E. Minehara, R. Nagai, T. Nishitani,
M. Sawamura, JAEA, Ibaraki, Japan.
Abstract
One of challenges that high-power FEL oscillators
driven by energy recovery linac (ERL) are facing is to increase the extraction FEL efficiency as high as possible.
The high-efficiency oscillation relaxes the total beam current needed for high-power lasing and makes the optical
micropulse length shorter, which is useful for various applications. Two triple bend achromatic arcs have been used
in a recovery loop for an ERL FEL at Japan Atomic Energy Agency (JAEA). The return arc after an undulator has
an energy acceptance of 15%, which is large enough to recover the electron beam used for high-efficiency FEL oscillation. Recently we have achieved the efficiency exceeding 2%, which accompanies large energy spread, by doubling the electron bunch repetition rate. The FEL efficiency
has been measured from the horizontal profiles of the exhausted electron beam with a wire scanner installed at adispersive point in the return arc. The other arc placed upstream of the undulator has been found to work as a bunch
compressor for the high-efficiency FEL oscillation.

INTRODUCTION
One of challenges that high-power FEL oscillators
driven by energy recovery linac (ERL) are facing is to increase the extraction FEL efficiency as high as possible.
The high-efficiency oscillation saves the total beam current needed for high-power lasing, which decreases thebeam load to various accelerator components and increases
the wall-plug efficiency. The high-efficiency oscillation is
also appropriate for producing broadband ultrashort optical pulses, and makes the optical micropulse length shorter,
which is useful for various applications [1].
In a high-power ERL FEL at Jefferson Lab, a highefficiency FEL oscillation has been achieved at near IR
wavelength region [2, 3, 4]. The exhausted beam is transported to accelerators through a Bates type recovery loopwith energy acceptance of 15%, and full energy recovery
has been successfully established [5]. A recovery loop
which consists of two triple bend achromatic arcs has beenused for an ERL FEL at Japan Atomic Energy Agency(JAEA) [6]. The energy acceptance of the return arc after an undulator was 7% before June 2006 [7, 6]. Recently
we have achieved the efficiency exceeding 2%, which accompanies large energy spread beyond the energy acceptance of the arc, by doubling the electron bunch repetition
rate [8]. The optical pulse can now interact with a fresh∗ nishimori.nobuyuki@jaea.go.jp

Energy Recovery FELselectron bunch every round trip, while it overlapped withan injected electron bunch every two round trips before thedoubling.
In this paper, first we give brief description of the configuration and recent upgrade of JAEA ERL for a high-power
FEL oscillation with the doubled beam current. Then ourrecent experimental results on the FEL efficiency and thebeam dynamics through the energy recovery loop are reported in details. The FEL efficiency has been measured
with a wire scanner installed at a dispersive point in the
return arc, which can serve as a monitor of the energy distribution of the exhausted electron beam. The wire scanners have been also installed at other dispersive points forstudy of the beam dynamics through the triple bend achromatic arcs. A measurement of the energy distributions at
the first arc, which is placed upstream of the undulator, asa function of the accelerator phase has revealed that magnetic bunch compression in the first arc is indispensable fora high-power FEL oscillation at the JAEA ERL. Finally,
applications planned in JAEA FEL are presented.

CONFIGURATION OF JAEA ERL
The JAEA FEL facility has been developed as a highpower FEL at wavelength in far infrared region around 20
μm. The laser output power exceeded 1 kW within 500 μs
macropulse duration without energy-recovery in 2000 [9].
In order to increase the FEL output power higher than 10
kW and demonstrate the technology and commercial profitof high-power FELs for industrial applications, we have developed an ERL FEL as an extension of the original superconducting accelerator [10].
The layout of the JAEA ERL is shown in Fig. 1. An injector, main super-conducting accelerator (SCA) modules,
an undulator, and the first arc are from the original FEL.
An injection merger, a half chicane before the undulator,
and the return arc were installed for the ERL. The injector
consists of 230 kV electron gun with a thermionic cathode,83.3 MHz subharmonic buncher (SHB), and two cryomodules, each of which has a single cell SCA cavity driven at499.8 MHz. An electron bunch of 0.5 nC with full widthhalf maximum (FWHM) length of 600 ps is generated bya grid pulser at a 10.4 MHz repetition rate, that is 5 mA
average current, and compressed by the SHB followed by a
4.5-m drift. The electron bunch is accelerated to 2.5 MeV
by two single cells, and further compressed by ballistic
bunching through a 9-m drift. A two-step staircase is used
for the injection merger, because this configuration fulfills
the design requirements, achromaticity and small emittance265

TUAAU03

Proceedings of FEL 2006, BESSY, Berlin, Germany

optical cavity

the first arc
half chicane

undulator

the return arc
SHB

SCA P1 SCA P2

electron gun

beam dump

merger chicane

SCA M1SCA M2

Figure 1: The layout of JAEA Energy-Recovery Linac. An electron bunch generated by 230 kV electron gun is accelerated
to 2.5 MeV and injected into the energy-recovery loop. The electron bunch is accelerated to 17 MeV by main superconducting cavities and transported to the FEL undulator. The electron bunch is, then, re-injected to the main cavities anddecelerated down to 2.5 MeV and collected by a beam dump.

growth, and fits in the existing space. The achromaticity ofthe merger is realized by setting three quadrupole magnets
to the appropriate strengths. An electron bunch injected to
two main cryomodules, each of which has five cell SCA
cavities driven at 499.8 MHz, is accelerated up to 17 MeV
and transported to the undulator through the first arc andthe half chicane. After the FEL interaction, the electron
bunch is re-injected into the main cryomodules at a deceleration phase for the energy recovery. The re-injection
phase can be controlled by changing the recirculation path
length. The return arc has been placed on movable tables
for this purpose. Both arcs used in the recirculation loop
have two families of quadrupole magnets which enable one
to vary M56 while maintaining achromaticity. This variable
M56 can be used for bunch compression in the first arc andfor energy compression in the return arc. The return arc
also has two families of sextupole magnets to compensate
second-order aberrations T 166 , T266 , T566 arising from thelarge energy spread due to the FEL interaction.
The JAEA ERL-FEL has been operated in pulsed modeof 1 ms macropulse length in maximum and 10 Hz repetition rate, because of the following reasons. 1) The coolingpower of the refrigerator system for the SCA modules is not
sufficient enough to operate in CW mode. 2) The shield of
the building for the linac is not thick enough for the radiation protection.

UPGRADE OF JAEA ERL
Gun Grid Pulser and Injector RF sources
Increasing the injector beam current is a straightforward approach to increase the FEL power by taking fulladvantage of the energy-recovery. The JAEA gun has athermionic cathode driven by a grid pulser. In the original configuration, the gun was designed to produce 0.5 nC
electron bunches at 10.4 MHz repetition. We installed a
new grid pulser working at 20.8 MHz, doubled repetition266

of the original one, and a 10 mA beam is now available[11]. The new grid pulser is designed at Budker Institute of
Nuclear Physics and can be operated in CW-mode as wellas pulsed mode [12]. The electron beam properties with
the new grid pulser keep similar performance to the original one. The pulse width and the normalized rms emittanceat the gun are 590 ps (FWHM) and 20 πmm·mrad, respectively [11].
Two single-cell cavities of the injector were driven by
8 kW solid state amplifier for each, enough capacity for 5
mA operation. The solid state amplifier was replaced by an
IOT-klystrode of 50 kW, which enables one to inject a 40
mA beam into the ERL [13].

RF low-level controllers
Stable operation of an FEL relies much on the stabilityof an accelerator. An RF low-level controller for a SCA
is one of the key components for achieving good stability. The original JAEA FEL was equipped with a low-level
controller, which kept phase flatness at ±1 degree within a
1 ms macropulse. The low-level controller was replacedby new one, which provides the following functions forthe better stability: the feedback gain and bandwidth canbe varied during operation to obtain good flatness of RFphase and amplitude, and all the circuits are contained inboxes with temperature stabilization. The new controller
is installed in the vicinity of the SCA cavity to make thecable length between the controller and the SCA as short
as possible. Furthermore the cables between the controller
and the cavities are contained in a temperature-controlled
pipe to suppress the temperature drift. After these upgrade,the accuracy and stability of accelerating RF has been improved. The flatness of RF phase and amplitude within a
1 ms macropulse are 0.06 deg. rms and 0.013% rms, respectively, while those for the old system were 0.20 deg.
and 0.013% [14]. Phase and amplitude fluctuations for 5
minutes in the new system are measured as 0.15 deg. andEnergy Recovery FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

FEL EFFICIENCYThe FEL wavelength at the JAEA FEL is around 20 μm
and a holed mirror is used to couple FEL out of the optical cavity. The coupling efficiency of the holed mirror
is estimated to be around 30% [15]. It is however difficult to exactly determine the FEL efficiency from the measured FEL power only. The FEL efficiency can be obtained
from a measurement of the beam centroid shift of the exhausted beam from the position without lasing at a dispersive point. A non-destructive method is indispensable forthe energy analyzer, since the exhausted beam has to be recovered under an ERL operation. A synchrotron radiation(SR) monitor allows for continuous monitoring of the energy spectrum of the beam for an ERL operated even at afull power [16, 5]. The SR wavelength at the JAEA ERL
is however longer than 20 μm, where no monitor camera
is available. A beam position monitor is also a promising
candidate for measuring the shift of the beam centroid [17].
It does not however provide information about the energy
distribution of the exhausted beam, which is also importantfor beam energy recovery. We decided to use a wire scanner, which is appropriate for measuring profiles of pulsed
or low-current-CW beams, although it is a partially intercepting device.

0.1

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δL (μm)

-20

20

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0
10
wire position (mm)

δL=+10μm
0μm
-1μm
-2μm
-4μm
-6μm
-10μm
-20μm
-30μm

20

30

0.8

FEL power at δL= 0 μm (W)The doubled beam current has enabled us to operate the
JAEA ERL FEL with efficiency higher than 2%. The resulting large energy spread of the exhausted electron beam
exceeded the energy acceptance of the return arc, whichcaused a radiation problem when the FEL was operated
for a long time period at a macropulse length longer than
250 μs. We made minor modification of the return arc
to increase the beam energy acceptance. The bore ofquadrupole magnets of the return arc was enlarged from
64 mm to 102 mm. The beam pipe diameter was enlarged from 55 mm to 100 mm. The energy acceptanceof the return arc has been increased from 7% to 15%. The
quadrupole magnets in the first arc were also replaced withthose used in the return arc. The energy acceptance of thefirst arc has been increased from 3.5% to 4.3%.

total current (μA)

Increased energy acceptance of the arcs

to measure large dynamic range beam profile in an ERL
where small beam loss like beam halo represents significant amount of beam power [18]. A wire array based on
secondary electron emission current is used to provide time
resolved electron spectrum, which is useful to study theevolution of the energy spectrum from a narrow to a broad
spectrum as a result of the FEL interaction [19, 20].
The wire scanner used in the present study is based ona linear movement of a copper wire in 0.6 mm diameter
through the beam at a speed of 0.39 mm/s by 100 mmstroke. The copper wire is mounted on an aluminium fork
with a gap of 26 mm and electrically floated from theground. The secondary electron emission current is measured with a current meter (TR8641 electronic picoammeter, ADVANTEST). The wire position is measured with alinear potentiometer and is recorded in an ADC (WE7272
isolated digitizer, YOKOGAWA) together with the secondary electron current.

secondary emission electron current (μA)

0.015%, respectively.

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0.0
40

Figure 2: Horizontal beam profiles for various cavity
detuning lengths measured with a wire scanner (WIRE#1) placed in the middle of the drift space between two
quadrupole magnets just after the first bending magnet in
the return arc, where horizontal dispersion is measured tobe η = 0.376 m. The vertical axis shows secondary electron emission current and horizontal axis shows wire position. The total secondary emission electron current integrated along the wire position is plotted with respect tooptical cavity detuning length in the inset. The FEL powerat δL = 0 μm during a wire scan is represented by a blacksolid line.

Wire Scanners
A wire scanner consists of a thin wire that is moved
across the beam path. The local density of the electrons
traversing the wire is detected by measuring such secondary particles as secondary electrons and bremsstrahlung
photons produced by the interaction of the electron beamwith the wire. Detection of the secondary particles allows one to measure the beam profile, and wire scanners are widely used as beam profile monitors. Detecting bremsstrahlung photons with a scintillator and a photomultiplier placed downstream of the wire has enabled one

Energy Recovery FELs

Electron energy distributions and FEL efficiency
Figure 2 shows horizontal beam profiles measured forvarious detuning lengths (δLs) of an optical cavity withthe wire scanner, which is installed in the middle between
two quadrupole magnets placed just after the first bending
magnet in the return arc. This wire is called WIRE #1 in
the present paper. The horizontal dispersion at the wire
scanner is measured to be η = 0.376 m from the shift ofthe beam centroid with respect to the magnetic field of thefirst bending magnet. This is similar to the value of η =267

TUAAU03

Proceedings of FEL 2006, BESSY, Berlin, Germany

0.41 m calculated from a first-order matrix of beam transport (see Fig. 5). The vertical axis shows secondary emission electron current from the wire scanner and horizontal
axis shows wire position. The polarity of the secondary
electron current is positive. The inset shows the total secondary emission current integrated along the wire position
as a function of δL. The total secondary current is 1.5 μA,
which is almost independent of δL. The secondary electron
production rate for 17 MeV electron on our wire scanner isestimated to be 8%, since the incident electron beam current during the measurement was 18.5 μA. The production
rate is similar to that for for 30 MeV electron on carbon,
which is measured to be 3% [21]. The peak secondary electron current measured by the wire is less than 0.07 μA (seeFig. 2), indicating that the beam loss due to the presence of
the wire is small (less than 5%). This explains our observation that the FEL power at δL = 0 μm remains unchanged
during the wire scan, which is shown by a black solid line
in Fig. 2,

0.5

20
2.4
15
2.0

10
5

1.6

0
-100 -80 -60 -40 -20
0cavity detuning length (μm)

1.2

FEL efficiency (%)

1.0

2.8
beam dump current (μA)

FEL power (W)

1.5

0.8
0.4
0.0
-100

0.0
-80

-60
-40
-20
cavity detuning length (μm)

0Figure 3: FEL power measured as a function of δL at
macropulse length of 230 μs. FEL efficiencies obtained
from the energy distributions of the exhausted electron
beam are shown by open squares. The efficiencies nearzero detuning length cannot be measured with our energy
analyzer due to the limited energy acceptance, and they are
determined from measured FEL power. The inset shows
the beam dump current with respect to δL.
The FEL power changes as a function of δL, as shownin Fig. 3, and the energy distributions of the exhausted
electron beam changes as well (see Fig. 2). The shift ofthe beam centroid from the position without lasing yields
the FEL efficiency together with the dispersion η = 0.376
m. The measured FEL efficiencies are plotted as open
squares in Fig. 3. The efficiency higher than 2% cannot
be measured with our present wire scanner, since the scanner is placed downstream of the focusing quadrupole magnet where the dispersion is maximum of η = 0.6 m. The
sharp edge of the beam profiles seen around the wire position of −34 mm in Fig. 2 represents the beam loss in thelower energy side at the first quadrupole. The amount of
the beam loss is considered to be small, since the total sec-

268

ondary electron current is almost constant with respect toδL (see inset of Fig. 2). The maximum FEL efficiency isestimated to be 2.8%, as shown in Fig. 3.
Table 1: JAEA ERL FEL parameters
Parameter
Measured
Beam energy at undulator
17 MeV
Average current at undulator
8 mA
Bunch charge at undulator
0.4 nC
Bunch length at undulator
12 ps (FWHM)
Peak current
35 A
Energy spread before undulator 1.5% (FWHM)
after undulator> 15% (full)
Normalized emittance (rms)
40 mm mrBunch repetition
20.8250 MHz
Macropulse
1 ms × 10 Hz
Undulator period
3.3 cmNumber of undulator periods
52
Undulator parameter (rms)0.7
Optical cavity length
7.2 m
Rayleigh range
1.00 mMirror radii
6 cm
Output wavelength
22 μm
FEL extraction efficiency> 2.5%
The coupling efficiency of the holed mirror is obtained
from the present efficiency measurement. The measured
FEL power is 1.5 W for macropulse length of 230 μs. The
FEL power during the macropulse is estimated to be 0.75
kW, since the FEL power for the first 30 μs is negligibly
small. The FEL is extracted through a KRS5 window, thathas the transmittance of 70% in normal incidence. The
beam current measured at the beam dump is 18.5 μA corresponding to the average beam current of 8 mA. From thoseexperimental results, the coupling efficiency of the holed
mirror is estimated to be 28% and agrees well with the calculated value of 30% [15]. The JAEA ERL FEL parameters
are listed in Table 1.

Thermal effect on the wire scanner
Heating of the wire might be a concern when attempting to measure the profile of high average power electron
beams [22]. The stopping power for 17 MeV electrons incopper is 2.5 MeV cm 2 /g. [23], and the specific gravity ofcopper is 8.94 g/cm 3 . We assume that the copper wire in
0.6 mm diameter is regarded as a foil with width of 0.532
mm and depth of 0.532 mm. The energy loss of 17 MeV
electron in the copper wire is estimated to be 1.2 MeV. The
total charge struck by the electron beam during a wire scanis measured to be less than 25 μC when macropulse lengthis 230 μs, and the maximum power deposited on the wire
during the scan is 30 J. The specific heat of copper is 0.385
J/g/K at 25◦ C. Thus the temperature rise of the wire canbe estimated to be 15000 K in maximum when we assume
that the heat accumulates in the wire within a vertical distance of 2 mm, which is similar to the vertical beam size.

Energy Recovery FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany
30

WIRE #1

20

WIRE #2βxβ(m)However we need to take thermal radiation power, thermal
conductivity of copper, power of secondary emission particles, and others which can alleviate the temperature riseof the wire, into account. Although the wire scanner canbe used as an energy analyzer as long as heating is not a
problem, we need to study this thermal effect in details.

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βy

20

4

0

1

5

0
-150

-100

-50

0

50

δL (μm)Figure 4: FEL efficiencies as a function of δL obtained
from a one-dimensional time-dependent FEL simulation(solid line) and corresponding beam energy spread (dottedline). Measured FEL efficiencies are also plotted as open
squares for comparison.

FEL simulation
We have conducted an FEL simulation for comparison
with the experimental result. We use one-dimensional
time-dependent FEL simulation code, which was used in
our previous studies [24] and agrees well with experimental results obtained without energy recovery. The electron
bunch length measured at the undulator center is 12 ps(FWHM). The electron bunch shape used in the simulation
is assumed to be triangular with the peak Colson’s dimensionless beam current of j 0 = 25. A mono energetic electron beam is assumed in the simulation, since the peak FEL
efficiency depends little on initial energy spread [24]. The
optical cavity loss is measured to be 4.2% from a cavity
ring down of the FEL pulse with a Ge:Cu detector. Figure
4 shows calculated FEL efficiency and full energy spreadof an electron bunch as a function of δL. The measured
FEL efficiencies are much smaller than those obtained in
the simulation at large detuning lengths. This may be dueto the large energy spread of the incident electron beam.

BEAM TRANSPORT IN THE RETURN
ARCTransverse and longitudinal beam dynamics through thereturn arc for JAEA ERL has been already studied to finda matched beam envelope from the undulator to the beam
dump [7]. In order to roughly estimate dispersion and
M56 in the return arc, we calculate the beam envelope

Energy Recovery FELs

0

1

2

3

4

5

6

Z(m)

from
undulator

tomerger chicane

return-arc

Figure 5: Beam envelopes from the undulator exit throughthe return arc to the merger chicane calculated from a firstorder matrix of beam transport. The positions of wire scanners are indicated by arrows.

from the undulator to the entrance of main SCA modules
based on magnet parameters used for actual beam transport. Courant-Snyder parameters at the exit of the undulator are given from the matched beam condition for the undulator, αx = 0; βx = 0.33 m; αy =−1; βy = 1.7 m. Figure
5 shows obtained betatron functions for the beam envelope,
where M56 = −0.56 m from the undulator to the entranceof the merger chicane.
0.1

0.08

0.06

total current (μA)

10

-10

secondary emission electron current (μA)

2

0
-200

10ηx

15
full energy spread (%)

FEL efficiency (%)

32
δL=+20μm
0μm
-2μm
-6μm
-10μm
-30μm

1
0
-40

0.04

-20
0
δL (μm)

20

0.02

0
-40

-30

-20

-10

0

10

20

30

40

wire position (mm)Figure 6: Horizontal beam profiles for various cavity
detuning lengths measured with a wire scanner (WIRE#2) placed in the middle of the drift space between two
quadrupole magnets just after the second bending magnet
in the return arc, where horizontal dispersion should be thesame as that of WIRE #1, η = 0.376 m, when the return arc
is achromatic. The inset shows the total secondary emission electron current integrated along the wire position withrespect to δL.

269

Proceedings of FEL 2006, BESSY, Berlin, Germany

MAGNETIC BUNCH COMPRESSION IN
THE FIRST ARC
A high peak current electron beam, which can be accomplished by means of magnetic, ballistic, or velocity bunch
compression, is indispensable to realize a high-efficiency

270

2.0

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θ=-17
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FEL power when θ=0 (W)secondary emission electron current (μA)

(a)

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10
wire position (mm)

20

30

2.0

2.0

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0.5

total secondary electron current (μA)(b)

FWHM energy spread (%)

A drawback of a triple bend achromatic arc is that
quadrupole magnets have to be properly set not only toadjust M56 for energy compression, but also to establish
achromaticity in the arc. This is in contrast to the Bates
type end loop where a pair of quadrupole magnets and apair of sextupole magnets are used just to control M 56 ,T566 , respectively, since the end loop is intrinsically achromatic [5]. Therefore achromaticity has to be carefully
checked in a triple bend achromatic arc. We have measured horizontal beam profiles downstream of the second
bending magnet in the return arc with a wire scanner (seeFig. 6). This wire scanner is called WIRE #2 in the present
paper and has been installed in the middle of the drift space
between two quadrupole magnets after the second bending magnet and should have the same dispersion function
as WIRE #1 when the return arc is achromatic. However,the beam profiles shown in Fig. 6 are similar to those in
Fig. 2 only when the FEL efficiency is less than 1%, andthey are quite different from each other when the efficiency
is higher than 1%, requiring chromaticity correction. The
total secondary electron current measured with WIRE #2,
which is shown in the inset of Fig. 6, is almost the same asthat with WIRE #1. The beam loss is thus expected to besmall in the return arc. In the measurement shown in Fig.
6, sextupole magnets are not used to compensate second
order aberrations T 166 , T266 , T566 arising from the large
energy spread due to the FEL interaction. We will performa systematic measurement of the horizontal beam profiles
with various parameter sets of sextupole magents soon.
A current transformer placed downstream of the returnarc, which picks up an induction current, is also used asa beam loss monitor for the return arc. The current transformer signal remains almost the same when the FEL efficiency is low, but some beam loss is observed for theefficiency higher than 2%. The beam dump current withrespect to δL should be constant when the full energy recovery is established. However the beam current gradually drops as the efficiency increases over 2%, as shown in
the inset of Fig. 3. One possible reason is that the energy
spread of the recovered beam is beyond the energy acceptance of the beam dump. Although the dump can collectthe beam with four times different momentum, the energy
spread of the recovered beam can exceed the acceptanceunder high-efficiency FEL oscillation. Without sufficientenergy spread compression, the energy spread can remain
2.5 MeV, which corresponds to 15% of 17 MeV beam,
while the mean energy of the recovered beam is lower than
2.5 MeV. We need to study carefully how much beam isrecovered through the main SCA modules and how muchof the recovered beam is collected by the beam dump.

difference of mean energy (%)

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0.0
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0

5

θ (deg.)Figure 7: The top figure (a) shows horizontal beam profiles measured with a wire scanner placed just after the firstbending magnet in the first arc, where horizontal dispersion
is calculated as η = 0.50 m, with respect to the RF phase of
the last SCA module M2 defined as θ. The black dottedline shows measured FEL power during a wire scan when
θ = 0◦ , where the FEL power is maximum. The bottom
figure (b) shows relative difference of the beam centroid
energies (solid line), FWHM energy spreads (dotted line),
and the total secondary emission electron current from thewire scanner as a function of θ. Those data are obtained
from the top figure (a).

FEL oscillation. At the JAEA ERL, ballistic bunching,which is performed before the main SCA modules, hadbeen considered to play a major role in the bunch compression [25]. Recently we measured powers of coherent
synchrotron radiation (CSR) generated from three bending
magnets in the first arc and found that the CSR power at thelast magnet is much stronger than the remaining two. This
indicates that another bunch compression occurs in the firstarc. In order to confirm this magnetic bunch compression,
we measured horizontal beam profiles with a wire scannerat a dispersive point as a function of the RF phase of thelast SCA module (SCA M2). Hereafter we use θ as the RFphase of SCA M2. The horizontal dispersion at the wire
scanner located just after the first bending magnet is estimated to be η = 0.50 m from the first-order matrix calculation. The measured beam profiles are shown in Fig. 7(a).
Here we set θ = 0◦ where the FEL power is maximum. The

Energy Recovery FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

Energy Recovery FELs

3000

2500

(a)
θ=-14.2
-10
-5
0
2
4
6

counts/ch

2000

1500

1000

500

0
-60

-40

-20

0

20

40

60

80

time (ps)
20

40

10

30

0

20

-10

10

FWHM bunch length (ps)(b)
bunch arrival time (ps)black dotted line shows FEL power with respect to the wire
position when θ = 0 ◦ . The power decreases by 10% when
the wire passes the beam centroid. The ratio of FEL power
loss is consistent with the ratio of beam loss due to the presence of the wire scanner, which is calculated from the peaksecondary current of 0.1 μA divided by the total secondary
current of 1.4 μA.
Figure 7(b) shows difference of the mean energy,
FWHM energy spread, and total secondary electron current with respect to θ. The energy spread is 1.5% when
θ = 0◦ , but it decreases down to 0.8% as θ decreases to−12◦ . The energy of beam centroid shifts toward higher
energy side with decreasing phase and reaches maximum
around θ = −10 ◦ . The energy difference between θ = 0 ◦and θ = −10◦ is 0.8% corresponding to 0.14 MeV for 17
MeV electron. Since the energy gain for each main SCA
module is roughly 7.5 MeV, 11 degree off-crest acceleration yields the same amount of energy difference. Fromthese results, we can conclude that θ = 0 ◦ is about 10 degree off-crest of the SCA M2 phase. The total secondary
electron current gradually increases with decreasing θ, andthe ratio of the current increases by 20% when θ = −17 ◦ .
The similar amount of beam loss is observed in another experiment. We have measured beam currents with a Faraday
cup both in the straight section along the main SCAs andafter the first arc, and observed that the beam loss throughthe first arc amounts to roughly 20% when the RF phaseis adjusted for the FEL power to become maximum. This
indicates that the lower energy side of the electron beamarising from the off-crest acceleration is lost at the beam
duct of the first bending magnet in the first arc. We have aplan to replace the beam duct with one having larger bore
and repeat the same measurement to study the energy spectra of the accelerated electron beam with respect to θ inmore details.
We have also measured temporal beam profiles at the undulator center as a function of θ with a synchroscan streak
camera (M1954-10, Hamamatsu) at macropulse length of
30 μs, as shown in Fig. 8(a). The centroid of beam profiles changes as a function of θ, since the beam arrival time
shifts due to M56 from the SCA M2 to the undulator. The
shift of arrival time and rms bunch length are shown in Fig.
8(b). The shortest FWHM bunch length of 12 ps is obtained
when θ = 0◦ , indicating that high peak current is indispensable for the high-efficiency FEL oscillation. The arrival
time difference between θ = 0 ◦ and θ = −10◦ is 10 ps, andthe corresponding momentum difference between the two
acceleration phases is 0.8% from Fig. 7(b). This leads to
M56 = 0.38 m, where the sign of M 56 is determined fromfirst-order matrix calculation of the first arc based on themagnet parameters used for actual operation. The calculation yields M56 = 0.6 for the first arc and M 56 = 0.07 forthe half chicane.
We will perform the same measurement somewhere
downstream of the second arc to obtain M 56 from the undulator center to the entrance to the main SCA modules. The
value of M56 in the return arc should be the same as that to

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θ (deg.)Figure 8: The top figure (a) shows temporal beam profiles
measured with a synchroscan streak camera at the undulator center with respect to the RF phase of the SCA M2 (θ).
The bottom figure (b) shows relative difference of the beam
arrival time (solid line), and FWHM bunch length (dottedline). Those data are obtained from the top figure (a).

the undulator from the exit of SCA M2 except for its sign,
if the energy compression in the return arc is properly executed. It is worth to mention that such a longitudinal phasespace manipulation using magnetic bunch compression anddecompression is performed in JLab FEL in an elegant way[5], where M 56 = −0.3 m from the exit of SCA modules tothe undulator for the bunch compression and M 56 = 0.3 m
from the undulator to the entrance of SCA modules for theenergy compression.

APPLICATION
A laser-beam transport line has been built to deliver FEL
pulses to an experiment room. We have upgraded an optical beam expander, which consists of two elliptic mirrors,
at the end of FEL optical cavity to convert a diverging beamfrom a center-hole on a FEL cavity mirror into a parallel
beam. The expanded beam is transported to the experimental room through a 24 m-long evacuated pipe. FEL
transport efficiency 50% has been achieved [1].
For FEL applications, we investigate material processing
using ultrashort FEL pulses. By using FEL pulse shorter
than pico-second, it is possible to avoid thermally induced

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stress and debris generation, which has been unavoidable inmaterial processing with Q-switched YAG lasers or CO2
lasers [26]. Recently we found that non-thermal surface
peeling of stainless steel by ultrashort laser pulses canbe adopted to eliminate stress-corrosion-cracking (SCC),
which is a critical problem in nuclear power plants [27].
A pilot experiment using Ti:sapphire laser showed that we
can remove the residual stress and SCC susceptibility ofcold-worked and hardened stainless steel by the laser peeling. Application of self-chirped FEL pulses is also studied. We reported that frequency chirp is induced in an FEL
pulse, when the FEL oscillator has large gain and is operated at perfectly synchronized cavity length [28]. We
demonstrated generation of an FEL pulse with frequency
chirp of 14% and duration of 320 fs. A laser pulse withsuch large frequency chirp can be used for quantum control of chemical reaction: the resonant excitation of atomic
or molecular systems, which have an anharmonic potential
ladder [29].

REFERENCES[1] H. Iijima et al.,“ Development of frequency-resolved optical gating for measurement of correlation between time andfrequency of chirped FEL”, in these proceedings.
[2] S. Benson et al.,“High power lasing in the IR Upgrade FEL
at Jefferson Lab”, Prof of the FEL-2004, 229 (2004).
[3] S. Benson,“Design challenges in high power free-electron
laser oscillators”, abstract of the FEL-2005, (2005).
[4] G.R. Neil et al.,“The JLab high power ERL light source”,
NIM A 557, 9 (2006).
[5] D. Douglas,“The Jefferson Lab 1kW IR FEL”, Prof of the
LINAC-2000, 716 (2000).
[6] R. Hajima et al.,“First demonstration of energy-recovery operation in the JAERI superconducting linac for a high-powerfree-electron laser”, NIM A 507, 115 (2003).
[7] R. Hajima, E.J. Minehara,“Electron beam dynamics througha return-arc and a deceleration path of the JAERI energyrecovery linac”, NIM A 507, 141 (2003).
[8] R. Nagai et al.,“Beam current doubling of JAEA ERL-FEL”,
in these proceedings.
[9] N. Nishimori et al.,“High extraction efficiency observed at
the JAERI free-electron laser”, NIM A 475, 266 (2001).
[10] R. Hajima et al.,“Design of energy-recovery transport for
the JAERI FEL driven by a superconducting linac”, NIM A
445, 384 (2000); T. Shizuma et al.,“Simulated performanceof the energy-recovery transport system for JAERI-FEL”,
ibid 475, 569 (2001).
[11] N. Nishimori et al.,“20.8 MHz electron gun system for anenergy recovery linac FEL at JAERI”, Proc. of the APAC2004, 625 (2004).
[12] V.P. Bolotin et al.,“Status of the Novosibirsk energy recovery linac”, NIM A 557, 23 (2006).
[13] M. Sawamura et al., “Status and development for the JAERIERL-FEL for high-power and long-pulse operation”, Prof of
the EPAC-2004, 1723 (2004); Masaru Sawamura and Ryoji
Nagai, “Status of RF system for the JAERI energy-recovery
linac FEL”, NIM A 557, 287 (2006).

272[14] R. Nagai et al.,“Improvement of RF low-level controller for
JAERI ERL-FEL”, Prof of the 1st annual meeting of Part.
Acc. Soc. of Japan, 293 (2004) (in Japanese).
[15] R. Nagai et al., “Optical resonator optimization of JAERIERL-FEL”, NIM A 528, 231 (2004).
[16] P. Chevtsov et al., “Non-invasive energy spread monitoring
for the JLAB experimental program via synchrotron lightinterferometers”, NIM A 557, 324 (2006).
[17] A.P. Freyberger and G.A. Krafft, “Summary report on synchronization, diagnostics and instrumentation”, NIM A 557,
370 (2006).
[18] A.P. Freyberger, “Large dynamic range beam profile measurements”, Proc of the DIPAC-2005, 12 (2005).
[19] T.I. Smith et al., “Status of the SCA-FEL”, NIM A 296, 33(1990).
[20] W.A. Gillespie et al.,“Time-resolved electron spectrum
measurement on the FELIX facility”, NIM A 331, 786(1993).
[21] R.I. Cutler et al., “Performance of wire scanner beam profile monitors to determine the emittance and position ofhigh power CW electron beams of the NBS-Los Alamos
racetrack microtron”, Proc of the PAC-1987, 625 (1987);
M.A. Wilson et al., “Performance of the 5 MeV injector
for the NBS-Los Alamos racetrack microtron”, ibid, 322(1987); D.B. Barlow et al.,“Prototype flying-wire beamprofile monitor”, Proc of the PAC-1993, 2480 (1993).
[22] J. Camas et al.,“Observation of thermal effects on the LEP
wire scanners”, Proc of the PAC-1995, 2649 (1995).
[23] http://www.physics.nist.gov/PhysRefData/Star/Text/
contents.html[24] R. Hajima et al.,“Analyses of superradiance and spikingmode lasing observed at JAERI-FEL”, NIM A 475, 270(2001).
[25] R. Hajima et al.,“Development of an energy-recovery linac
for a high-power FEL at JAERI”, Proc. of the APAC-2004,
245 (2004).
[26] A. Nishimura et al., “Demonstration of material processing
using JAERI-FEL”, Proc of the FEL-2003, II-57 (2003).
[27] E.J. Minehara et al., “Preparation femtosecond laser prevention for the cold-worked stress corrosion crackings on reactor grade low carbon stainless steel”, Prof of the FEL-2004,
665 (2004); E.J. Minehara et al., “JAERI 10kW high power
ERL-FEL and its applications in nuclear energy industries”,
Prof of the FEL-2005, 305 (2005).
[28] Ryoichi Hajima and Ryoji Nagai, “Generation of a selfchirped few-cycle optical pulse in a FEL oscillator”, PRL
91, 024801 (2003).
[29] S. Chelkowski et al.,“Efficient molecular dissociation bya chirped ultrashort infrared laser pulse”, PRL 65, 2355
(1990).

Energy Recovery FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUAAU04

ON THE DESIGN IMPLICATIONS OF INCORPORATINGAN FEL IN AN ERL
G. R. Neil, S. V. Benson, D. Douglas, P. Evtushenko, and T. Powers
Thomas Jefferson National Accelerator Facility, Newport News VA 23606 USA.
proven to be a great learning tool in the path toward thenext generation ERLs. Key areas for discussion include:
1) impact of longitudinal phase space manipulation
on rf phase and amplitude control and srf cavity
specifications2) magnetic field quality, higher order term
management for transverse and longitudinal
acceptance3) wakefields and resistive wall effects

Abstract
Encouraged by the successful operation of the JLab
Demo in 1998, many high current ERLs are now being
designed with not only short pulse synchrotron beamlines
but also FELs. Such inclusion has major implications onmagnet quality, rf feedback requirements, wiggler design,
srf cavity QL, halo, etc.
Measurements on the JLab ERL FEL have identified
new challenges. The JLab Upgrade was designed with a
160 MeV beam of 10 mA in 75 MHz, 300 fs bunches.
FEL designers set transverse emittance and longitudinalbunching requirements, but to accommodate an FEL in
our ERL also means setting stringent phase stability
requirements of (<6x10-9/fm rms) based on a desired FEL
detuning tolerance of 1.2 microns. Recovered beam RF
loading on the subsequent accelerated beam complicatessatisfying these requirements. Gain in the rf feedback
limits the accuracy of energy stability when loaded Qs are~107. Energy recovery to <10 MeV sets magnetic field
tolerances at 10-4. We present measurements on the JLabERL showing how to set system requirements to toleratesuch FEL lasing.

LONGITUDINAL PHASE SPACE
For an FEL ERL it is generally desirable to let the bunch
length remain long during initial acceleration to minimize
longitudinal emittance growth. By operating off crest, acorrelated energy spread in imposed on the beam that canbe used to compress the beam to high peak current at the
wiggler. The FEL then imposes an energy spread duringlasing with a full width on the order of 6 times theextraction efficiency. This large energy spread must betransported to the dump during energy recovery. In
addition the centroid of the distribution loses energy
according to the FEL efficiency. If an appropriate M56
and path delay in the transport is applied before
deceleration the energy spread of the beam can becompressed as the beam decelerates so that the ultimate
energy spread as a fraction of the energy is not muchlarger than the FEL-imposed spread. The offset
deceleration angle must be chosen to be sufficient tohandle the full energy spread of the beam or successfultransport to the beam dump will not be possible (Figure1). Given the large energy spread of the decelerating
beam it is also necessary to match the higher order termsof the magnetics. The Upgrade FEL utilizes sextupoles tohelp match the rf curvature and minimize dE/E at the
dump [2-4].

BACKGROUND
Given the rising interest in Energy Recovered Light
Sources incorporating Free Electron Lasers [1], it is
helpful to review what specifications of the light source
may need revision in order to accommodate the strict
demands of the FEL. The discussion below should not beviewed as inclusive but rather is a starting point for
further analyses based on experience to date. We give
examples of specific criteria based primarily on our
experience with the JLab IR Upgrade machine, which has

φ0
E

t

E li n ac c os φ 0?
Figure 1. Electron distribution on the acceleration and deceleration rf phase. If the energy spread of the beam exceeds(ΔE/E)FEL/2 < Elinac cos φ0 then there is not sufficient rf gradient to decelerate those electrons.

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60

5442 W

7W
591

W

72
44

0W

911 W

20

911 W

W

2237 W

911 W

Klystron Power“Cavity” Power“Beam” Power
Figure 2. Loading of the rf with a) perfectly matched acceleration and deceleration, b) when the FEL turns on andinstantaneously shifts in phase, c) after the srf cavity tunes its resonance to minimize power draw.

A practical rf control system must be able to managetransients associated with the FEL turning on and off.
Figure 2 illustrates the beam load phasors in a typical rf
cavity with the accelerated and decelerated beam initiallyperfectly canceling. For the example parameters, when
the FEL turns on a phase shift of 7.2 degrees results andinitially the rf power draw goes from 911 W at zero
degrees to 7244 W at 50 degrees in the rise time of thelaser: ~ 10 microseconds. Given time the srf cavity canretune to minimize the power draw (Figure 2c, 3). The
resultant is then 2237 W at zero degrees. The energy of

the accelerated beam must not change substantially during
this transient or a relaxation instability between the FEL
and accelerator can be initiated. It is important to notethat although an ERL with perfectly opposed accelerating
and decelerating beams can operate in principle with avery high loaded Q >> 107 such an arrangement makes
this turn on and management of the FEL much moredifficult. In practice, it may be more practical to trade thehigh CW power draw for ease of operation by having alower QL [5].

RF power as a function of beam current cavity FEL3-4,
first pass -10d second pass +160d off crest, CW, tuners on

3

RF Power (kW) .

2.5

2

1.5

1

0.5

Predicted After Tuner Nulls Out Imag Part
Predicted With Fixed Tuner Position
Actual Vaules Taken Every Two Seconds During the Run

0
0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Beam Current (mA)

Figure 3. Measured and calculated RF power draw during lasing with cavity tuning for rf power minimum.

274

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Proceedings of FEL 2006, BESSY, Berlin, Germany
Having excess power available to stabilize fluctuations
is crucial. The optical cavity must have its round trip
travel time precisely matched to the arrival time of theelectron bunches for stable lasing. To keep the peak-topeak fluctuations smaller than 10% it is necessary to keep
the cavity length stable to less than 0.05GNλ. For
example, in the JLab IR Upgrade for G of 0.5, a N of 32,
and λ at 1.5 µm one must keep the cavity length constantto <1.2 µm peak to peak. The micropulse arrival timemust be kept constant to the same precision:δω δL 1.2 ×10 −6<<= 3.8 × 10 −8
ω
L
32

(1)

From the frequency modulation constraint you get aδτ < 6x10-9/fm. Note thattiming jitter constraint of
the FEL is fairly tolerant of slow timing jitter since theoptical cavity can follow this.

FIELD QUALITY
Since the FEL and energy recovery is sensitive to thephase of the rf it goes without saying that magnetic field
quality affects the path that any electron takes andtherefore must have tight tolerances. A transverse
variation in field ΔB leads to an erroneous angular spread

TUAAU04

across the beam of magnitude δx’ = ΔBl/Bρ ∼ ΔBl/(33.3
kG-m/GeV * Elinac). This evolves, via M52 a path length

spread δl, which differential path length spread in turntranslates to a final energy spread ΔEdump which equals

2π sinφ0 Μ52(ΔBl/33.36 kG-m)/λRF (GeV). From thisone can conclude that the allowed error field integral ΔBl
is independent of linac length/energy gain. In otherwords the tolerable relative field error falls as energy(required field) goes up. Higher energy ERLs will haveincreasing difficulty meeting this requirement. For the
JLab Upgrade the tolerances are of order ΔEdump ~ 3400

MeV * (ΔB/B) and ~ 0.16 keV/G-cm * (ΔBl); thus a 10-4
relative field error budget leads to a remnant momentum
spread of 340 keV after energy recovery. This has led to
the necessity of careful design, mapping, and hysteresis
control of the magnets in the Upgrade. Major dipoles(seemust be spectrometer grade with dB/B of 10-4
Figure 4 for an example of one of our IR Upgrade
magnets).
A substantial amount of effort has gone into making the
IR Upgrade FEL transport have the ability to linearize andcontrol higher order transport terms so as to achieve theshortest possible bunch length at the wiggler andsuccessfully transport beam energy spreads of up to 15%
all the way to the beam dump with current losses less than
10-4. A full discussion of this system is beyond the scopeof this paper. We refer the reader to [3].

Figure 4. Measured field contours of a GX dipole at 0.4 G resolution. Precision measurements such as these must be
made at all desired operating points (or ranges) and B• dl calculated for high order transport.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

WAKEFIELDS
The wakefield produced by relativistic particles is an
issue often dealt with in storage rings so techniques toaddress this are well known in the community. The issues
with an ERL can be more severe than with such storagerings because of the short bunch lengths required at the
FEL itself. This causes the high frequency collective
emission cutoff to move to much higher frequencies, abenefit if one is looking for THz emission but a detrimentin terms of resistive wall heating and excitation of
unintended cavities along the beam pipe. Transitions
between different size and shape chambers must be
engineered to minimize wakefield problems or significant
heating of the electron beam can result.
In addition, the narrow chamber required for wigglers
exacerbates the problem since the longitudinal wake goesinversely with the square of the pipe diameter. Sucheffects can have dramatic consequences even at themodest currents (5 to 10 mA) of our first generation ERLs
(Figure 5).

SUMMARY
We have illustrated a number of ways in which thedemands of high longitudinal brightness at the input of
the FEL, and large energy spread at the output of the FEL
can drive tight specifications for the magnetic transportsystem and its apertures. In addition the need for output
stability and the impact of laser transients sets additional
strict requirements on the RF control system, and phaseand timing stability of the beam.
While existing
engineered solutions meet the need of first generation
machines, improvements will be needed to extend theperformance to systems presently in the planning stage.

Figure 5. An image of the IR Upgrade wiggler chamber in the visible and infrared during 4.6 mA of beam.
Heating is estimated at 35 W/m with the chamber reaching 42oC on top and 100oC at midplane.

ACKNOWLEDGEMENTS

REFERENCES

We had the support of the entire FEL team in developing
this work. We especially appreciate the help of Rui Li
and Eduard Pozdeyev of CASA in analyzing thewakefield effects. This work was supported by U.S. DOE
Contract No. DE-AC05-84-ER40150, the Office of Naval
Research, the Air Force Research Laboratory, the Army
Night Vision Laboratory, the Commonwealth of Virginia
and the Laser Processing Consortium.

[1] G.R. Neil, et al., Nucl. Inst. And Meth. In Phys. Res.
A557, 9-15(2006).
[2] D. R. Douglas, et al., Proc. Linac 2000, Monterey,
August 21-25, 2000.
[3] D. R. Douglas, JLab Technical Note JLABTN02002,(2002).
[4] S. Benson, Nucl. Inst. And Meth. In Phys. Res., A507,
40-43 (2003).
[5] A.M. Vetter, Nucl. Inst. And Meth. In Phys. Res
A429, 52-57(1999).

276

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TUAAU05

OPTICAL DESIGN OF THE ENERGY RECOVERY LINAC FEL ATPEKING UNIVERSITY*
Zhenchao Liu#, Kexin Liu+, Xiangyang Lu, Shengwen Quan, Guimei Wang, Baocheng Zhang,
Jiankui Hao, Kui Zhao, Jiaer Chen
Institute of Heavy Ion Physics & MOE laboratory of Heavy Ion Physics, Peking University, Beijing,
100871, China.
Abstract
Peking University is currently designing an Energy
Recovery Linac FEL (PKU-ERL-FEL). The system isconsisted of a DC-SC photocathode injector, asuperconducting linac which is composed of two nine cell
TESLA-type cavities, an undulator and beam transportsystem. The objectives of the PKU-ERL-FEL areproviding infrared FEL and building a test-bed for the
study of beam dynamics and accelerator technology forenergy recovery. In this paper the main parameters of the
PKU-ERL-FEL are described and the optical design forthe beam transport of PKU-ERL-FEL is presented. The
simulation is carried out using the typical particle tracking
codes such as elegant.

INTRODUCTION
Energy Recovery Linac (ERL) for FEL was approvedin Jlab [1]. It is an economical operation mode for widely
use in scientific research, industrial and other areas. As
the benefit of reducing most of the energy loss, ERL
would make it possible to construct large accelerators

which need huge power and increase the beam current toa very high level that seems difficult nowadays. Recently
many laboratories are developing ERL technology andsome facilities are under constructing such as ERLP in
Daresbury Laboratory [2][3][4]. Peking University alsoplan to build an Energy Recovery Linac FEL (PKU-ERLFEL) based on the research work of RF superconducting
technology. This facility will not only provide infrared
FEL (IR-FEL) for users but also be used as a test-bed forthe study of beam dynamics and superconducting linac
techniques for energy recovery. In this paper we mainly
discuss the optical issues of the PKU-ERL-FEL.

DISCRIPTION OF PKU-ERL-FEL
Similar with other facilities, PKU-ERL-FEL consists ofa DC-SC photocathode injector, a superconducting linac
which is composed of two nine cell TESLA-type cavities,
an undulator with mirrors in each side and beam transportsystem. PKU-ERL-FEL is under design and the generalparameters are determined. Figure 1 shows the layout andtable 1 gives the main parameters of the PKU-ERL-FEL.

Figure 1: Layout of PKU-ERL-FEL.
___________________________________________*Work supported by National Basic Research Project#lzhchao@pku.edu.cn+
kxliu@pku.edu.cn

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Table 1: Main parameters of the PKU-ERL-FEL

Transport system
Considering the limited space, the transport loop should
be at a smaller scale. The length between the outer side of
the outward arc and return arc is near 17 meters and thewidth of the trajectories is about 4.2 meters. 3 bend
merger is adopted for beam injecting to the linac.
Following the linac is the extraction chicane which bends
the decelerated beam to the dump. After the first arc
which contains three 60° bending magnets the beam will
be turned 180° to the opposite direction. Then the beam
goes through the chicane with a bending angle of 15° andthe undulator. The beam comes out from the second arc
and goes back to linac through the merger chicane. Theenergy is recycled and the exhausted electron beam goesto the dump with an energy of about 5MeV.

Injection Energy

5MeV

Maximum Energy

30MeV

Bunch Frequency

26MHz

Bunch Charge~60pC

Bunch length at Entrance of Undulator~1ps

Macro Pulse Length

2ms

Rep. Frequency of Macro Pulse

10Hz

Energy Spread (rms)0.24%Transverse Emittance （rms, n.）~3μm

Length of Undulator

1.5m

λu of Undulator

3cm

DESIGN CONSIDERATION

K of Undulator

0.5-1.4

Optical Cavity Length11.52mWavelength of FEL

4.7-8.3μm

It is well known that the lattice of an ERL-FEL systemshould be achromatic and the whole loop should be
isochronous. Keeping the matrix elements

Injector
The injector is a three and half cell DC-SC
photocathode injector working at 2K with a frequency of
1.3GHz. DC-SC photocathode injector has been studied at
Peking University since 1999 and demonstrated with a
one and half cell model [5]. The accelerating gradient of
this three and half cell DC-SC photocathode injector willreach 15MV/m and the transverse emittance of the beamfrom the photocathode is less than 3.0μm.

Linac
The linac is composed of two nine cell TESLA-type
cavities also working at 2K. Electron will be accelerated
to 30 MeV from 5 MeV at a gradient of about 13MV/m.
Then it goes through the whole loop and back to the linac
to be decelerated to 5MeV at 180° phase shift which isexactly achieved by adjusting the length of the whole loop.
The linac will be operated in pulse mode due to thelimitation of the capability of the cryogenic system.

Undulator
The undulator is 1.5m long and with 50 periods. The
wave length of the IR-FEL produced by the undulator isfrom 4.7μm to 8.3μm. As the bunch frequency is 26MHz,
the length of the cavity is currently set at 11.52m. Before
the undulator is a magnet compressor to compress thebunch length to about 1.0ps. The bunch length has to belengthened for effective deceleration. There are two ways
to lengthen the bunch after undulator, one is using a
decompressing chicane and another is adjusting the R56 ofreturn arc. We adopt the second way for saving cost andspace. Therefore the undulator is put close to the second
arc to make one mirror in the chicane and the other in theoutside of the first bending dipole of the second arc.

278

R16 = R26 = 0(1)

in each section is necessary to ensure the lattice to be
achromatic. Keeping the matrix element

R56 = 0(2)

will make the whole loop isochronous. Because we will
use the return arc to lengthen bunches, the R56 of thesecond arc should compensate the R56 coming from thecompression chicane and other parts:

R56,arc 2 = −( R56,chicane + R56,other )(3)

The waist of the beta function should be removable andthe beta function should match with the requirements of
the undulator.
Energy spread is another important parameter to realize
FEL and energy recovery successfully. The beam energy
spread is determined by [6]

δ<

1
4N

(4)

N is the undulator period. The undulator in PKU-ERLFEL has 50 periods so that the beam energy spread shouldbe less than 0.5%.
Space Charge and Coherent Synchrotron Radiation(CSR) can cause the increase of beam emittance.
Therefore they should be taken into account in our design.
In the optical design we also need to consider thesecond order matrix terms of T166, T266 and T566.
Sextupoles should be used in the two arcs to reduce thevalue of second order matrix terms to a tolerable degree.

Energy Recovery FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

OPTICAL LAYOUT

80

b e ta x w ith S C
b e ta y w ith S C
b e ta x w ith o u t S C
b e ta y w ith o u t S C

70

Beta function/m

60

Injector to linac

50
40
30
20
10
0
0

1 00

200

30 0

4 00

500

60 0

7 00

rms,n.emittance /mmmrad

le n g th /m

1 1 .01 0 .5
1 0 .0
9 .5
9 .0
8 .5
8 .0
7 .5
7 .0
6 .5
6 .0
5 .5
5 .0
4 .5
4 .0
3 .5
3 .0
2 .5

x w ith S C
y w ith S C
x w ith o u t S C
y w ith o u t S C

0

100

200

300

400

500

600

50 0

6 00

700

9.5
9.0

w ith S C
w ith o u t S C

8.5

Considering the space charge, we have optimized thebeam transmission with parmela in the injection line.
Simulation has been carried out with and without spacecharge. The result shows that space charge takes little
influence on beta function and emittance in x plane. In yplane, the emittance also doesn’t change a lot but beta
function changes obviously with and without spacecharge. Figure 2 shows the beta functions from theinjector to the linac.
A waist of the transverse beta function has been madeat the entrance of the linac but this requirement is not very
strict. Simulation shows that the beta function does notchange a lot in the exit of the accelerator when the waist
is at different positions around the entrance of the linac.

Arc1 to arc2

le n g th /mlongitudinal rms emittance/deg-keV

TUAAU05

In the first arc the beta function is symmetric but in thesecond arc is not. The beta function in x plane makes a
waist in the middle of the undulator and keeps small
within the undulator for higher radiation power gain. Theenergy spread is 0.24% (rms) at the entrance of theundulator which fulfills the requirement of lasing. The
emittance and energy spread will increase greatly after
undulator. We assume that the second arc has an
acceptance of 30μm in emittance and 7% full width inenergy spread according to the experiences of Jlab and
JAERI [7]. The radius of beam envelope is up to 3.5cm inthe outer quadrupole of the second arc due to this increase

8.0
7.5
7.0
6.5
6.0
5.5
5.0
4.5
4.0
3.5
0

1 00

20 0

30 0

4 00

70 0

le n g th /m
0 .5 0w ith S C
w ith o u t S Clongitudinal beta function/deg/keV

0 .4 5
0 .4 00 .3 5
0 .3 00 .2 50 .2 00 .1 50 .1 00 .0 50 .0 0
0

10 0

200

30 0

4 00

50 0

6 00

70 0

le n g th /m

Figure 2: Beta functions and emittance from the injector
to the linac
Energy Recovery FELs

Figure 3: Twiss parameters in the two arcs (Top one is thefirst arc and bottom one is the second arc)
279

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Proceedings of FEL 2006, BESSY, Berlin, Germanyof emittance and energy spread. The diameter of theaperture of this quadrupole should be ~10cm forcompletely acceptance of the beam. Figure 3 shows thebeta function and the dispersion in the two arcs.
CSR effect is taken into account from the first arc to thesecond arc in our simulation and it takes little influenceon the emittance of the beam.
The second order matrix terms of T166 , T266 and T566
are decreased by using sextupoles in the two arcs. T166
and T266 are less than 0.02m and T566 is less than 1m after
optimization.

Arc2 to linac and dump
The beta function of this section is well behaved in ourdesign. The beta function of the beam from the second arc
is adjusted by four quadrupoles and goes through the linac.
After extraction it goes to the dump and the envelope iscontrolled well by three quadrupoles.

SUMMARY
The preliminary optical design of the PKU-ERL-FEL
is carried out and the beta function of whole loop has
been obtained. The result will be checked by further
careful simulation with different particle tracking codes
before the construction of the beam line of the PKU-ERLFEL.

REFERENCES
[1]

[2]

[3]
[4]
[5]
[6]
[7]

280

Lia Merminga, David R. Douglas, “HIGHCURRENT ENERGY-RECOVERING ELECTRON
LINACS”, Annu. Rev. Nucl. Part. Sci. 2003.
53:387–429.
R. Hajima , M. Sawamura, “JAERI ERL-FEL: status
and future plans”, The 14th Symposium on
Accelerator Science and Technology, Tsukuba,
Japan, November 2003.
M.W. Poole, E.A. Seddon, “4GLS and the Prototype
Energy Recovery Linac Project at Daresbury”,
EPAC’04, Lucerne, July 2004.
G. H. Hoffstaetter, I.V. Bazarov, “Status of a Plan for
an ERL Extension to CESR”, Prodeedings PAC05,
Knoxville/TN (2005), ERL-05-02.
K. Zhao, et al, NIM, A475 (2001) 564.
W. Colson, R. Freedman, “Oscillator evolution in
free-electron lasers”, Phy. Rev. A, V.27 N.3, 1983.
R. Hajima, T. Shizuma, “First Demonstration ofEnergy-Recovery Operation in the JAERISuperconducting Linac for a High-Power FreeElectron Laser”, FEL 2002, presentation.

Energy Recovery FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

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PROSPECTS OF CASCADED HARMONIC GENERATION FELS∗
G. Penn, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
Abstract
Harmonic generation in Free Electron Lasers (FELs) encompasses many techniques for using an input seed laser
to produce FEL radiation at a frequency that is multiples
above that of the seed laser itself. This allows for the advantages of seeded FELs to be preserved, while extending thereach of these FELs to photon energies far above those produced by conventional laser sources. Many new projects
are underway to make use of these methods, including the
FERMI@Elettra [1] facility which envisions the use of two
harmonic generation stages to reach photon energies above
100 eV. Different methods of harmonic generation are discussed, as well as the technical challenges to overcome inattempting to chain together multiple harmonic stages in an
FEL.

INTRODUCTION
Harmonic generation in an FEL [2] is a promising technique for achieving high-intensity photon sources at shortwavelengths. Among the benefits of this design is that theoutput is seeded by a laser signal, allowing for excellent
frequency and timing control. The resulting output has thepotential of being a transform-limited pulse, and the output power is not limited by the input power but instead by
the saturation level of the FEL itself. In addition, the FEL
output is at a harmonic of the laser signal, so that the required laser wavelength is longer than the desired output
wavelength.
Multiple stages of harmonic generation can be combined
into a cascade, where the output from each stage is used as
the input seed for the next stage. A harmonic cascade allows conventional laser sources to be used to produce photons at extremely high energies. There are several facilities
which plan to use a harmonic cascade as a source for experiments. Among these are FERMI@Elettra, which is toconsist of two FELs, one with a single harmonic stage producing radiation in the 100 – 40 nm range, and one with
two harmonic stages producing radiation in the 40 – 10 nm
range. BESSY [3] is developing an FEL with up to fourstages of harmonic generation, yielding wavelengths ranging from 50 nm down to as low as 1.2 nm. Both of thesefacilities plan to use conventional laser sources. An additional possibility is seeding with a High-Harmonic Generation (HHG) signal [4], which uses a short, intense laser
pulse passing through a gas jet to generate many high harmonics of the initial laser. Such sources would drasticallyreduce the total harmonic conversion required in an FEL,
∗ This work was supported by the Director, Office of Science, High Energy Physics, U.S. Department of Energy under Contract No. DE-AC0205CH11231.

The Challenge of fs Pulses and Synchronisation

but much work remains to be done to ascertain their suitability for use in this way.
This paper will begin with the FERMI@Elettra design
to illustrate the harmonic generation process and to show
some of the fundamental issues which need to be considered for a harmonic cascade. Sources of noise can degrade
the FEL output, and phase noise is particularly important toconsider for large harmonics. Simplified models are used
to characterize the major constraints which must be considered for a harmonic cascade. Future prospects are

FERMI@ELETTRA SIMULATIONSThe electron beam parameters for FERMI@Elettra are:
1.2 GeV energy, 1.5 micron emittance, and depending on
the beam compression the current can range from 400 A to
1 kA and the energy spread can range from 100 to 200 keV.
The seed laser is tunable in the range 240 – 360 nm, has apeak power of 100 MW, and the pulse duration can be up to
1 ps. The first modulator has a period of 16 cm and is 3.04
m long. At the first harmonic, the undulators have a periodof 6.5 cm and are in sections of 2.34 m length. The final
radiator for the second harmonic has a period of 5 cm andis in sections of 2.4 m length. The initial modulator produces an energy oscillation in the electron beam with thesame period as the wavelength of the seed laser, as the relative phase between the undulator field and the laser field
when they both overlap the electrons determines the energy
transfer. A dispersive chicane follows this modulator, converting the energy modulation into bunching at the wavelength of the seed laser. When this bunching is sufficiently
strong, there are significant components at harmonics of thefundamental wavelength. Subsequently, the electron beam
passes through undulators tuned to a harmonic of the seedlaser, and radiates at that harmonic.
For the two-stage FEL, termed FEL-2, there are then two
possibilities, as shown in Fig. 1. In the “fresh-bunch” approach, the radiation produced at the end of the first stage
is made to overlap the electron beam in another modulating undulator after passing through a delay chicane. As aresult, the radiation pulse produces an energy modulation
in a region of the electron beam closer towards the headof the bunch, which was relatively unperturbed by the firststage of the FEL. The second stage produces a harmonic of
the output from the first stage in the same way as the firststage generates a harmonic of the seed laser. In the “wholebunch” approach, the first stage is continued until there issufficient energy modulation at the harmonic to continue tothe next stage. The electron beam is then passed through adispersive chicane to enhance the bunching at the desired
final harmonic. In the final radiator, the same section of281

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electron beam radiates at this higher harmonic.

ENERGY AND PHASE ERRORS
A simplified view of harmonic generation in an FEL
serves as a useful starting point for considering the challenges faced in designing a harmonic cascade FEL, as
touched on above. In Fig. 5, a slice of the electron beam
is modelled as a collection of mono-energetic beamlets,
each one with a uniform distribution in longitudinal position (here expressed as phase). Note that phase increases
towards the head of the bunch. After the modulator anddispersive chicane, the phase space distribution is folded
over to produce significant bunching centered at the zero
phase.
The spread in energies for the original beam results ina finite width for the microbunch, as a consequence of the

282

0.5
0.45
0.4
output power (GW)An example from the FERMI@Elettra optimization
study will motivate the topics discussed below. A realistic
longitudinal beam distribution from accelerator studies isshown in Fig. 2. The central current is roughly 500 A. Notethat there is a strong parabolic shape to the slice energy as afunction of longitudinal position. More recent designs haveadvanced far towards removing this feature, but it serves asa useful reference. A whole-bunch configuration startingwith a 240-nm seed laser with 1 ps duration FWHM produces 10 nm output with 0.1 mJ per pulse, and with peak
power of 400 MW. The output power and phase (modulo2π) resulting predicted by simulations using GENESIS [5]are shown in Fig. 3. The phase shows a strong quadratic
dependence which mirrors the energy variation, and whichleads to a broad, fluctuating spectrum as shown in Fig. 4.
Applying an appropriate linear chirp to the seed laser isquite effective at cancelling the phase variation, resulting
in the sharp spectrum shown on the same figure. While
this demonstrates that a parabolic energy profile can becancelled with a linear frequency chirp in the seed laser,
proper tuning may be challenging and more complex phasespace distributions will not be amenable to this type of afix. Avoiding such features in the beam profile therefore
becomes a high priority when high longitudinal coherence
and spectral brightness are desired.

Figure 2: Preliminary phase space distribution fromFERMI@Elettra study.

0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-1000

-500

0
t (fs)

500

1000

500

1000

4
3
output phase (radian)Figure 1: Two possible configurations for the FEL-2 line of
the FERMI@Elettra facility: fresh-bunch (top) and wholebunch (bottom).

2
1
0
-1
-2
-3
-4
-1000

-500

0
t (fs)

Figure 3: Output power and phase at 10 nm using wholebunch approach.

conservation of phase space. There are more subtle issues
which can be understood with this picture, however. Effective bunching, especially at higher harmonics, requires
an energy modulation much larger than the initial energy
spread. Roughly, this requires that the energy modulation,
γM , satisfyγM ≥ (n − 1)σγ ,(1)

The Challenge of fs Pulses and Synchronisation

Proceedings of FEL 2006, BESSY, Berlin, Germany
5e+11

1.5

no laser chirp
optimized chirp
Energy Deviation (a.u.)

4e+11# photons / meV

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3e+11
2e+11
1e+11

1
0.5
0
-0.5
-1

0

-1.5
123.9

123.95124

124.05

124.1

-3

-2

-1

photon energy (eV)

0

1

2

3

1

2

3

Phase

where n is the harmonic number and σ γ is the energy
spread. The degree of bunching generated at the harmonic
will be sensitive to the slice energy spread. Furthermore,because each energy value corresponds to a different phasefor the microbunching, longitudinal variations in the average beam energy will lead to offsets in the timing of the
microbunches. As the microbunches are separated by nwavelengths in terms of the harmonic output, these fractional timing offsets can have a large effect on the coherence of the output radiation.
To further understand the effect of longitudinal energy
variation in the beam, we consider a similar effect wherephase offsets are introduced within the seed laser itself.
In Fig. 6, the bunching produced by a seed laser with alinear frequency chirp is compared to that produced by aseed laser with no chirp, but for an electron beam witha quadratic energy chirp. Both variations are greatly exaggerated compared to that which would be encounteredin practice. The vertical bars indicate the phases of successive microbunches. It is apparent that a chirped seedlaser can produce the same changes in timing structure asa chirp in the electron beam energy. This explains how
a linear chirp in the seed laser can fix the output from anelectron beam having a parabolic energy profile. Note thata linear energy chirp would simply produce a uniform offset in output wavelength. This is generated as the modulated electron beam passes through the dispersive chicane,where it is either compressed or stretched depending on thesign of the energy variation. Curvature in the energy profile leads to more complicated perturbations, as some sections of the beam are compressed and others are stretched.
This can lead to sidebands in the spectrum or broadening,which would degrade the output radiation to be no longer
transform-limited. This effect is made worse at high harmonics, as seen in Fig. 7. Here, an arbitrary small phaseerror is introduced to a pure Gaussian pulse. The effect isbarely visible in the spectrum of the fundamental, but atthe 24th harmonic the spectrum is drastically altered. At
the fundamental, the signal is still transform limited, but

The Challenge of fs Pulses and Synchronisation

Energy Deviation (a.u.)

1.5

Figure 4: Output spectrum using laser seed with no chirp(red) and with optimized chirp (green).

1
0.5
0
-0.5
-1
-1.5
-3

-2

-1

0
Phase

Figure 5: Illustration of bunching process as it affects electrons having different energies.

the pulse is still unsuitable for harmonic generation beyonda certain limit. This introduces added complexity to the design of the seed laser, as the constraints are more stringent
than usual and are not a typical part of the vocabulatory oflaser sources. In particular, even short pulses (i.e., a small
number of wavelengths) will require a clock-like regularityof the field oscillation in order to function optimally as an
FEL seed.

Macroparticle Noise
Because electrons at different energies are bunched at
different phases, there are additional concerns for theproper simulation of harmonic generation. Typically,
macroparticle noise in FEL simulations are controlled bystarting with pseudorandom particle distributions, and using subsets of particles uniformly spaced in phase. Deviations from this uniform spacing are chosen to mimic
the expected statistical fluctuations. However, an efficientbunching process will put most particles of a given energy
at a single phase, so the final phase distribution will only
depend on the initial energy distribution. In the example above, there will only be five bunches centered about
the zero phase. Different choices of modelling the energy distribution will thus lead to different bunching pa-

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Energy Deviation (a.u.)5

POWER FLUCTUATIONS AND ENERGYOFFSETSlinear laser chirp
quadratic energy chirp

4
3
2
1
0
-1
-20

-10

0

10

20

Phase

Figure 6: Comparison of bunching process for a flat beam
seeded by a chirped laser, versus a beam with quadraticenergy variation and no laser chirp. Vertical bars indicate
the phases of successive microbunches.

1

Spectral Intensity

0.8
0.6
0.4
0.2

no noisefundamental
24th harmonic
0.1
0.08
0.06
0.04
0.02
0
-0.01

0

0.01

0
-0.04 -0.03 -0.02 -0.01
00.01 0.02 0.03 0.04
Frequency Offset

Figure 7: Spectra of Gaussian pulse with oscillating phaseerror, at original frequency and at 24th harmonic.

While phase distortions can reduce the longitudinal coherence of the FEL output, power fluctuations are also amajor concern. There are many possible sources of powerfluctuations, but typically the most important one is energy
offsets in the beam. Note that while phase errors accumulate due to longitudinal variation of the slice beam energy,
it is the difference between the slice energy and resonant
energy which determines the output power. Shot-to-shotjitter in beam energy is thus a significant concern for output power flucuations. The sensitivity of the FEL to relative energy offsets is typically the larger of 1/N U or the
FEL parameter [6], ρ FEL = λU /LG . Here, NU is thenumber of undulator periods, λ U is the undulator period,and LG is the exponential gain length, all for the final undulator where the gain length is longest and the number ofundulator periods is largest.
Reducing the sensitivity of the FEL involves a trade-off
with trying to optimize the peak output power. One method
is simply to reduce the number of undulator periods, at thecost of greatly reduced average power. A more efficientmethod is to introduce either variations in the magnetic
field strength of the undulator, or phase offsets between undulator sections. Examples are shown in Figs. 8 and 10; thelatter example is from a pseudorandom variation in the undulator field strength which drastically reduces the dependence on beam energy and reduces the peak power by a factor of 30. The evolution of the power and bunching for theexample labelled “phase 3” are shown in Fig. 9. Note thatthe configuration is specific to the given length of undulator, at which point the various beam energies come close toeach other in performance, but after passing through different dynamics.

1.6

flat
linear taper
phase 1phase 2phase 3

1.4

284

1.2
Power (GW)

rameters. Furthermore, especially for large energy spreadand harmonic number, the discrete nature of the bunching
will lead to noise in the bunching parameter as the gaps
between energy levels become resolved. The macroparticle noise for an optimally bunched beam will be given by
nσγ /Nγ γM , where Nγ is the number of energies sampled
by the distribution. Sampling more phases will not reduce
this macroparticle noise, and may even make the problem
worse if it is done at the expense of the number of discrete energies sampled. There is as of yet no known robust
method to control this effect in simulations. It becomes increasingly difficult to get simulation results to converge as
the initial energy spread in the electron beam is increased,
especially when the nominal seeded bunching is already
low.

1
0.8
0.6
0.4
0.2
0
-5

-4

-3

-2

-1

0

1

2

3

4

5

-3

delta gamma / gamma (10 )Figure 8: Sensitivity of FEL output power to beam energy
offsets, for variations of the fine tuning.

The Challenge of fs Pulses and Synchronisation

Proceedings of FEL 2006, BESSY, Berlin, Germany
0.7

0.5
Power (GW)

length and γ is the relativistic factor of the beam. This isdue to a combination of reduced electron density and increased spread in longitudinal velocities. Another is thechallenge of satisfying the resonance condition,-0.4%-0.25%-0.1%+0.05%
+0.2%

0.6

0.4

λU =

0.3
0.2
0.1
0
0

2

4

6

8

10

12

14

16

18

20

10 12
z (m)

14

16

18

20

z (m)
0.4

-0.4%
-0.25%-0.1%+0.05%+0.2%

0.35

Bunching

0.3
0.25
0.2
0.15
0.1
0.05
0
0

2

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6

8

Figure 9: Power and bunching evolution in the FEL, for different electron beam energies, using the “phase 3” example
in the previous figure.

Figure 10: An example of extreme reduction in the sensitivity of FEL output to electron beam energy through pseudorandom tapering. Peak power in the tapered example (blue)
is a factor of 30 below that in the nominal case (red), but isstable to much larger energy variations. Courtesy of G. De
Ninno and E. Allaria.

CHALLENGES FOR HARMONICCASCADES
The desire for even shorter wavelengths leads one to consider more ambitious harmonic cascade FEL designs, asin the BESSY multi-stage FEL. As the goal is moved toshorter wavelengths, the tendency is to consider more energetic electron beams. One motivation is the reduced effectiveness of the FEL when the normalized emittance ismuch larger than λ r /4πγ, where λr is the radiation wave-

The Challenge of fs Pulses and Synchronisation

2γ 2
λr ,
1 + a2U(2)

where aU is the normalized strength of the undulator field.
The FEL parameter also tends to drop drastically as thebeam energy is reduced, which further constrains tolerances on energy jitter and energy spread.
The high harmonic numbers involved also introduce
complications. Attempting to take a single, large harmonic
jump becomes very impractical, as the required energy
modulation must be extremely large or the energy spreadmust be very low in order to satisfy Eq. 1. This leads toan additional problem, that for larger energy modulations
the beam will debunch more rapidly. If the gain length islonger than the debunching length, the electrons will not
be trapped in the ponderomotive well and the FEL will notreach saturation. A rough requirement to reach saturationis(3)
γM ≤ γλU /16LG.
Together with Eq. 1, this limits the range of acceptable energy modulations, and also imposes a maximum allowed
energy spread.
Ultimately, many smaller harmonic stages become required. This adds to the complexity, and does not eliminate the sensitivity to phase noise and energy variations
which depend on the total harmonic multiplication factor. The noise-to-signal power ratio within a given bandwidth can be expected to grow as the square of the total
harmonic power through the harmonic generation process.
The seeded FEL process must also compete with spontaneous FEL emission which may amplify the noise along
the FEL, as well as spontaneous growth in energy spread.
As the energy modulation itself increases the slice energy spread with each harmonic multiplication stage, freshbunch delays between stages will ultimately be required.
Each delay to an unseeded section of the electron beam
introduces constraints on synchronization and reduces the
maximum duration of the output pulse for a given electron distribution. While it may be possible to alternate between fresh-bunch and whole-bunch stages, these considerations lead to challenging electron source and acceleration
requirements. Numerical simulations also require more resources and care when large harmonics are desired.
One attractive option is to take advantage of rapid advances in HHG sources, and seed the FEL at much shorter
wavelengths than conventional lasers can achieve. There
has been much recent activity studying the feasibility of
HHG sources as an FEL seed [7, 8, 9]. While further characterization of these sources is clearly needed to make reliable predictions, some facts are already apparent. First,
the typically low peak power in these signals is not an obstacle to their use. In particular, amplifying a signal is285

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much less difficult than conversion to a harmonic (hence
the (n − 1) factor in Eq. 1). In addition, the HHG sources
typically have durations of less than 100 fs, which favors
experiments based on timing rather than spectral widths,
and slippage between the radiation and the electrons willsmooth out some phase noise components. Ultimately,
HHG sources could be used to seed X-ray FELs which use
only a single stage of harmonic generation.
While the challenges for developing cascaded harmonic
FELs are daunting, they link together a large range of technologies; small improvements on many fronts may open
up new horizons for seeded FELs in the future. It is clearthat the lasers used as seeds for the FEL require more detailed characterization. In addition to improved or novel
sources for seeding, advances in electron sources, acceleration, undulator design, and optics will enable more ambitious projects in the future. In the meantime, current
facilities on the horizon will offer experience and testing
grounds for new ideas, as well as provide opportunities for
performing advanced scientific research.

ACKNOWLEDGMENTS
This paper discusses work performed in collaboration
with many individuals, and much of this work came out of
the collaboration to produce the FERMI@Elettra technicaloptimization study. The author would like to express his
gratitude to Bill Fawley, Jonathan Wurtele and Sasha Zholents for their guidance in FEL studies, and John Corlett
and Bill Barletta for their support and encouragement.

REFERENCES[1] C. Bocchetta et al., Proceedings of the 2005 FEL Conference,(2005) 682.
[2] L.-H. Yu et al., Science 289 (2000), 932–934.
[3] The BESSY Soft X-ray Free Electron Laser, TDR BESSY
March 2004, eds.: D.Krämer, E. Jaeschke, W. Eberhardt,
ISBN 3-9809534-08, BESSY, BERLIN (2004).
[4] H.C. Kapteyn, M.M. Murnane, and I.P. Christov, Physics Today (March 2005) 39–44.
[5] S. Reiche, Nucl. Instr. Methods A 429 (1999), 243–248.
[6] R. Bonifacio, R. Corsini, and P. Pierini, Physical Review A
45 (1992), 4091–4096.
[7] G. Lambert et al., Proceedings of the 26th International Free
Electron Laser Conference (FEL04), Trieste, Italy (2004), paper MOPOS21.
[8] B. Sheehy et al., Proceedings of the FLS 2006 Workshop,
WG333.
[9] M. Gullans, J. Wurtele, G. Penn, Z. Zholents, submitted toPhys. Rev. ST:AB.

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FEMTOSECOND SYNCHRONIZATION AND
STABILIZATION TECHNIQUES ∗J. Kim† , F. Ludwig‡ , J. Chen, Z. Zhang§ and F. X. Kärtner, MIT, Cambridge, MA 02139, USA.
Abstract
High-precision synchronization and stabilization techniques are crucial for future advances in next generation
light sources, seeded x-ray free electron lasers. In thispaper, we present long-term stable femtosecond-precision
optical-to-RF and optical-to-optical synchronization andstabilization techniques. For optical-to-RF synchronization, we demonstrate an optical-microwave phase detector
that is capable of extracting an RF-signal from an opticalpulse train in a long-term drift-free way. Extraction of an
RF-signal with 3-fs in-loop timing jitter, integrated from
1 Hz to 10 MHz, from an optical pulse train is demonstrated. Optical-to-optical synchronization of two femtosecond lasers with sub-femtosecond precision over 12hours is demonstrated. We also discuss how to use optically stabilized fiber links for timing distribution. Together
with low-noise mode-locked lasers, a flexible femtosecond
timing system can be constructed.

INTRODUCTION
Seeding of free electron lasers operating in the xray regime with radiation generated from ultrafast laser
sources, either directly, via nonlinear crystals, or via highharmonics from noble gases, may result in a fully coherent x-ray laser. For seeding of such large-scale facilities
spanning over several hundreds meters to a few kilometers,
it is critical to synchronize low-level RF-systems, photoinjector lasers, seed radiation and potential probe lasers
with low timing jitter, preferably in sub-10-femtosecond
range, in a long-term stable arrangement [1].
Figure 1 shows the schematic of the envisioned timing distribution and synchronization system for the futurenext generation light sources, seeded x-ray free electron
lasers (XFELs). The pulse repetition rate of an opticalmaster oscillator implemented as a mode-locked laser isstabilized to an optical and/or microwave frequency standard. The pulse train is distributed to all critical subsystems, i.e., the pulsed klystron, the photo-injector laser,
the low-level RF systems for linear accelerator, the seedlaser as well as probe lasers, by use of timing stabilized
fiber links. Finally, low-jitter, drift-free optical-to-RF and
optical-to-optical synchronization between the distributed
timing pulse trains and the remote RF- or optical subsystems will result in a tightly synchronized timing systemover the large-scale accelerator facility.
∗ Supported by ONR, AFOSR, and EUROFEL.
† jungwon@mit.edu‡ Permanent address: DESY, Hamburg, Germany§ Permanent address: Peking University, Beijing, China

The Challenge of fs Pulses and Synchronisation

Microwave
Standard

Optical Master Oscillator
Mode-Locked Laser

Optical Fiber Links for Timing Distribution

Optical-to-RF
Synchronization

Optical-to-Optical
Synchronization

Pulsed KlystronPhoto-Injector
Laser

Optical-to-RF
Synchronization

Optical-to-Optical
Synchronization

Optical-to-Optical
Synchronization

Low-Level RF
Systems

Seed Laser

Probe Laser

High-Level RF
Systems

Electron Gun

LINAC

Undulator

fs X-raypulsesFigure 1: Schematic outline of timing distribution and synchronization for seeded X-ray free electron laser (XFEL)
facilities.
Currently, the most promising candidates for ultra-low
jitter optical master oscillators are passively mode-locked
Er-doped fiber lasers [2], Yb-doped fiber lasers [3] andEr/Yb-glass lasers [4, 5]. Erbium and Ytterbium gain materials have long upper-state lifetime in the ms-range, andtherefore, the high frequency fluctuations of the laser output in amplitude and timing are quantum noise limited [6].
Thus the timing jitter of mode-locked lasers is superior tothat of conventional microwave oscillators in the high frequency range.
The crucial performance indicator for the optical master oscillator is the phase noise or timing jitter in the highfrequency range. The bandwidth of optical/microwave reference locking is typically limited to tens of kHz range,
and the high-frequency noise beyond locking bandwidthfollows that of the free-running master oscillator. In addition, timing stabilization of fiber links based on the crosscorrelation of the back-reflected pulse from fiber end withthe fresh pulse also has a bandwidth limitation from thetravel time of the reflected pulse. These limitations assurethat a very low jitter mode-locked laser is a prerequisite fora high-precision timing system.
In Refs. [7] and [8], the timing jitter is characterized bymeasuring the phase noise of one harmonic (at 1.3 GHz)of the microwave signal obtained by direct photodetectionof the pulse train. For standard Er-doped stretched pulse
fiber lasers, the integrated timing jitter from 1 kHz to 22
MHz (Nyquist bandwidth) is measured on the order of 10
fs, which is already better than most commercial highquality microwave signal generators (for example, Marconi
2041 signal generator). Note that the measurements areoften limited in precision by the amplitude-to-phase (AMto-PM) conversion from direct photodetection. A more detailed discussion on this conversion will be given in the next
section. In theory, the high frequency timing jitter of pulse
trains from mode-locked lasers can be below one femtosec-

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ond.
Once a timing signal in form of an optical pulse train
is generated from a master oscillator, it should be distributed to the remote RF- or optical-subsystems that we aim
to synchronize with minimal excess noise. Precise transferof timing signals through fiber links for timing information
dissemination has been demonstrated recently [7, 9, 10, 11]
for short time spans, typically less than a minute. If thefiber length is L, we assume that no length fluctuations are
faster than 2L/c, where c is the speed of light in the fiber.
Relative fiber expansion by temperature change is typicallyon the order of 10−7 /K, which can be compensated by afiber length control loop by referencing the back reflected
pulse from the fiber end with the later pulse from the modelocked laser. Recently, the demonstration of timing distribution over 500 meters in an accelerator environment wasdone with pure RF-techniques [7]. When the feedback loop
is open, the jitter integrated from 0.1 Hz to 5 kHz is 66
fs; when the loop is closed, the in-loop jitter is suppressed
down to 12 fs. More detailed information on this timing
distribution experiment can be found in Ref. [7].
Although a short-term stabilization on the order of few
tens of femtoseconds can be achieved with RF-techniques
only, for long-term stabilization of fiber links with sub10 fs accuracy over hours, balanced cross-correlation techniques [12] can be employed, as discussed later in this paper. Work is in progress to demonstrate long-term stablefiber links.

OPTICAL-TO-RF SYNCHRONIZATION
Once precise timing information encoded as an opticalpulse train arrives at each remote location, the next task
is to synchronize it with, for example, RF-subsystems. It
is crucial to convert this optical signal into a low-jitter,
drift-free RF-signal with a satisfactory power level in along-term stable way. Recently, it has been shown thatthe extraction of an RF-signal from an optical pulse train
using direct photodetection is limited in precision by excess phase noise [13]. The major contribution to this excess
noise was identified to be the amplitude-to-phase (AM-toPM) conversion in the photodetector. The intensity noiseof the laser can be converted into a significant amount ofphase noise and phase drift by this process. In Refs. [8]and [14], the AM-to-PM conversion factor was measured
and it typically ranges 1 to 10 ps/mW depending on the bias
and the bandwidth of the photodetector. The intensity noiseof the delivered pulse train can be converted into a significant amount of excess timing jitter by this process. For a
12-GHz InGaAs photodetector at 6 V reverse bias that we
tested, the AM-to-PM conversion factor was measured as
1.6 ps/mW [8]. For an Er-doped fiber laser with 0.03 %rms
relative intensity noise (RIN), this may already result in 5fs excess jitter when 10 mW of power is applied to the photodetector. In addition, direct photodetection has a limited
extractable RF-power and signal-to-noise ratio (SNR) due
to the damage threshold for the input optical power to the288

Optical-Microwave Phase Detector
OpticalInput
rep ratefR.
. 2

Tapping
couplerfR

fR/2

Photodiode 1

Isolator

50:50
Coupler

RF-combiner

+

Phase
Modulator
SagnacLoop

Downconversion
Mixer
Loop
Filter

~

NfR

VCO

fR/2

RF-Input

Photodiode 2

Figure 2: Schamatic of a balanced optical-microwave
phase detector and its use for RF-signal regeneration froman optical pulse train. VCO, voltage-controlled oscillator.

photodetector. Moreover, phase drifts in the diode due totemperature change as well as post-amplification to reachthe required signal level can prevent a long-term stable regeneration of RF-signals.
Therefore, it is highly desirable to develop a phaselocked loop between an optical pulse train and a highquality RF voltage-controlled oscillator (VCO) to prevent
those undesired AM-to-PM conversion and drifts due tothe photodetection process. In addition, one can leverage
the fly-wheel effect of VCO. In doing so, the key issue
is the development of drift-free, low-jitter phase detector
which compares the relative phase between pulse trains andRF-signals in the optical domain before the photodetection
is involved. Previously, we proposed and demonstrated ascheme to avoid the excess noise from direct photodetection by transfer of timing information in the optical domain[15]. However, due to acoustic vibrations and poor phasenoise properties of the free-running VCO, the relative jitter
was limited to 60-fs measured from 100 Hz to 10 MHz.
For the extraction of low-jitter, high-power, and driftfree RF-signals from optical pulse trains, a balanced
optical-microwave phase detector is proposed and demonstrated. This phase detector is still based on the timing information transfer in the optical domain. The timing information transfer in the optical domain is implemented byuse of a differentially-biased Sagnac fiber-loop and synchronous detection. We used the phase error signal fromthis balanced optical-microwave phase detector, which isrobust against drifts and photodetector nonlinearities, to regenerate low-jitter RF-signals from optical pulse trains.
Figure 2 shows the schematic of the balanced opticalmicrowave phase detector. Part of the input pulse train istapped off by Photodiode 1. This photodiode is used togenerate a synchronous detection signal at half the repetition rate (fR /2) of the optical pulse source. This signal is applied to both the phase modulator and the downconversion mixer. The rest of the input pulse train is sent to

The Challenge of fs Pulses and Synchronisation

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUBAU02els as well as optimizing loop characteristics. In addition,
the construction of a second loop is in progress to perform
long-term out-of-loop measurements by mixing two VCO
outputs in quadrature.

OPTICAL-TO-OPTICALSYNCHRONIZATION

Figure 3: The single-sideband (SSB) phase noise spectra
at 10.225 GHz. (a) Free-running VCO. (b) In-loop phasenoise when it is locked. (c) Signal analyzer noise floor.
the Sagnac-loop with a phase modulator. The phase modulation in the Sagnac loop is converted into an amplitude
modulated signal at fR /2 at the output of the Sagnac-loop.
The amplitude of this signal is, to the first order, proportional to the phase error between the optical pulse train andthe RF-signal (which is, the output from the VCO). The detected signal at Photodiode 2 is band-pass filtered at fR /2and down-converted to the baseband by mixing with thereference signal. This error signal is filtered and controls
the low-noise VCO to close the phase-locked loop.
For the demonstration experiment, a standard stretchedpulse Er-doped fiber laser [2] (repetition rate fR = 44.26
MHz) is used as the optical pulse source. All optical components in the phase detector are implemented using commercial 1550-nm optical fiber and components. In the experimental implementation, we generated a signal with thefrequency 10.5fR for the phase modulation in the Sagnacloop in parallel with fR /2 component to reduce the necessary fiber loop length. By closing the loop with a 10.225GHz (231st harmonic of the fundamental repetition rate)
VCO (PSI DRO-10.225), a long-term stable locking between the laser and the VCO is achieved.
Figure 3 shows the measured in-loop phase noise spectraat the output of down-conversion mixer. The voltage signal from the phase detector was amplified with a low-noise
amplifier (G=10 non-inverting amplifier with AD797) andmeasured with a low-noise vector signal analyzer (Agilent
89410A), and converted into single-sideband (SSB) phasenoise at 10.225 GHz. This measurement shows that the integrated in-loop jitter is 3.0 fs ± 0.2 fs integrated from 1
Hz to 10 MHz when it is locked. Currently, the system islimited by the thermal noise from electronic amplifiers andhas not yet reached shot noise limited performance yet. We
are currently pursuing to further suppress the timing jitter to below 1 fs by increasing optical and RF power lev-

The Challenge of fs Pulses and Synchronisation

Tight synchronization is necessary not only between optical and RF-subsystems but also between different optical systems, for example, the photo-injector laser, the seedlaser and the probe lasers as shown in Fig. 1. Conventional
timing synchronization between two mode-locked lasers
based on microwave mixers [16] suffers from high residual jitter and thermal drifts in the electronic amplifiers andmixers. To overcome this limitations, a balanced opticalcross-correlator [12] can be used for the long-term opticalto-optical synchronization. This technique uses nonlinear
optical processes for an extremely sensitive detection oftiming differences between optical pulses.
Figure 4 shows the schematic of the balanced crosscorrelator. The combined pulses from two mode-locked
lasers with different spectra, denoted as wavelengths λ1
and λ2 , are splitted by a broadband 50:50 beam splitter. The two beam paths have a different group delay(GD), for example, by inserting a glass plate in one of thearms. This group delay offsets the relative position between two pulses. Each combined pulse is focused into
a nonlinear crystal to generate a sum-frequency component
1= λ11 + λ12 . After bandpass filtering the sumat λSFGfrequency generation (SFG) components, a balanced detector measures the intensity imbalance. For small timing
differences (within the range of the group delay of the GD
element), the output from the balanced detector is nearly
proportional to the time difference between the two pulses.
At the zero-crossing of the balanced detector output, theamplitude noise from each laser is balanced and does notaffect the detected error signal. The signal from the balanced detector is used to lock the repetition rates of thetwo lasers by controlling the cavity length of one laser
with cavity mirrors mounted on piezo-electric transducers(PZTs). This finally closes the loop. This method enables
a drift-free and temperature-independent synchronization
between two independent lasers.
The long-term timing synchronization performance using balanced optical cross-correlation is demonstrated using a 5-fs Ti:sapphire laser (centered at 830 nm) and a 30fs Cr:forsterite laser (centered at 1250 nm). The pulses are
combined and splitted by use of a broadband 50:50 beam
splitter with matched group delay dispersion. LBO crystals
with 1-mm thickness are used for SFG at 499 nm (1/830nm+ 1/1250nm = 1/499nm). To generate a group delay offset
of 45 fs between 830 nm and 1250 nm, a 3-mm thick fusedsilica plate is used.
Figure 5 shows the out-of-loop cross correrlation result
for a timing jitter measurement between the Ti:sapphireand Cr:forsterite lasers. The black line shows the cross-

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Dt
GD

SFG

l1 l2

Dt

SFG

GD
1

l SFG

=

GD/2

1
1
+
l1 l 2

Figure 4: Schematic of a balanced cross-correlator. GD:
group-delay element between two color pulses. SFG: sumfrequency generation.

to-optical synchronization techniques. We proposed anddemonstrated the use of a balanced optical-microwave
phase detector and balanced optical cross-correlator. By
use of optical techniques, we could achieve a long-term
femtosecond and sub-femtosecond accuracies which was
not achievable with conventional pure RF-techniques.

REFERENCES[1] J. Kim, F. Ö. Ilday, F. X. Kärtner, O. D. Mücke, M. H. Perrott, W. S. Graves, D. E. Moncton, T. Zwart, “Large-Scale
Timing Distribution and RF-Synchronization for FEL Facilities,” Proceedings of Free Electron Laser Conference 2004,
p. 329, August 2004.
[2] G. Lenz, K. Tamura, H. A. Haus and E. P. Ippen, Opt. Lett.
20, 1289 (1995).
[3] F. Ö. Ilday, J. R. Buckley, H. Lim, F. W. Wise and W. G.
Clark, Opt. Lett. 28, 1365 (2003).
[4] J. B. Schlager, B. E. Callicoatt, R. P. Mirin, N. A. Sanford, D.
J. Jones and J. Ye, Opt. Lett. 28, 2411 (2003).
[5] S. C. Zeller, L. Krainer, G. J. Spuhler, R. Paschotta, M.
Golling, D. Ebling, K. J. Weingarten and U. Keller, Electron.
Lett. 40, 875 (2004).
[6] S. Namiki and H. A. Haus, IEEE J. Quantum Electron. 33,
649 (1997).
[7] A. Winter, P. Schmüsser, H. Schlarb, F. Ö. Ilday, J. Kim, J.
Chen, F. X. Kärtner, D. Cheever, T. Zwart, D. Wang, “HighPrecision Optical Synchronization Systems for X-Ray Free
Electron Lasers,” Proceedings of Free Electron Laser 2005,
p. 676, August 2005.

Figure 5: Long-term optical-to-optical synchronization result between Ti:sapphire and Cr:forsterite lasers. Drift-free
sub-femtosecond synchronization over 12 hours were measured.
correlation trace when two lasers are not locked. The
red line shows the cross-correlation trace when two lasers
are locked adjacent to each other so that timing fluctuations are transferred into intensity fluctuations in the crosscorrelation signal [16]. The pulse trains from the two lasers
are locked with 380 attoseconds rms timing jitter over 12hours without thermal drift in the bandwidth from 0.02
mHz to 2.3 MHz. Note that the duration of 12 hours does
not constitute a limit to the locking scheme but was merely
the duration of the experiment. In principle, as long as thelasers stay mode-locked, the timing lock can be maintained
if the mechanical perturbations to the system are below acertain threshold value.

CONCLUSION
In summary, we reported on the progress toward a longterm stable and scalable timing distribution and synchronization system for future accelerator and seeded x-ray freeelectron laser facilities proposed in Ref. [1]. In particular,
we demonstrated high-precision optical-to-RF and optical-

290[8] F. X. Kärtner, F. Ö. Ilday, J. Kim, A. Winter, F. Grawert,
H. Byun, J. Chen, “Progress in Large-Scale Femtosecond
Timing Distribution and RF-Synchronization,” Proceedingsof 2005 Particle Accelerator Conference, p. 284, May 2005.
[9] J. Ye, J. Peng, R.J. Jones, K.W. Holman, J.L. Hall, D.J. Jones,
S.A. Diddams, J. Kitching, S. Bize, J.C. Bergquist, L.W.
Hollberg, L. Robertsson, and L. Ma, J. Opt. Soc. Am. B 20,1459 (2003).
[10] K. W. Holman, D. J. Jones, D. D. Hudson, J. Ye, Opt. Lett.
29, 1554 (2004).
[11] D. D. Hudson, S. M. Foreman, S. T. Cundiff and J. Ye, Opt.
Lett. 31, 1951 (2006).
[12] T. R. Schibli, J. Kim, O. Kuzucu, J. Gopinath, S. N. Tandon,
G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen,and F. X. Kärtner, Opt. Lett. 28, 947 (2003).
[13] E. N. Ivanov, S. A. Diddams and L. Hollberg, IEEE J. Sel.
Top. Quantum Electron. 9, 1059 (2003).
[14] A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C.
Bergquist, W. H. Oskay and L. Hollberg, Opt. Lett. 30, 667(2005).
[15] J. Kim, F. X. Kärtner, and M. H. Perrott, Opt. Lett. 29, 2076
(2004).
[16] R. K. Shelton, S. M. Foreman, L. Ma, J. L. Hall, H. C.
Kapteyn, M. M. Murnane, M. Notcutt and J. Ye, Opt. Lett.
27, 312 (2002).

The Challenge of fs Pulses and Synchronisation

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUBAU03

CROSS-CORRELATION BETWEEN A VUV-FEL AND AN OPTICALLASER
Theophilos Maltezopoulos, Ulrike Fruehling, Elke Plönjes, DESY, Hamburg;
Markus Drescher, Roland Kalms, Maria Krikunova, Marek Wieland, Uni HH, Hamburg;
Stefan Cunovic, Norbert Müller, Universität Bielefeld, Bielefeld

Abstract
At the Free Electron Laser in Hamburg (FLASH) a synchronized 800 nm optical laser is available for time-resolved
VUV/vis pump-probe experiments. We crossed both femtosecond pulses in a Kr gas target and imaged the createdphotoelectrons with an energy-dispersive electron spectrometer. In the region where both pulses overlap in space andtime, the photoelectrons are energetically shifted and form
spectral sidebands. The imaging electron spectrometer projects
the spectral- into an intensity modulation, thus, mapping
time into space. This way, the technique delivers information about the relative timing between VUV- and visible
pulse and is non invasive for both pulses. While observation of the cross-correlation signal currently requires dataaveraging, with proper focussing single shot capability shallbe reached, thereby enabling pulse-to-pulse jitter measurements.

PAPER NOTAVAILABLE

The Challenge of fs Pulses and Synchronisation

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Proceedings of FEL 2006, BESSY, Berlin, Germany

INVERSE FREE ELECTRON LASERS
FOR ADVANCED LIGHT SOURCES
P. Musumeci, F. Germoni, M. Serluca, M. Mattioli
INFN-Roma1, P.le Aldo Moro 2, 00100, Rome, Italy.
Abstract
Laser accelerators hold the promise for high gradient acceleration and production of ultra short electron bunches.
Among these, the inverse free-electron laser has recently
demonstrated to be a mature and reliable scheme ready tostep up from successful proof-of-principle experiments to
cutting-edge applications. The very high gradient and themulti kAmp peak current of the output beam make it an attractive option in the hundreds of MeV to few GeV energy
region. We examine the feasibility of using an IFEL driven
by an high power Ti:Sa laser source to generate soft x-raysby FEL interaction in an undulator. A control of the slippage of the radiation over the ultrashort spikes of the IFELmicrobunched beam current is implemented to increase thegain and maintain the 200 as-long pulse structure in the radiation profile.

INTRODUCTION
While the wall plug efficiency of laser based accelerators still falls short of the requirements needed to costeffectively build a high energy physics linear collider, highgradient, short-wavelength advanced accelerator schemes
are an attractive option to produce electron beams suitableto drive 4th generation x-ray lasers where one can choose
peak brightness over average brightness. The small transverse emittances and high peak currents of current conventional radiofrequency based designs [1, 2] are within thereach of advanced state-of-the-art laser based accelerators.
The requirements on the beam relative energy spread (lessthan few thousandths) could be tougher to satisfy but the
progress in the experimental results in these last few years[3] brings closer to reality an advanced accelerator driven
x-ray laser with an attractive reduction of the footprint andhenceforth of the costs of such machines.
Among the various advanced accelerator schemes, theinverse free-electron laser (IFEL) is one of the mostpromising and well understood in terms of control of longitudinal phase space, trapping efficiency and final energy
spread [4]. Using a high power laser and a properly designed undulator the IFEL has recently demonstrated accelerating gradients superior to conventional rf accelerators and very high energy gains [5]. Moreover, the IFEL
is a far-field vacuum acceleration scheme which preserves
the beam emittance through acceleration and it is in principle free of optics damage threshold limitations. Finally,
the energy transfer mechanism, just the inverse of the wellknown FEL principle at the basis of the last generation light292

source facilities, is very efficient and one can design undulators able to transfer more than 75 % of optical power tobeam power [6]. The final efficiency is in fact only limitedby the wall-plug to optical conversion efficiency which forcommon high power laser systems is still quite low (below
1 %).
Even though many limitations arise when one considers
the IFEL for multi-GeV energies mostly due to the synchrotron radiation losses from the wiggling electron trajectories, the tremendous progress and commercial availability of ultrahigh power laser sources makes the IFEL schemea very feasible and convenient choice in the hundreds of
MeV to few GeV energy, which is just the energy region
for x-ray FEL drivers.
The detailed control over the electron beam longitudinal
phase space obtainable with the interaction of a powerfullaser and relativistic electrons passing through an undulator has already captured the interest of FEL physicists. In
fact the IFEL mechanism in its not-accelerating prebunching version has been already proposed to be used at LCLS
to enhance the SASE characteristics (ESASE). The shorthigh current spikes obtained converting the IFEL-induced
energy modulation into density modulation at the scale ofthe optical wavelength are foreseen to shorten the undulator distance needed to reach saturation and to produce sub
femtosecond X-ray pulses [7].
In this paper we conjugate the advantages of using an
IFEL as a prebuncher with its high gradient capabilities todesign a soft X-ray source based on an IFEL accelerator.
The design aims at producing coherent radiation in the socalled water window region of the electromagnetic spectrum (λ = 3-4 nm) and it is tailored on the SPARC linac
which is a state-of-the-art injector delivering a high brightness electron beam at 200 MeV energy in its final stage of
construction at Frascati [8].

IFEL DESIGNIn Table 1 we report the input parameters considered forthe IFEL design.
The electron beam input parameters like energy, energy spread and peak current are the nominal values of the
SPARC linac [9]. In this design exercise we have considered to use a portion (20 TW out of 100 TW) of the highpower laser foreseen to be installed in the same experimental area of the high brightness injector [10]. The ratio between the laser rayleigh range and the undulator length has
been set to maximize the integrated gradient and so the final energy gain [11]. The choice for the IFEL coupling is

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TUBAU04

20

Table 1: IFEL input parametersparameter
fixed value
Energy210 MeV
Energy spread
0.5 %
1 kA
Current
Wavelength
800 nmPeak Power
20 TW
2m
Wiggler length
wiggler gap
7 mm
0.2 m
Rayleigh range
Waist position
1m

15
10
5

a)
0

1.5

2

Resonant energy (MeV)

1500
1000
500

b)
0

0

0.5

1

1.5

2

Distance along the undulator (m)Figure 1: Variation of period and magnetic field amplitude
along the undulator (a). The resonant energy is also shown
(b).
4000

4000

3000

3000

γi 2000

2000

1000

1000

(1)

which yields the maximum attainable magnetic field amplitude for a given gap g and period λ w has been used as an
upper bound for the magnetic field. [12]. The optimized
variations for period and field amplitude are reported inFig. 1a. The resulting resonant energy
λw (1 + K 2 )
(2)
γr =
2λ
along the helical undulator is also shown (Fig. 1b). In (2)K is the normalized peak magnetic field amplitude and λis the driving laser wavelength.
In order to guarantee an high quality final longitudinal
phase space for the accelerated beam the ponderomotive
resonant phase is varied along the undulator. In Fig. 2 weshow the longitudinal phase space and its projection on theenergy and time axis obtained tracking particles throughthe undulator and laser electromagnetic fields with the 3D
IFEL code TREDI[13]. At the beginning the resonant phaseis close to zero to improve capture efficiency while later inthe undulator after the particles have been already captured
and bunched its value grows to π/3 to maximize the accelerating gradient and reduce the final energy spread. The
latter in particular is one of the most sensitive parameters
for a 4th generation light source driver. The stable accelerating region of phasespace formed by the ponderomotive
IFEL potential ensures that small variations in driving laser
power and time/spatial jitter only affect the capture efficiency reducing slightly the final peak current and not theother parameters of the accelerator like final energy and

The Challenge of fs Pulses and Synchronisation

0.5
1
Undulator period (cm)Magnetic field amplitude (kGauss)

2000

a permanent magnet helical undulator. The particle transverse velocity is always different than zero and parallel tothe electric field of a circularly polarized laser (easily obtainable from a linearly polarized pulse, using a high power
quarterwave plate) so that the energy transfer mechanism
between photons and electrons is always turned on. The
undulator gap is set to 7 mm in order to be able to propagate without clipping along the undulator length both thelaser and the electron beam. To ensure feasibility of theundulator construction, the Halbach relation
Bmax = 1.79e−λw /g [T esla]

0

00

1

2

80

3

φi

4

5

6

0 0

20

40

energy distribution

60
40
20
0 0

1

2

3

4

5

6

Phase distribution

Figure 2: Simulated longitudinal phase space of the electron beam at the exit of the IFEL accelerator.
energy spread [13]. The output accelerator parameters are
summarized in Table 2.
The average gradient obtained in this design is quite
large, more than one order of magnitude larger than conventional rf-based designs. A length of just 2 m of undulator is sufficient to reach an energy of 1.5 GeV suitable todrive a x-ray laser at the water window wavelength (3 nm)
which is the goal of our design exercise. The high peakcurrent results from the bunching at the optical wavelengththat takes place in the IFEL (see Fig. 3).

SLIPPAGE DOMINATED FEL
The undulator magnet envisioned to be used to generate
the soft x-ray radiation is the same of the one being built

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Proceedings of FEL 2006, BESSY, Berlin, Germany
Table 2: IFEL output parameters
Energy1.7 GeV
Energy spread< 0.5 %
250 asmicrobunch length
Peak current
6 kAmpAvg. gradient
750 MeV/m

25

2

20

1.5

Energy (GeV)
Current(kA)E-spread (10^-3)

15
1
10
0.5

5

0

0

-0.2

0.8

1.8

2.8

3.8

Distance along the bunch (μm)

Table 3: FEL parameters
Radiation wavelength
3 nm
Undulator period
2.8 cmUndulator K
1.65
77
Periods per section
Number of sections
6
ρ parameter
4.5 ·10 −3

294

Figure 3: Electron beam current along the bunch. The current spikes are very short (250 as) and distant an optical
period 2 fs between eachother.

z = 14.8 m

2
1
0

0

1

2

3

4

30
20
10
0

0

1

2

3

4

Coordinate along the bunch (μm)

0.1

x offset (mm)

3

0
-0.1

Average power (MW)Current (kA) Peak Power (MW)and installed for the SPARC project. The FEL parameters
are reported in Table 3.
Start-to-end simulations of the entire system are performed using the output phase space from TREDI as thestarting distribution in Genesis 1.3 [14]. Even though thephysical mechanism of the interaction is the same along
the system, it is required to use a different code to model
the IFEL interaction since due to the strong tapering theperiod-averaged classical FEL approximation is not valid
anymore, and the explicit 3d Lorentz-force equation solver
is used for the particle dynamics in the simulation of the
IFEL with TREDI. At the same time for the light generation
section of the system, TREDI does not take into accountthe evolution of the electromagnetic field which has to be
calculated using Genesis. The longitudinal phase space isperiodic with period equal to the driving laser wavelength.
The FEL simulation is performed over a window including a portion of the accelerated beam of a length such toinclude 6 to 8 periods of 800 nm. In Fig. 3 we show thebeam parameters along the electron bunch coordinate inside the simulation window. The energy spread at the peakof the current is almost as large as the FEL ρ parameter andthis degrades the interaction. Further work is needed in the
optimization of the last section of the IFEL accelerator inorder to minimize this effect.
The Genesis simulation result is shown in Fig. 4. The
final peak power is limited to only few MW and in the longitudinal profile of the newborn radiation there is no traceof the attractive sub-fs structure of the incoming electron
beam.
To explain these results, we must keep in mind that thethe duration of the current spikes is only 1/10th of the optical wavelength, that is 250 attoseconds or ∼ 90 nm. Considering the fact that in the undulator the radiation slips one
radiation wavelength each undulator period, after only 30
periods of undulator the radiation has slipped over the peak

0

2

4

6

8

10

12

14

2

4

6

8

10

12

14

1
0.1
0.01
0

Distance along the undulator (m)Figure 4: Output of the SASE simulation.

of its gain medium. An FEL driven by such beam would
operate in a strongly slippage dominated regime. Clearly
the problem is reduced if the IFEL accelerates the electron
beam to higher energies enabling the production of shorter
wavelength radiation. In this case in fact the length of eachcurrent spike would be the same, being fixed by the IFEL
driver wavelength) and the shorter wavelength FEL radiation would experience a high gain for a larger number ofundulator periods before slipping away of the high peakcurrent region. Unfortunately the IFEL accelerator design
gets more complicate for higher final energies since it requires a larger laser power and it also involves staging of
two different IFEL modules. Moreover the planned extension of the SPARC photoinjector, SPARX [15], is foreseen
to deliver coherent soft X-rays and user and diagnostics
availability make attractive the few nm region of the electromagnetic spectrum.
One possible solution to the slippage problem is to takeadvantage of the microbunch train structure of the electron
beam. In principle one could retard the charged particles
inserting a magnetic path length between different undulator sections so that the radiation would slip faster over theelectrons and take over the next high current spike at the
beginning of the next undulator section. A cartoon illustration of this scheme is shown in Fig. 5. The advantage inthis configuration is twofold: i) the FEL radiation only experience high gain and is amplified over the entire undulator length and ii) the magnetic chicane inserted to delay theelectrons between undulator sections is a positive R 56 element which helps the conversion of energy modulation into

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CONCLUSIONSElectron current spikesa)Undulator sectionsb)

Radiation

Figure 5: Schematics of chicane to compensate slippage
inserted between undulator sections.

density modulation and so accelerates the microbunchingprocess enhancing the FEL instability in a optical-klystron
like configuration [16].
Without a coherent seed over all the electron bunch, on
the other hand, the enhancement of the FEL interaction will
not take place since the phase of the electromagnetic field
and of the induced bunching starting in the different highgain high current regions is completely random being determined by the shot-noise in the electron beam. Suitableseeds at these short wavelengths are of course lacking at
this time, but the strong progress in high harmonic generation in gas [17] could help in this regard. In Fig. 6 we show
the results of the GENESIS simulation obtained introducing a coherent seed over the entire macrobunch length sothat there is a definite phase relationship between the radiation and the bunching in the different current spikes andthe FEL interaction can start constructively at the beginningof each undulator section. In the upper right corner the xtrajectory of the electron beam is represented. The bumps
represent the magnetic chicanes located in between different undulator sections. The final peak power is > 1 GW
and the radiation is composed by a train of sub-fs spikes
locked with the 800 nm IFEL drive laser phase.

We propose the use of an inverse free electron laser todrive a 4th generation light source in the soft X-ray region of the electromagnetic spectrum. Taking advantageof the high gradient and of the precise control over the longitudinal electron beam phase space, the inverse free electron laser accelerator delivers a high current, high energy
electron beam. The sub-fs structure on the current induces
strong limitations due to the slippage on the FEL dynamics. If one wants to preserve the structure and increase thefinal power, some special precautions have to be taken. It
is worthwhile to note that even if in this paper we considered the inverse free-electron laser as the advanced accelerator scheme to generate the electron beam, a similar output
beam structure is likely to be found using other laser and/or
plasma based accelerators. The considerations and the solutions discussed here are applicable to those cases also.
Another benefit of the proposed laser driven source is thesynchronization and phase-locking of the x-ray pulse withan external high power laser for pump-probe experiments.

REFERENCES[1] J. Galayda et al. Linac Coherent Light Source Conceptual
Design Report, SLAC-R-593, 2002.
[2] TESLA Technical Design Report TESLA-FEL-2002-9,
DESY-2002-167, 2002.
[3] C. G. R. Geddes et al. Nature, 431:538, 2004.
[4] W. Kimura et al. Phys. Rev. Lett., 92:054801, 2004.
[5] P. Musumeci et al. Phys. Rev. Lett., 94:154801, 2005.
[6] P. Musumeci. Proc. of 2006 Advanced Accelerator Concepts, Lake Geneva, WI, 2006.
[7] A. A. Zholents and W. M. Fawley.
92:224801, 2004.

Phys. Rev. Lett.,[8] M. Bellaveglia. In these proceedings, 2006.
[9] D. Alesini et al. Nuclear Instruments and Methods inPhysics Research A, 507:345, 2003.
[10] L. Serafini et al. In Proc. of 2006 EPAC Conference, 2006.

[12] K. Halbach. Journal de Physique, C1:211, 1983.
1.5

z = 14.8 m

1
0.5
0

0

1

2

3

4

30
20
10
0

0

1

2

3

4

Coordinate along the bunch (μm)

Average power (MW) x offset (mm)Current (kA)

Peak Power (GW)[11] W. Kimura et al. In AIP Conf. Proc., volume 737, page 251,
2004.
0.1

[13] P. Musumeci et al. In Proc. of 2001 Particle Accelerator
Conference, Chicago, Illinois, page 4008, 2001.

0-0.1 0

2

4

6

8

10

12

14

100

[14] S. Reiche. Nuclear Instruments and Methods in Physics Research A, 429:243–248, 1999.
[15] C. Vaccarezza et al. In Proc. of 2006 EPAC Conference,
Edinburh, Scotland, 2006.

10
1
0.1
0.01
0

2

4

6

8

10

12

14

Distance along the undulator (m)[16] Y. Ding et al. PRSTAB, 9:070702, 2006.
[17] J. Seres et al. Nature, 433:596, 2005.

Figure 6: Output of the GENESIS1.3 simulation with aseed and with the magnetic chicanes between the undulator
sections.

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TECHNICAL ASPECTS OF THE INTEGRATION OF THE OPTICALREPLICA SYNTHESISER FOR THE DIAGNOSTICS OF ULTRA-SHORTBUNCHES INTO FLASH AT DESY*
P. van der Meulen, N. Javahiraly, M. Larsson, Department of Physics, AlbaNova, Stockholm
University, Stockholm, Sweden
V. Ziemann, Department of Nulcear and Particle Physics, Uppsala University, Uppsala, Sweden
H. Schlarb, A. Winter, E. Saldin, E. Schneidmiller, M. Yurkov, DESY, Hamburg, Germany.
Abstract
In this paper we present an overview of current statusof the Optical Replica Synthesiser at DESY. The method
is based on producing an "optical copy" of the electron
bunch with its subsequent analysis with optical techniques[1]. To this end, a near-IR laser beam is superimposed on
the electron beam in the first undulated of an optical
klystron. In the following dispersive section the laserinduced energy modulation is transformed into a density
modulation. The modulated electron bunch then produces
a strong optical pulse in the second undulator. Analysis of
this near-IR pulse (the optical copy) then provides
information about the profile, the slice emittance and theslice energy spread of the electron bunch. We discuss theimplementation of such a measurement set-up at the
FLASH facility at DESY and investigate the influence ofvarious parameters on the performance of the device.
Topics we address include the dispersive chicane, as wellas the requirements for the seed laser pulses and thedetection and analysis of the near-IR pulse.

INTRODUCTION
Monitoring and tuning the bunch properties are
essential for the reliable operation of linac-based SASE
free-electron lasers such as FLASH [2], XFEL [3], and
LCLS [4]. This need has triggered the development of
new diagnostic methods based on a transversely
deflecting cavity [5] or electro-optical sampling [6]. The
Optical Replica Synthesiser (ORS), a complementary
scheme that was introduced in reference 1, is similar to an
optical klystron FEL seeded by an infrared laser as isshown in figure 1. In the modulator the interaction of thelaser with the transversely oscillating electrons causes anenergy modulation. A dispersive section turns this energy
modulation into a density modulation at the wavelengthof the light. In a following radiator undulator the microbunched beam radiates coherently and the emitted lightpulse has the same longitudinal profile as the electron
beam. Hence the name optical replica synthesiser.
The optical replica pulse is analysed in a FROG
(frequency resolved optical gating) device [7], which isbased on recording the spectrally resolved signal of theauto-correlation. Subsequent application of a pulse
retrieval algorithm reveals both amplitude and phase of
the incident electric field and thus of the longitudinal
profile of the electron bunch. A very compact second

296

harmonic FROG device, Grenouille [8], which performs
the analysis, is available commercially.
Following up on the signing of a letter of intent by
DESY and the vice-chancellors of three Swedish
universities in Uppsala and Stockholm the recently
established SU-KTH-UU Free Electron Laser Centre hasentered a collaboration with DESY to design andimplement a prototype of the ORS in FLASH in order toestablish the feasibility of the device for the X-FEL. In
this note we present the status of the project as of August
2006.

SPACE AND TIMEThe ORS will be installed in the beam line of FLASH
between the collimating dog-leg and the VUV-undulator.
The seed laser will be coupled in into the beam line justdownstream of the dog-leg where a vacuum window isavailable. The modulator will be located about 10 m
downstream of the vacuum window. The magnets will fit
into 1.5m long unoccupied sections between quadrupoles
and other equipment and the magnet gap of 40mm is
sufficiently large to allow installation without modifying
the existing beam pipe. The chicane consisting of fourstandard dipole magnets will also fit in between
consecutive quadrupoles and can be mounted without
breaking the vacuum. The housing of the extraction
coupling mirror and some extra diagnostic for beam size
measurements and alignment of laser and electron beam
will require some vacuum intervention.
The distance between the modulator and the radiator
will be on the order of 15m and it should indeed be short,because collective effects such a plasma oscillations [9]perturb the micro-bunching, caused by modulator, before
it can generate the optical replica pulse in the radiator.
The replica pulse in this case would not be a faithful
replica of the electron bunch profile.
The laser system will be placed outside the linac
tunnel with the shortest possible laser transfer line. For
that an additional tunnel into the beam-tunnel will be
drilled near the dog-leg. The installation of the ORS in the
beam line is foreseen for a shutdown during spring 2007
which will be followed by commissioning and operating
until the self-seeding option for FLASH will be installedin the beam line between the collimating dog-leg and theundulator.

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Figure 1: Schematic view of the Optical Replica Synthesiser.

SEED LASER
The seed laser will be based on an 1550 nm Erbium
fiber oscillator that can be synchronised to the RF systemof the linear accelerator. This oscillator has recently been
constructed and the first, preliminary tests show that it isfunctioning properly. Stable mode locking is achieved
and the pulse has the desired characteristics regarding
pulse energy and spectral width. A schematic diagram of
the Erbium fiber laser is shown in figure 2. As a next step
the pulses will be compressed and frequency doubled.
Subsequently the active synchronisation will be
implemented and its effect on the laser operation will betested.
todiagnostics
FC

λ4 λ4

λ4 λ2

FC
SMF

PBS
SMF

stretcherisolator-5% coupler

WDM

pump
diode

ErF

Figure 2: Schematic view of the Erbium fiber oscillator.
FC: fiber coupler; SMF: single mode fiber; ErF: Erbium
doped fiber, PBS: polarising beam splitter, WDM:
wavelength division multiplexer, λ4: quarter lambda
plate, λ2: half lambda plate.
As an amplifier we will use an existing Clark-MXR
CPA2001 Ti:Sapphire laser from Stockholm University.
The interfacing of the home-built oscillator and theamplifier will start soon. The choice for this amplifier ismainly motivated by budgetary reasons, as the CPA2001
is a highly compact laser system that is not easily adapted
to this particular application. On the other hand, it has
performed very reliably in our lab, with little maintenanceand without major malfunctions for many years. The
doubled output pulses of the Erbium fiber oscillator will
be stretched before injection into the Ti:Sapphire
amplifier cavity. We will attempt to use the stretcher
currently installed inside the CPA2001. This means that
we will have to separate the two layers of the CPA2001 inorder to gain access to the lower level. No modifications

The Challenge of fs Pulses and Synchronisationof the amplifier cavity or the compressor are envisaged
and only slight changes of control electronics arenecessary, predominantly in the Pockels cell driver. The
normal operating frequency of the CPA2001 is 1 kHz, but
it can easily be reduced to 1-10 Hz to match the frequencyof FLASH.
A seed laser intensity of about 4.5 GW/cm2 isnecessary to achieve required energy modulation of theelectron bunch in a five period modulator undulator [1]. If
we account for reflection losses during transport, theestimated maximum pulse energy of the modified
CPA2001 laser system will be approximately 700 μJ
inside the accelerator vacuum tube. The pulse length will
be set to about 2 ps to attain a stable temporal overlap
between the laser pulse and the electron bunch. This isachieved by deliberately misaligning the compressor of
the CPA2001. The resulting longitudinal chirp on thelaser pulse is not expected to influence the operation of
the ORS significantly.
In order to estimate the beam diameter inside themodulator undulator we have performed a straightforward
calculation using Gaussian optics. The results of thiscalculation, in which the beam is focussed by a Galilean
telescope consisting of two achromatic lenses with focal
lengths of 1.0 m and -0.8 m separated by 0.26 m, areshown in figure 3. The beam from the CPA2001 wasassumed to be diffraction limited with an initial diameterof 6 mm (FWHM). From figure 3 we can see that a beam
diameter of about 0.8 mm (FWHM) can be expected at
the position of the modulator undulator located about 10
m downstream from the second telescope lens. This leads
to a laser peak intensity of about 45 GW/cm2 a factor often in excess compared to what should be required. A
more realistic simulation that takes into account thetransversal mode structure of the femtosecond pulses isunder way using commercial beam propagation software.
This simulation will also address the transport form the
CPA2001 laser system to the focussing telescope.
In principle even higher laser intensities could bereached by focussing tighter, but here we are limited by
the requirement that the intensity is essentially constantover the entire length (ca. 1.5 m) of the modulator and by
the dimensions of the input vacuum window (16 mm
diameter). Furthermore, the laser beam should easily
accommodate the whole electron bunch, which has adiameter of 0.1-0.2 mm (FWHM), even while it isperforming its oscillatory motion in the modulator, and by
making the diameter of the seed laser beam too small we

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may simply become too sensitive to the pointing stabilityof the laser system. In any case, the distance between thelaser and the modulator is so large that probably active
beam position stabilisers are required to maintain spatial
overlap between the laser and the electron beam forextended periods of time. Existing beam position
monitors and screens will be used to monitor the spatial
overlap between the laser and the electron beams.
Diagnostic stations to monitor the laser before thevacuum window as well as after the radiator undulator areforeseen, but not yet finalised.

-3

beam diameter (FWHM, 10 m)

2.4

1.8

1.2

0.6

4

6

8

10

12

14

16

distance (m)Figure 3: Seed laser beam diameter as a function of the
distance to the focussing telescope showing a focus of 0.8
mm diameter (FWHM) inside the modulator.
One point of concern is the presence of a spatial chirp
and / or a tilted wavefront on the CPA2001 seed laser
pulse. At the moment it is not entirely clear how this willaffect the detailed micro-bunching process or thesubsequent analysis of the radiator pulse using theGrenouille FROG apparatus. We will perhaps be forced totake steps to correct the seed laser pulse for theseimperfections.

UNDULATOR AND CHICANEThe undulators for the modulator and radiator withperiod l0 and K=93.4B0l0 must fulfil the FEL resonancecondition λ=l0(1+K2/2)/2γ2 with an IR laser operating at λ
= 780 nm and beam energies E = γmc2 between 500 and1000 MeV. Together with the constraint to be shorter than
1.5 m we arrive at electromagnetic magnets that have 5
full periods plus two extra periods to zero the fieldintegrals with a period of 20 cm and a peak field B0 below
0.5 T. In order to allow separating the high power seedlaser from the weaker replica pulse by a polariser we will
have one horizontal and one vertically polarised
undulator. Both magnets are now ordered from
Scanditronix in Sweden and will be delivered to DESY in
spring 2007. The support structure for the undulators tomove them in and out of the beam line will be designedby staff at DESY.

298

The standard steering dipoles with a peak excitation of
33x10-3 Tm are sufficient for chicane to provide an R56 of
up to 0.3 mm. The transverse offset ( ca. 10 mm) of thebeam in the chicane can also be used to insert a mirror
and extract a major portion of the seed laser pulse to
avoid irradiating downstream equipment and disturbing
the weak replica pulse.

LASER DIAGNOSTICS
Once the replica pulse is generated in the radiator
undulator it has to be extracted from the beam pipe andtransported to the diagnostic section with the Grenouille.
Presently we are discussing several options to extract thelight, either by pointing the radiator undulator at adownstream off-axis mirror. This option, however, would
introduce significant wavefront distortion and is notfavoured. In another option we add a second chicane
downstream of the radiator with steering magnets to steer
around an off axis screen. A third option would be toinsert a mirror with a hole into the beam pipe such thatthe electron beam can pass the mirror, but the IR pulse isdeflected out. These options will be scrutinised in the
coming months.
The placement of the Grenouille either in theaccelerator tunnel or in the new laser housing has notbeen decided yet. Placement of the Grenouille inside thetunnel has the advantage of a shorter beam path for the
replica pulse as well as easier alignment and construction,
but access to the tunnel during accelerator operation is
impossible and parasitic operation without impeding otheractivities is, of course, much favoured.

CONCLUSIONS AND PROSPECTS
We have taken the first steps towards implementing
the ORS in FLASH at DESY. Ordering the magnets
which have a long lead time was the first major step andbuilding the laser will be the next, together with solving
all the other issues that we only mentioned in passing.
The infrastructure of lasers and undulators created for the
ORS provides a fertile ground for further experimentswith beams and lasers, especially regarding
synchronisation. For example, using the FIR-undulator
that will be installed downstream of the VUV-undulator
as the radiator instead of the original radiator will allow to
generate a coherent light pulse at the wavelength of theseeding laser close to the experimental hall where it canbe cross-correlated with an external laser used for pumpprobe experiments. This will yield information about therelative timing of the external laser and the bunch arrivaltime, which also caused the VUV-pulse. In this way the
relative timing between VUV-pulse and external laser canbe determined.
Furthermore, passing the micro-bunched electron beam
after the chicane through an optical transition radiation
screen, will yield information about the bunching and thissignal can be used for tuning.

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REFERENCES[1] E. Saldin, E. Schneidmiller, M. Yurkov, ``A simple
method for the determination of the structure ofultrashort relativistic electron bunches,'' Nucl. Inst.
and Methods A 539 (2005) 499.
[2] J. Rossbach, Nucl. Inst. Meth. A475 (2001) 13.
[3] P. Audebert, et.al., ``TESLA XFEL: The first stageof the X-ray laser laboratory - Technical Design
Report,'' DESY 2002-167.
[4] The LCLS Design Study Group, ``LCLS Design
Study Report’’, SLAC-R-593, 2002.
[5] O. Grimm et al., ``Longitudinal bunch shapediagnostics with coherent radiation an a transverse
deflecting cavity in TTF2'', Proceedings of the 2004
FEL conference, 395.
[6] G. Berden, et al., ``Electro-Optic Technique with
Improved Time Resolution for Real-Time,
Nondestructive, Single-Shot Measurements of
Femtosecond Electron Bunch Profiles,'' Phys. Rev.
Lett. 93 (2004) 114802.
[7] R. Trebino, ``Frequency Resolved Optical Gating'',
Kluwer Academic, Boston, 2000.
[8] www.swanoptics.com[9] G. Geloni, E. Saldin, E. Schneidmiller, M. Yurkov,``Theory of space-charge waves on gradient-profile
relativistic electron beam: An analysis inpropagating eigenmodes,'' Nucl. Inst. and Methods
A 554 (2005) 20.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

INVESTIGATIONS OF THE LONGITUDINAL ELECTRON BUNCHSTRUCTURE AT THE FLASH LINAC WITH A TRANSVERSE
DEFLECTING RF-STRUCTURE
Michael Röhrs∗ , Christopher Gerth, Holger Schlarb
Deutsches Elektronen-Synchrotron DESY, D-22603 Hamburg, Germany.
Abstract
In the single-pass Free-Electron Laser FLASH, SelfAmplification of Spontaneous Emission (SASE) occurs ina small fraction of an electron bunch with a length inthe order of micrometers. As a consequence, there is aneed for bunch diagnostics with a time resolution in the
femtosecond regime for understanding and improving themachine performance. At FLASH, a vertically deflecting structure (LOLA) is used to measure the longitudinal charge density profile and phase space distribution of
single bunches with high time resolution. The horizontal slice emittance can be determined by additionally using
quadrupole scan techiques. In this paper, we present resultsof measurements under conditions close to SASE operation
at 13.7 nm. We reached a RMS resolution of 20 fs for thelongitudinal profile measurements, and resolved the longitudinal phase space distribution and slice emittance with
50 fs and 60 fs, respectively. Strong indications for a substructure within the horizontal phase space distribution of
the peak current region have been found.

INTRODUCTION
At the Free electron LASer in Hamburg (FLASH), electron bunches with peak currents of 1-3 kA are produced
by longitudinal bunch compression in two magnetic chicanes. This results in a narrow high current region at thefront of the bunch (“spike”) with a width of less than 100
fs (FWHM) and a long trailing tail. The SASE process
may be initiated within the spike, if transverse slice emittance and slice energy width are sufficiently small. However, these parameters are significantly degraded by coherent synchrotron radiation (CSR) effects in the dipoles ofthe magnetic chicanes, and by space charge forces along
the linac. The SASE signal with a duration in the order of
10 fs suggests that only a fraction of the charge in the spike
contributes to the lasing process. To resolve the longitudinal structure, bunch diagnostics with an appropriate time
resolution is necessary.
The most powerful and multifunctional tools for this purpose are currently transverse deflecting rf-structures called
LOLA [1, 2, 3]. LOLA structures operate in a hybrid
mode (a superposition of a TM 110 and a TE110 mode),which propagates with a phase velocity equal to the speedof light. A passing relativistic electron is subject to a deflecting force in vertical direction, which is independent of∗ michael.roehrs@desy.de300

the transverse position of the electron within the structure
and constant in time. The force sensitively depends on thephase of the fields at the arrival time due to a high frequency time variation at 2.856 GHz. Injection of a bunchat zero crossing of the deflecting force results in a shearingor “streaking” of the bunch without centroid deflection. As
a consequence, the vertical positions of the bunch electrons
downstream of the structure are linearly correlated with
their longitudinal coordinates. Standard OTR screens thenallow for measurements of the particle distribution in thelongitudinal-horizontal plane. Alongside the measurementof the longitudinal charge density profile, this techniquepermits to determine the horizontal slice emittance by scanning quadrupoles upstream of LOLA [4]. Furthermore, thelongitudinal phase space distribution can be obtained in asingle shot measurement at locations with significant horizontal dispersion. An estimate for the time resolution is
given by the vertical size of the bunches at the screen location without streak, i.e. with LOLA being switched off.
Parameters of the LOLA structure are listed in Table 1 [3].

Table 1: Properties of LOLA [3]Length
3.64 mFrequency
2.856 GHz
Max. operating power
25 MW
Deflecting voltage at 20 MW
26 MV
Filling time
0.645 μs
Aperture
44.88 mm

EXPERIMENTAL SETUP
A schematic of the FLASH linac and the sections used
for the measurements is shown in Fig. 1. Electron bunches
are generated in an rf photocathode (gun) and accelerated
in five superconducting modules ACC1 to ACC5. The
bunches are longitudinally compressed in two magnetic
chicanes BC2 and BC3 at energies of typically 127 MeV
and 360 MeV, respectively. A dispersive section (dogleg)
is used to collimate the beam before it enters the undulator section. For the presented measurements, the linac wasoperated with a bunch charge of 0.5 nC and a final energyof 677 MeV to produce a SASE signal at 13.7 nm wavelength. We obtained an average radiation energy of 5 μJ
per electron bunch. The phase of module ACC1 was set to-7.6◦ from minimum energy width operation, which is 4.4 ◦above the phase for maximum peak current (-12 ◦). The

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UND6

….

UND1

Dogleg

LOLA

ACC45

BC3

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ACC1 GUN

ACC23
BC2

Beam direction

CAMERALOLAOTRSCREENQUADRUPOLEDIPOLE
OFF-AXISSCREENKICKERCOLLIMATORS

Figure 1: Schematic of the FLASH beamline and a zoom into the regions used for the measurements. Longitudinal profileand slice emittance have been measured on an off-axis screen (bottom right), the distribution in longitudinal phase spacewith a screen in the dogleg section (bottom left).
phases of modules ACC23 and ACC45 were set to -25 ◦and 0◦ , respectively.
LOLA is located at the end of the linac. An off-axis
screen with a hight of 17 mm has been used in combination with a horizontal kicker preceding LOLA to measure
the longitudinal profiles. The time scale on the vertical axisof the screen has been calibrated by measuring the verticalbunch position while varying the phase of LOLA aroundzero crossing. The calibration constant or “streak strength”
was 4.9 mm/ps in case of the density profile measurement.
The input power of LOLA has been adjusted to observe entire bunches on the screen, including the long tails. In thisway additional quantities may be infered, e.g. the charge
portion within the spike, whereas the time resolution isslightly degraded. The horizontal slice emittance has beenmeasured by varying quadrupoles upstream of LOLA. Several quadrupoles had to be scanned simultaneously in orderto minimize the changes in time resolution (vertical beam
size with LOLA switched off) while the phase advance inhorizontal direction was varied.
An OTR screen in the horizontally dispersive dogleg section has been used for measuring the longitudinal phasespace distribution. The dispersion generated by the upstream dipole has been determined to be 233 mm by measuring the horizontal beam position on the screen for different dipole currents.
Before the measurements, the optics downstream of BC3
had been modified in order to improve the resolution of
the measurements. However, we expect only a negligible

The Challenge of fs Pulses and Synchronisation

modification of the longitudinal bunch properties and thehorizontal emittance. In case of longitudinal phase spacemeasurements, also the optics upstream of BC3 had to bemodified slightly, which may have altered CSR effects inthe dipoles of BC3.

RESULTSLONGITUDINAL PROFILE
Fig. 2 shows the measured longitudinal charge density
profile of a single bunch. It consists of a sharp leading spikeand a long tail. The width of the spike is ∼70 fs (FWHM).
The time resolution is ∼50 fs FWHM and ∼20 fs RMS.
The properties of the spike change slightly from bunch tobunch most likely due to phase and / or amplitude fluctuations of the first acccelerating module. An analysis for 100
successive bunches reveals a nearly gaussian-shaped distribution of the spike width with a mean of 74 fs and a sigmaof 9 fs. The same applies to the charge in the spike defined by the coloured area in Fig. 2 and the corresponding
current, which are 0.13 ± 0.01 nC (25 ± 1 % of the total
bunch charge) and 1.7 ± 0.1 kA.

LONGITUDINAL PHASE SPACE
The particle distribution of a single bunch in longitudinal phase space, which is directly obtained from an OTR
image of a streaked bunch in the dispersive dogleg section,is presented in Fig. 3 (top). It shows the expected overall

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Proceedings of FEL 2006, BESSY, Berlin, Germany

1
0.4

0.9

high

0.2

0.8

0
δ [%]

0.7

−0.2

ρ / ρmax

0.6
−0.4

0.5
−0.6

0.4
−0.8

0.3

0

0.5

1
Δ t [ps]

1.5

low

2

0.2
0.1
0

0.3

0

0.5

Δ t [ps]1

1.5

density profile [a.u.]slice boundaries

20.25

σx [μ m]σδ [%]

400
0.15

300
0.1

200

0.05

100

0

0
0

302

0.5

1
Δ t [ps]

1.5

2

Figure 3: Longitudinal phase space distribution for a single
bunch (top) and corresponding RMS slice energy width σ δ(bottom). In the bottom image, the slice boundaries and thedensity profile are drawn in.
0.8
0.6

energy profile [a.u.]
long. profile (lp) [a.u.]
lp:low energy part
lp:high energy part

50 fs

0.4
0.2
δ [%]

correlation, which is characterized by a rapid energy variation at the head of the bunch leading to the observed sharp
spike in the longitudinal profile, and an increasing energy
along the tail due to off-crest acceleration. Within the highdensity region, there are deviations from the ideal shapein terms of spikes in time and energy direction. Tracking calculations with ASTRA [5] and CSR-Track [6] arein qualitative agreement with these results [7]. Some distinct distortion patterns are mostly related to longitudinal
space charge (LSC) forces: On the way from BC3 to thescreen, LSC causes an increase in energy width, which canclearly be seen in Fig. 3. The spike at the very front of thebunch in time direction is due to energy spread generatedby LSC during the passage from BC2 to BC3, which is thensheared in longitudinal phase space in BC3.
The slice energy widths and the longitudinal density profile calculated from the measured phase space distribution
are shown in the bottom plot in Fig. 3. The chosen slice
widths is equal to the RMS resolution of 50 fs. The slice
energy spread reaches a maximum value of ∼0.26 % or
∼1.8 MeV at the bunch head and decreases to ∼ 0.06 %(∼406 keV) in the tail. Here, the values are limited by theresidual transverse beam size without dispersion and provide an estimate for the energy resolution of the measurement.
The increase in energy width at the front is largely due
to a non-gaussian energy distribution. Within this region,
two local maxima of the energy profile can be observed(Fig. 4). This structure may arise from both, LSC and CSR,
but we expect the LSC effects to be dominant. By dividing the phase space distribution between the two maxima
as indicated by the dashed line in Fig. 4, the longitudinaldensity profile in the high current region can be consideredseperately for the two regions, revealing a separation of thecharge density maxima in time by ∼50 fs (see Fig. 4). It
may be speculated that this is a true substructure of the
spike in the longitudinal density profile, which could not
be resolved here.

600
500

0.2

Figure 2: Normalized longitudinal charge density profile
measured with LOLA. The width of the coloured region
is equal to the width of the spike (FWHM). The specified
charge fraction in the spike refers to this area.

700

0
−0.2
−0.4
−0.6
−0.8

−200

−150

−100

−50
Δ t [fs]

050

Figure 4: Projections of the longitudinal phase space distribution within the peak current region ( Fig. 3) onto thetime and energy axis. The longitudinal profile is splitted
into two parts, as is indicated by the dashed horizontal line:
The one for the low energy part and the one for the highenergy part. The maximas of the profiles are seperated intime by ∼50 fs.

SLICE EMITTANCE
Figure (5) shows the measured horizontal 1σ slice emittance (normalized) along the bunch (bottom) with a resolution of 60 fs, and an OTR image of a bunch during thescan (top). Within the bunch tail the slice emittance ranges
from 2 μrad to 3 μrad. There is a dramatic increase in slice
emittance at the front of the bunch with a value of ∼16 μrad
within the density spike, which is significantly larger than
expected for SASE operation. Assuming an RMS energy

The Challenge of fs Pulses and Synchronisation

Proceedings of FEL 2006, BESSY, Berlin, Germany1highΔ x [mm]

0.5
0
−0.5
−1
−1.5

low
0

0.5

Δ t [ps]

1

1.5

20
density profile [a.u.]slice boundaries

10

ε

norm
[mm mrad]
x

15

5

0

0

0.5

Δ t [ps] 1

1.5

Figure 5: OTR image of a bunch during the quadrupole
scan (top) and 1σ slice emittance along the bunch (bottom).
In the bottom image, the slice boundaries and the density
profile are drawn in.

180

TUBAU06

explained by dispersion in the order of 50 mm, which isa possible value at this location. The dispersion causedby the kicker amounts only to ∼10 mm and does therefore not explain this behaviour. In case CSR forces significantly contribute to the separation of the energy maxima, this would lead to a horizontal displacement as well.
However, we have no proof yet that there is a connection
between the observed structures in the energy profile andthe horizontal profile.
Another contribution may come from a systematic error of the absolute emittance values. The accuracy ismainly determined by quadrupole gradient errors, since six
quadrupoles have been used for the scan. Figure (6) shows
the result of a Monte Carlo simulation for 3 % peak to peakerrors of all quadrupole gradients (independently), which isa rather pessimistic assumption. The probability of having
an error larger than 30 % is accordingly 15 %. The ratios of
the given slice emittance values are not affected by gradienterrors.
The shown results for the slice emittance suggest that areasonable analysis of the emittance in the high current region can, at least for the time resolution given here, only bedone by reconstructing the transverse phase space distribution. A main goal for the future is therefore to apply phasespace tomography methods. Moreover, quantitative comparisons with simulations using ASTRA and CSR-Track
will be done.

160

ACKNOWLEDGEMENTS

140

We would like to thank the FLASH team, in particular
B. Faatz, M. Hüning and B. Beutner, for their support.

120

N

100
80

REFERENCES

6040[1] P. Emma et al, “A Transvers RF Deflecting Structure for
Bunch Length and Phase Space Diagnostics”, SLAC-PUB8864, August 2000.

20
0
0.4

0.5

0.6

0.7

ε/ε

0.8

0.9

1

1.1

0

Figure 6: Result of a Monte Carlo simulation with 1000
seeds for the relative emittance error assuming 3 % peak topeak quadrupole gradient errors.
width of ∼0.2 % as measured in the spike, the emittancewould have to be about ∼5 μrad to obtain the observed
SASE power [8].
One contribution to this increase in slice emittance isdue to a substructure in the horizontal profile of slices in
the high current region. For certain quadrupole settings,
two separate density maxima appear, as can be seen on thebunch image in Fig. 5. This suggests that there are twoislands with high charge density in the horizontal phasespace distribution, each for its own having a smaller emittance. Assuming that these density maxima correspond tothe observed maxima in the energy profile of the head, thehorizontal displacement of the two density maxima may be

The Challenge of fs Pulses and Synchronisation[2] M. Hüning et al,“Observation of femtosecond bunch length
using a transverse deflecting structure”, FEL Conference
2005, Stanford, August 2005.
[3] A. Bolzmann, “Investigations of the Longitudinal Charge
Distribution of Electron Bunches at the VUV-FEL using the
Tranverse Deflecting Cavity LOLA”, Diploma thesis, Universität Würzburg,2005.
[4] M. Röhrs at al, “Measurement of Slice-Emittance using a
Transvers Deflecting Structure”, FEL Conference 2005, Stanford, August 2005.
[5] K. Flöttmann,“ASTRA - A Space ChargeTracking Algorithm”
2006, http://www.desy.de/ mpyflo/Astra dokumentation/[6] M. Dohlus , “Two Methods for the calculation of CSR
Fields”, TESLA-FEL-2003-05.
[7] M. Dohlus, “Modelling of Space Charge and CSR Effects in
Bunch Compression Systems”, EPAC 2006, Edinburgh.
[8] B. Faatz, private communication.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

A 3D MODEL OF THE 4GLS VUV-FEL CONCEPTUAL DESIGNINCLUDING IMPROVED MODELLING OF THE OPTICAL CAVITY
N. R. Thompson and D. J. Dunning, ASTeC, Daresbury Laboratory, Warrington WA4 4AD, UK ∗B. W. J. Mc Neil, SUPA, University of Strathclyde, Glasgow G4 0NG, UK
J. G. Karssenberg, P. J. M. van der Slot and K.-J. Boller, Twente University, Enschede, Netherlands.
Abstract
The Conceptual Design Report (CDR) for the 4th Generation Light Source (4GLS) at Daresbury Laboratory in the
UK was published in Spring 2006. The proposal includes
a low-Q cavity (also called a regenerative amplifier) FEL
to generate variably-polarised, temporally-coherent radiation in the photon energy range 3-10eV. A new simulation
code has been developed that incorporates the 3D FEL code
Genesis 1.3 and which simulates in 3D the optical components and radiation propagation within the non-amplifying
sections of an optical cavity. This code is used to estimate
the optimum low-Q cavity design and characterise the output from the 4GLS VUV-FEL.

INTRODUCTION
4GLS is a 4th Generation Light Source [1] proposed
by CCLRC Daresbury Laboratory to meet the needs ofthe ‘low photon energy’ community. The Conceptual Design Report (CDR) was published in 2006 [2]. 4GLS
will comprise synchrotron radiation sources, free-electron
lasers and conventional lasers which will be combined synchronously to allow innovative pump-probe experiments.
A 600MeV high average current branch operating in energy recovery mode (80pC bunches at up to 1.3GHz) will
feed spontaneous sources and a VUV-FEL. A 750-950MeV
high peak current branch (1nC bunches at 1-10kHz) will
feed a XUV-FEL[3]. There will also be an IR-FEL operating over 2.5–200μm.
This paper first summarises the VUV-FEL CDR design.
The proposal is a low-Q cavity FEL, or Regenerative Amplifier FEL [4, 5], in which the high gain allows saturation to be reached in a few passes with mirrors of low reflectivity. It has been shown from 1D simulations [6] thatthe optimum outcoupling fraction is ∼ 75% for mirrors of
60% reflectivity, using a hole for outcoupling. This fraction
gives a near maximum output power but is a stable working
point, such that the output power is relatively insensitive tosmall changes in outcoupling fraction or mirror reflectivity.
The next section presents 3D simulations of the CDR design, using Genesis 1.3 [7] and a new 3D optics simulation
code developed at Twente University [8]. These simulations confirm the validity of the CDR design and the earlier 1D simulations which investigated the parameter space.
The last section presents simulations to optimise the resonator.
∗ n.r.thompson@dl.ac.uk

304

Table 1: Baseline VUV-FEL parameters, as presented in
the 4GLS CDR.
U NDULATOR
Undulator Period λw
Periods per module
Number of modules
E LECTRON B EAMElectron Beam Energy
Relative Energy Spread (rms)
Bunch Charge
Peak Current
Normalised emittance
O PTICAL C AVITY
Cavity length Lcav
Upstream ROC r1
Downstream ROC r2
Rayleigh length zr
Fundamental mode waist w0
Waist position (measured from US mirror)
Outcoupling hole radius
Cavity stability g1 × g2

60 mm
37
5
600 MeV
0.1%
80 pC
300 A
2 mm-mrad34.6 m
12.85 m22.75 m2.8 m
0.34 mm
12.2 m2 mm
0.88

CDR PARAMETERS
The VUV-FEL will produce radiation of variable polarisation using APPLE-II undulator modules. The minimum
gap is 10mm and the undulator period 60mm. The photon energy range 3–10eV is covered by gap tuning from
10–19mm in helical mode and 12–25mm in planar mode.
For high enough gain for RAFEL operation, the undulator length, expressed in the universal scaling of [9], must
give z̄ ≡ 4πρNu ≥ 4 over all wavelengths and polarisations. The required length is then 11m, achieved with five
2.2m modules of 37 periods. The intermodule gap is 0.6m
to allow space for a quadrupole, BPM and phase matchingunit. A FODO lattice is used with quadrupoles of length
0.12m and strength 9T/m. The electron beam parameters
have been derived using the FEL design formulae of Ming
Xie [10].
The resonator parameters are derived from simple assumptions, with the expectation they will be revised after
3D optics modelling. The fundamental cold cavity modeis focussed to maximise the overlap between radiation andelectron beam over the first two undulator modules. This isdone with a waist at the end of the first module, 12m fromthe upstream (US) mirror as shown in Fig.1. The optimum
Rayleigh length z R (for maximum overlap) is then approximately one third the total length of the two modules plus

Energy Recovery FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH001

Figure 1: A schematic of the 4GLS VUV-FEL with the baseline CDR parameters. The fundamental cavity mode is shownon the same longitudinal scale as the engineering representation. The electron beam direction is right to left.
gap, i.e. around 1.7m. However, this z R pushes the cavity
geometry close to instability and gives an excessive spot
size at the downstream mirror and some diffraction losseson the undulator aperture for the longer wavelengths. In
addition the hole size on the downstream mirror is larger
than the spot size of the spontaneous radiation emitted on
the first pass and does not allow sufficient feedback. The
Rayleigh length is therefore chosen so that the spot sizeof the fundamental cavity mode is the same as the estimated spot size of the spontaneous emission. This gives
a Rayleigh length of 2.8m, somewhat larger than the value
for maximum overlap.
The hole size is such that the outcoupling fraction of thefundamental cold cavity mode is 65%. This is slightly lessthan the optimum value (from 1D simulations) of 75% but
the high gain FEL interaction is expected to guide the radiation reducing the spot size and increasing the outcoupling
fraction towards its optimum value. The mirror material
is protected aluminium with a reflectivity of 60% at 10eV.
The CDR parameters are given in Table 1 and a schematicshown in Fig.1 where the fundamental cold cavity mode isshown on the same longitudinal scale as the machine layout.

3D SIMULATIONS
A new simulation code has been developed at Twente
University that incorporates the 3D FEL code Genesis 1.3
and which simulates in 3D the optical components and radiation propagation within the non-amplifying sections of
the optical cavity. Full details of the code are given elsewhere [8]. The code has been used to model the 4GLSVUV-FEL using Genesis 1.3 in steady-state mode. All thesimulations presented here are for 10eV operation. Simulation results for 3eV will be presented in a later work.

Simulations of baseline design
The CDR parameters have been used for the initial simulations. The growth of output power and the measured
outcoupling fraction, both as a function of pass number,are shown in Fig. 2. At saturation the output power is
350MW with a measured outcoupling fraction of 68%. The

Energy Recovery FELs

85
1 GW

Outcoupling (%)

Output power

100 MW

80

10 MW
1 MW

75

100 kW
10 kW

70

1 kW
100 W
0

5

10
Pass

15

65
20

Figure 2: The growth of output power and the measured
outcoupling fraction, both as a function of pass number,
for the CDR parameters.
normalised power profiles at saturation, for different points
within the optical cavity, are shown in Fig.3. A modal expansion algorithm is under development and will calculate
the power distribution between the fundamental and higher
order modes. It is clear however from Fig.3 that there issignificant transverse HOM content in the radiation field.
It is interesting to note that although the on-axis power ofthe radiation reflected from the downstream (DS) outcoupling mirror is zero, due to the large hole, by the time theradiation is reflected back off the upstream (US) mirror andback into the undulator the power is concentrated on-axis
allowing good coupling with the electron beam for the next
pass.

Cavity optimisation
Fig.4 shows the effect of varying the radius of the outcoupling hole and the mirror reflectivity on the output
power after 20 passes (by which time the FEL has reachedsaturation for almost all parameter sets used here). The
results show that the CDR working point (hole radius
2mm, reflectivity 60%) is satisfactory and stable—the output power is near optimum, yet small changes in hole sizeor reflectivity have a correspondingly small effect on the305Proceedings of FEL 2006, BESSY, Berlin, Germany
Hole radius (mm)TUPPH001

Undulator exit
P (a.u.)

1
0.5
0
−2

−1

0
Output1

2

P (a.u.)

1
0.5
0
−10

3
4e+08
2.5
2

3e+08

1.5

2e+08

1

1e+08

0.5
0
9

−5

0
5
Incident DS Mirror

10

10

11

12

13

14

Waist position (m)P (a.u.)1

Figure 5: Output power (W) as a function of hole radius
and waist position.

0.5
0
−10

−5
0
5
Reflected DS mirror

10

Hole radius (mm)P (a.u.)

1
0.5
0
−10

−5

0
5
Incident US Mirror

10

P (a.u.)

1
0.5
0
−10

−5
0
5
Undulator entrance

10

P (a.u.)

3e+08

1.5

2e+08

1

1e+08

0.5
0

Waist radius (mm)

−1

0

1

Figure 6: Output power (W) as a function of hole radius
and waist size, for waist position 12.19m.

2

x(mm)

Figure 3: The normalised intensity cross sections at saturation, for different points within the optical cavity. The
parameters are the CDR values (waist position 12 m, waist
radius 0.34mm).
Hole radius (mm)

2

0.5
0
−2

3
4e+08
2.5
2

3e+08

1.5

2e+08

1

1e+08

0.5
0
0.3

0.4

0.5

0.6

0.7

0.8

0.9

Mirror reflectivity

Figure 4: Output power (W) as a function of hole radiusand mirror reflectivity. The CDR hole radius is 2mm andmirror reflectivity is 60%.

output power. In fact a reduction in reflectivity would causea small increase in output power, as predicted by the earlier
1D simulations.
Different cavity configuration have been investigated bychanging the ROC of the mirrors such that either waist
size or waist position of the lowest order cold-cavity mode
is kept constant and the other is varied. The dependence

306

4e+08
2.5

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

1

0.2

3

of the output power on hole radius and waist position isshown in Fig.5. It appears that moving the waist back 1mtowards the undulator entrance (from 12m to 11m from the
upstream mirror), i.e. to the centre of the first undulator
module, gives a working point in a broader region of near
maximum output power which would be beneficial.
The results of varying the waist radius from its CDR
value of 0.34mm are shown in Fig.6 for a waist position of
12m where it is seen there is little dependence on waist radius even when the waist radius is 0.1mm which representsa cavity on the boundary of instability with g 1 g2 = 1.00.
Extensions of geometry into unstable resonator configurations will be investigated in the future. Similar results havebeen obtained for a waist position of 10.5m. These results
demonstrate that considerations of cold cavity resonatormodes are not very relevant to this design—the gain guiding of the high-gain FEL interaction strongly dominates.
This interpretation is supported by simulations investigating the effect of changes in waist position on the radiation profiles at different cavity positions. Shown in Fig.
7 are the far field intensity cross sections (calculated at
14m beyond the outcoupling hole, this being the positionof the VUV-FEL optical diagnostic bench) and at the undulator entrance. The cross sections are displayed in arbitrary
units. Again, the dependence on waist position is weak.
It is noted that the far field cross section in Fig.7 displays clear higher order transverse mode structure, with a

Energy Recovery FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

4

x (mm)

2e+05
2
0
1e+05

-2
-4
0e+00
9

10

11

12

13

14

Waist position (m)TUPPH001

minimum intensity on axis. A scan of the effect of holeradius on far-field cross section is shown in Fig.8 where
it is seen that the far field cross section can be improved(i.e. brought closer to a fundamental gaussion mode) byreducing the hole radius. Further optimisation will now bedone to maximise the output power while maintaining the
optimum far-field cross section, including investigation of
unstable resonators.
Finally, the total power within the undulator as a function of waist position is shown in Fig.9. The baseline waist
position of 12m gives the strongest power growth.

2e+05

CONCLUSION

x (mm)

1

0

1e+05

-1
0e+00
9

10

11

12

13

14

Waist position (m)Figure 7: Intensity (a. u.) cross sections in the far field(top) and at the undulator entrance (bottom) as a functionof the waist position of the cold-cavity fundamental modeof the resonator. The hole radius is 2mm.
1e+06

x (mm)

4
2
0

5e+05

-2
-4
0e+00
0.5

1

1.5

2

2.5

3

Full 3D modelling of the VUV-FEL has been madepossible with the new optics simulation package. The main
conclusions are:
• The CDR parameters are close to the optimum values
found with steady state simulations;• The far field cross-section and total output power depend on hole radius but, for each hole radius, are otherwise relatively insensitive to the resonator configuration over a large range of ROC’s around the CDR
values;• The high gain of the FEL ensures that optical guiding
within the undulator and hole size are far more dominant in defining the radiation profile than the ROC ofthe mirrors.
These conclusions demonstrate that the VUV-FEL shouldbe treated as a self-seeding amplifier FEL rather than as an
oscillator FEL.
After 3eV simulations are complete it is expected that 3
mirror sets will be specified, one optimised for 10eV output, one for 3eV output and one for scanning over the fullrange.

Hole radius (mm)REFERENCES

Waist position (m)Figure 8: Intensity (a. u.) cross section in the far field as afunction of hole radius, for waist position 12.19m.
14

6e+08

13

5e+08
4e+08

12
3e+08
11
2e+08
10

1e+08

9

0e+00
0

2

4

6

8

10

12

Distance from undulator entrance (m)Figure 9: Power (W) growth along undulator as a functionof waist position. The vertical bands are due to the gaps
between the undulator sections.

Energy Recovery FELs

[1] M. W. Poole and E. A. Seddon, 4GLS and the ERLP Projectat Daresbury Laboratory, PAC05 Proceedings, (2005)[2] 4GLS
Conceptual
DesignReport,CCLRC,
http://www.4gls.ac.uk/documents.htm#CDR, (2006)[3] B. W. J. McNeil et al, The Conceptual Design of the 4GLSXUV-FEL, (ibid), (2006)[4] B. W. J. McNeil, IEEE Journal of Quantum Electronics, 26,
6, 1990, p1124[5] D. C. Nguyen et al, Regenerative Amplifier FEL, Proceedingsof the XX International Linac Conference, p731 (2000)[6] N. R. Thompson et al, A VUV-FEL for 4GLS, Proc. 27th FEL
Conf., Stanford (2005)[7] http://corona.physics.ucla.edu/~reiche/[8] J. G. Karssenberg et al, FEL-Oscillator Simulations with
Genesis 1.3, (ibid), (2006)[9] R. Bonifacio et al, Opt. Commun. 50, p373 (1984)[10] Ming Xie, PAC Proceedings 1995, p183.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

DEVELOPMENT OF FREQUENCY-RESOLVED OPTICAL GATING FOR
MEASUREMENT OF CORRELATION BETWEEN TIME AND
FREQUENCY OF CHIRPED FEL
H. Iijima, R. Hajima, E. J. Minehara, R. Nagai and N. Nishimori, Japan Atomic Energy Agency, 2-4
Shirakata-Shirane, Tokai, Naka, Ibaraki, Japan.
Abstract
A femtosecond infrared-chirped free-electron laser(FEL) is an effective tool of dissociating molecules
without the intramolecular vibrational redistribution. The
ultrashort FEL pulse with the broadband spectrum isachieved operating the long-pulse electron beam from anenergy recovry linac at Japan Atomic Energy Agency.
Until now, the broadband spectrum of ultrashort pulse
was measured to be 'Z /Z0 = 14% with the central
wavelength of 23 Pm and the pulse duration of 320 fs at
FWHM by an autocorrelation of fringe-resolved second
harmonic generation. However the information of pulse
shape and variation of frequency depending on the time
during the pulse were not obtained. Since it is essential toknow both information in the pulse for the dissociation of
the molecule, we will measure them by frequencyresolved optical gating (FROG).

INTRODUCTION
A femtosecond infrared-chirped free-electron laser(FEL) is an effective tool of dissociating polyatomic
molecules without the intramolecular vibrational
redistribution [1,2]. Coherent vibrational climbing
proceeds from exciting a molecular vibration transitions
by the ultrashort infrared pulse with the broadband
spectrum which encompasses several vibrationaltransitions of the molecule. Indeed, these transitionenergies become smaller and smaller with climbing theladder because of molecular anharmonicity. Therefore, theclimbing efficiency can be increased dramatically whenusing a negatively chirped pulse so that its high-frequency
components which resonant with the lower transitions of
the ladder precede its low-frequency components which
resonant with the upper transitions of the ladder. Coherent
vibrational climbing can be viewed also as a rapid
adiabatic passage leading to efficient excitation of theupper vibrational states with an efficiency that in theory
can be close to 100% because of the coherent nature of
the interaction.
At Japan Atomic Energy Agency (JAEA), an energy
recovery linac (ERL) driven by superconducting
accelerators has been constructed to produce a highpower far-infrared FEL(~20Pm) [3,4]. Operating thisdevice, it succeeds in generating ultrashort pulses with thebroadband spectrum using a long macro pulse of electron
beam by JAEA-ERL.
Until now, the broadband spectrum was measured to be'Z /Z0 = 14% at the central wavelength of 23 Pm and thepulse width of 320 fs at FWHM by an autocorrelation offringe-resolved second harmonic generation (FRSHG) [3].
308

However the intensity and the variation of frequency
depending on the time during the FEL pulse were notobtained. Since it is essential to know both of the intensity
and the variation of frequency in the pulse for the
dissociation of the molecule, we will measure them byfrequency-resolved optical gating (FROG) [5].

FREQUENCY-RESOLVED OPTICALGATING
Principle of FROG
FROG is a technique to completely determine theintensity and phase versus time or frequency. The
apparatus of FROG is only an autocorrelator followed bya spectrometer. In the autocorrelation and related
techniques, the ultrashort pulse is measured purely in thetime domain (autocorrelator), or in the frequency domain(spectrometer). In all these measurements, detectors canonly measure the intensity of the signal. As a result, it isinevitable to lose the phase information, if themeasurement is taken only in one domain. The
measurement of FROG trace is taken in a  hybrid
domain: time-frequency domain. As time and frequency
are two reciprocal domains connected by Fouriertransform, the phase information in time domain is
encoded into the intensity information in frequency
domain, and vise versa. Therefore FROG trace contains
the information of both intensity and phase of ultrashort
FEL pulse by doing only intensity measurement in timefrequency domain.
As the time-dependent component of the pulse can be
written in

E (t ) Re^ I (t ) exp(iZ t  iM (t ))`,
0(1)

where I(t) and M(t) are the time-dependent intensity andthe variation of frequency, and Z0 is a carrier frequency,
FROG trace is described as
2f

I FROG (Z ,W )³ E (t,W ) exp(iZt )dt ,
sig

(2)

f

where a quantity Esig(t,W) is a signal field defined by
E(t)g(t-W) . The function g(t-W) is a gate function withrespect to the gate delay W. Now, consider the Fouriertransform of Esig(t,W) with respect to W, Eq. (2) istransformed toEnergy Recovery FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany
2f

I FROG (Z ,W )³ Eˆ sig (t , :) exp(iZt  i:W )dtd: . (3)fSince Eq. (3) is the 2-dimensional Fourier transform withrespect to t and :, the signal field Esig(t) implementing
IFROG is determined uniquely due to the fundamental
theorem of algebra. As a result, the information of I(t) andM(t) in Eq. (1) are obtained from the quantity IFROG(Z,W).
Various non-linearities such as second-harmonic
generation (SHG), third-harmonic generation, selfdiffraction and polarized-gate are well known as the gatefunction [6]. In our measurement, SHG autocorrelation isused as the gate for FROG trace.

Simulation of SHG-FROG
In the SHG-FROG geometry, the pulse is split into twopulses which are then spatially overlapped in a piece of
frequency-doubling crystal. In the frequency-doubling
crystal, the two pulses induce a second harmonic due tothe second-order optical non-linearity. Hence the signal
field for SHG-FROG is given by Esig(t,W) = E(t)E(t-W). The(a)

TUPPH002

main advantage of SHG-FROG is sensitivity: it involves
only the second-order nonlinearity. Consequently, for agiven amount of input pulse energy, SHG-FROG will
yield more signal pulse energy.
In order to evaluate retrieval of the intensity I(t) andphase M(t) of the ultrashort pulse from SHG-FROG trace,
a numerical simulation for SHG-FROG was carried out
using the JAEA-FEL parameters. As a temporal profile of
input intensity, the previous simulation result was used [7].
The carrier frequency Z0 was determined by anexperimental measurement of O0 = 21Pm. Three types of
input variation of frequency were assumed for thesimulation.
The simulation results are shown in Fig. 1, in which the
top row shows false-color FROG trace for each phase; redmeans high intensity and violet means low intensity. The
images of FROG trace in Fig. 1 are cropped, but thesimulation was achieved in double range. The bottom row
shows retrieval results of FEL pulse, where red closed(open) circle indicates the retrieval intensity (phase)respectively, and blue lines mean the input shape of FEL
pulse. The each column indicates the difference of the

(b)

(c)

41.38

1.0

28.65

0.0

15.92
-2.5

0.0

2.5 -2.5

0.0

2.5 -2.5

0.0

2.5

Delay [ps]Time [ps]Figure 1: The top row shows false-color FROG trace for each phase; red means high intensity and purple means low
intensity. The bottom row shows the retrieval result, where red closed (open) circle indicates the retrieval intensity(phase) and blue line indicates the initial parameter. The each column (a), (b), (c) indicates Fourier transformerlimited, negative chirp, self-phase modulated pulse respectively.

Energy Recovery FELs

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Proceedings of FEL 2006, BESSY, Berlin, Germany

variation of frequency; (a) is a Fourier transformerlimited, (b) is a negative chirp, and (c) is a self-phasemodulated pulse respectively. The retrieval intensity andphase were good agreement with the input intensity andphase.

MEASUERMENT SETUP

Focus and transport system
Since the FEL pulse is diverged by optical diffraction
due to a I2-mm pinhole on an output coupler mirror of
FEL optical cavity, a pair of Au-coated elliptical mirrors
is used to parallelize the FEL pulse with large beam size
(approximately 5 cm in diameter). This optical focusing
system is located near the output coupler. In an
experimental room, the transported FEL is focused again
by a pair of Au-coated parabolic mirrors. The whole setup is mounted in vacuum boxes, which are evacuated up
to 10-7 Torr, in order to avoid distortion of the FEL pulse
due to absorption of the infrared radiation by ambient
water vapour, and is connected to the 24-m FEL transport
ducts. The optics design was determined to be close to100% optical transport efficiency by a numericalsimulation code GRAD [8].

STATUS OF MEASUREMENTS

Spectrum of FEL pulse
Now, the whole optics is being adjusted precisely toprovide the SHG signal from the Te crystal, therefore thefocus, transport, and measurement system are inatmosphere. The atmospheric transport efficiency wasmeasured to be 40 ~ 50 % due to the absorption by theambient water vapour, and the average power of FEL
pulses was measured to be 500 mW, typically.
Figure 3 shows a spectrum of the FEL pulse measured
by a spectrometer. One can find the absorption by theambient water vapour at 21.1, 21.8 and 22.6 Pm.

Experimental setup of SHG-FROG
Figure 2 shows a schematic view of SHG FROG
apparatus constructed now. As shown in Fig. 2, theincoming FEL pulse is split by a polyethylene
terephthalate (PET) film, whose thickness is 23Pm, into
two beams. One of them is delayed by a movable retroreflector; the other has a fixed path length. The movablereflector can be achieved by a stepper-motor-driven linear
stage on which the retro reflector is mounted. A parabolic
mirror focuses both pulses onto the frequency doubling
crystal consisting of 2mm thickness Tellurium (Te). The
second harmonic generated in the crystal when bothpulses have a temporal and spatial overlap propagates
through a slit to the spectrometer. Finally a mercurycadmium telluride (MCT) detector detects the intensity ofsignal.
RR

Cry: SHG Crystal (Te)
BS: Beam Splitter
RR: Retro Reflector
OD: Optical Delay (Stepper-Motor-Driven Stage)
PM: Parabolic Mirror

FEL pulse

RR
BS

OD

Spectrometer

PM

MCT
Detector

Cry

Figure 2: The schematic view of the SHG-FROG setup.

310

Figure 3: The spectrum of FEL pulse. The absorption of
the infrared radiation by the water vapour can be seen at
21.1, 21.8 and 22.6 Pm.

Polarization
High efficiency SHG is one of important points toperform SHG-FROG trace. The efficiency depends on anangle between a Te crystal orientation and a polarizing
plane, and an input power of the FEL pulse dominantly.
On the other hand, the surface of Te crystal is damaged if
the pulse is strongly focused to generate the second
harmonic. Therefore the angle between the Te crystal
orientation and the polarizing plane of FEL pulse should
be adjusted precisely.
Figure 4 shows a measurement result of polarizing
angle of the FEL pulse at position of Te surface. The
measurement was done using a polarizer. In this figure,zero degree corresponds to the horizontal direction. In ourcase, the FEL pulse has a vertical polarization at theoutput coupler. At the surface of Te crystal, the polarizing
direction rotates to 133 degree due to the refractions via
the mirrors in the transport system. The measurement
value is good agreement with the designed value.

Energy Recovery FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH002

consider to measure them by SHG FROG. The numericalsimulation of SHG FROG using the FEL parameters cancompletely retrieves the intensity and phase of the pulse.
In the following, we have start to develop the apparatus ofSHG FROG. Now we are measuring basic parameters of
the FEL pulse (beam size, power, wavelength,polarization and so on) in the experimental room.

ACKNOWLEDGEMENTS
This research is partially supported by MEXT
KAKENHI 18740265.
Figure 4: Polarizing angle on the surface of the doubling
crystal.

SUMMARY
The femtosecond infrared-chirped FEL is the effective
tool of dissociating molecules without the intramolecularvibrational redistribution. JAEA ERL-FEL has been
constracted to provide a high-power far-infrared FEL. The
ultrashort FEL pulse with the broadband spectrum isachieved operating the long-pulse electron beam fromJAEA ERL-FEL. Since it is essential to know both of theintensity and the variation of frequency in the pulse forthe high-efficiecny dissociation of the molecule, we

Energy Recovery FELs

REFERENCES[1] S. Chelkowski, et al., Phys. Rev. Let., 65 (1990) 2355.
[2] Y. Fujimura, O plus E, No. 176, p. 102.
[3] R. Hajima and R. Nagai, Phys. Rev. Let., 91 (2003)
024801.
[4] N. Nishimori, et al., Nucl. Instrum. and Meth. A, 475(2001) 266.
[5] R. Trebino, et al., Rev. Sci. Instrum., 68 (1997) 3277.
[6] B. A. Richman, et al., Opt. Lett., 22(1997)721.
[7] R. Hajima, et al., Nucl. Instrum. and Meth. A, 475(2001) 270.
[8] GRAD; General Laser Analysis and Design program(Applied Optical Research, AOR).

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Proceedings of FEL 2006, BESSY, Berlin, Germany

BEAM CURRENT DOUBLING OF JAEA ERL-FEL
R. Nagai#, R. Hajima, H. Iijima, N. Kikuzawa,
E. Minehara, N. Nishimori, T. Nishitani, M. Sawamura,
Japan Atomic Energy Agency, Tokai, Ibaraki, Japan
Abstract
An energy-recovery linac (ERL) R&D program for ahigh-power free-electron laser (FEL) is in progress at
Japan Atomic Energy Agency (JAEA; formerly JAERIand JNC). The first energy-recovery operation and FEL
lasing was demonstrated in 2002 by remodeling thesuperconducting linac of the JAERI-FEL driver. In thefirst demonstration, the accelerated beam current wassame as the original linac. One of the advantages of an
ERL is that the accelerating beam current can beincreased by only changing micro-pulse repetition rate
without increasing the RF power of the main linac. The
advantage of an ERL has been demonstrated by thecurrent doubling.

INTRODUCTION
For the high-power free-electron laser (FEL), the FEL
extraction efficiency or the drive beam power should be
increased. Increasing of the drive beam power is more
effective than increasing of the FEL extraction efficiency
because the FEL extraction efficiency is limited in several
percent. For the beam power increasing in a usual linac,
there are some problems as follows: high-power RF
source and coupler corresponding with the beam power
are needed, high-power and high-energy beam should be
dumped, radiation shield at the beam dump is very tough.
A high-power beam can be accelerated by small RF
power in an energy-recovery linac (ERL) because thebeam power not extracted to the FEL light is recovered
and used to the acceleration. The radiation shield andthermal design of the beam dump becomes easy because

Sub-Harmonic Buncher

Recovery TBA Arc

the dumped beam power and energy is reduced by thedeceleration at the linac. Using an ERL as an FEL driver
therefore solves the problems for the beam powerincreasing.
An ERL-FEL R&D program is in progress at Japan
Atomic Energy Agency (JAEA; formerly JAERI and
JNC). The first energy-recovery operation and FEL
lasing was demonstrated [1] in 2002 by remodeling thesuperconducting linac of the JAERI-FEL [2]. In the first
demonstration, the accelerated beam current was same as
the original linac. One of the advantages of the ERL is
that the accelerating beam current can be increased byonly changing micro-pulse repetition rate without
increasing the RF power of the main linac.
Todemonstrate the advantage, the e-gun, the injector RF
source, the low-level RF (LLRF) controller, and theoperation system have been improved. As a result of the
improvement, the doubled beam acceleration and the FEL
power improvement have been successfully achieved.

IMPROVEMENT OF THE JAEA ERL-FEL
The layout of JAEA ERL-FEL is shown in Fig. 1. The
injector consists of a DC electron gun with thermioniccathode driven by a grid pulser, an 83.3 MHz subhermonic buncher, and two 499.8 MHz 1-cellsuperconducting modules. The merger is a two-stepstaircase type that consists of four bending magnets andthree quadrupole magnets. The main linac consists of two
499.8 MHz 5-cell superconducting modules. The beamtransport system to the undulator consists of a triple-bend
achromatic (TBA) arc and a half-chicane achromatic
system. The undulator is a hybrid type with period

Undulator & Optical Resonator

Pre-Accelerator

Electron Gun

Main Linac

Beam Dump

Merger
RF Source for the Pre-Accelerator

RF Source for the Main-Linac

Figure 1: Layout of JAEA-ERL.
___________________________________________#

Email: nagai.ryoji@jaea.go.jp

312

Energy Recovery FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany
number of 52 and period length of 33 mm. The opticalresonator is a near-concentric Fabry-Perot type thatconsists of two gold-coated mirrors with center-hole
output coupler. The recovery beam transport system is a
TBA arc.
In the original linac, the electron beam was accelerated
in burst mode with 10 Hz macro-pulse and 10.4125 MHz
micro-pulse repetitions. The macro-pulse average current
was 5 mA that was mainly limited by the RF powersources and the grid pulser. To demonstrate that thehigher beam current than the RF source capacity of themain linac can be accelerated, the ERL has been
improved.
The electron gun is equipped with a thermionic cathodeand operated at 230kV DC voltage. A train of electron
bunch is generated by the grid pulser. To generate 20.825
MHz bunch train, doubled repetition of original one, amain-circuit of the grid pulser was replaced to new circuit[3]. The bunch length and timing jitter of the electron
beam at the electron gun are 590 ps-FWHM and 12.8 psrms, respectively. The bunch length and timing jitter arecompressed into about 1/100 through the beam transportsystem to the undulator.
In the original linac without energy-recovery, two 1cell superconducting modules were driven by two 8 kW
solid-state amplifiers for each, enough capacity for 5 mA
operation. The solid-state amplifiers were replaced by
two IOT of 50 kW [4], which is enough capacity for 40
mA operation.
Stable operation of an FEL depends much on thestability of an accelerator.
In a superconducting
accelerator, a LLRF controller is one of the key
components for achieving good stability. The original
LLRF controller was designed for phase flatness at ±1
deg. within a 1 ms macro-pulse. This LLRF controller
contributed to the 10-year operation of JAERI-FEL. Afterthe remodeling into the ERL, however, the original LLRF
controller performance was insufficient for the ERL
operation. The LLRF controller was replaced by new one.
The new controller is based on analog phase andamplitude control of the cavity RF field coupled with atuner controller, which is same as the original controller.
In the new controller, the following functions wereintroduced for the better stability: the feedback gain, time
constant and loop phase offset can be varied during
operation to obtain good flatness of RF phase andamplitude within a macro-pulse, all the circuits arecontained in a temperature regulated oven [5]. By the
new controller, the phase and amplitude stabilities at thebeam acceleration are 0.07 %-rms and 0.07 deg-rms,
respectively. The original controller was placed at thecontrol room, and the feedback loop involved 50 m cables
to connect the controllers and the RF cavities. These longcables have large phase drift due to the temperaturedependence of the electrical length. The new controller
are installed just beside the cavities to make the cable
length as short as possible. Furthermore the cables
between the controllers and the cavities are contained in atemperature-regulated pipe to suppress the effect of theEnergy Recovery FELs

TUPPH005

changing of the room temperature [6]. The phase stability
in any season has been achieved less than 0.1 deg-rms by
the temperature-regulated cable system.
The electron motion in the longitudinal and transversal
phase space is very complex because the injector has long
drift spaces before and after the pre-accelerator. The
achromaticity of the merger and the bunch length of theelectron beam are sensitive to the quadrupole magnets
parameter. Therefore, the beam transport parameter
adjustment of the injector and the merger is not easy. To
support systematic parameter search, the accelerator
operation system of the JAEA-ERL is equipped with adata-logging system and database services [7]. The initial
parameter set of the injector was decided by the numerical
optimization [8]. In the result, the electron bunch lengthof less than 10 ps has been achieved at the undulator.
The length of the optical resonator was changed alongwith remodeling to the ERL. The optical resonatorgeometry was optimized by a Fox-Li procedure utilized
simulation code[9]. In the optimization, the center-hole
thickness was not taking into account. The center-hole
thickness causes additive loss.
If the center-hole
thickness is taking into account, the radius should beenlarged more than the ideal case. The center-hole radiusof 1.0 mm was adopted in consideration of the loss by thecenter-hole thickness because the optimum radius was 0.8
mm in the ideal case. The misalignment tolerance of theresonator was estimated by the Fox-Li simulation code[10]. The offset and tilt tolerance for the FEL powerfluctuation of 1% are 0.1 mm and 40 μrad, respectively.
The vibration of the floor is less than 1 μm. The accuracyof the He-Ne alignment system of the optical resonator isless than 20 μrad. The offset and tilt tolerance of the
optical resonator is therefore sufficiently large for the FEL
power fluctuation of less than 1%.

ERL AND FEL DEMONSTRATIONSIn the adjustment of the beam transport, the higher
current beam than the RF source capacity cannot be
accelerated because the energy-recovery is not enough.
The energy-recovery acceleration and beam transport
have been adjusted in the condition of original micropulse repetition of 10.4125 MHz. Under the micro-pulse
repetition in 10.4125 MHz, because the beam lost isallowed, the screen monitor can be used for the beamtransport adjustment. After the adjustment, doubled beamin the repetition frequency of 20.825 MHz has been
accelerated only changing of the micro-pulse repetition.
The current increase only by changing the micro-pulse
repetition is scalable. The successful current doublingshows that the current can be increased easily up to 40
mA corresponding with the repetition of the SHB
frequency. Typical signal of the current monitor at theentrance of the main linac is shown in Fig. 2. Thesesignals are the injection beam to the main linac and the recirculated beam from the recovery beam transport systemin the repetition of 20.4125 MHz. The amplitudes of the

313

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Proceedings of FEL 2006, BESSY, Berlin, Germany

injection and the re-circulated beam signal are the almost
same.

20.825MHz

than the RF power source capacity. The detune curve of
the FEL extraction efficiency is shown in Fig. 4. The
Maximum efficiency and power are 2.7 % and 0.7 kW,
respectively.
The output efficiency of the opticalresonator is about 30 %. The output efficiency of the
optical resonator is about 37 % in the numericalsimulation. The difference of the measured value andcalculated one is caused by the thickness of the output
center-hole, and misalignment of the resonator.
3.0

Figure 2: Typical signal of the current monitor at theentrance of the main linac.
Typical signal of output power of the main linac RF
source is shown in Fig. 3. The RF source is operated in
the pulse mode in the repetition of 10 pps and the pulse
width of 2 ms. The electron beam has been accelerated
with 1ms in the latter half. In the case of Fig. 3, themacro-pulse width of the electron beam is 230 μs. The
RF output power with and without the electron beam are
the almost same because the RF power is recovered by
the decelerated electron beam. As shown in Fig. 3, thehigh-current electron beam can be accelerated if there isan RF power only of the amount of exciting theacceleration field. The spike at the edge of the electron
beam macro-pulse is caused by the feedback of the RF
low-level controller. In the pulse mode, the RF power tocompensate the disturbance such as the edge of theelectron beam macro-pulse is needed as shown in Fig. 3.

2.0
1.5
1.0
0.5
0.0
-120

-100

-80 -60-40-20
Detuning Length [μm]020Figure 4: Detune curve of the FEL extraction efficiency.
105

Recovery Rate [%]Recovery Beam

FEL Efficiency [%]

2.5

100
95
90
85

with Beamwithout Beam

80
0.0

0.5

1.0
1.5
2.0
FEL Efficiency [%]

2.5

3.0

Figure 5: Recovery rate of the electron beam at the beam
dump.

Figure 3: Typical signal of output power of the main linac
RF source.
After the energy-recovery acceleration, the FEL lasing
is successfully achieved by adjusting the length and thebeam position of the optical resonator. The beam positionis adjusted while monitoring the stored spontaneousemission with a liquid-nitrogen-cooled HgCdTe detector.
The FEL extraction efficiency is obtained by measuring
the energy loss of the electron beam. The energy loss andenergy spectrum of the electron beam is measured by awire-monitor set up on the way of the recovery TBA arc.
The amount of the beam lost by the wire monitor is less314

The recovery transport system with a large energy
acceptance is necessary because after lasing the electron
beam has large energy spread. The energy spread is about
5 times of the extraction efficiency. The recovery rate ofelectron beam at the beam dump is shown in Fig. 5. The
electron beam is almost recovered up to the extraction
efficiency about 1 %. Under the present condition, thebeam loss at the FEL lasing is less than the RF source
capacity. To increase the beam current, the recovery rateshould be close to 100 %. Measured energy spread at the
maximum output power is about 13.5 % (tail to tail). Theenergy acceptance of the recovery TBA arc is about 16 %in the calculation, and almost electron beam can betransported. There is actually little bremsstrahlung
radiation in the arc part. The beam is therefore lost
mainly in deceleration at the main linac. To recover the

Energy Recovery FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH005

almost electron beam, after lasing the energy spread of theelectron beam should be compressed because it is toolarge into the energy after decelerating [11]. Therefore,
R56 of the recovery TBA arc and deceleration phaseshould be optimized to achieve fully recovery. The
optimization of the energy compression is in progress.

CONCLUSION
One of the advantages of an ERL is that the high beam
current over the RF source capacity of the main linac canbe accelerated. The advantage of an ERL has beensuccessfully demonstrated by the current doubling with
only changing of the micro-pulse repetition rate. The
current increase only by changing the micro-pulse
repetition is scalable. The successful current doublingshows that the current can be increased easily up to 40
mA corresponding with the repetition of the SHB
frequency.
To achieve in the future the 10 kW class high-power
FEL, the beam current will be increased by solving the
problem of the recovery rate and increasing the repetitionof micro-pulse up to the SHB frequency of 83.3 MHz.
The RF sources of the pre-accelerators are ready for 40
mA beam. For the 83.3 MHz operation, the drive
frequency of the grid pulser should be improved up to
83.3 MHz. Design of a grid pulser for the higher
repetition rate is under investigation. A photo cathodeelectron gun driven by a laser as another option for the83.3 MHz operation is under investigation also.

REFERENCES[1] N. Nishimori, et al., Nucl. Instr. and Meth. A475
(2001) 266-269.
[2] R. Hajima, et al., Nucl. Instr. and Meth. A507 (2003)
115-119.
[3] N. Nishimori, et al., Proc. of the APAC2004 (2004)
625-627.
[4] M.Sawamura, et al., Nucl. Instr. and Meth. A557
(2006) 287-289.
[5] R. Nagai, et al., Proc. of the Annual Meeting of Part.
Acc. Soc. (2004) 293-295.
[6] R. Nagai, et al., Proc. of the 14th Symposium on Acc.
Sci. and Tech. (2003) 362-363.
[7] N. Kikuzawa, Proc of the FEL2003 (2004) II-5.
[8] R. Nagai, et al., Proc. of the Annual Meeting of Part.
Acc. Soc. (2004) 420-422.
[9] R. Nagai, et al., Nucl. Instr. and Meth. A528 (2004)
231-234.
[10] R. Nagai, et al., Proc. of the FEL2004 (2004) 255257.
[11] R. Hajima, E. Minehara, Nucl. Instr. and Meth. A507
(2003) 141-145.

Energy Recovery FELs

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Proceedings of FEL 2006, BESSY, Berlin, Germany

PERFORMANCE OF A CONVENTIONAL ANALOG Φ-A TYPE LOWLEVEL RF CONTROLLER
R. Nagai#, R. Hajima, H. Iijima, N. Kikuzawa,
E. Minehara, N. Nishimori, T. Nishitani, M. Sawamura,
Japan Atomic Energy Agency, Tokai, Ibaraki, Japan
Abstract
For a free-electron laser application and energyrecovery linac based light source, high-stability ofaccelerator RF amplitude and phase is required. A lowlevel RF controller of the JAEA-ERL has been improved
to ensure high-stability accelerating RF field. The
controller is a conventional analog Φ-A type controller.
The controller performance is evaluated with a 499.8
MHz superconducting cavity and a 1300 MHz copper
cavity. The phase and amplitude stabilities of the 499.8
MHz superconducting cavity within latter half of an RF
pulse are 0.0055 deg-rms and 7.64×10-5, respectively. For
the 1300 MHz copper cavity, the performance of pulse
and CW modes are evaluated. In the case of pulse mode,the phase and amplitude stabilities are 0.011 deg-rms and7.64×10-5, respectively. In the case of CW mode, thephase and amplitude stabilities are 0.011 deg-rms and6.68×10-5, respectively. Therefore, the performance of theanalog Φ-A type low-level RF controller is sufficient for afree-electron laser stable operation and an energyrecovery linac based light source.

INTRODUCTION
Stable operation of a free-electron laser (FEL) andperformance of an energy-recovery linac (ERL) based
light source depend much on the stability of an accelerator.
In a superconducting accelerator, a low-level RF (LLRF)
controller is one of the key components for achieving
good stability. An ERL R&D program for a high-power
FEL is in progress at Japan Atomic Energy Agency(JAEA; formerly JAERI and JNC). A LLRF controller
based on analog phase and amplitude feedback system
was improved in the R&D program. An analog Φ–Asystem has the faster response than a digital feedback
system because there is no delay caused by thecomputation.
There is however the following
disadvantages: the feedback parameters are not adjustableeasily, the temperature coefficient of the circuit parts arelarger than the digital feedback system. To solve thedisadvantages, the following functions were introduced:
the feedback gain, filter time constant and phase-lockloop (PLL) offset phase can be varied during operation,
all the circuits are contained in a temperature regulatedoven. As a result of the improvement, the accelerator
phase stability of 0.06 deg-rms was achieved within latter
half of an RF pulse [1].
The feedback filter of the LLRF controller is a lowpass filter of a single-pole RC circuit type. Only the___________________________________________#

Email: nagai.ryoji@jaea.go.jp

316

resistance can be varied to change the time constant. The
operation frequency of the PLL is 499.8 MHz, which isthe same frequency of the superconducting cavity. To
satisfy the requirements of the ERL based next generation
light source, the following functions are added: the filter
time constant can be varied by changing the resistanceand capacitor, the frequency converter and band-passfilter can be added for the various frequency operation.
The improved controller performance is evaluatedwith a 499.8 MHz superconducting cavity and a 1300
MHz copper cavity. The stabilities are measured by theerror signal of the controller. For the 499.8 MHz
superconducting cavity, the RF mode is a pulse mode
which is the same mode with the JAEA-ERL usual
operation mode. For the 1300 MHz copper cavity, thephase and amplitude stabilities are measured in the pulse
and CW modes. In the CW mode, the phase stability is
estimated by also the phase noise measurement.

STABILITY MEASUREMENTS
Stability of the 499.8 MHz Superconducting
CavityThe RF field stability is measured for the 499.8 MHz
superconducting cavity used as a pre-accelerator of the
JAEA-ERL. The JAEA-ERL is operated by pulsed RF
mode in the width of 2 ms and the repetition of 10 pps.
The stability in the part of latter half used to accelerate theelectron beam is measured in the setup as shown in Fig. 1.
The setup is similar to the usual operation of the JAEAERL. The signal of 499.8 MHz from the master oscillator(Hewlett-Packerd 8665A) is input to the controller as areference signal. The output of the controller is amplified
with 400 W pre-amplifier (THAMWAY T145-56AAA)
and 50 kW IOT (CPI CHK2500W5508) [2], and input tothe superconducting cavity. The monitor signal of thesuperconducting cavity is returned to the controller for the
feedback loop. The signals of the phase and amplitude of
the cavity are output from the controller and measured bya signal monitor. The signal monitor consists of adigitizer (Yokogawa WE7000) and a computer. The
signals of the phase and amplitude from the controller are
digitized and acquired to the computer. The phase andamplitude stabilities are calculated with real-time fromthe digitized data. The feedback gain, filter time constantand PLL offset phase of the controller are adjusted in realtime monitoring of the stabilities.
Typical signal of the phase and amplitude within apulse is shown in Fig. 2. The phase and amplitude
stabilities within latter half of an RF pulse are 0.0055 deg-

Energy Recovery FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany
rms and 7.64×10-5 rms, respectively. The accelerating
gradient and loaded Q of the superconducting cavity are
5.2 MV/m and 1.3×106, respectively. In this case, main
disturbance is an RF shaking due to the pulse operation.
400W Pre-Amplifier

Master Oscillator

50kW-IOT

TUPPH006

For the CW mode measurement, the feedback parameters
are re-adjusted. The phase and amplitude stabilities are
0.011 deg-rms and 6.68×10-5 rms, respectively.
Frequency Converter & Band-Pass Filter+28dBm Amplifier

Master Oscillator

LLRF Controller

Test Cavity

LLRF Controller

Local Oscillator

Superconducting Cavity
Signal Monitor

DC Signal

Figure 1: Stability measurement setup for the 499.8 MHz
superconducting cavity.

0.00

σA=7.64×10-5rms

4
3
2
1
0

0

1

2
3
Time [ms]

-0.05

4

5

1

2
Time [ms]

3

0.8

3.50

0.6
0.4
0.2
0.0

3.45

-0.2

-1

0

1
2
Time [ms]

3.40

3.30

3

4

σφ=0.011deg-rms

-1

0

1
2
Time [ms]4

Figure 2: Typical result of the phase and amplitude (inset)
within a pulse for the 499.8 MHz superconducting cavity.

Stability of the 1300 MHz Copper Cavity
To evaluate the performance of the LLRF controller atthe 1300 MHz operation, the phase and amplitude
stabilities are measured using a copper cavity in the pulse
and CW modes. The loaded Q of the copper cavity is
about 5800. The measurement setup is shown in Fig. 3.
The signal of 1300 MHz from the master oscillator(Hewlett-Packerd 8341B) is input to the controller as areference signal. The signal of 800.2 MHz from the local
oscillator (Agilent 8662A) is input to the controller for afrequency conversion. The output of the controller isamplified with +28 dBm amplifier (Mini-Circuits ZHL4240W), and input to the copper cavity. The monitor
signal of the copper cavity is returned to the controller for
the feedback loop. A part of the returned signal is input toa spectrum analyser (Tektronix RSA230) for the phasenoise measurement in the CW mode. The master
oscillator, local oscillator and spectrum analyzer aresynchronized with the local signal of the master oscillator.
For the pulse mode measurement, the phase andamplitude stabilities are measured with the width of 3 ms
and the repetition of 10 pps. The feedback parameters areadjusted according to the similar procedure of thesuperconducting cavity case. Typical signal of the phaseand amplitude within a pulse is shown in Fig. 4. The
phase and amplitude stabilities within latter half of an RF
pulse are 0.011 deg-rms and 7.64×10-5 rms, respectively.

Energy Recovery FELs

σA=7.64×10-5rms

1.0

3.35

σφ=0.0055deg-rms
0

1.2

3.55
Phase [deg.]

Amplitude [MV/m]

Phase [deg.]

0.05

-0.10

3.60

6
5

DC Signal

Figure 3: Stability measurement setup for the 1300 MHz
copper cavity.

Amplitude

0.10

RF Signal

Spectrum
Analyzer

Signal Monitor

RF Signal

3

4

Figure 4: Typical result of the phase and amplitude (inset)
within a pulse for the 1300 MHz copper cavity.
For the CW mode, the phase stability is estimated byalso the phase noise measurement. The phase fluctuation(phase stability), σφ over a frequency range from f1 to f2 isgiven by1/ 2

σ ϕ = ⎛⎜ ∫ 2 L( f ) df ⎞⎟
f2

⎝ f1

⎠

[rad ] ,(1)

where L(f) is a single sideband (SSB) phase noise [3]. In
this measurement, the frequency range is 2 Hz to 10 kHz.
The measurement accuracy of the spectrum analyzer used
for this measurement is about -100 dBc/Hz. The phasenoise of the master oscillator is not negligible small. The
phase stability of the cavity is therefore estimated by

σ ϕ = (σ ϕ2m − σ ϕ20 )

1/ 2

,

(2)

where σφm is measured phase stability and σφ0 is phasefluctuation of the oscillator and spectrum analyzer. The
measured SSB phase noise against offset from the carrier
frequency (offset frequency) is shown in Fig. 5. The inset
is a phase noise of the oscillator and the spectrum
analyzer. The phase stability is 0.013 deg-rms as a resultof the measurement. Even if two phase noises in Fig. 5
are compared, the difference is hardly seen. The phasenoise of the spectrum analyzer and the oscillator is not
small enough to measure such a very high stability (lessthan 0.01deg-rms). The high-accuracy measurement of
the phase noise by a low-noise measurement system isunder arranging.

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CONCLUSION

0-20

L(f) of Osc. [dBc/Hz]

L(f) of Cavity [dBc/Hz]

0

-40
-60

-20
-40
-60
-80
-100
-120

1

10
100
1000
Offset Frequency [Hz]

10000

-80
-100
-120

1

10
100
1000
Offset Frequency [Hz]10000

Figure 5: SSB phase noise of the copper cavity and theoscillator (inset).
The main disturbance of the ERL is a minute vibrationof the acceleration cavity which is called microphonic[4,5]. To evaluate the microphonic disturbance, the phasenoise is measured with the mechanical vibrated cavity.
The phase and amplitude stabilities measured by the error
signal of the controller are 0.014 deg-rms and 7.60×10-5,
respectively. The measured phase noise is shown in Fig.
6. The large phase noise (-37 dBc/Hz) due to themechanical vibration is observed around 25 Hz without
the feedback. When feedback is on, the phase noise isalmost the same as the background level (-75 dBc/Hz).
Therefore, the feedback gain of the phase around thisfrequency is 38 dB or more. The phase stability estimatedfrom the phase noise is 0.034 deg-rms. The estimatedvalue differs from the measured by the error signal due tothe accuracy of the measurement system in this condition.

L(f) of Cavity [dBc/Hz]0The phase and amplitude stability requirements for an
ERL based light source are 0.06 deg-rms and 3×10-4 rms,
respectively [5]. The performance of the conventional
analog Φ-A type LLRF controller is sufficient for the
ERL-FEL stable operation and the ERL based light source
as a result of the stability measurement.
The measurement of the SSB phase noise is useful forthe performance evaluation of the controller withfrequency resolved disturbance analysis.

REFERENCES[1] R. Nagai, et al., Proc. of the Annual Meeting of Part.
Acc. Soc. (2004) 293-295.
[2] M. Sawamura, R. Nagai, Nucl. Instr. and Meth. A557
(2006) 287-289.
[3] E. Ezura, ‘Characterization and Measurement ofFrequency Stability’ KEK Report 2000-6.
[4] C. Hovater, et al., Proc of the 20th Linac Conf. (2000)
518-520.
[5] M. Liepe, et al., Proc. of the PAC2003 (2003) 13291331.

Feedback-Off

-20
-40
-60
-80
-100
-120

1

10
100
1000
Offset Frequency [Hz]10000

L(f) of Cavity [dBc/Hz]

0

Feedback-On

-20
-40
-60
-80
-100
-120

1

10
100
1000
Offset Frequency [Hz]10000

Figure 6: SSB phase noise with mechanical vibration.

318

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TUPPH007

JAEA PHOTOCATHODE DC-GUN FOR AN ERL INJECTOR
T. Nishitani, R. Hajima, H. Iijima, R. Nagai, M. Sawamura, N. Kikuzawa, N. Nishimori, E.
Minehara, Japan Atomic Energy Agency, Tokai, Ibaraki, Japan
M. Tabuchi, Y. Noritake, H. Hayashitani, Y. Takeda, Nagoya Univ., Nagoya, Aichi, Japan.
Abstract
An ERL-based next-generation synchrotron lightsource and free electron laser require an electron beam oflarge current and small emittance. In order to realize anelectron gun satisfying such requirements, we aredeveloping an NEA-GaAs photocathode DC-gun. The
gun is based on an existing DC-gun of Japan Atomic
Energy Agency (JAEA) ERL-FEL and designed toprovide a beam with energy of 250 keV and average
current of 50 mA. Conditioning of a high voltage power
supply has been completed up to design the target
voltage of 250 kV. We have also decided to use
superlattice semiconductor as a new type ofphotocathode with higher performance than an existing
technology. We fabricated bulk-AlGaAs photocathodesamples by molecular beam epitaxy in order to optimize
the superlattice structure. We measured quantum
efficiency and lifetime of the samples and achieved twice
QE of a bulk-GaAs photocathode and longer NEA
surface life than that of the bulk-GaAs photocathode.

INTRODUCTION
NEA-GaAs photocathodes have played very importantroles as polarized electron sources in several fields offundamental science [1]- [5], because polarized electrons
is generated from an NEA-GaAs photocathode can be
through the excitation of electrons by polarized photons
tuned to the band-gap energy.
Now, an NEA-GaAs photocathode is also expected asa high-brightness electron source for ERL-basednext-generation synchrotron X-ray light sources(ERL-LS). Ultimately high-brightness electron beam isrequired to realize the ERL-LS [6]. In order to realize
such a high-brightness electron source, we need tocontrol initial momentum spread of electrons as small as
possible. An NEA photocathode can generate electron
beam with such small initial momentum spread by
excitation energy corresponding to the band-gap.
However, a conventional NEA-GaAs photocathodeusing a bulk type of GaAs semiconductor (bulk-GaAs)
has serious problems, small quantum efficiency (QE) andshort lifetime of the NEA surface.
In JAEA, we are developing a high-brightness electron
gun for future ERL LS and FEL. In this study, we havedecided to use a superlattice semiconductor for ahigh-brightness photocathode to fulfill the requirementof future ERL LSs. In the design of superlattice structure,
we can optimize its electron affinity, band-gap energy
and quantum confinement effect to improve thephotocathode performance: higher QE, smaller
momentum spread and longer lifetime.

Energy Recovery FELs

DEVELOPMENTAL STATUS OF THE
JAEA PHOTOCATHODE DC-GUN
An NEA photocathode has a fragile surface consistingof thin layer of cesium-atoms attached to gallium-atoms,
which form electric dipole field to pull down the vacuum
potential barrier. The NEA surface is easy to destroy byion back-bombardment, which is ion generation bycollision of extracted electrons and residual gas
molecules followed by acceleration of the ions toward
the cathode surface. Therefore, extreme high vacuum isessential to make an NEA surface of good quality andpreserve it for long time.
A field emitting electrons also causes the ion
back-bombardment. The field emission current can besuppressed using titanium and molybdenum as electrodematerials [7] and isolating gun chamber from NEA
activation chamber to prevent cesium contamination to
the electrode.
The JAEA photocathode DC-gun consists of the gunchamber, the NEA surface preparation chamber and theload-lock system for transporting photocathode between
these chambers. The preparation chamber is equippedwith 200l/s NEG pump modules and a 500l/s ion pump.
The gun chamber is equipped with 2000l/s NEG pumpmodules and two ion pumps, 500l/s and 200 l/s.
We have decided to use titanium alloy for theelectrodes and these chambers. The titanium alloy shows
out-gassing rate of 6×10-13 Pa m/s, which is much lower
than that of standard vacuum materials by three orders ofmagnitude [8]. In our estimation of the ultimate pressureusing the pumping speed and the out-gassing rate, thechambers is expected to be below 5×10-10Pa
The ceramic insulator of the gun and the high voltage
stack of the 250kV-50mA power supply are locatedside-by-side in a pressure vessel filled with SF6 gas of
2kgf/cm2.
Figure 1 shows the gun chamber and the high voltage
power supply.

Figure 1 : JAEA photocathode DC-gun.

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Conditioning of the high voltage power supply has
been completed up to the design voltage of 250kV.
Figure 2 shows leakage current of high-voltage terminal
as a function of applied voltage. We confirmed the linear
relationship between leakage current and supplying
voltage without severe corona discharge.
120

higher energy photons to achieve high-QE operation at
the expense of large momentum spread of electrons. A
superlattice photocathode, on the other hand, enable one
to achieve high-QE and small momentum spread
simultaneously by choosing a photon energy just above
the step energy of DOS [11].

NEA-ALGAAS PHOTOCATHODE

Leakage current [uA]100

Advantages of bulk-AlGaAs in a high QE and alonger lifetime

80
60
40
20
0

0

50

100

150

200

250

Voltage [kV]Figure 2 : Leakage current of the high-voltage terminal
as a function of applied.

STRATEGY OF A NEW TYPE OF
PHOTOCATHODE
Superlattice photocathodeWe have decided to use a superlattice photocathode asa new type of photocathode with higher performance
than the existing technology [9]. A superlattice structure
has periodically interchanging solid layers, well-layer
and barrier-layer, thickness of which is less than 10nm.
By selecting appropriate semiconductor for a each layer,
a superlattice is possible to have larger band-gap energy
and smaller electron affinity than that of a bulk-GaAs.
We consider the superlattice has intrinsic advantages
in realization of higher QE, smaller initial momentum
spread of photoelectrons and a longer lifetime of the
NEA surface than those of a bulk-GaAs photocathodedue to the following two reasons.
(1) Larger band-gap and smaller electron affinity
than those of a GaAs is possible by optimization of asuperlattice structure.
Experimental results of polarized electron sources
have suggested that larger band-gap photocathode ismore suitable for higher QE photocathode [10].
Moreover, we predict smaller electron affinity is moresuitable for longer NEA life. Because a semiconductor
with smaller electron affinity has lower vacuum level
when the surface is NEA-activated.
(2) Electron density of state (DOS) for a superlattice
is a step function of excitation photon energy because ofquantum confinement effect.
In a semiconductor photocathode, QE is proportional
to its DOS integrated from the band-gap energy to theexcitation photon energy. A bulk GaAs, which has amonotonically increasing DOS function, requires rather

320

In order to confirm the effect of band-gap energy andelectron affinity on the photocathode performance, wehave measured QE and lifetime of different materials:
bulk GaAs and bulk AlGaAs, which has larger band-gap
energy and smaller electron affinity than GaAs. It is
known that the AlAs semiconductor has larger band-gap
energy and smaller electron affinity than the GaAs
semiconductor [12].
The measurement of the QE and the NEA surface
lifetime as a function of band-gap energy and electron
affinity is essential for optimization of the material
fraction in the barrier layer of a superlattice structure.
The bulk AlGaAs cathode is also expected to be a higher
QE and a longer lifetime in comparison with aconventional GaAs photocathode.

Fabrication of crystal samples
We fabricated bulk-GaAs and bulk-AlGaAs samples
with various Al fractions (=0.10, 0.17. 0.28). Thesesamples have the same active-layer thickness for thephotoelectron generation. Figure 3 shows samples
fabricated by Molecular Beam Epitaxy at Nagoya
University.
Exposure of a cathode surface to atmosphere results inadsorption of impurities such as oxide and carbide,
which are harmful for NEA activation and hard to
remove by heat cleaning. The samples have, therefore,
covered by arsenide film in their preparation at the MBE
chamber. The film is removed by heating in a vacuum
chamber just before the NEA activation.

Figure 3 : Photocathodebulk-AlGaAs.

samples:bulk-GaAs

and

Energy Recovery FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

The measurements of QE and life time for GaAs and
AlGaAs have been made at a test bench as shown in
Figure 4.
The main chamber keeps extreme high vacuum of
3×10-9 Pa using the combination of a 500 l/s ion pump
and a 1300 l/s NEG pump. The surface of samples iscleaned by radiation heating using a tungsten heater. The
NEA surface is activated by alternatively adsorption ofcesium and oxygen (yo-yo method).
Ti:Sapphire laser (720-870nm), He-Ne laser (633nm)
and laser diode (690nm and 670nm) is used as a
excitation laser.

band-gap energy (1.42eV) and QE of 2~3% from theband-gap energy to 0.1eV above the band-gap energy.
These results are consistent with previous experiments
[13].
2

10

1

10
Quantum Efficiency(%)

Experimental setup

TUPPH007

0

10
10

-1

10

-2

10

-3

10

-4

1.4

1.6
1.8
Excitation Energy(eV)2Figure 6 : Quantum efficiency of the bulk-AlGaAs
sample.
Figure 6 shows QE spectrum of the bulk AlGaAs
sample. We can also see a threshold around the band-gap
energy (1.79eV) calculated from the content ofaluminum.. The QE from the band-gap energy to 0.1eV
above the band-gap energy is 5~8%, which is two times
higher than that of the bulk-GaAs sample.

NEA-surface life measurement
Figure 7 shows measurement results of NEA surface
lifetime of samples, where laser photon energy waschosen at 0.1 eV above the band-gap for each sample.
Photocurrent was below 100 nA and applied voltage was
as low as 200 V to avoid NEA surface degeneration by
ion back bombardment.

Figure 4 : Experimental set up.

Quantum efficiency measurement
2

Quantum Efficiency(%)

10

1

10

0

10

-1

10

1.4

1.5
1.6
Excitation Energy(eV)

1.7

Figure 5 : Quantum efficiency of the bulk-GaAs sample
Figure 5 shows measured QE spectrum of thebulk-GaAs sample. We can see a threshold around theEnergy Recovery FELs

Figure 7 : NEA-surface lifetime of bulk-GaAs (laser
wavelength of 804nm) and bulk-AlGaAs (laser
wavelength of 633nm).

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In the case of the bulk-GaAs, QE, initially 3.5%,
decreases below 1% 4hours after the NEA activation andthe photocurrent ceases after 6 hours. In the case of thebulk-AlGaAs, QE shows initial drop from its initial value
of 8% to 3% during 5 hours, but keeps 3% QE more than
26 hours.
From these results, we have found the bulk-AlGaAs
has a longer lifetime of NEA surface than the bulk-GaAs.
These results agree with our prediction that smaller
electron affinity is suitable for longer NEA life.

SUMMARY
In JAEA, we are developing an electron gun for future
ERL X-ray light sources and FELs. Fabrication of a DC
gun and study on a photocathode for small emittance andhigh average current are in progress. We have proposednovel approaches, titanium alloy for the DC gun
chambers and superlattice for the photocathode. The
superlattice produces electrons with small initialmomentum spread due to its quantum confinement effect,and realizes high QE, small emittance and long life timeby optimizing well- and barrier-layers so that it has large
band-gap and small electron affinity. Preliminary resultsfrom the measurements of QE and lifetime for the bulk
GaAs and the AlGaAs photocathodes support our
strategy. We will measure QE and NEA surface ofsamples with various fraction of aluminum to optimize
the superlattice structure322

ACKNOWLEDGEMENT
This work has been supported in part by Grant-in-Aid
for Scientific Research for Ministry of Education,
Culture, Sports, Science and Technology (Nos.
18740253).

REFERENCE[1] D.T. Pierce et al., Appl. Phys. Lett. 26 (1975) 670.
[2] C.Y. Prescott et al., Phys. Lett. 77B (1978) 347.
[3] M. Meyerho¤ et al., Phys. Lett. B 327 (1994) 201.
[4] SLD Collaboration, Phys. Rev. Lett. 74 (1995) 2880.
[5] S. Mayer, J. Kessler, Phys. Rev. Lett. 74 (1995) 4803.
[6] Sol M. Gruner, et al., Review of Scientific
Instruments, Vol. 73 Issue 3 pp. 1402-1406, 2002
[7] F. Furuta et al., NIM A 538 (2005) pp. 33–44[8] H. Kurisu, et al., J. Vac. Sci Technol. A21 (2003) L10[9] T. Rao, et al., Nuclear Instruments and Methods inPhysics Research A557 pp.124–130, 2006[10] T. Nakanishi, et al., AIP Conference Proceedings 421,
(1998) pp. 300-310[11] T. Nishitani et al. J. Appl. Phys. 97 (2005) 094907[12] Sadao Adachi, J. Appl. Phys. 58 (3), (1985) pp.
R1-R12[13] T. Maruyama, et al., Appl. Phys. Lett. Vol82, 23,(2003) pp.4184-4186

Energy Recovery FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH008

HARMONIC LASING CHARACTERIZATION AT JEFFERSON LAB
S. V. Benson and M. D. Shinn, Jefferson Lab, Newport News VA 23606.
Abstract
Harmonic lasing is normally suppressed because oflasing at the fundamental wavelength. It can, however, beachieved using any of several methods that suppress fundamental lasing. In this paper we discuss two methods
used at Jefferson Lab. The first is to use the characteristics of dielectric coatings to allow harmonic lasing at cavity lengths longer than the synchronous length for thefundamental. The second is to use a dielectric coatingthat has little reflectivity at the fundamental. This allows
us to directly compare fundamental and harmonic lasing
with the same optical resonator and electron beam. We
present measurement carried out at Jefferson Lab using
the IR Upgrade FEL operating at 0.53, 0.94, 1.04, 1.6, and
2.8 microns in which both schemes are used to produce
lasing at both the 3rd and 5th harmonic of the fundamental.

INTRODUCTION
Harmonic lasing was predicted in 1980[1][2] and third
harmonic lasing was demonstrated at Stanford and Los
Alamos [3][4] in 1988. Since then many groups havedemonstrated 3rd harmonic lasing and Jefferson Lab has
demonstrated 2nd and 5th harmonic lasing as well [5][6].
In all cases the challenge has been two-fold: produce asufficiently bright electron beam with high gain at harmonic wavelengths, and somehow suppress fundamental
lasing. Photocathode injectors now routinely produce
electron beams bright enough to lase well at harmonics.
There are also several techniques that are available tosuppress the fundamental. The first harmonic lasing
demonstrations used a dispersive element to force theharmonic lasing to a longer cavity length or an aperture topreferentially diffract away the fundamental. Anotherway, more appropriate for a high power system, is to use
dielectric mirrors to provide a high resonator Q at theharmonic and little or no Q at the fundamental. This is
how lasing at the second and fifth harmonic wereachieved at Jefferson Lab. In either case the gain wasquite low so two high reflectors were used to produce
lasing.
In this paper dielectric mirrors were used to produce
harmonic lasing with relatively high gain at the third andfifth harmonic and a new mechanism was discovered that
produces harmonic lasing using a resonator with high Q at
the fundamental.

FEATURES OF DIELECTRIC MIRRORSRELATED TO HARMONIC LASING
Most high power resonator mirrors consist of a stack oflayer pairs. The layers alternate between high and low
refractive index materials, for example silicon dioxide/hafnium dioxide or thorium fluoride/zinc selenide.
The thickness of each layer is one quarter of the center

Energy Recovery FELs

wavelength, or /4n where n is the refractive index of thecoating. The peak reflectivity is a function of the ratio of
the refractive indices and the number of layer pairs. The
spectral width of the reflectivity band is proportional to
the square root of the ratio of the refractive indices. Notethat the third harmonic center wavelength is not exactly
one third of the fundamental wavelength because the refractive indices vary with wavelength, however in practice, if a quarter wave stack has good reflectivity for one
wavelength, it will have similar reflectivity at the third
harmonic of that wavelength.
As for the laser cavity, if a resonator has a high resonator Q at the fundamental wavelength, then it usually has
high resonator Q for the third harmonic and possibly thefifth harmonic if the fundamental is a long wavelength.
In our case the resonator Q is actually slightly higher forthe third harmonic than for the fundamental. Since thegain at the fundamental wavelength is typically muchhigher than the third and fifth harmonic gain, the laser
will almost always lase at the fundamental with a quarterwave stack. If the wiggler is set to a wavelength 5/3 aslong as the center wavelength of the quarter wave stackcoating, the third harmonic of the coating will be coincident with the fifth harmonic of the FEL. There is very
little resonator Q at 5/3 of the center wavelength or at 5/9of the resonator wavelength where the third harmonic isresonant. The laser then lases at the fifth harmonic of the
FEL and the third harmonic of the coating. Note that it isalso possible to lase at the fundamental of the FEL withthe third harmonic of the coating.

CASE 1. LASING AT HARMONICS AT A
FIXED WAVELENGTH
The first measurements were performed with the same
resonator and center wavelength, while varying the wiggler strength. The resonant wavelength of the wiggler
was set to 1.02 microns, 3.06 microns, and 5.1 microns.
All three settings produced strong lasing. The detuning
curves for the three settings are show in figure 1. It isvery interesting to note that the fundamental, which has
the highest gain of the three, has the shortest detuning
curve. According to G. Dattoli’s formulas [7], the detuning curve length should be proportional to GhNW. where
G is the small signal gain, h is the harmonic number, N W
is the number of wiggler periods and  is the laser wavelength. The ratio of the detuning curve lengths using themeasured gain should be 3.5:6.0:5.7 according to the formula. The third and fifth are a bit shorter than this would
indicate but they are also closer to threshold, which shortens the detuning curve.
Table 1 shows a comparison of measured and predicted
gain and power, where predicted values were obtainedusing Dattoli’s formulas. The measured gain was inferred from the minimum turn-on time in the detuning

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curve. Simulations indicate that the turn-on time to half
power is 22.5 e-foldings and direct measurements of thegain support this observation. The power was measured
using a high power laser power meter accurate to 5%.
The gain and power are in good agreement for the fundamental and fifth harmonic but the experimental gain islower and power is much larger than predicted for thethird harmonic. This may have been due to differences inaccelerator setup though no single accelerator parametercan explain the discrepancy.
Detuning curves vs. Harmonic number
2.5
Fundamental
3rd Harmonic
5th Harmonic

Power(arb. units)

2
1.5
1
0.5
0
-0.5
216

217

218

219

220

221

222

223

224

L(μm)

Figure 1. Power vs. cavity length for lasing at the fundamental, third, and fifth harmonic, with fundamental
wavelength ~1.04 μm.
Spectra vs. Harmonic number

cate that the lasing wavelength is typically a fraction
1/hNW longer than the resonant wavelength. Since h ischanging but the resonant wavelength is not, one expects
the laser wavelength to get closer to the resonant wavelength. The fundamental is shifted further from the resonant wavelength because it is lasing harder than the harmonics, as is evident from the weak sideband at 1.11 μm.

CASE 2: LASING ON THE FIFTH HARMONIC OF THE LASER AND THE THIRDHARMONIC OF THE COATING
For both the 2.8 and 1.6 micron mirrors, it was possible
to lase at the third harmonic of the laser coating and thefifth harmonic of the laser. For the 2.8 micron mirrors the
wiggler was set to 4.65 microns and lased at 0.935 microns. For the 1.6 micron mirrors the wiggler was set to2.74 microns and lased at 0.53 microns. In both cases thelasing was quite robust. Note that both mirror sets havehigher reflectivity at the third harmonic than at the fundamental. The detuning curve at 0.53 μm was as long as
5 microns, which is comparable to the fundamental lasing
curve. Dattoli’s formula noted above, implies that the 5th
harmonic gain is 3/5 of the fundamental gain. The gain
inferred from the turn-on time and losses is about 1/3 thefundamental gain. Direct gain measurements will be necessary to resolve these discrepancies. The efficiency was
not as good as the 1.06 micron lasing but we did obtain 35
W of CW light in the green.

1.4

1

Fundamental
3rd Harmonic
5th Harmonic

1

Power(arb. units)

Power(arb. units)

1.2

0.8
0.6
0.4
0.2

Fund. Lasing at 2.8 μm
Fund. Lasing at 0.93 μm
Fifth Harm. Lasing at 0.93 μm

0.8
0.6
0.4
0.2

0
0.950

1.00

1.05

1.10

1.15

0

Wavelength(μm)-72.0Figure 2. Spectra while lasing with 1.06 micron mirrors
with the resonant wavelength equal to 1.02, 3.06, and 5.1
microns. The resonator losses were 3.5%/pass. Note themovement towards 1.02 microns as the harmonic number
is increased.
Table 1. Measured and predicted gain and power whenlasing at harmonics at ~1.04 microns.
h
1
3
5

Meas.
Gain
48%
20.4%
11.6%

Calc.
Gain
48%
24%
11%

Meas.
Power(W)
700
275
63

Calc.
Power (W)
885
180
65

Spectra for these three cases are shown in Figure 2. Notethat the wavelengths are not the same. Simulations indi-

324

-70.0

-68.0

-66.0

-64.0

-62.0

-60.0

-58.0

L(μm)

Figure 3. Detuning curves for three different configurations using the 2.8 micron mirrors.
In figure 3 we show the detuning curves while lasing at
the fundamental using both the 2.8 μm and 0.935 μm reflectivity peaks. The detuning curves for the fundamental
have a three to one ratio. Dattoli’s formula then would
indicate similar gain. In fact the gain at 2.8 microns isabout 50% larger than at 0.935 microns. This apparent
discrepancy has been seen before when varying the electron beam repetition rate [8]. Both curves have a convex
shape (negative second derivative), which is common
when the gain is well above threshold. The fifth harmonic curve at 0.935 μm should be five times as long as

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Proceedings of FEL 2006, BESSY, Berlin, Germany
the fundamental if the gain is similar. In fact it is only
twice as long indicating a gain 40% of the fundamental.
It also has a concave shape, which is typical for lasingclose to threshold. The ratio between the fifth harmonic
gain and fundamental gain is extremely sensitive to theenergy spread. The ratio is 0.4:1 for an energy spread of
0.3%. This is a typical value for our machine, though the
spread was not measured the day of these measurements.

TUPPH008

3rd Harmonic Lasing Spectrum

Intensity (counts)

Master

7000
6000
5000
4000
3000
2000
1000
510

520

530

540

550

560

Wavelength (nm)CASE 3: A NEW WAY TO LASE AT THE
THIRD HARMONIC
When the laser is very well tuned and the wavelength isvery close to or slightly longer than the center wavelengthof the mirror coatings, we see a very interesting phenomenon. The laser starts to lase sporadically at the third
harmonic when the cavity length is very close to the synchronous cavity length where the round trip time in theresonator matches the arrival time of the electron
bunches. This occurs for both the 1.6 micron and 2.8
micron mirrors. We sometimes use this as a measure of
how well the laser is optimized. If the laser optimizationis poor, harmonic lasing will not occur.

Figure 5. Lasing spectrum using an Ocean Optics visible
spectrometer array. This is a single macropulse shot.
This behavior is shown in figure 4. In figure 4a we see
the pattern of coherent spontaneous radiation that is always present when lasing at 1.6 microns. In figure 4b wehave lengthened the optical cavity by a fraction of a micron and see very strong green emission with a TEM00
profile. The image here completely saturates the CCD
camera. The spectrum of the third harmonic lasing isshown in Figure 5. This signal at 530 nm is not present
when the cavity is tuned for strong fundamental lasing.
With the 2.8 μm mirrors the lasing can occur over alarger range of detuning and can be quite stable. In figure
6 we show a detuning curve obtained using a spectrometer at 0.935 microns. The detector did not show any signal when lasing at the fundamental but showed a strong
signal when lasing at the 3rd harmonic.

a.

Figure 6. Detuning curve taken through a spectrometer
set to 935 nm. The lasing occurs over about 0.5 microns
in cavity length. The fundamental is not lasing over thisrange.
b.
Figure 4. (a) coherent harmonics emitted during fundamental lasing on the output coupler of the laser. (b)Harmonic lasing at 0.53 microns obtained by lengthening
the optical cavity by a fraction of a micron.

Energy Recovery FELs

We do not understand exactly how this new lasing
phenemonan works. It seems as though the round trip
time in the resonator is less for the third harmonic than for
the fundamental. This suggests that the fundamental light
penetrates more deeply into the coating than the third
harmonic light. The interference that produces the outgoing wave should be the same for the third harmonic as
for the fundamental. The different penetration depth may

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be related to the higher reflectivity of the coating at thethird harmonic. Future experiments will study the wavelength dependence of the harmonic lasing and comparewith reflectivity models of the coating.

CONCLUSIONS
The availability of a high brightness electron beam anda wiggler with large tuning range has opened up an interesting diagnostic device for free-electron lasers. Since theharmonic lasing is far more sensitive to beam parametersthan the fundamental it allows one to more carefully optimize the laser. The presence of lasing at harmonics
greatly restricts the laser modeling since the model must
fit both the fundamental and harmonic lasing with thesame optical resonator and electron beam.
In the future we plan to try to lase with an electron
beam with half the energy spread of the one now used.
This reduces the fundamental gain but greatly increases
the harmonic gain. We should have a situation where theharmonic gain actually exceeds the fundamental gain.
This should also allow lasing at the seventh and possibly
the ninth harmonic.

ACKNOWLEDGEMENTS

REFERENCES[1] J. M. J. Madey, R. C. Taber, "Equations of Motion
for a Free-electron Laser with a Transverse Gradient", In Free-electron generators of coherent radiation, 7, Addison-Wesley (1979) 741.
[2] W. B. Colson, IEEE J. of Quant. Elec. QE-17, (1981)
1417.
[3] S. V. Benson, J. M. J. Madey, Phys. Rev. A39, (1989)
1579–1581.
[4] R. W. Warren, L. C. Haynes, D. W. Feldman, W. E.
Stein, S. J. Gitomer, Nucl. Inst. and Meth. A296
(1990) 84–88.
[5] George R. Neil, S. V. Benson, G. Biallas, J. Gubeli,
K. Jordan, S. Myers, and M. D. Shinn, “Second Harmonic FEL Oscillation, Phys. Rev. Lett. 87, (2001)
084801.
[6] S. Benson, M. Shinn, G. R. Neil, and T. Siggins,“First Demonstration of 5th Harmonic Lasing in a
FEL”, presented at the 21st International FEL Conference, Hamburg Germany, August 1999.
[7] G. Dattoli, S. Cabrini, L. Gianessi, V. Loreto, and C.
Mari, Nucl. Inst. and Meth. A318 (1992) 495.
[8] S. Benson et al., Nucl. Inst. and Meth. A429 (1999)
27–32.

George Neil was quite helpful in setting up the laser totake data. Shukui Zhang operated the Ocean Optics
spectrometer to get the visible spectrum. This work was
supported by U.S. DOE Contract No. DE-AC05-84ER40150, the Office of Naval Research, the Air Force
Research Laboratory, the Army Night Vision Laboratory,
the Commonwealth of Virginia and the Laser Processing
Consortium.

326

Energy Recovery FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

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A DESIGN STUDY OF A FIR/THZ FEL FOR HIGH MAGNETIC FIELDRESEARCH
M. Tecimer, L.C. Brunel, J. van Tol, NHMFL / FSU, Tallahassee, FL 32310, USA,
G. Neil, TJNAF, Newport News, VA 23606, USA.
Abstract
Presently a conceptual design for a NIR-FIR FEL
system at the National High Magnetic Field Lab. - Florida
State University (NHMFL-FSU) is being undertaken incollaboration with the FEL group at the Thomas Jefferson
Laboratory. The system is expected to combine highmagnetic field research with an intense, tuneable photon
source spanning the spectral region ~ 2 - 1100 microns.
Here, a design study involving the FIR/THz part of the
NHMFL-FEL design proposal is presented. The
suggested long-wavelength FEL encompasses in the firstphase a thermionic injector with a ~2 mA average current
and a ~10 MeV superconducting rf linac module
operating at 1.3 GHz. The broadband outcoupling overthe envisaged FIR/THz spectral range (100 - 1100
microns) can be accomplished by adopting a variableoutcoupler scheme in a waveguided cavity. Besides theperformance predictions of the suggested long wavelength FEL, techniques for the generation of high peak
power, nanoseconds long THz pulses (for magnetic
resonance applications) are also briefly discussed.

INTRODUCTION
In the framework of the NHMFL FEL initiative thedesign efforts for the construction of FIR/THz FEL
radiation sources are twofold; the main effort is directed
towards the generation of high peak power micropulses
for time resolved measurements in the (tens of)picoseconds range. The planned rf-linac based systemrelies on relatively mature technologies developed at
FELIX (FOM), Stanford, Jefferson Lab. and
FZRossendorf. The use of superconductive rf-linac cavities
enables quasi-cw operation with the associated higher
average THz radiation power levels (tens of Watts) andTable 1:FIR FEL Specifications
PARAMETERFIR FEL

UNITS

100 to 1100μm

Micropulse Energy

1 to 3μJ

Micropulse-width~ 5 to 60

ps

Fract. bandwidth~ 0.3 - 5%

Resonator
Outcoupling
Pulse rep. rate
Macropulse-width
Beam energy
Wiggler period
Wiggler K
Periods

pp- waveguide, ~ 5.8
Variable (others?)
26 (13)

Wavelength

100μs to CW
10 - 1170 (hybrid.)
0.6-3.5
40

m
MHz
MeV
mm

offers the possibility of an extension to an energy
recovery linac (ERL) system (considered for the NIRMIR FELs) as well. The second part of the FEL effort
focuses on the development of techniques in producing
relatively long ((sub-) nanoseconds), kW - level tuneable(sub-)millimetre wave pulses, in order to generate spin
excitations at high magnetic fields and for possible
pulsed magnetic resonance applications. While it has
been shown that the FIR-FEL technology developed by
the TeraHertz Center at UCSB with an electrostatic
accelerator (EA) [1,2], this long wavelength range at theenvisioned power levels have not yet been achieved witha rf linac system.
Here, we give an overview of the studied outcoupler
design options and report on the simulated performanceof a rf-linac driven waveguide FIR-FEL based on
specified system settings. Finally, we discuss briefly on
the current status of search for methods that would allow
us to extend the inherently short pulse durations in thestudied sc rf linac driven FIR FEL configuration into thens range.

RF LINAC-FIR FEL DESIGN ISSUES
Figure 1: Layout of the FIR-FEL beamline option.

mtecimer@magnet.fsu.edu

FEL Oscillators and Long Wavelength FELs

In the current design , the beam energy for the FIR
FEL is provided by the first cryomodule (~10 MeV,
operating at 1.3 GHz) which constitutes, along with thethermionic injector, the injector section of the NIR-MIR
FELs. The thermionic injector system (a grid modulated
DC gun followed by subharmonic and fundamental

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Proceedings of FEL 2006, BESSY, Berlin, Germany

a.)

b.)

c.)
Figure 2 a-c: The lateral dimension of the outcoupler mirrors shown in a.) , b.) amounts to ~14 cm. The radius ofcurvature is ~3.5 m. The outcoupler mirror shown in c.) isconstructed for an FIR FEL operating at ~230-650 μm.
bunchers) [3] is similar to the ones in use at FZRossendorf and Stanford University. It is planned toprovide ~2 mA average current at 26 MHz repetition rate.
The NHMFL FIR-FEL is being designed to cover a large
portion of the THz spectrum while employing a single
wiggler, (possibly) a single cylindrical outcoupler mirror
along with a waveguide structure that extends over theentire cavity (~5.8 meters). The latter option reduces thediffraction losses inherent in this long wavelength spectral
region and avoids oversized cavity mirrors and mirror
vacuum chambers. It requires the injection of the beam
into the parallel-plate waveguide cavity (gap:10 mm)
prior matching the beam into the undulator. After leaving
the interaction section, the spent beam is directed into abeam dump. The design specifications along with the
major system parameters are listed in Table 1.

-4

2.0x106

Intracavity Pulse Energy [J]Peak Power [W]Intensity

10

Pulse length10

The continuous tunability offered by the FEL over theenvisaged large spectral range ideally would incorporate abroad-band feedback/outcoupling which can be accomplished by adopting a variable outcoupler scheme on one of
the cylindrical metal-mirrors. The outcoupler option
illustrated in Fig. 2a is a modified version of the variableheight outcoupler (Fig. 2c) studied and realized in [4,5].
Adjusting the slot aperture in the vertical dimension
between 0. – 3.0 mm continuously, the power output canbe optimised over the entire 100 - 1100 microns. Hereby,
the use of inserts with different lateral sizes (1.5mm,
3.0mm) allows one to keep the ratio of horizontal tovertical dimensions of the aperture < ~1.5 , at any slot
aperture/wavelength configuration. In the second option,
depicted in Fig. 2b, the middle insert (thus the centre of
the hole aperture) is displaced in the vertical, sampling
different areas of the hybrid waveguide mode on the
mirror surface. The latter scheme covers the targeted
wavelength range using max. three different hole
apertures (or, alternatively, three cylindrical mirrors that
could be moved up and down in the vertical, each having
a different hole aperture). The optical beam transport
accounts for the small (max. ~ 2 - 3 mm) off-axis
displacement of the optical beam centre behind theoutcoupler. Other variable outcoupler options such as
FPI-meshes are being considered (as far as they remain
operational at cw multi-kW level intracavity power),particularly for wavelengths above 500 microns.
The performance modelling of the FIR-FEL system isbased on electron beam parameters (bunch charge, norm.
transverse emittance, longitudinal emittance, energy
spread) that are similar to those implemented at FZRossendorf FEL, with the exception of an increase in theelectron bunch repetition frequency up to 26 MHz, thelatter being relevant in determining the resonator lengthand the average radiation power. Using the waveguide
FEL code described in [5,6], that models the physics of a
rf-linac driven, highly slippage dominated short pulse
THz-FEL oscillator, the FEL performance for various

5

13 MHz26 MHz-4

1.5x10-4

1.0x10-5

5.0x10

0.0

10

0

4

0

200

400

600

800

1000

1200

Wavelength [microns]

Figure 3: The upper peak power values (blue dots) are
obtained at the peak of the detuning curve whereas thelower data points at cav. Detuning ~ -0.4·λ.

328

20

40

60

80 100 120 140 160 180
Roundtrip #Figure 4: FEL operation at 13 MHz and 26 MHz pulse
rep. rates with ~5.8 m cavity length , λ ∼ 155 μm.

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany
wavelength/wiggler settings (assuming a FEL operating at
a fixed beam energy of 10.8 MeV) and outcoupling ratios(optimised by using the transmission characteristics of thescheme shown in Fig. 2a) are studied. An aspect that
affects strongly the intracavity radiation build-up process
and the evolution of the optical pulse structure is the useof ps-short electron bunches for the generation of (for rflinac based systems unusually) long wavelength radiation
in a waveguided propagation medium. Fig.3 shows thepredicted (approximate) peak power levels achievable in
the generated THz micropulses. The inset illustrates thesimulated pulse shape whose leading edge exhibits adistinct exponential decay deviating from the Gaussian.
Another possible operational mode is driving the FIR
FEL with 13 MHz rep. rate (limiting the average current
to ~1mA), while keeping the waveguide resonator length
5.8 meters. In this case, the optical pulse interacts withthe electron beam every other roundtrip, thus experiencing nearly twice as much cavity losses for each
amplifying pass. The simulated evolution of the intracavity micropulse energy up to the saturation is shownin Fig. 4 at 155 microns (as an example) for both, 13
MHz and 26 MHz rep. rates. In the ‘13 MHz case’ theoutcoupling ratio is set to ~ 0.6 % (optimised to obtain
the highest pulse energy coupled out), while the ‘26 MHz
case’ employs ~ 3.0 %. The calculated outcoupled pulse
energies at different wavelengths indicate that 13 MHz
rep. rate in combination with 5.8 m resonator length does
not lead to a satisfying FEL operation. It results in asignificant reduction in the pulse energies obtained. In
addition, the micropulse energy fluctuations in subsequent
roundtrips (by an amount defined by the cavity losses)
may not be tolerable in many applications. In thefollowing, simulated pulse energies are given for the ‘13
MHz and 26 MHz repetition rates’ at two different
wavelengths, 155 microns and 1080 microns respectively:• ‘13 MHz ‘case:- outcoupled max. pulse energy ~0.7 μJ (@155 μm)- outcoupled max. pulse energy ~0.3 μJ (@1080 μm)• ‘26 MHz’ case:- outcoupled max. pulse energy ~3.1 μJ (@ ~155 μm)- outcoupled max. pulse energy ~1.6 μJ (@ ~1080 μm)

GENERATION OF (SUB-) NS PULSESFor pulsed magnetic resonance excitations, the pulse
length condition is given by γB1τ ≈ 0.5 in which γ is
28 GHz/Tesla, B1 is the amplitude of the oscillating
magnetic field, and τ is the FIR pulse length. For theenvisioned time resolution and the available power, thepulse length is of the order of 1 ns. At the present design
stage, having optical pulse rep. rates of max. 26 MHz, theplanned superconductive rf-linac FIR FEL configuration
is not suitable for the implementation of interpulse phaselocking techniques described in [7] to generate narrow
bandwidth, ns - long pulses. On the other hand, the

FEL Oscillators and Long Wavelength FELs

TUPPH009

Table 2: Grating Stretcher specificationsm
Z
Initial Final
d
λ
[m]
[ps]
[ns]
[μm]
[μm]
100

80

1

3.0

5.0

1.5

100

80

3

1.34

5.0

3.1

500

400

1

3.0

25.0

1.6

500

400

3

0.57

25.0

3.1

1000

800

1

3.0

65.0

1.2

1000

800

3

0.78

65.0

3.1

flexibility offered by the variation of cavity
desynchronization on modifying the pulse durations (thusthe Fourier transform limited spectral bandwidth) falls
short of providing the pulse lengthening effect thatwould be necessary to meet the requirements posed on thepulse durations and the associated spectral bandwidths. A
possible (standard-) solution to lengthen the (rf-linac
generated) picoseconds long optical pulses with
sufficiently broad bandwidths is the use of grating
stretchers [8], ending up with frequency chirped pulses of
ns-duration. However, due to the introduced time
frequency correlation within the pulse and the still
existent broad bandwidth (not Fourier transform limited
pulses), frequency chirped pulses remain restricted intheir applications in the area of pulsed magnetic
resonance experiments. Table 2 illustrates the parametersof a grating stretcher and the stretching factors achievable
upon application of the device on the outcoupled
FIR FEL pulses specified in Table 1. In Table 2,parameters d, m, Z denote the groove spacing of theblazed grating, the order at which the grating is used andthe variable distance between the grating and thetelescope mirror used in the setup, respectively.

ACKNOWLEDGMENTS
We thank G. Ramian for helpful discussions. One of theauthors (M.T.) acknowledges the input provided by P.
Michel and J. Teichert regarding the sc rf-linac system at
FZR-ELBE. This work has been supported by the NSF
under grant no DMR-0520481.

REFERENCES[1] G. Ramian, Nucl. Inst. and Meth. A 318, (1992) 225.
[2] Doty et al., Rev. Sci. Instrum., Vol.75, (2004) 2920.
[3] http://www.FZ-Rossendorf.de/ELBE[4] M. Tecimer et al., Nucl. Instr. and Meth. A 528,
(2004) 146.

329

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Proceedings of FEL 2006, BESSY, Berlin, Germany[5] http://www2.hawaii.edu/~mtecimer[6] M. Tecimer et al., Nucl. Instr. and Meth. A 528,
(2004) 139.
[7] D. Oepts and W.B. Colson, IEEE QE-26, (1990) 723.
[8] E.B. Tracy and A.J. DeMaria, Phys. Lett., Vol. 29 A,
369.

330

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH012

EXPERIMENTAL STUDY OF A VOLUME FREE ELECTRON LASERWITH A ”GRID” RESONATOR
V.G. Baryshevsky ∗ , N.A.Belous, A.A.Gurinovich, A.S.Lobko, P.V.Molchanov, V.I.Stolyarsky,
Research Institute for Nuclear Problems, 11 Bobryiskaya str., 220050, Minsk, Belarus
Abstract
Operation of Volume Free Electron Laser with a ”grid”
photonic crystal, built from periodically strained metallic
threads, was studied in the backward wave regime. Generation threshold was observed for different ”grid” photonic
crystals. Dependence of the generation threshold on theresonator length was investigated.

INTRODUCTION”grid” photonic crystal of metal threads is almost transparent for the electromagnetic waves in the wavelength range,
where the skin-depth is less then the thread radius. The
conclusions of [14] declared possibility of development of
VFEL with the ”grid” photonic crystal of metal threads.
First lasing of the volume FEL with a ”grid” volume
resonator, which was formed by the periodic set of metalthreads inside a rectangular waveguide, was observed in
the proof-of-principle experiment [15] and completely confirmed conclusions of [14].
In the present paper dependence of the generation intensity as a function of the grid photonic crystal length is studied for the backward wave oscillation regime.

Generators using radiation from an electron beam in aperiodic slow-wave circuit (travelling wave tubes, backward wave oscillators, free electron lasers) are now
widespread [1].
THE CONCEPT
Diffraction radiation [2] in periodical structures is in the
Waves propagation through photonic crystals is the subbasis of operation of travelling wave tubes (TWT) [3, 4],
backward wave oscillators (BWO) and such devices as ject for numerous studies both theoretical and experimental
Smith-Purcell lasers [5, 6, 7] and volume FELs using two- [17, 18, 19, 20].
Challenges, which appears when considering interactionor three-dimensional distributed feedback [8, 9, 10, 11].
A challenge of precise electron beam guiding over the of an electromagnetic wave with such a photonic crystal,slowing structure (the electron beam should pass at the dis- are as follows: It is well known that a metal grid reflects
electromagnetic waves perfectly. Therefore, the questiontance δ ≤ λβγ
4π over the diffraction grating, here δ is theso-called beam impact parameter, λ is the radiation wave- arises as to whether a wave penetrate deep into resonator,
length, β = v/c , v is the electron beam velocity, γ is especially since resonator contains a set of grids. Theoretthe electron Lorentz-factor) restricts application of Smith- ical analysis [14, 16] showed that periodic metal grid does
Purcell lasers and the similar devices. Electrical endurance not absorb electromagnetic radiation and the ”grid” phoof resonator limits radiation power and current of accept- tonic crystal, made of metal threads, is almost transparent
able electron beam. Conventional waveguide systems are for the electromagnetic waves in the frequency range fromessentially restricted by the requirement for transverse di- GHz to THz. In this range the skin depth δ is about 1 mimensions of resonator, which should not significantly ex- cron or less for the most of metals (for example, for 10 GHz
δCu = 0.66 μm, δAl = 0.8 μm, δW = 1.16 μm and so on).
ceed radiation wavelength.
The most of the above problems can be overcome in Thus, in this frequency range the metallic threads can be
VFEL [8, 9, 10, 11, 12]. In VFEL the greater part of elec- considered as perfect conducting.
According to [14, 16] the refraction index for the ”grid”
tron beam interacts with the electromagnetic wave due tovolume distributed interaction. Transverse dimensions of photonic crystal, can be expressed as:
η(⊥)
(1)
VFEL resonator could significantly exceed radiation waven2(⊥) = 1 + 2 ,klength D  λ. In addition, electron beam and radiation
power are distributed over the whole volume that is ben- where4π
A0η(⊥) =,
(2)
eficial for electrical endurance of the system. One of theΩ2 1 + iπA0 − 2CA0
VFEL types uses a ”grid” volume resonator (”grid” phon and n⊥ are the refraction indices for the waves withtonic crystal) that is formed by a periodically strained either
polarization parallel and perpendicular to the thread axis,
dielectric or metallic threads.
respectively, k = 2π/λ is the wave number, R is the thread
The ”grid” structure of dielectric threads was experi- radius, Ω = d · d , where d and d are the photonic
2
y
z
y
z
mentally studied in [13], where it was shown that such crystal periods along the axis y and z, respectively, C =”grid” photonic crystals have sufficiently high Q factors 0.5772 is the Eiler constant. The values A
0() and A0(⊥)(104 − 106 ).
for perfectly conducting threads are defined as [15, 16]:
Theoretical analysis [14, 16] showed that periodic metali
1 J0 (kR) N0 (kR)
J02 (kR)
grid does not absorb electromagnetic radiation and the A0() =+π J02 (kR) + N02 (kR) π J02 (kR) + N02 (kR)∗ bar@inp.minsk.by,

FEL Oscillators and Long Wavelength FELs

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TUPPH012

Proceedings of FEL 2006, BESSY, Berlin, Germany(3)i
1 J0 (kR) N0 (kR)J02 (kR),+
A0(⊥)=
π J02 (kR) + N02 (kR) π J02 (kR) + N02 (kR)
where J0 , N0 , J0 and N0 are the Bessel and Neumannfunctions and their derivatives, respectively.
To consider threads with finite conductivity one should
use the following expressions:√
i J0 (kt R)J0 (kR) − εt J0 (kt R)J0 (kR),
A0() =
π J0 (kt R)H (1) (kR) − √εt J  (kt R)H (1) (kR)
0
0
0
(4)
1


√
J
(k
R)J
(kR)
−
J
(k
R)J
(kR)
0 t
0
0
i
εt 0 t,A0(⊥)=
π J0 (kt R)H (1) (kR) − √1 J  (kt R)H (1) (kR)00
εt 0where εt is the dielectric permittivity of the thread material,√(1)
kt = εt k, H0 is the Hankel function of the zero order.
The expressions (3) can be obtained from (4) considering
εt → ∞.
Difference in the refraction indices for different wave
polarizations (n = n⊥ ) indicates that the system owns
optical anisotropy (i.e. possesses birefringence and dichroism). To escape this anisotropy we can alternate the treads
position in the grid: threads in each layer are orthogonal tothose in the previous and following layers.
Smith - Purcell (diffraction) radiation in photonic crystal
for an electron beam with the velocity v passing throughthe ”grid”arises when the radiation condition is fulfilled:ω − kn(k)v = τ v ,(5)where τ is the reciprocal lattice vector and n(k) is the refraction index (see (1)). Suppose the electron beam velocity is directed along the axis OZ, then (5) can be presented
in the form:k − τz β = k n(k) β cos θ,(7)where η is determined by (2) and the eigenvalues κmn aredetermined by the waveguide transverse dimensions (widtha and height b):πm 2πn) + ( )2 .
κ2mn = (
(8)
a
b

332

ω2 (m, n) =τz v
1 − β2




1+β

1−

(κ2mn − η) 1 − β 2
τz2
β2

(9)

.

h
It should be reminded here that τz = 2πmdz , where mh =1, 2, ... is the number of harmonic. From (9) it follows thathigher harmonics provide for getting radiation with higher
frequencies. For example, for the electron beam with theenergy 200 keV, considering θ ∼ 20◦ and dz = 1.6 cm, thefirst harmonic (mh = 1) gives radiation frequencies ∼ 10
GHz and ∼ 40 GHz for the roots 1 and 2 of the equation(7), respectively, the 30-th harmonic (mh = 30) provides∼ 230 GHz and ∼ 1 THz.

EXPERIMENTAL SETUP
The ”grid” photonic crystal is built from tungsten threads
with the diameter 0.1 mm strained inside the rectangular
waveguide with the transversal dimensions a = 35 mm,
b = 35 mm and length 300 mm (see Fig.1). The distance
between the threads along the axis OZ is dz = 12.5 mm.
A pencil-like electron beam with the diameter 32 mm, energy ∼200 keV and current ∼2kA passes through the above
structure. The magnetic field guiding the electron beam is∼ 1.55 − 1.6 tesla. Period of grating is chosen to provide radiation frequency ∼ 8.4 GHz. The ”grid” structure(6)

where β = vc , the angle between k and the electron beamhvelocity is denoted by θ and τz = 2πmdz , where mh =1, 2, ... is the number of harmonic. The roots of this equation give the spectrum of frequencies of diffraction (SmithPurcell) radiation, which is induced by a particle moving in
the above ”grid” photonic crystal.
Diffraction radiation in a metal waveguide of the rectangular cross-section with the ”grid” photonic crystal placed
inside it is shown in [14, 16] to be described by the equation
similar to (6):ωω − τz v 2) = ( )2 − (κ2mn − η),(vcThe roots of equation (7) for τ 2ηβ 2  1 can be obtained as:
z



τz v
(κ2mn − η) 1 − β 2
1−β 1−,
ω1 (m, n) =1 − β2τz2
β2

Figure 1: The ”grid” diffraction grating placed inside thewaveguide.
is made of separate frames each containing the layer of 1,
3 or 5 parallel threads with the distance between the next
threads dy = 6 mm). Frames are joined to get the ”grid”
structure with the distance dz between layers.
Frequency range was evaluated by means of tunablewaveguide filters, which were tuned in the band 7.8 - 12.4
GHz with passbands 0.25 GHz, 0.5 GHz and 1 GHz. Attenuation of radiation in the suppressed band of this filteris ∼ −25 dB.

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH012

EXPERIMENTAL RESULTS
The objective of the experiment is to study dependenceof the generated radiation intensity on the ”grid” photonic
crystal length.
The maximal radiation power of VFEL generator in thethis experiment was about 1.5 kiloWatt for one thread in
the frame, 5 kiloWatts for three threads in the frame and 10
kiloWatt for five threads in the frame.
The sample oscillogram is shown in Fig.2, where signals
marked 1 and 2 are the signals obtained from microwave
detectors. Other two curves are the electron gun voltage
and electron beam current. Time scale is 80 ns.

single frame with a strained threadframes with threads

Figure 3: Photonic crystal with frames each containing one
thread equidistant from waveguide top and bottom walls.
L / l0
1

2

3

4

5

6

7

8

80 ns

Figure 2: The sample oscillogram.

normalized power

1,0
0,8
0,6
0,4
0,2
0,0
50

Two types of experiments are reported.
1.
The radiation power was measured for photonic
crystal with 4, 8, 10 and 24 frames each containing one
thread equidistant from waveguide top and bottom walls(see Fig.3). The result of these measurements is presented
in Fig.4, where the radiation power is normalized to the
maximal detected power (1.5 kiloWatt).
2.
The radiation power is measured for photonic
crystal with 4, 6, 10, 12, 14 and 22 frames each containing
five threads distant dy = 6 mm each from other (see Fig.5).
The result of these measurements is presented in Fig.6,
where the radiation power is also normalized to the maximal detected power (10 kiloWatt). The solid curve in thisfigure shows the numerically simulated radiation power,
which also normalized.

CONCLUSION
Operation of Volume Free Electron Laser with a ”grid”
photonic crystal, built from periodically strained metallic
threads, was studied in the backward wave regime. Generation threshold was observed for different ”grid” photonic crystals. Dependence of the generation threshold on
the resonator length was investigated. Use of volume resonators of the described type provides to weaken requirements for the electron beam shape and guiding precision,

FEL Oscillators and Long Wavelength FELs

100

150

200

250

300

Length, mm

Figure 4: Dependence of the generation intensity on thelength of the ”grid” photonic crystal with one thread in
the frame, the upper scale show the resonator length in thenumber of wavelength L/λ0 , where λ0 = 3.6 cm.
because the electron beam passes directly through the photonic crystal.

REFERENCES[1] V.L.Granatstein, R.K.Parker and C.M.Armstrong, Proceedings of the IEEE 87, no.5 (1999).
[2] B.M.Bolotovskii and G.V.Voskresenskii, Usp. Fiz. Nauk. 88,
209 (1966) (Sov. Phys. Usp. 9, 73 (1966)).
[3] R.Kompfner, Wireless World 52, 369 (1946).
[4] R.Pierce, Proc. IRE 35, 111 (1947).
[5] S.J.Smith and E.M.Purcell, Phys. Rev. 92, 1069 (1953).
[6] W.W.Salisbury, US Patent 2,634,372 (1953); J.Opt. Soc.Am.
60, 1279 (1970).
[7] G.Doucas, J.H.Mulvey, M.Omori, J.Walsh and M.F.Kimmit,
Phys.Rev.Lett. 69, 1761 (1992); John E. Walsh US Patent
5,790,585 (1996).

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Proceedings of FEL 2006, BESSY, Berlin, Germany[20] E. I. Smirnova and C. Chen, M. A., J. Appl.Phys. 93(10),5859 (2003).
[21] R.W. James, The Optical Principles of Diffraction of X-Rays(Ox Bow Press, 1982).
[22] Shih-Lin Chang, Multiple diffraction of x-rays in crystals(Springer-Verlag, 1984).
[23] V.V. Nikolsky , Electrodynamics and propagation of radiowave (Nauka, 1978)

Figure 5: Photonic crystal with frames each containing fivethreads distant dy = 6 mm each from otherL / l0
1

2

3

4

5

6

7

8

normalized power

1,0
0,8
0,6
0,4
0,2
0,0
50

100

150

200

250

300

Length, mm

Figure 6: Dependence of the generation intensity on thelength of the ”grid” photonic crystal with 5 threads in theframe marked with squares and numerically simulated dependence of the wave amplitude on the ”grid” photonic
crystal length for the electron beam with the energy ∼200
keV and current density ∼ 2 kA/cm2[8] V.G.Baryshevsky, NIM 445A, 281 (2000); LANL e-printarchive physics/9806039.
[9] V.G.Baryshevsky, K.G.Batrakov, A.A.Gurinovich et al., NIM
483A, 21 (2002).
[10] V.G.Baryshevsky, K.G.Batrakov, A.A.Gurinovich et al.,NIM 507A, 137 (2003).
[11] V.G.Baryshevsky et al., Eurasian Patent no. 004665.
[12] V.G.Baryshevsky, I.D.Feranchuk, Phys.Lett. 102A, 141(1984).
[13] V.G.Baryshevsky,K.G.Batrakov,I.Ya.Dubovskaya,V.A.Karpovich,
V.M.Rodionova, NIM 393A, 71 (1997).
[14] V.G.Baryshevsky, A.A.Gurinovich LANL e-print archive:
physics/0409107[15] V.G. Baryshevsky, K.G. Batrakov, N.A. Belous, A.A. Gurinovich, A.S. Lobko, P.V. Molchanov, P.F. Sofronov, V.I. Stolyarsky, LANL e-print archive: physics/0409125.
[16] V.G.Baryshevsky, A.A.Gurinovich, to be published in NIM
B, Topical Issue RC2005.
[17] A. L. Pokrovsky and A. L. Efros, Phys. Rev. B 65, 045110(2002).
[18] A. L. Pokrovsky, Phys. Rev. B 69, 195108 (2004).
[19] E. I. Smirnova, C. Chen, M. A. Shapiro et al., J. Appl.Phys.
91(3), 960 (2002).

334

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH013

ELECTRODYNAMICAL PROPERTIES OF A VOLUME
FREE ELECTRON LASER WITH A ”GRID” RESONATOR
V.G. Baryshevsky, A.A.Gurinovich ∗Research Institute for Nuclear Problems, 11 Bobryiskaya str., 220050, Minsk, Belarus.
Abstract
The electrodynamic properties and lasing in Volume
Free Electron Laser with a ”grid” resonator (”grid” photonic crystal) with changing in space parameters are considered. The equations describing lasing of VFEL withsuch a resonator are obtained. It is shown that use ofdiffraction gratings (photonic crystal) with variable period
increases radiation intensity and provide to create the dynamical wiggler with variable period. This makes possible
to develop a double-cascaded FEL with variable parameters, which efficiency can be significantly higher then thatof conventional system.

INTRODUCTION
Diffraction radiation [1] in periodical structures is in thebasis of operation of travelling wave tubes (TWT) [2, 3],
backward wave oscillators (BWO) and such devices as
Smith-Purcell lasers [4, 5, 6] and volume Free Electron
Lasers [7, 8, 9] (see also [10]).
Volume Free Electron Laser (VFEL) is a radiation generator using non-one-dimensional distributed feedback,which is created with the aid of Bragg diffraction gratingsor photonic crystals.
One of the VFEL types uses a ”grid” volume resonator(”grid” photonic crystal) that is formed by a periodicallystrained either dielectric [11] or metallic threads [12, 13,
14, 15].
In the present paper the electrodynamic properties andlasing in Volume Free Electron Laser with a ”grid” resonator (”grid” photonic crystal) with changing in space parameters are considered. The equations describing lasingof VFEL with such a resonator are obtained. It is shownthat use of diffraction gratings (photonic crystal) with variable period provide to create the dynamical wiggler withvariable period. This makes possible to develop a doublecascaded FEL with variable parameters changing, whichefficiency can be significantly higher that of conventional
system.

THEORY OF LASING FOR VFEL WITH A”GRID” PHOTONIC CRYSTAL WITH
VARIABLE PERIOD
To obtain equations, which describe VFEL lasing in the”grid” photonic crystal (see Fig.1), the Maxwell equations∗ gur@inp.minsk.by

FEL Oscillators and Long Wavelength FELs

and motion equations for a particle in an electromagnetic
field should be considered:


4π
1 ∂D
 = − 1 ∂H ,+ j, rotE
c ∂t
c
c ∂t
∂ρ
 = 4πρ,divD+ divj = 0,
∂t

 =
rotH

(1)

 and H
 are the electric and magnetic fields, j andhere Eρ are the current and charge
densities, the electromagnetic

induction Di (r, t ) = εil (r, t − t )El (r, t )dt and, therefore, Di (r, ω) = εil (r, ω)El (r, ω), the indices i, l = 1, 2, 3
correspond to the axes x, y, z, respectively. The current andcharge densities are respectively defined as:j(r, t) =e vα (t)δ(r−rα (t)), ρ(r, t) =e
δ(r−rα (t)),αα

where e is the electron charge, vα is the velocity of theparticle α (α numerates the beam particles),


e 
1
dvα
 rα , t)) , rα , t)]− vα (vα E(=E(rα, t) + [vα×H(dt mγαcc2v2

1 rα , t) andhere γα = (1 − cα2 )− 2 is the Lorentz-factor, E(H(rα , t) are the electric and magnetic field in the point oflocation rα = rα (t) of the particle α.

front viewside view

Figure 1: A ”grid” photonic crystal.
The dielectric permittivity tensor can be expressed asε̂(r) = 1 + χ̂(r), where χ̂(r) is the dielectric susceptibility.

335

TUPPH013

Proceedings of FEL 2006, BESSY, Berlin, Germany

When χ̂  1 the system (1) can be rewritten as:1 ∂2
 r, t )dt =ε̂(r, t − t )E(ΔE(r, t) − 2 2c ∂t1 ∂j(r, t) + ∇ρ(r, t) .
= 4π
c2 ∂t

(2)

When the grating is ideal χ̂(r) = τ χ̂τ (r)eiτ r , where τ
is the reciprocal lattice vector [16, 17].
Let the diffraction grating (photonic crystal) period issmoothly varied with distance, which is much greater thenthe diffraction grating (ptotonic crystal lattice) period. It isconvenient in this case to present the susceptibility χ̂(r) in
the form, typical for theory of X-ray diffraction in crystals
with lattice distortion [18]:eiΦτ (r) χ̂τ (r),(3)χ̂(r) =

A0(⊥)
4π,
Ω2 k 2 1 + iπA0(⊥) − 2CA0(⊥)(4)

the symbols  and ⊥ indicate the waves with polarization
parallel and perpendicular to the thread axis, respectively,k = 2π/λ is the wave number, R is the thread radius, C =0.5772 is the Eiler constant, Ω2 = dy · dz , where dy anddz are the photonic crystal periods along the axis y and z,
respectively. The values A0() and A0(⊥) for the threads
with finite conductivity are defined as[14]:√J0 (kt R)J0 (kR)− εt J0 (kt R)J0 (kR)
,
√
(1)
(1)
J0 (kt R)H0 (kR)− εt J0 (kt R)H0 (kR)
√1 J  (kt R)J0 (kR)
(k
R)J
(kR)−
J
0
t
0
0
ε
i

A0() = πiA0(⊥) = π(1)J0 (kt R)H0t(1)(kR)− √1ε J0 (kt R)H0 (kR),twhere εt is the dielectric permittivity of the thread material,√(1)
kt = εt k, H0 is the Hankel function of the zero order,J0 and J0 are the Bessel functions and their derivatives,
respectively.
In contrast to the theory of X-rays diffraction, in the caseunder consideration χ̂τ depends on r. It is to the fact thatχ̂τ depends on the volume of the lattice unit cell Ω2 , which
can be significantly varied for diffraction gratings (photonic crystals), as distinct from natural crystals.
It should be reminded that for an ideal crystal withoutlattice distortions, the wave, which propagates in crystal
can be presented as a superposition of the plane waves:
 r, t) =E(∞ τ ei(kτ r−ωt) ,
A

(5)


τ =0

where kτ = k + τ .
In the case under consideration the solution of (2) can be
written in the form (compare with [18]):∞ τ ei(φτ (r)−ωt) , r, t) = Re
(6)
A
E(

τ =0

336

 2 ei(φ2 (r)−ωt) + .. ,(7)
 1 ei(φ1 (r)−ωt) + A
E(r, t) = Re A r
k1 (r  )dl,(8)
φ1 (r) =0τwhere Φτ (r) = τ (r )dl , τ (r  ) is the reciprocal lattice
vector in the vicinity of the point r  . The expressions for χ̂
for the ”grid” photonic crystal were obtained in [12, 14]:χ(⊥) =

 rwhere φτ (r) = 0 k(r)dl + Φτ (r) and k(r) can be foundas solution of the dispersion equation in the vicinity of thepoint with the coordinate vector r, integration is done overthe quasiclassical trajectory, which describes motion of the
wavepacket in the photonic crystal with lattice distortion.
Let us consider now case when all the waves participating in the diffraction process lays in a plane (coupledwave diffraction, multiple-wave diffraction [17, 16]) i.e. all
the reciprocal lattice vectors τ lie in one plane. Suppose
the wave polarization vector is orthogonal to the plane ofdiffraction.
 r, t) = e E(r, t), where
Let us rewrite (6) in the form E(φ2 (r) = r0k1 (r  )dl + r0τ (r  )dl.

(9)Then multiplying (2) by e one can get:
1 ∂2
ΔE(r, t) − 2 2c ∂tε̂(r, t − t )E(r, t )dt =1 ∂j(r, t) + ∇ρ(r, t) .
= 4πe
c2 ∂t

(10)
(11)

Substitution of (7) to (11) gives the following system:
1 i(φ1 (r)−ωt)  1 + i∇ k1 (r)A1 − k 2 (r)A1 +e[2ik1 (r)∇A
12
ω2
1 ∂ω 2 ε0 (ω, r) ∂A1 ω 2+ 2 ε−τ (ω,r )A2+
+ 2 ε0 (ω, r)A1+i 2
c
c
∂ω
∂t
c
1 ∂ω 2 ε−τ (ω, r) ∂A2+i 2] + conjugated terms =c  ∂ω∂t
1 ∂j(r, t) + ∇ρ(r, t) ,(12)
= 4πec2 ∂t
1 i(φ2 (r)−ωt)  2 + i∇ k2 (r)A2 − k22 (r)A2 +e[2ik2 (r)∇A2
ω2
1 ∂ω2 ε0 (ω, r) ∂A2 ω 2+ 2 ετ (ω, r)A1 ++ 2 ε0 (ω,r)A2+ i 2
c
c
∂ω
∂t
c
1 ∂ω 2 ετ (ω, r) ∂A1] + conjugated terms =+i 2c  ∂ω∂t
1 ∂j(r, t) + ∇ρ(r, t) ,= 4πec2 ∂twhere the vector k2 (r) = k1 (r) + τ , ε0 (ω, r) = 1 + χ0 (r),here notation χ0 (r) = χτ =0 (r) is used, ετ (ω, r) = χτ (r).
Note here that for numerical analysis of (12), if χ0  0, it
is
convenient to take the vector k1 (r) in the form k1 (r) =2

n k 2 + ωc2 χ0 (r).
For better understanding let us suppose that the diffraction grating (photonic crystal lattice) period changes along
one direction and define this direction as axis z.

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany
Considering the right part of (2) let us take into accountthat microscopic currents and densities are the sums ofterms, containing delta-functions, therefore, the right partcan be rewritten as:
1 ∂j(r, t) 
−i(
k⊥ 
r⊥ +φ1z (z)−ωt)+ ∇ρ(r, t) =
4πe
e
c2 ∂t
4πiωe = − 2 evα (t)δ(r − rα (t))e−i(k⊥ r⊥ +φ1z (z)−ωt)×cα× θ(t − tα ) θ(Tα − t),(13)here tα is the time of entrance of particle α to the resonator, Tα is the time of particle leaving from the resonator,
θ−functions in (13) image the fact that for time moments
preceding tα and following Tα the particle α does not contribute in process.
Let us suppose now that a strong magnetic field is applied for beam guiding though the generation area. Thus,
the problem appears one-dimensional (components vx andvy are suppressed). Averaging the right part of (13) overthe particle positions inside the beam, points of particle entrance to the resonator r⊥0α and time of particle entrance
to the resonator tα we can obtain:
1 ∂j(r, t) 
−i(
k⊥ 
r⊥ +φ1z (z)−ωt)+ ∇ρ(r, t) =
e
4πe
c2 ∂t

4πiωρ ϑ1 u(t) e 1
1=−d2r⊥0 ×
(14)
c2
S
T
 t

×
e−i(φ1 (r,r⊥ ,t,t0 )+k⊥ r⊥0 −ωt) dt0 =0=−4πiωρ ϑ1 u(t) e −i(φ1 (r,r⊥ ,t,t0 )+k⊥ r⊥0 −ωt)edt0 ,c2

where ρ is the electron beam density , u(t) is the mean electron beam velocity,which depends on time due to energy2
losses, ϑ1 = 1 − β 2ωk2 c2 , β 2 = 1 − γ12 ,   indicates1
averaging over transversal coordinate of point of particle
entrance to the resonator r⊥0α and time of particle entrance
to the resonator tα .
According to [19] averaging procedure in (14) can be
simplified, when consider that random phases, appearing
due to random transversal coordinate and time of entrance,
presents in (14) as differences. Therefore, double integration over d2r⊥0 dt0 can be replaced by single integration [19].
The system (12) in this case converts to:∂k1z (z)∂A122+i
A1 − (k⊥+ k1z(z))A1 +∂z∂zω2
1 ∂ω 2 ε0 (ω, z) ∂A1+ 2 ε0 (ω, z)A1 + i 2
+
c
c
∂ω
∂t
ω2
1 ∂ω 2 ε−τ (ω, z) ∂A2+ 2 ε−τ (ω, z)A2 + i 2
=
c
c
∂ω
∂t
2ω
(15)
= i 2 J1 (k1z (z)),
c

2ik1z (z)FEL Oscillators and Long Wavelength FELs

TUPPH013∂k2z (z)∂A222+iA2 − (k⊥+ k2z(z))A2 +
∂z
∂z
2
2
ω
1 ∂ω ε0 (ω, z) ∂A2+ 2 ε0 (ω, z)A2 + i 2
+
c
c
∂ω
∂t
ω2
1 ∂ω 2 ετ (ω, z) ∂A1+ 2 ετ (ω, z)A1 + i 2
=
c
c
∂ω
∂t
2ω
= i 2 J2 (k2z (z)),
cwhere the currents J1 , J2 are determined by the expression 2π
2π − p −iφm (t,z,p) −iφm (t,z,−p)
(e
+e
)dp,
Jm = 2πjϑm
8π 2
0

ω2
1
ϑm = 1 − 2 2 2 , m = 1, 2, β 2 = 1 − 2 ,(16)
β km cγ
2ik2z (z)j = en0 v is the current density, A1 ≡ Aτ =0 , A2 ≡ Aτ ,
k1 = kτ =0 , k2 = k1 + τ . The expressions for J1 for k1
independent on z was obtained in [19].
When more than two waves participate in diffraction
process, the system (15) should be supplemented withequations for waves Am , which are similar to those for A1
and A2 .
Now we can find the equation for phase. From the expressions (8,9) it follows thatdkm
km d2 z
1 dv dφm
d 2 φm=++,dz 2
v dz dzdz
v 2 dt2
Let us introduce new function C(z) az follows: z 1 dv 
v0
dφm
−
dz
= Cm (z)e 0 v dz
Cm (z),
=
dz
v(z)
 z
v0
Cm (z  )dz φm (z) = φm (0) +
0 v(z )

(17)

(18)

Therefore,v(z)dCm (z)=dz
v0km d2 z
dkm
+ 2 2
dz
v dt


.

(19)

In the one-dimensional case the motion equation can be
written as:eϑd2 zαReE(zα , t),=dt2mγ(zα , t, p)(20)

therefore,v(z) dkm
dCm (z)
=
+
(21)
dz
v0 dz
km
eϑm
+
Re{Am (z, t(z))eiφm (z,t(z),p) },3v0 v(z) mγ (z, t(z), p)ωdφm (t, z, p)|z=0 = kmz − , φm (t, z, p)|z=0 = p,dzv
A1 |z=L = E10 , A2 |z=L = E20 , Am |t=0 = 0, m = 1, 2,
t > 0, z ∈ [0, L], p ∈ [−2π, 2π],
L is the length of the photonic crystal.

337

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Proceedings of FEL 2006, BESSY, Berlin, Germany

These equations should be supplied with the equationsfor γ(z, p). It is well-known that
2 dγ

mc

dt


= ev E.

(22)

Therefore,dγ(z, t(z), p)  eϑl=Re{
Al (z, t(z))eiφl (z,t(z),p) }.
2
dz
mc
l

l

The above obtained equations (15,18,21,22) provide todescribe generation process in FEL with varied parameters of diffraction grating (photonic crystal). Analysis of
the system (21) can be simplified by replacement of theγ(z, t(z), p) with its averaged by the initial phase value
 2π1γ(z, t(z), p) dp.
γ(z, t(z)) =2π 0Note that the law of parameters change can be both smoothand stepped.
Analysis of such a system shows that its efficiency significantly exceeds efficiency of a system with constant parameters. Use of photonic crystals provide to develop different VFEL arrangements (see Fig.2). It should be noted
photonic crystal

kt2

kt1
k
kt2

kt3

kt1
k

e-beamkt

The electrodynamic properties and lasing in Volume
Free Electron Laser with a ”grid” resonator (”grid” photonic crystal) with changing in space parameters are considered. The equations describing lasing of VFEL withsuch a resonator are obtained. It is shown that use ofdiffraction gratings (photonic crystal) with variable period
increases radiation intensity and provide to create the dynamical wiggler with variable period. This makes possible
to develop a double-cascaded FEL with variable parameters, which efficiency can be significantly higher then thatof conventional system.

REFERENCES[1] B.M.Bolotovskii and G.V.Voskresenskii, Usp. Fiz. Nauk. 88,
209 (1966) (Sov. Phys. Usp. 9, 73 (1966)).
[2] R.Kompfner, Wireless World 52, 369 (1946).
[3] R.Pierce, Proc. IRE 35, 111 (1947).
[4] S.J.Smith and E.M.Purcell, Phys. Rev. 92, 1069 (1953).
[5] W.W.Salisbury, US Patent 2,634,372 (1953); J.Opt. Soc.Am.
60, 1279 (1970).
[6] G.Doucas, J.H.Mulvey, M.Omori et al., Phys.Rev.Lett. 69,
1761 (1992); John E. Walsh US Patent 5,790,585 (1996).
[7] V.G.Baryshevsky, NIM 445A, 281 (2000); LANL e-printarchive physics/9806039.
[8] V.G.Baryshevsky, K.G.Batrakov, A.A.Gurinovich et al., NIM
483A, 21 (2002).

k

Figure 2: An example of photonic crystal with thethread arrangement providing multi-wave volume distributed feedback. Threads are arranged to couple several
waves (three, four, six and so on), which appear due todiffraction in such a structure, in both the vertical and horizontal planes. The electronic beam takes the whole volumeof photonic crystal.
that, for example, in the FEL (TWT,BWO) resonator withchanging in space parameters of grating (photonic crystal)
the electromagnetic wave with depending on z spatial period is formed (see eq. (6)). This means that the dynamical
undulator with depending on z period appears along thewhole resonator length i. e. tapering dynamical wiggler
becomes settled. It is well known that tapering wiggler cansignificantly increase efficiency of the undulator FEL. The
dynamical wiggler with varied period, which is proposed,
can be used for development of double-cascaded FEL withparameters changing in space. The efficiency of such system can be significantly higher that of conventional system.
Moreover, the period of dynamical wiggler can be donemuch shorter than that available for wigglers using static
magnetic fields. It should be also noted that, due to dependence of the phase velocity of the electromagnetic wave on
time, compression of the radiation pulse is possible in sucha system.

338

CONCLUSION[9] V.G.Baryshevsky, K.G.Batrakov, A.A.Gurinovich et al., NIM
507A, 137 (2003).
[10] V.L.Granatstein, R.K.Parker and C.M.Armstrong, Proceedings of the IEEE 87, no.5 (1999).
[11] V.G.Baryshevsky, K.G.Batrakov, I.Ya.Dubovskaya, et al.,
NIM 393A, 71 (1997).
[12] V.G.Baryshevsky, A.A.Gurinovich, LANL e-print archive:
physics/0409107.
[13] V.G.Baryshevsky, K.G.Batrakov, N.A.Belous et al., LANL
e-print archive: physics/0409125.
[14] V.G.Baryshevsky, A.A.Gurinovich, to be published in NIM
B, Topical Issue RC2005.
[15] V.G. Baryshevsky, N.A. Belous, V.A. Evdokimov et al.,LANL e-print arXiv: physics/0605122.
[16] R.W. James, The Optical Principles of Diffraction of X-Rays(Ox Bow Press, 1982).
[17] Shih-Lin Chang, Multiple diffraction of x-rays in crystals(Springer-Verlag, 1984).
[18] S.Takagi, Acta Crystall. 15, 1311 (1962).
[19] K.G.Batrakov and S.N.Sytova, Computational Mathematics
and Mathematical Physics 45, No.4, 666 (2005).

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH014

LASER GAIN AND INTRA-CAVITY LOSSES OF THE ELBE MID-IR FEL
U. Lehnert, P. Michel, W. Seidel, J. Teichert, R.Wünsch
Forschungszentrum Rossendorf, PF 510119, 01328 Dresden, Germany.

20

beam onbeam off

beam onThe U27-FEL of the ELBE radiation source allows tochoose between five mirrors with different outcouplingholes. This allows to adapt the optical resonator to the required wavelength range to ensure the needed laser gain
and to optimize the outcoupled laser power.
Another parameter which influences the achievable laser
gain and output power is the detuning length of the opticalcavity. While for CW operation often the minimum detuning point is choosen which maximizes the outcoupledpower, for pulsed-mode operation about one wavelength ofcavity detuning maximizes the laser gain and yields best
stability of the laser.
To gain some insight into the behavior of the optical resonator we have measured the round-trip losses and the net
laser gain and compared both to calulations. We have useda fast-readout MCT detector to measure the decay and risetime of the outcoupled infrared beam caused by a 10 s
break in the electron beam micro-pulse train. We show gain
and loss for 5, 10 and 20 m wavelength with the typicaldetuning curves of an FEL.

power [a.u.]

Abstract

40

60

80
time [µs]100

Figure 1: Decay and rise of the optical power caused by a
10 s break of the electron beam.

ROUND-TRIP LOSSES
Round-trip losses inside the optical cavity were computed using the GLAD [1] code (see Fig. 2). The computation (totals shown with red triangles) includes the outcoupling of optical power (blue circles) as well as diffraction
losses due to the aperture limits of the optical beam path inlosseslossesThe U27 mid-IR FEL of the ELBE radiation source wasdesigned to cover a wavelength range from 3 to 20 m.
The optical resonator is equipped with two spherical mirrors with a free propagating optical mode of fixed Rayleighlength. Therefore, the optical mode size at the mirrors
shows a big variation over the whole wavelength range. To
achieve a suitable outcoupling different sizes of the outcoupling hole are required. The mirror chamber containing
the outcoupling mirror was designed with a mirror wheel
which allows to choose between 5 different mirrors. At
present outcoupling holes from 1.5 to 4 mm are available.
Now, the fraction of outcoupling can be adjusted to ensure
the needed laser gain and to optimize the outcoupled laser
power.

lossesINTRODUCTION

GAIN AND LOSS MEASUREMENTS
For measurements of the laser gain and round-trip lossesof the optical cavity we switch off the electron beam for a
10 s period. An MCT detector with a fast readout electronics is used to measure the decay and rise of the opticalpower (see Fig. 1). The decay can easily be fitted by a single exponential giving the optical losses per round-trip.

FEL Oscillators and Long Wavelength FELs

wavelength [µm]Figure 2: Comparison of measured and computed values of
the round-trip losses inside the FEL resonator.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

out-coupling hole size

1.5 mm

2.0 mm

3.0 mmmeasured average power

16.8 W

24.8 W

13.9 Wmeasured round-trip losses

5.25  0.25 %7.25  0.25 %10.0  0.6 %computed round-trip losses

2.9 %

6.6 %

5.8 %

out-coupled fraction

1.1 %

2.0 %

4.4 %

average intra-cavity power

1600 W

1300 W

330 W

intra-cavity saturated power

62 MW

50 MW

13 MW

100
50

0.06
0.05

power [MW]net gain per round-trip

Table 1: Parameters of the optical resonator of the U27 FEL measured at 10 m wavelength for different sizes of theoutcoupling hole. The intra-cavity power is estimated using the computed fraction of outcoupling. To scale it to thesaturation power a pulse length of 2 ps was assumed which was previously measured for a minimum-detuning setting of
the optical resonator.

0.04
0.03
0.02
0.01

10
5
1
0.5

0
0.5

1.0

5

10
50
power [MW]0.1

Figure 3: Analytical model of the gain drop at high laser
powers approaching saturation.

50

55

60
time [µs]65

Figure 4: The rise of the optical power computed from themodel in Fig. 3 very well fits the measured power data.
particular inside the undulator. The amount of outcouplingvery well agrees with a simple geometrical model (blueline) except for very short wavelengths where the opticalmode has a tendency to avoid the outcoupling hole. The latter effect was seen experimentally as well. At 5 m wavelength the measured losses were significanly smaller whenusing the 3 mm outcoupling hole than with the 1.5 mm or
2 mm holes. In general, the measured round-trip losses
show a quite reasonable agreement with the computation.

LASER GAIN AND POWER
The rise of the optical power is determined by the net
laser gain. However, the rise curves shown in Fig. 1 need amore involved analysis as the gain itself depends on the optical power. We use a simple analytical model (see Fig. 3)
to simulate the gain drop at high powers caused by overbunching and wave-breaking effects. This model very wellfits the measured curves of the laser turn-on as shown in
Fig. 4. In the example shown we have a 6% small-signal
gain over 7% round-trip losses. The laser saturates at
50 MW optical power. At this point the gain has dropped
to just match the losses.

340

THE OPTIMAL OUTCOUPLING
The measurements performed at 10 m wavelength
demonstrate that there exists an optimal outcoupling hole
for a given cavity and beam setup. The data shown in Table 1 were measured with a 22 MeV electron beam with
50 pC bunch charge. The round-trip losses roughly correspond to the computed ones considering that the losses
at the mirror surfaces are not included in the calculations.
Going from 1.5 mm to 2 mm outcoupling hole size one
sees the expected rise of the losses (approx. 2%) due to theoutcoupling and the increased diffraction losses at the hole.
At this power level the gain changes quite rapidly with thepower. So the needed 2% higher gain translates only into asmall drop of the intra-cavity power. The outcoupled power
is increased. But when going further to 3 mm hole size theincreased losses yield a much lower saturation power inside the cavity. Despite the higher outcoupling fraction theoutcoupled power drops. The measured power levels again
roughly confirm the gain model shown in Fig. 3.

REFERENCES[1] GLAD, Applied Optics Research, Woodland, WA 98674,
USA.

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH015

REMOTE CONTROLLED IR-DIAGNOSTIC STATION FOR THE FEL AT
ROSSENDORF
W. Seidel, S. Friebel, R. Jainsch, M. Justus, K.-W. Leege, D. Proehl, D. Stehr, H. Weigelt,
S. Winnerl, D. Wohlfarth
Forschungszentrum Rossendorf, Dresden, Germany
Abstract
The remote controlled diagnostic station delivers a small
amount of the IR radiation by means of a system of relocatable mirrors, scraper mirrors and beam splitters to thespectrometer and to various power detectors working indifferent power ranges. Furthermore, a long wavelength
MCT detector is integrated in the diagnostic station for gain
and loss measurement in the whole wavelength range of
the U27-FEL. The average FEL power for the users canbe reduced by a remote controlled attenuator. We havebuilt a non-collinear background-free autocorrelator as apart of the diagnostic station to characterize the optical
micropulse duration. By using a CdTe single-crystal forsecond-harmonic generation a broad wavelength coverage
is obtained. In order to decrease the average radiation
power of the Rossendorf FEL, as required for certain experiments, the repetition rate can be reduced from 13 MHz
to 1 kHz. For that aim a semiconductor plasma switch excited by a synchronized Nd:YAG amplifier is under commissioning and first results will be presented.

INTRODUCTION
The Radiation Source ELBE [1] at the Forschungszentrum Rossendorf in Dresden is centered around a superconducting Electron Linear accelerator of high Brilliance andlow Emittance (ELBE), constructed to produce CW electron beams up to 1 mA beam current at 40 MeV. The electron beam is used to generate various kinds of secondary
radiation, mainly to drive free-electron lasers in the infrared region (3-150 μm). Starting in the summer 2005,
beam time is offered to external users in the frame of the
EC funded ”Integrating Activity on Synchrotron and Free
Electron Laser Science” (FELBE project [2]). It is of great
importance for routine user operation at ELBE that after
changing the beam path or after beam interruptions stable
operation in all wavelength ranges can be provided withina very short time (some minutes). Extensive diagnostics
for the optical components of the FEL are very importantto achieve fast availability.

DIAGNOSTIC STATION
Remote Controlled Power and Wavelength Measurement
We have developed an optical beam diagnostic system(see Fig. 1) to properly characterize and adapt the outputof the two FELs (U27 and U100). The present system is

FEL Oscillators and Long Wavelength FELs

Figure 2: Interface of the remote controlled part of the IRdiagnostic station. One attenuator, two scraper mirrors on
stepper controlled stages, one mirror and one beam splitteron a common pneumatic stage, spectrometer and different
power meters are indicated. The red lines show different
paths for the radiation when both scraper mirrors are notentirely within the beam.

compatible with a tuning range from 3 μm to 150μm, andcan be extended beyond 150 μm, if necessary.
The FEL beam from each undulator will be transported
separately from the resonator to the diagnostic area throughbeam pipes using reflective optics. Both lines will bemerged on the diagnostic table, which may be purged withdry nitrogen to avoid absorption in air, if necessary. From
here both the beams follow the same path. From the main
beam, approximately 1-5 percent of the total power will
be separated by a scraper mirror on a translation stage
for wavelength measurement and power monitoring. The
transmitted beam passes an attenuator and can be delivered
to 6 optical laboratories. In this attenuator precisely fabricated metal grids diffract a calibrated (3,5, and 3 × 10dB) percentage of power out of the beam. The rejected
power is absorbed in the walls of the housing. The mode
structure and other properties of the transmitted beam in-

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Figure 1: Arrangement of the different optical components and devices on the table.
μm to about 200 μm. The monochromator will be equippedin near future with a 48-channel pyroelectric linear array detector. We use the second side exit slit equippedwith a single Hg-Cd-Te or Ge-Ga detector for measurements with higher sensitivity. The part reflected from thepneumatic device is distributed with an other scraper mirror and two flipper mirrors to different power meters andreference detectors for monitoring the lasing process (seeFig. 2). The FEL diagnostic instrumentation has been
integrated into the existing Programmable Logic Control(PLC) and Human-Machine-Interface (HMI) environmentof ELBE (see Fig. 3). It ensures the access both for operators and users of the FEL. The basic technologies used are
the WinCC server/client system, the SIMATIK PLC system and distributed I/O by Beckhoff Automation for control of pneumatic components (i.e. attenuators), analogue
data logging (FEL power, MCT) and other instrumentation.
The stepper control drivers for the scraper mirrors are integrated system components, whereby using (expensive) separate controllers could be avoided.

Characterization of the Optical Pulse
Figure 3: The existing Programmable Logic Control(PLC) and Human-Machine-Interface (HMI) environmentof ELBE with the integrated FEL diagnostics instrumentation.
cluding the divergence and the M 2 parameters are fully
preserved, the polarisation as well. The deflected part ofthe power goes through a synchronized chopper for measurement in CW-mode. Next to this the outcoupled beam
is deflected by a mirror or a diamond beam splitter (350μm thick, under 45 degrees, deflection 15 %) at a pneumatic translation stage. The beam transmitted through the
diamond beam splitter (85 %) is transported to the spectrometer. The spectrum is measured with a Czerny-Turnertype spectrometer which contains a turret with three different gratings to cover the whole wavelength range from 3

342

The optical pulse length can sensitively be tuned byvarying the resonator length with respect to the nominal
length resulting from the electron bunch repetition rate. At
minimum detuning one yields the highest saturated power
and the shortest optical pulse length. By detuning theresonator the spectral width can be decreased simultaneously increasing the pulse length. To characterize the ultrashort pulses generated by the FEL we built a non-collinear
background-free autocorrelator system. We used a CdTe
crystal as SHG medium [3], since it is transparent for awide wavelength range in the FIR. We measured the autocorrelation function at maximum power in the detuning curve at a wavelength of 11.09 μm (see Fig. 4, upperpart). We deduced a pulse duration of 0.89 ps (FWHM),
assuming a Gaussian temporal pulse shape. The measured
FWHM of the spectrum is approx. 176 nm. The cal-FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH015

Figure 5: Setup for the plasma switch (see below).

Extraction of Single FEL Radiation Pulses Usinga Laser-Activated Plasma Switch

Figure 4: Pulse duration and the corresponding FWHM of
the wavelength of 11 μm at maximum of the detuning curve(upper part) and from a detuned resonator (lower part).

culated time-bandwidth product is about 0.4 which indicates Fourier-transform limited operation. Long IR pulses
with narrow bandwidth can be obtained from a detuned resonator (see Fig. 4, lower part).

FEL Oscillators and Long Wavelength FELs

In order to decrease the average radiation power of theRossendorf free-electron laser FELBE, as required for certain experiments (high pulse energies but moderate or low
average power), the FEL repetition rate can be reduced
from 13 MHz to 1 kHz. To this end, plasma switchingof FEL radiation pulses was demonstrated. The plasma
switch bases on the principle of photo-induced reflectivity
by an optically excited electron-hole plasma [4, 5]. Germanium serves as semiconductor material for the switch. The
semiconductor was illuminated by a Nd:YAG laser amplifier system (1 kHz, λ = 1064 nm, τ ∼ 16 ps, ≤1 Watt), generating an electron-hole plasma on the front surface of thesemiconductor. The generation of sufficient plasma density leads to a variation of the optical semiconductor properties for the infrared FEL-radiation (strongly focused andunder Brewster’s angle). For realizing the pulse selection
the frequencies of both laser sources (FEL and Nd:YAG)
were synchronised with RF electronics. For the exact timing of both laser pulses, when they hit the semiconductor,
they were detected with a photon-drag detector or a fastpyroelectric detector (FEL) and a photo diode (Nd:YAG)
and were adjusted on each other with cables, phase-shifter(trombone) and through moving a precision linear stage.
Fig. 5 shows the experimental set-up. A gold mirror served
as a reference for determining the reflectivity of the Germanium. The selected FEL pulses were detected by afast MCT detector with a bandwidth of 20 MHz. Fig. 6
shows the switched pulse in two amplitude scales. The signal from the switch laser (photo diode) is shown in red.
From the comparison of the black and blue curves we obtained an amount of dark pulses in the switched beam ofabout 0.5 % due to the angle of beam spread from the focussing. The time-resolved measurement of the reflectivity
yields an exponential decay with a time constant of 590 ps.
For the highest value of the Nd:YAG laser amplifier peakfluence of 25 mJ/cm 2 , a reflectivity of Ge for FEL radi-

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Proceedings of FEL 2006, BESSY, Berlin, Germany

ation (λ = 11μm) of 100 % was achieved (see Fig. 7).
We thus succeeded to extract single FEL radiation pulses
out of the 13 MHz pulse train, indicating that this plasma
switch is most suitable for the Rossendorf FEL. Further examinations will concentrate on achieving similar results for
shorter wavelength. To integrate this plasma-switch into
the existing diagnostic station we have to build an additional by-pass to the Germanium or Silicon slab which isunder Brewster’s angle (see Fig. 1). The selcted micropulse will be refocused to the waist parameters outside of
the by-pass line and transported to the user stations.

Figure 7: Dependence of reflectivity on the pump-laser
peak fluence.

REFERENCES[1] P. Michel et al., Proceedings of the 2004 FEL Conference, p.
8-13, Trieste, Italy[2] www.fz-rossendorf.de/felbe

Figure 6: The switched FEL pulse at 11 μm in two different
amplitude scales is measured by a fast MCT detector with [3] J. Xu, G.M. Knippels, D. Oepts, and A.F.G. van der Meer,
Opt. Comm. 197 (2001) 379-383
a bandwidth of 20 MHz. The signal from the switch laser(photo diode) is shown in red. From the comparison of the [4] P. Haar, Ph.D. thesis, Standford University (1996)
black and blue curves we obtain an amount of dark pulse in [5] E.H. Haselhoff et al., Nucl. Instr. and Meth. A358 (1995)
the switched beam of about 0.5 %.
ABS28

344

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH016

THE PARTIAL-WAVEGUIDE RESONATOR OF THE U100-FEL
AT FZ ROSSENDORF
M. Freitag, R. Schlenk, W. Seidel, U. Willkommen, D. Wohlfarth, R. Wuensch, B. Wustmann,
FZ Rossendorf, Dresden, Germany.
THE U100-FEL
At the radiation source ELBE [1] an FEL with a permanent magnet undulator (U100) [2] has been constructed toextend the wavelength range to above 150 μm. Its lowest
wavelength (20 μm) overlaps with the existing U27-FEL(Fig. 1). There is a first experimental evidence that wavelengths below 20 μm, maybe down to 15 μm, can also bereached.
The undulator is composed of 38 magnetic periods, each
100 mm long. The hybrid structure consists of SmCo magnets and soft-iron poles. It guarantees a sufficiently highFigure 2: Scheme of the U100 resonator with partial waveguide. The electron beam enters the resonator at the dipole
magnet D1 and leaves it at D2.
beam the optical beam propagates freely - both horizontallyand vertically - through quadrupole and dipole magnets up
to the toroidal mirror M1 with an outcoupling hole in thecenter.
The partial waveguide causes a series of problems which
are not present in the case of an open resonator. The mirrors must have different curvatures in horizontal and vertical direction. Although embedded in the waveguide, thedownstream mirror M2 must be movable to adjust beam direction and resonator length. The narrow waveguide complicates the entering of screens and mirrors for beam diagnostics, and impedes the evacuation of the vacuum chamber.

RESONATOR MIRRORS

Figure 1: Wavelength λ 1 (fundamental harmonic) of the
U27- and U-100 FELs as a function of the kinetic electronenergy Eekin calculated for the indicated undulator parameters Krms .
magnetic field at a reasonable undulator gap, and a high radiation resistance. Increasing the gap from 24 to 85 mm
the undulator parameter K rms varies from 2.7 to 0.3.
A waveguide was installed to fit the optical resonatormode into the undulator gap. It is 10 mm high andspans over 7.92 m from the undulator entrance to the resonator mirror M2 on the opposite side of the resonator(Fig. 2). The waveguide consists of two parallel plates,
each 5 mm thick and divided into three pieces made outof non-magnetic stainless steel. In the horizontal direction
the waveguide is wide enough to allow a free propagationof the optical beam. On the upstream side of the electron

FEL Oscillators and Long Wavelength FELs

In the horizontal direction the infrared beam has a Gaussian shape. The curvature of the resonator mirrors corresponds to a Rayleigh length of 180 cm with a waist in thecenter of the undulator. Within the waveguide the verticalpropagation is confined by the upper and lower plate of the
waveguide. The downstream mirror M2 is cylindrical andfocuses the beam only in horizontal direction. On the opposite side the vertical beam size increases rapidly behind theexit of the waveguide. The size of the beam at the surfaceof mirror M1 depends strongly on the wavelength. This is
illustrated in Fig. 3. The size of the mirrors (black rectangle) covers more than 99% of the beam intensity even at
150 μm.
At the entrance into the waveguide, the optical modemust be converted from a freely propagating one into awaveguide mode and vice versa. This conversion causes
optical losses which reduces the net gain of the laser. In
general, the curvature of mirror M1 which minimizes themode conversion losses depends on the wavelength. In ourcase, the waveguide is sufficiently far away from M1 andwe can use a common radius of curvature for all wave-

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Proceedings of FEL 2006, BESSY, Berlin, Germany

MIRROR ALIGNMENT AND CONTROLSYSTEM
Fig. 5 shows the scheme of the resonator alignment control system. It is similar to the system developed and used
for the U27-FEL [4]. The correct location of the resonator
axis is checked by means of two HeNe laser beams introduced into the resonator by auxiliary and pop-in mirrors.

Figure 3: Transverse distribution of the light intensity at thesurface of the outcoupling mirror M1 in comparison withthe mirror size (black rectangle) calculated for the shortest(20 μm) and the longest wavelength (150 μm). The various
colors represent the relative intensity in percent while thesmall circles in the center indicate the various outcouplingholes.

M
M
M

P
P

Figure 5: Schematic view of the resonator alignment system. M1,2 : resonator mirrors, L 1,2 : HeNe alignment
lasers, B1,2 : beam expander, S 11,12,21,22 : steering mirrors,
P1,2 : pop-in mirrors, T: adjustment apertures, C: monitoring camerasLoutcoupling
mirror M1

waveguideL

DC-Mot.

70%
30%
splitterFigure 4: Support for the three mirrors M1. M: mirror, P:
piezoelectric drives, L: linear translation stage,

Mirror M2

undulator

PC
laser

setting ΔLÆ cavity detuning
stabilization δ (L+ ΔL) <"0.5 μm

interferometer

Figure 6: Schematic view of the resonator length control
system.
lengths of the operating range of the U100-FEL. Above
35 μm the calculated coupling losses per round trip are below 5% [2]. Only at wavelengths below 25 μm they exceed
10% (simulations by means of the code GLAD [3]).
The beam is outcoupled through a circular hole in thecenter of mirror M1. Because of the large variation of thebeam radius (factor 3) and of the expected laser gain (factor5) in the operational range of the U100-FEL we need outcoupling holes of different size. We chose a set of 3 mirrors
with the same curvature and holes with a diameter of 2, 4.5
and 7 mm. They are mounted on a support (Fig. 4). Using a linear translation stage the appropriate mirror can beshifted into the right position. The mirrors are gold-coatedcopper mirrors and cooled by water. They can be tilted horizontally and vertically by means of piezoelectric drives.

346

A Hewlett-Packard interferometer system [5] is used formonitoring the resonator length (Fig. 6). It has also beentaken from the U27-FEL.
The resonator has to be set and stabilized to a certain
length and its axis has to be aligned to the electron beam.
For that aim the mirrors are gimbal-mounted and can betilted horizontally and vertically by means of piezoelectric(M1) and DC drives (M2). They allow the mirrors to betilted up to 15 mrad in steps of 1 μrad. Moreover the cylindrical mirror M2 can be shifted along the resonator axis by
3.6 mm in steps of 100 nm (hysteresis 2 μm) by means ofremote controlled DC drives (Fig. 7). Steps and hysteresis can additionally be reduced by a factor of about 30 bymeans of a beam in bending. Fig. 8 shows the opened mirror chamber M2.

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

D

B
B

TUPPH016

tem (Fig. 5). CCD cameras in lead housings are used forobserving the screens and markers through the viewports(Fig. 9).

R

Dl
D
B

Dl

VC
P
R

Figure 7: Back side of the flange of mirror chamber M2
with control elements. The mirror is mounted on the center of the front side. Schematic view with DC drives (D)for mirror tilting and shifting (D l ). The broken line (R) indicates the hidden driving rod, which transfers the motion
onto the mirror on the front side. The beams in bending arelabelled by B.

M WG

VP

Figure 9: Diagnostic mirror for resonator axis tuning insertable into the waveguide. M: mirror, R: rod, P: pneumatic cylinder, VC: vacuum chamber, WG: waveguide,
VP: view port.
Beam positioning monitors with an aperture of 75 mm
have been developed for the online measurement of theelectron beam position. One of them is located in frontof the waveguide entrance.

VACUUM MANIFOLD

Figure 8: Open mirror chamber M2 with the rectangularcylindrical mirror (left side) and the end of the waveguide(right side).

BEAM DIAGNOSTICS
There is an extensive beam diagnostics system within
the resonator region consisting of 20 view screens, markers and auxiliary mirrors. Most of them have to be inserted
into the waveguide. They are not allowed to touch the polished surface of the waveguide, which is only 10 mm high.
Fig. 9 shows the scheme of an auxiliary mirror with thecorresponding insertion unit. The mirror is mounted at theend of a rod extending into the waveguide. The rod canbe shifted into the waveguide by means of a pneumatic
cylinder. It can precisely be moved along and perpendicular to the resonator axis, and allows an additional torsionof the rod which leads to a controlled and extremely sensitive tilting of the mirror at its head. The accuracy is 30 μm
and 5μrad, respectively. Similar insertion units are used
for OTR screens (7 mm high) made of beryllium with a
1 mm hole, foil screens consisting of a stretched aluminum
foil, and markers (8 mm high) with a hole for the alignment and interferometer lasers. Among them are the pop-in
mirrors and apertures used for the resonator alignment sys-

FEL Oscillators and Long Wavelength FELs

The presence of the waveguide does not allow to place
the getter pumps directly below the beam line. A vacuum
manifold with 6 getter pumps and 7 ports (Fig. 10) is installed below the waveguide instead. Their total throughput amounts to 520 l/s. An additional getter pump with
350 l/s throughput is fixed below each mirror chamber. The
electron beam line can be separated by vacuum valves upstream and downstream the resonator. Another valve separates the mirror chamber M1 with the outcoupling window. Additionally, four powerful turbomolecular pumps

Figure 10: Collective vacuum line with getter pumps andconnectors to the waveguide.
are linked to the manifold and to both mirror chamber as

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Proceedings of FEL 2006, BESSY, Berlin, Germany

well. They ensure to hold the vacuum in the whole systemin the case of a local rise in pressure. Membrane pumps
serve as fore-vacuum pumps. In stand-by mode the turboand membrane pumps can be switched off.
The system can be vented by means of needle valves
with dry and particle-free nitrogen gas. A mass spectrometer allows to analyze the residual gas. The pressure in thevacuum line and in the mirror chambers is measured bymeans of Penning and Pirani vacuum gage heads.

SUMMARY
At the radiation source ELBE, another free-electron laser
has started to produce light in the far infrared region. It iscapable of producing IR radiation between 20 and 200 μm.
Its resonator was equipped with a partial waveguide to allow a small undulator gap. Curvature and size of the resonator mirrors were adapted to minimimum optical losses.
To optimize the outcoupled laser power three mirrors withcircular holes of different size were installed on a linear
translation stage. The resonator was equipped with a control and alignment laser system which allows to adjust andstabilize the resonator length and to align the resonator mirrors. Special beam diagnostic elements, which can be inserted into the waveguide, and a vacuum manifold were developed to fix the beam position and to ensure an extreme
vacuum within the narrow waveguide.

REFERENCES[1] http://www.FZ-Rossendorf.de/ELBE[2] E. Grosse et al., FEL’05, Aug. 2005, SLAC, TUPP031,
http://www.JACoW.org[3] GLAD, Applied Optics Research, Woodland, WA 98674,
USA.
[4] U. Lehnert et al., FEL’05, Aug. 2005, SLAC, MOPP032,
http://www.JACoW.org[5] U. Lehnert et al., FEL’05, Aug. 2005, SLAC, TUPP030,
http://www.JACoW.org

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FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH018

NEW RESONATOR FOR THE ISRAELI FEL
A. Faingersh, Y. Socol, E. Dyunin, J. Dadoun, Kh. Garb, A.Gover#,Dept. of Physical Electronics - Faculty of Engineering, Tel-Aviv University,
Tel-Aviv, Israel
M. Einat, B. Litvak, B. Kapilevich, Y. Pinhasi, A. Yahalom,
Dept. of Electrical and Electronic Engineering - The College of Judea and Samaria, Ariel, Israel
G. Denisov, M. Shmelev,
Institute of Applied Physics, Nizhniy Novgorod, Russia
Abstract
The Israeli FEL resonator (W-band 75-110 GHz) was
re-designed in order to reduce the overall round-trip
losses and to control the radiation out-coupling.
In its new configuration, the resonator consists of an
overmoded corrugated rectangular waveguide and two
radiation mode splitters, separating the high-energy ebeam from the mm-wave radiation. The electron input
splitter is based on Talbot effect in an overmoded
rectangular waveguide. The radiation out-coupling takes
place in the output splitter. The splitter is based on anovel design. It combines Talbot effect between twoparallel plates with free space propagation and withfocusing by two curved cylindrical mirrors in a confocal
imaging scheme.
The waveguide and the splitters were tested, showing
improved performance in comparison with the former
resonator. The measured unloaded Q-factor of the newresonator is increased by a factor of ~3, up to Q=25,000.
Accordingly, the round-trip losses are ~23%. Rotating
grids control the radiation out-coupling, allowing
optimization of the radiation power and the extraction
e-beampropagation
direction

efficiency. The design layout and the testing results arepresented.

NEW RESONATOR DESIGNThe Israeli FEL with Curved Parallel Plate (CPP)
waveguide-based resonator was reported earlier [12]. Only a small part (~5%) of the generated RFenergy was coupled out in these configuration. In
order to minimize the total round-trip losses of theresonator, it was re-designed. The previously used
CPP waveguide was substituted by a twocorrugated-walls
rectangular
waveguide.
Toseparate the laser RF radiation from the electron
beam and to out-couple the desired part of the RFenergy, the beam output confocal splitter was also
designed.

General Layout
The resonator consists of several waveguidesections of different profiles. It is integrated into

Wiggler

Confocal Splitter

Straight Talbot
Splitter

Rectangular CorrugatedWaveguide

Fig. 1. The resonator lay-out and the scheme of installation of the resonator into the wiggler system.
___________________________________________#

Corresponding author. Email: gover@eng.tau.ac.il

FEL Oscillators and Long Wavelength FELs

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Proceedings of FEL 2006, BESSY, Berlin, Germany

the wiggler system, so that the interaction between
the electron beam and the wiggler magnetic field of
takes place inside the waveguide cavity rectangular corrugated waveguide. The latter isassembled from 4 separate walls, 2 smooth and 2
mill-machined corrugated. This waveguide wasdesigned in such a way that the electron beam at
the design energy (1.4 MeV) can interact only withthe fundamental mode TE 01 according to thedispersion relation. The resonator layout installed
into the wiggler system is schematically shown in
Fig. 1.
In order to obtain positive feedback from theresonator mirrors, two wave splitters were placed atboth terminations of the corrugated waveguide.
These splitters are reflectors, based on overmoded
rectangular waveguides shorted with a mirror at
one end.

Confocal Splitter
The confocal splitter is a quasi-optical mm-wave
component that based on a novel design. The splitterconsists of an overmoded rectangular waveguide and two
curved metallic mirrors. The splitter scheme provides thecontinuous waveguide propagation and Talbot effect in
one dimension, and free-space propagation of theradiation in the other dimension (both orthogonal to thedirection of propagation). The two parabolic (shaped in
the plane of free space propagation) mirrors provide thedispersion-free focusing. The splitter prototype design
and the manufactured model photo are shown at fig. 2.
Computer simulation of the radiation propagation throughthe confocal splitter was also performed. The round-trip
losses in the splitter were theoretically estimated as 12%,and later measured experimentally to be about 15 %.

Fig. 2. Confocal splitter design (left) and the fabricated prototype (right).

The length of the input splitter equals to half of
the Talbot-effect-optical-imaging length. At thisdistance, the overmoded (oversized) rectangular
waveguide provides splitting of the original field
distribution at the termination plane of the
waveguide, where the reflecting mirror is placed.
This effect allows to make a hole in the metallic
mirror (as there is no field in the center), therefore
to pass the electron beam through this hole.
The output confocal splitter is of the Talboteffect-optical-imaging length and it provides thefundamental mode’s field reconstruction at theplane of coupling grids that terminate the resonator.

350

MEASUREMENTS RESULT
After manufacturing of the resonator components, thewhole resonator was assembled in the laboratory in orderto enable experimental investigation outside the FEL
tank. The round-trip reflectivity of the resonator wasmeasured using excitation by special designed corrugatedhorn mode exciter through the 3-grid tuneable couplersystem. In this experiment, the reflected signal from theexcited resonator cavity was measured directly and theround trip reflectivity was calculated according to thetheory presented in [2], [3].

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Calculation of the round trip reflectivity
The algorithm of the round trip reflectivity is based on
measurement of the reflection coefficient resonance curveand uses “optical” formulation. The reflection coefficientof the shorted Fabri-Perot resonator isΓ = 1−( R1 − Rrt )(1 − R1 ) / R1
2
(1 − Rrt ) + 4 Rrt sin 2 (δ/2 )f0
δλ= 1/ 2
δ f1/ 2λ0

were λ g and ν g are the wavelength and velocity ofwave propagation inside the resonator accordingly.
The total round-trip reflectivity R rt of the FEL
resonator was calculated in the present work basedon Eq. 4 and the direct measurement of the FWHM
linewidth δ f 1/2 of the resonant peaks. This linewidth
was obtained from measurement of the power
spectral reflection pattern.

(1)

CONCLUSIONS

were Γ is the power reflection coefficient, R1 – reflectionof the entering mirror (coupling condition), Rrt is the totalround trip reflectivity and δ is a phase. On the other hand,choosing the Q factor definition as the ratio between
the frequency f 0 (resonant wavelength λ 0 ) andbandwidth of the resonator mode δ f 1/2 (or δ λ 1/2 ):Q=

TUPPH018(2)

The Israeli FEL resonator was re-designed in order todecrease the internal round-trip losses and thus to achievethreshold current reduction. The novel reflector andsplitter based on the quasi-optical confocal scheme, were
designed, manufactured and characterized. The round trip
losses of the confocal splitter are about 15% (in good
agreement with the theoretical limit estimation of 12%).
The round trip losses of the overmoded corrugatedwaveguide and straight Talbot section were measured to
be about 8 % for both waveguides. The total losses of thewhole resonator system are therefore about 23%.

As it shown in [2], one can derive:

Q=

2π L

4

REFERENCES

Rrt

(3)

λ 1 − Rrt

were L is the resonator length and λ is wavelength. It
should be noted that in Eq. 3 above, Q is the loaded
Q-factor since both internal and external (coupling
mirror) losses are included. Finally, the round trip
reflectivity (or total losses, since Rrt = 1-Loss) can befound in terms of Qloaded or directly in terms of FWHM
(δf1/2) of the measured resonator peaks:⎡
2π L+
Rrt = ⎢ −⎢ λ Q
g loaded⎢⎣⎡
2π Lδ f1/ 2
= ⎢−
+
⎢
vg
⎢⎣

⎛ 2π L ⎞⎜⎟⎜λ Q⎟⎝ g loaded ⎠

2

⎤
+ 1⎥
⎥
⎥
⎦

⎛ 2π Lδ f ⎞
1/ 2
⎜
⎟
⎜
⎟
v
g
⎝
⎠

2

4

⎤
+ 1⎥
⎥
⎥
⎦

(4)

[1] A. Faingersh, A. Gover, A. Eliran, and B.Kapilevich“Concluding report: measurements and calculation ofround-trip reflectivity in the FEL waveguideresonator before and after modification and estimateof threshold current improvement”, Internal report of
the FEL group, 25-Aug-06, Tel-Aviv University.
[2] A. Gover, A. Faingersh, at al. “Radiation
measurements in the new tandem accelerator FEL”,
Nuclear Instr. And Methods In Physics Research, A
528 (2004), pp. 23-27.
[3] B. Kapilevich, A. Faingersh, and A. Gover,“Accurate determination of Q-factor of a quasioptical resonator”, Microwave and Opt. Tech. Lett.,vol.36, No.4, (2003).

4

FEL Oscillators and Long Wavelength FELs

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Proceedings of FEL 2006, BESSY, Berlin, Germany

PRESENT STATUS OF THE ISRAELI FEL: INCREASING FEL POWER BY
ELECTRON BEAM ENERGY BOOSTING
E. Dyunin, M. Volshonok, A.Gover#,Dept. of Physical Electronics - Faculty of Engineering, Tel Aviv University, Tel-Aviv, Israel
M. Einat, Y. Lurie, Y. Pinhasi, Y. Socol, A. Yahalom,
Dept. of Electrical and Electronic Engineering – The College of Judea and Samaria, Ariel, Israel
Abstract
The status of a R&D work aimed on increasing the FEL
power by boosting the electron beam energy after theradiation build-up is reported. A fine control of theelectron beam energy during the radiation pulse isdesigned to compensate the small energy degradation
during the pulse. Also, a controlled ramp (up or down) in
the electron energy during the pulse will be applicable.
Theoretical estimations of the output power in thepresence of an electron energy change during the pulse
are presented. Two models, showing agreement between
them are compared: Analytical model based on thependulum equation, and, Rigorous 3D FEL interaction
model solved numerically.
Another expected result of the design is to further
extend the pulse duration with stable conditions and toobtain improved coherency.
The electrical and mechanical lay-outs of the highvoltage boosting (leading to electron beam energy
boosting) are also presented.

ramp can also be used to compensate the small
degradation in the high voltage during the pulse topractically obtain constant electron energy for longer
periods. That will lead to improvement of the coherency
in the FEL radiation in view of the long pulse operation inconstant conditions. In the following sections the twodifferent models are presented and the results are given.
Also the designed experimental setup to support theenergy variations during the pulse is described.

THE FEL 3-D MODEL
The calculations were carried out in the framework ofsteady-state,
three-dimensional,
space-frequency
approach, described in more details in [1]. In theapproach, the total electromagnetic field oscillated at
signal frequency f s is presented in the frequency
domain as an expansion in terms of transverse eigenmodes ε q ( x, y ) of the cavity, in which the field is
excited and propagates:

INTRODUCTION
Electrostatic accelerator based FEL's (EA-FEL) are
Unlike RFcharacterised by long pulse operation.
linac FEL's having a pulse width limited by the RF part,the EA-FEL's pulse width is incomparably longer andpractically limited by the capability of the power supply
to support the system with the required energy. In
principle, an ideal power supply can support a CW operationof the FEL. Calculations of a long pulse operation of an
FEL, show a saturation regime obtained at the end of theenergy build up process, were the output power of the
FEL is stable at its maximum. This maximum is related to
the FEL characteristics and the operation conditions (suchas electron-energy) which are kept constant.
In this paper the possibility of changing the electronenergy during the pulse, after the radiation build-up, isconsidered. Calculations are made in two different
methods to estimate the variations in the EA-FEL output
power in saturation as a result of change in the electronenergy during the pulse. Schematic of a high voltage
boost system that supports a change in the electronsenergy during the pulse is presented. This system allows acontrolled ramp of the electron energy (up or down). This~− j k zq z
E(r ) = ∑ C q ( z ) ε q ( x, y ) eqHere the time-domain field is{~E(r, t ) = Re E(r ) e + j 2π f s t

}

(1)

(2)

and C q ( z ) is an amplitude coefficient of the mode q,
which could be found from the excitation equation:d
1 + j k zq z ~*Cq ( z ) = −e∫∫ J (r ) ⋅ ε q ( x, y ) dx dy
dz
2Nq

(3)

The power of the electromagnetic field emitted up to thepoint z can be found as follows:

PEM ( z ) = ∑ C ( z )
q

2 1

2

{ }

Re N q(4)

here N q is the mode normalization power of the mode q.

___________________________________________* Work supported by the Israeli Ministry of Defence#
Corresponding author. E-mail: gover@eng.tau.ac.il

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As usually accepted we consider the electron beam as
consisting of a number of electron clusters or charged
quasi-particles, distributed over the beam. Therefore theexcitation current can be given in such a form:

J(r, t ) = −∑ qi v i δ ( x − xi )δ ( y − yi ) δ [z − zi (t )] (5)ior in the frequency domain:v~
J (r ) = −2 ∑ qi i δ ( x − xi )δ ( y − yi ) e − j 2π f s ti ( z )
v zi
i
(6)
Substitution of the excitation current (6) into theexcitation equation (3) enables one to re-write the last as
follows:d
Cq ( z ) =dz+ j [k zq z − 2π f s t i ( z )]qi
1v i ⋅ ε q* ( xi , yi ) e∑(7)
N q i v zi
In Eq. (5)-(7)qi , v i and ri ≡ {xi , yi , zi } are thecharge, the velocity and the coordinates of the particle
with a number i, andz 1ti ( z ) = t 0 i + ∫dz'(8)0 v zi (z ')is the moment when the particle number i comes to thepoint z.
With a known field, a next phase-space position of theparticles can be found from the equations of motion:dv idγ ⎤ ⎫
1 ⎧e 1 ⎡=− ⎨E(ri , t ) + v i × B(ri , t ) + v i i ⎥ ⎬⎢dz
dz ⎦ ⎭
γ i ⎩ m v zi ⎣
(9)

dγ i
e 1
=−
v i ⋅ E(ri , t )dz
mc 2 v zi(11)qHere the expansion coefficient of the total field is

Cqtot ( z ) = ∑ Cq(n ) ( z )N

n =1

and the coefficients of the field emitted after n round tripsof the radiation are defined by the recursion relation:− j k z q Lc
C q(n +1) ( z = 0) = Γ C q(n ) ( z = Lw ) e(13)
The above equations form a closed set of non-linear
equations, which enables one to calculate the bothradiated field and the beam trajectory. The model was
realized in FEL3D numerical code and applied for the
calculations considered in the next section.

THE “PARAMETRIC” PENDULUM
EQUATION MODEL
The oscillation build-up and saturation process of the
FEL oscillator were analyzed numerically in Ref. [3,4].
At saturation the radiation field inside the cavity is built
up, and the small signal assumptions are not valid. The
electron dynamics is described in the combined wiggler
and radiation wave fields (the ponderomotive wave) interms of the pendulum model [5]:(10)

Figure 1 demonstrates schematically an FEL operated
in oscillator regime. In that case some part of the radiation
emitted by the beam is reflected by mirrors and returnedto the interaction region, been forced to interact with a
new portion of the driving current. Then the total
electromagnetic field, emitted after N round-trips of theradiation in the resonator, may be found by:~− j k zq z
Etot (r ) = ∑ Cqtot ( z ) ε q ( x, y ) e

Figure 1: Principal scheme of FEL in an oscillator regime.

d2Ψ
2= − K s sin Ψ
2
dz
θ=

dΨ
dz

(15)

where Ψ (z ) is the phase of the electron relative to thezponderomotive wave: Ψ (z ) = θ (ω, z ' )dz ' + Ψ0 , and the∫0

detuning parameter is θ (ω, z ) =

(12)

(14)

ω
v z ( z)

− k zq (ω ) − k w .

k zq (ω) is the axial wavenumber of mode q, andk w = 2π λ w

is

the

wigglerwavenumber.

The

Synchrotron oscillation wavenumber Ks is given by

FEL Oscillators and Long Wavelength FELs

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Proceedings of FEL 2006, BESSY, Berlin, Germany

P = Ap K s4
Ap =

1
2π

⋅
2

(16)
|

(γ γ β ) ⋅ A λ ⋅ (mc / e)
0 z

aw2

2 4
z

2

em
4

L

2

2

(17)

Zq

where E and P are the circulating radiation field andpower in the saturating oscillator cavity (we assume highround-trip resonator reflectivity, and therefore constant
power -P along the resonator).

Fig. 3: Dynamics of electron beam trapping andsynchrotron oscillation at steady state saturation stage ofan FEL oscillator.

As well known, the pendulum equation (14) can be
integrated once, resulting in a picture of open and closed
trajectories in θ − Ψ phase-space (Fig. 2). This picture
can also be viewed as a display of electron energy vs.
phase trajectories, if one uses the differential linear
relation between γ and θ near the synchronism energy γ0(Fig. 3).

Fig. 4: The oscillations build-up in EA-FEL withconstant electron energy and with a step in the energy
during the pulse after saturation:
Constant Terminal Voltage 1.42 MV (PE) – Green,
Voltage Step from 1.4 to 1.42 MV (PE) – Red,
Voltage Step from 1.4 to 1.42 MV (FEL3D) – Violet.

ENERGY BOOST SYSTEM

Figure 2: Phase-Space Trajectories of the Pendulum
Equation.

OSCILLATION BUILD-UP EA-FEL
The oscillation build-up dynamics as a result of the twomodels are presented in Fig. 4. all the calculations are
made for a single frequency. The result for a constantelectron energy (1.42 MeV)) is shown in green. This
calculation is done by the pendulum equation model. For
the same frequency, a case with a step in the electronenergy is calculated (red curve). The initial voltage is 1.4
MV and saturation is obtained. Than a voltage step isapplied to 1.42 MV. As a result a new saturation level isobtained which is higher that the former level of a stable
voltage. Thus, for the same final (i.e 1.42 MV) conditions
two saturation levels are possible.
A verification of the red curve behaviour is obtained by
the FEL 3D model (violet curve). Although different
levels of saturation are obtained, the behavior is similar,
where a jump in the saturation level is obtained. The
differences between the models can be related to thedifferences in the assumptions in the models.

354

Since the EA-FEL is capable of a long pulse operation,a coherent operation in high power is applicable [6]. Still.
A practical experimental difficulty is the electrons the hit
the terminal parts and reduce the voltage. These electrons
can be related to non-ideal transport conditions and toreturning electrons that could not reach the collector. Thisphenomena cause a drift in radiation frequency that is
related to the drift in the voltage drop. Correcting thisvoltage drop was one of the motivations to the work
presented here. But, if a correction system is designed, it
can be used to more than a voltage correction but also tovoltage control in a desired manner such as a ramp.
The voltage ramp control system is presented in Fig. 5.
it is placed in the high voltage terminal and its output isadded to the terminal voltage. A capacitor is charged tovoltage of up to 30 kV. During the pulse it is partly
discharge through a selected resistor to the terminal.
Therefore the voltage of the terminal is raised. By
selecting the resistor and voltage the rate of the voltage
raise can be determined. Therefore a compensation to theelectrons hitting the terminal can be achieved in order tostabilize the voltage conditions and as a result thefrequency as well.
Also a ramp (positive or negative) in the voltage can beapplied in order to enhance the saturation level as
predicted by the theory.

FEL Oscillators and Long Wavelength FELs

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Fig. 5: The voltage ramp control circuit.

CONCLUSION
The possibility to achieve higher extraction efficiency andtherefore higher operation power of the EA-FEL byelectron energy step is theoretically possible.
Bi-stable saturation conditions are obtained for different
initial conditions. An experimental setup is underconstruction in order to demonstrate the effect

REFERENCES[1] Y. Pinhasi, A. Gover, and V. Shterngartz, Phys. Rev.
E 54, 6774 (1996)[3] M.V. Krongaus, Y. Pinhasi, M. Tecimer, A. Gover,Nucl. Inst. and Meth .Phys. Res. A445, 28 (2000).
[4] M.V. Krongauz, Y. Pinhasi, A. Gover, "Dynamics
and control of power build-up in a pre-bunched
FEL", unpublished.
[5] A. Gover, E. Dyunin, Y. Lurie, Y. Pinhasi, M. V.
Krongauz, "Superradiant and stimulated superradiantemission in prebunched electron-beam radiators - part
II : Radiation enhancement schemes", Phys. Rev. ST– Acc. Beams Vol. 8, 030702 (2005).
[6] Y. Socol, A. Gover, A. Eliran, M. Volshonok, Y.
Pinhasi, B. Kapilevich, A. Yahalom, Y. Lurie, M.
Kanter, M. Einat, and B. Litvak, "Coherence limits
and chirp control in long pulse free electron laser
oscillator", Phys. Rev. ST – Acc. Beams Vol. 8,080701, (2005).

FEL Oscillators and Long Wavelength FELs

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Proceedings of FEL 2006, BESSY, Berlin, Germany

DYNAMICS CONTROL OF THE ELETTRA STORAGE RING FREEELECTRON LASER WITH DIGITAL FEEDBACKS
E. Allaria#, G. De Ninno, Sincrotrone Trieste, 34012 Trieste, Italy
A. Antoniazzi, D. Fanelli, Dept. of Energetics, University of Florence, Florence Italy.
Abstract
The laser dynamics of a storage-ring free-electron laser
has two main sources of instabilities. First of all,dynamical instabilities are developed as the free electron
laser is moved away from the exact tuning between the
period of the electron bunch(es) circulating into the ringand that of the photon pulse stored in the optical cavity. In
addition, external (low-frequency) noise sources have astrong influence on the dynamical behavior of the systemand can perturb its dynamics. Different feedback
techniques have been proposed in order to control
dynamical instabilities and stabilize the laser output. We
present here a numerical and experimental investigationon the control of the Elettra storage ring free electron
laser dynamics using different feedbacks techniques thatcan be experimentally implemented by means of a Field
Programmable Gate Array.

INTRODUCTION
In a storage ring free electron laser (SRFEL) the
electron bunch interacts with photons when passing
through the optical klystron (Fig.1). The photons are
stored in an optical cavity characterized by a travelingtime ΔT and bounded by the two mirrors. The electron
bunch, circulating in the storage ring, is characterized by
the revolution period ΔT+ε which is determined by thestorage ring radiofrequency.

bunches in the ring (some MHz).
On a “slow” time scale (ms), the SRFEL behavior isstrongly related to the temporal superposition of thephoton and electron bunches inside the optical klystron.
More precisely, the laser envelope displays a steady state
regime for a perfect electron-photon tuning (ε=0 in Fig.1).
Small light-electron detuning is sufficient to induce
intensity oscillations on a slow time scale (Fig.2).
Due to these instabilities the quality of the laser
temporal evolution is usually rather poor. Besides
temporal detuning, the environmental noise (which isusually related to a residual 50Hz modulation comingfrom the power network) also perturbs the system and canstrongly affect the SRFEL dynamics (Fig.2,5).
A simple model based on a recurrence map [1,2] can beused in order to describe the slow time-scale evolution ofa SRFEL:[]I j (τ ) = R 2 I j −1 (τ − ε ) ⋅ 1 + g j −1 (τ ) + is (τ ) (1)g j (τ ) = g 0

σ0
e
σj

⎛ σ 2 −σ 2 ⎞
0 ⎟
⎜− j
⎜
2σ 02 ⎟⎠⎝e⎛
τ 2 ⎞⎟⎜−⎜ 2σ⎟t, j ⎠⎝2ΔT(γI j + σ 02 − σ 2j )τsε = ε + F (t )σ 2j +1 = σ 2j +()⎡ dI t ⎤⎥⎣ dt ⎦F (t ) = A ⋅ ⎢

( 2)
(3)
( 4)
(5)

F (t ) = A1 ⋅ [I (t ) − I (t − Td 1 )] + A2 ⋅ [I (t ) − I (t − Td 2 )] (6)Figure 1: Layout of the storage-ring free-electron laser.
The photon pulse (red) stored in the optical cavity
interacts with the electron bunch (gray), circulating in thestorage ring. The light intensity is acquired using an
optical detector (Det). The resulting signal can beelaborated by an FPGA and used for slightly changing theelectron revolution period (from ΔT to ΔT+ε) by varying
the phase of the radio-frequency cavity (RF) of the ring.
Due to the impulsive character of the laser medium thelaser intensity of a SRFEL is characterized by a sequenceof micropulses whose duration is of the order of tens ofpicoseconds. Moreover its repetition rate is that of

Eq.1 describes the laser intensity at the jth passage
where τ is the temporal position with respect to thecentroid of the electron bunch, R is the cavity mirror
reflectivity, is stands for the spontaneous emission of the
optical klystron, ε accounts for the detuning. The gain
gj(τ) is described by Eq.2 where g0 and σ0 respectively
stand for the initial peak gain and energy spread
respectively, σt,j is the bunch length of the jth interaction.
The energy spread σj is described by Eq.3 where γ is thedifference between equilibrium and initial energy spread,
Ij the normalized laser intensity, ΔT the revolution periodof electrons on the ring and τs the synchrotron damping
time. For a more exhaustive description of the model werefer to Ref. [3].
Eqs.5,6 refers to the control signal F(t) for the case ofderivative and delayed feedbacks. Those signals are used
to modulate the detuning (ε) according to Eq. (4) where t= jΔT.

___________________________________________#

enrico.allaria@elettra.trieste.it356

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Table 1: Parameters used for the simulations of the Elettra
SRFEL.
Ω = 16 kHzστ , j =αΩσjΔT = 216 ns α = 1.6 ⋅10 −3

is = 4.3 ⋅10−7τ s = 86 ms

R = R1 ⋅ R2 = 0.96

γ = σ e2 − σ 02

σe

σ0

≈ 1.3

ε = ε 0 + δε ⋅ sin (2πνt ) ν = 50 Hz

The above model provides an ideal setting toinvestigate possible strategies for the stabilization of the
SRFEL dynamics. The signal proportional to the laser
output intensity extracted from the optical detector (Det in
Fig.1) can be instrumental to the control of the systemthrough dedicated feedback algorithms (Eqs. 4-6). Moreprecisely, this signal can be used ad hoc to modify theelectron revolution period (from ΔT to ΔT+ε) through the
RF cavity of the ring (Fig.1).

Detuning and noise effects on SRFEL dynamics
By using the above model one can investigate the roleof both the detuning and the external periodic noise
modulation on the SRFEL dynamics.
Here we numerically simulate the Elettra SRFEL byusing the model (Eq.1-3) assuming the values reported in
Tab.1. We first assume an ideal case and neglect theexternal noise modulation at 50 Hz. In order tocharacterize the effect of a simple detuning ε0 on the
SRFEL dynamics, the bifurcations diagram of the laser
output intensity (I) vs the detuning value (ε0) has beenreconstructed. Bifurcation diagrams are obtained byplotting the values of the laser intensity maxima andminima when dynamically varying the value of thephoton-bunch detuning ε0. In order to free our resultsfrom hysteresis effect we perform the scan bothincreasing and decreasing the values of ε0.
Fig.2 (black curve) displays the results for the case of anon modulated detuning ε0.

TUPPH020

intensity decreases up to a second transition point (ε0 =0.18fs). For larger detuning values the SRFEL achieves
again a stable regime which falls outside the region
considered in the subsequent analysis [4].
Results are instead different if one accounts for thepresence of the external periodic noise signal. In Fig.2(red curve) we report the bifurcation diagram of the
SRFEL intensity vs the detuning value (ε0) for a choice ofthe parameters which corresponds to the case of theElettra SRFEL, i.e. δε0 = 0.18fs [3]. The used value forthe noise strength is sufficient to destroy the initial (i.e.
small detuning) steady state region and the bifurcation
diagram now shows a cascade of transitions between
periodic and chaotic behaviors. However, depending on
the detuning value, there exists regions where the laser isalways turned on.
In the following we shall consider the Elettra SRFEL to
be represented by the model of Eq.s1-3 with ε0 and δεrespectively equal to 0.5fs and 0.18fs [10].

CONTROL ALGORITHMS
The sensitivity of the system to the detuning ε can be
exploited to implement a feedback system. A signal
proportional to the laser can be used as an input in a
feedback loop in order to control the system. To this aim
an appropriate change to the electron revolution period isapplied through the RF cavity of the ring (Fig.1, Eqs.1-6).
Recently, encouraging experimental results have beenreported for a derivative feedback based on a low-passfilter [5]. In the near future we plan to implement a moresophisticated feedback system, exploiting the intrinsic
flexibility of a FPGA to design innovative control
algorithm. In the following we shall provide a first
theoretical insight into this issue by comparing a digitalderivative feedback (Fig.3,4) and a digital delayed
feedback.

Derivative feedback
A derivative feedback enables to reduce the chaotic
oscillations of the SRFEL dynamics.

Figure 2: Bifurcation diagram of SRFEL intensity withrespect of the detuning parameter ε0. Black curve refers to
the case without external perturbation of the detuning
parameter (δε = 0, see table 1). Red points refers to thecase where also an external periodic perturbation ispresent (δε = 0.18fs).
Results clearly show the presence of a steady state
regime up to a detuning value of about 0.12fs where thetransition to a pulsed regime occurs. Starting from ε0 =0.12fs, the laser is characterized by high-intensity shortpulses followed by long periods where the laser is off. If
the detuning is further increased, the peak of the laser
FEL Oscillators and Long Wavelength FELs

4

4

3

3

2

2

0.1

0.1

6
5
4

6
5
4

3

3

2

2

0.01

0.01
0.00

0.05

0.10

0.15

0.20

0.00

0.05

0.10

0.15

0.20

Figure 3: Time trace of the Elettra SRFEL showing theeffect of the digital derivative feedback. a) Unstablebehavior of the Elettra SRFEL. b) Controlled regime.
As appear evident from inspection of the experimental
data reported in Fig.3, the digital derivative feedback
control is able to prevent the laser to turn off. However, asmall residual modulation at 50Hz is still present together
with higher frequencies spurious contribution. In figure 4
we characterize the transition from the unstable pulsed
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Proceedings of FEL 2006, BESSY, Berlin, Germany

regime to the controlled one as a function of the strengthof the control loop.
2.2

normalized std

2.0
1.8
1.6
1.4
1.2

0

500

1000
1500
2000
derivative gain (a.u)

2500

3000

Figure 4: Transition from uncontrolled (Fig.3a) tocontrolled (Fig.3b) regimes: the normalized standard
deviation of the SRFEL signal is reported as a function of
the strength of the control signal.
One of the limitations of the derivative feedback is thefact that the sign of the controlling signal necessary forthe stabilization of the SRFEL depends on the sign of thedetuning [3]. For that reason in cases where the detuning(ε0) is smaller or comparable to the perturbation of theexternal noise signal (δε), a strong control signal cannot
be employed. Otherwise, the control signal can induce
detuning with the wrong sign and move the system awayfrom the stability.

Delayed feedback
Delay control feedback can avoid the aforementioned
problem because it involves a low correlation between thevalues of the laser intensities used for the calculation of
the control signal.
Such a method consists in applying to the system acontrol signal F(t) described by Eq. (6): the loop gain A
and the delay times Td1,2 are the parameters to be set inorder to stabilize the laser evolution.
Delayed feedbacks have been originally proposed forthe stabilization of unstable periodic orbits of chaotic
oscillators [6]. Recently two different incommensurable
delays has been proposed to be used to obtain thestabilization of a steady state [7]. We further showed thepossibility of using such a strategy in a SRFEL [8]. We
are here interested in testing the robustness of the method
to small fluctuations of SRFEL and/or algorithm
parameters.
Figure 5 analyzes the performances of the method as afunction of the two delay times. Results clearly show theexistence of a region (blue) where the standard deviationof the signal has been strongly reduced (<0.5) thus
pointing to the stabilization of the SRFEL signal. It is
important to emphasize that those regions are located out
from the diagonal which in turn enables one to conclude
that at least two delays are necessary for the method toeffectively work.
The possibility, and advantages, of using additional
delay times should be addressed [9]. The robustness of the
proposed method has been verified with respect of thevariation of several input parameters.

358

Figure 5: Color-scale plot of the standard deviation of the
SRFEL output as a function of the delays used in the twodelay lines of the control algorithm (A=1.9e-6). The plots
clearly show the advantage of using two delays withrespect to one (diagonal).
Numerical simulations indicate that the stable region(blue in Fig.4) is maintained when the input parameters(loop gain A, noise frequency and amplitude, electronphotons detuning …) are changed, as one would expect tooccur in experimental conditions. This is a crucial
observation in view of possible experimental realizations.

COMPARISON BETWEEN DERIVATIVE
AND DELAYED FEEDBACK
In order to compare the performance of the delayed
control algorithm and the derivative one we numericallytested both methods as a function of the strength of theexternal noise signal.
Figure 6 show the behavior of the SRFEL with
ε0=0.05fs as a function of the noise strength (δε). The
pulsed chaotic dynamics, which is usual for the Elettra
SRFEL, is evident from the large range of fluctuation of
the laser maxima for δε in the range 0.15-0.20fs.

Figure 6: Bifurcation diagram of the SRFEL intensity as afunction of the external noise modulation strength (δε).
A proper setting of the derivative feedback [3] allows tostabilize the dynamics of the SRFEL in the region ofδε ∈ (0.15-0.20fs) which is characteristic of the Elettra
SRFEL. However, for larger values of δε the dynamics
remains chaotic (Fig.7).

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TUPPH020

without facing the risk of producing opposite effects,
reported instead for the case of the derivative feedback.

CONCLUSIONS

Figure 7: Bifurcation diagram of the SRFEL intensitywith the use of the derivative feedback set for thestabilization (A=3.0e-2) of the unstable oscillations
around the δε = 0.18fs case.
As clearly shown in figures 6,7,8 a dual delay
algorithm results in a better stabilization of the SRFEL
dynamics over a larger range of δε.

We presented a reliable model for the investigation ofboth detuned and noisy regimes in a SRFEL. The model
has been applied to testing possible feedback algorithm tobe developed with a FPGA. Preliminary experimental
results have been reported concerning the stabilization of
the Elettra SRFEL trough a digital derivative feedback. A
proposed feedback method based on delayed signal has
been presented and numerically investigated. The
comparison of the delayed method with the derivative one
shows the advantages of the former in terms of achieved
stability and robustness to noise.
On the basis of these encouraging results, theexperimental implementation of the delayed feedback
control on the Elettra SRFEL is planned for the near
future.

REFERENCES
Figure 8: Bifurcation diagram of the SRFEL intensitywith the use of the dual delay feedback set for thestabilization (A=1.9e-6, Td1= 3.11ms, Td2=4.24 ms ) of theunstable oscillations around the δε = 0.18fs case.
Although the ultimate goal of obtaining a perfect steadystate regime is beyond current possibilities, both methods
are capable to stabilize the laser intensity for a large
window of values of the noise strength δε, a crucial
quantity responsible for undesidered oscillations arisingin the uncontrolled case (Fig. 6). A comparison between
the proposed two methods in terms of extension of theallowed range of the noise strengthshow that the approachbased on the multidelay performs better. This conclusion
applies also as concerns the amplitude of the residual
oscillations.
As previously anticipated, the reason for the above
success is to be ascribed to the fact that the low
correlation between delayed values in the case of chaotic
signal allows us to implement a strong control term

FEL Oscillators and Long Wavelength FELs

[1] M. Billardon et al., Phys. Rev. Lett. 69, 2368 (1992).
[2] S. Bielawski et al., Phys. Rev. A, 47, 3276 (1993).
[3] G. De Ninno et al., Phys. Rev. E 71, 066504 (2005)[4] M.E. Couprie et al., Phys. Rev. E. 53, 1871 (1996).
[5] S. Bielawski et al., Phys. Rev. E, 69, 045502 (2004).
[6] K. Pyragas, Physics Letters A, 170, 421-428 (1992).
[7] A. Ahlborn and U. Parlitz, Phys. Rev. Lett. 93,
264101 (2004).
[8] E. Allaria et al., FEL05, JACoW/eConf C0508213,
THPP005 (2005)[9] Work in preparation.
[10] In the case of Elettra a detuning of 0.4fs correspondto a variation of 1Hz of the 500MHz RF frequency
which is the limit of the accuracy of the instrument.
Moreover to the time jitter of the master oscillator,that depending of the working conditions can be of
the order of 1ps, can be associated a detuning of
0.02fs if we simplify the jitter to a 50Hz signal.

359

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Q-SWITCH TECHNIQUES IMPLEMENTED AT THE ELETTRA
STORAGE-RING FREE-ELECTRON LASER
F. Curbis∗ , M. B. Danailov, B. Diviacco, L. Romanzin, M. Trovò, G. De Ninno
Elettra, Basovizza, Trieste, Italy.
Abstract
In a Storage-Ring Free-Electron Laser (SRFEL) giant
pulses can be produced by the interaction between the light
stored in the optical cavity and an electron beam with low
energy-spread (cold beam). This interplay produces theheating of the beam. After the generation of a single giant pulse the overlap between electrons and radiation isperiodically prevented for a time necessary to dump theenergy spread and recover the cold-beam condition. Two
different methods are now implemented at Elettra for giant pulse generation. In the first, by modifying the radiofrequency of the ring, a change of the revolution time ofelectrons is induced. This avoids the temporal overlap between the electron beam and the optical field in the mirror
cavity. The second method relies on a mechanical gating(chopper) which intercepts the light produced during previous interactions, inducing a periodic depletion of the optical cavity. The giant-pulses repetition rate is determinedby the periodicity of the radio-frequency changes and therotating velocity of the chopper, respectively. In this paper
we compare the different techniques mentioned above forthe case of the Elettra SRFEL.

INTRODUCTION
The customary layout of a Free-Electron Laser (FEL)in oscillator configuration takes advantage of an optical
klystron. This magnetic structure is made up of two undulators and a dispersive section in between (see Figure 1).
In the small gain case [1], which is indeed the oscillatorcase, the strong magnetic field of the dispersive section induces a delay between the radiation emitted in the first andin the second undulator. In comparison to the light the electrons spend longer time to pass through a magnetic chicane
and, once in the the second undulator, their emission will
have a different phase with respect to the light emitted formerly. This delay produces a constructive interference ofradiation, changing the optical klystron spectrum in a more
spiky structure and enhances the FEL process because its
gain is proportional to the derivative of this interference
structure. The other main component of an oscillator FEL
is the optical cavity, composed by two mirrors on axis withthe two undulators and the dispersive section, as depicted
in Figure 1.
In the normal operational mode of a storage-ring FEL
in oscillator configuration, the light emitted has a temporal structure depending on the ring filling and each pulse∗ francesca.curbis@elettra.trieste.it

360

dispersive section
radiatorcavity mirror

modulator

extractedlight

FEL light
radio-frequency

cavity mirror

electron bunch

Figure 1: Layout of the Elettra storage-ring FEL in oscillator configuration.
has a quite low power. When the electron beam interacts
with the light stored in the optical cavity, emitting coherently, its energy spread grows up. This effect, called beam“heating”, limits the maximum power achievable, because
the gain is proportional to the electron density. Between
the generation of two consecutive giant pulses it is necessary to wait few synchrotron damping times, this allows to
restore the cold beam condition. In this period of time, infact, if the light-electron interaction is prevented, the beamenergy spread decreases to the initial value.
Several methods have been studied and applied in oscillator FELs [2, 3, 4, 5] to create “giant pulses”. There arebasically three techniques that have been implemented:• the gain modulation [6];• the modulation of RF frequency [4, 5];• the mechanical gating (chopper).
The first method is presently employed at Duke, wherea dedicated magnet steers the electron beam orbit in thetransverse direction. When the electron beam orbit is offaxis with respect to the optical cavity, the lasing is stopped
and the electron beam can cool down. Once the electron
beam orbit returns on-axis, a new giant pulse starts. The RF
frequency modulation has been used in Super-ACO and iscurrently implemented at Elettra and UVSOR. This technique may excite synchrotron oscillations of the electron
beam, or enhance them if already present. The induced oscillations can reduce the net gain at the laser start. While
the first two techniques can be considered equivalent for
generating giant pulses (as demonstrated for Duke in [7]),the mechanical gating is still under investigation.
The purpose of the Q-switch technique is twofold: toconcentrate the average power of storage-ring FEL in a series of giant-pulses and to have a regular temporal dynamics of the light. This allows to use the light emitted forexperiments, for example synchronizing an external trigger
which drives the giant pulse repetition rate [8]. Besides, it

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany
is well known that the FEL light at the fundamental wavelength, which is reflected by the mirrors of the optical cavity, produces higher harmonics [9]. These harmonics survive just for a single pass in the optical cavity, because themirrors do not reflect light with their wavelength. In normal
operation mode the power of higher harmonics, which depends on the fundamental power, is too low to be detected.
Giant pulse production is therefore a suitable way to enhance the fundamental power and accordingly the higher
harmonic power. One example of harmonic generation incavity is reported in Figure 2.

Intensity (arb.units)x10

fundamental 660nm

3

-100

0

100

rd

harmonic 220nm

200

300x10TUPPH021

the system is detuned the lasing process is stopped. An external signal source induces the detuning and modifies theslope and the amplitude of the RF frequency jump. The detuned condition is maintained for few synchrotron damping
times to allow the electron beam to cool down and the gainof the amplification process to recover its initial (i.e. laseroff) maximum value. Once this situation is reached, thesystem is led back to the perfect tuning condition which ismaintained for a long enough time (order of dozens of milliseconds) to induce the onset of the laser giant pulse. Thenthe system is detuned again and the process repeated.
The main advantage of this technique is the fast transition time. The RF modulation is driven by a signal generator, therefore one can choose the slope of the signal to reachthe maximum power. The unfavorable aspect is the beam
perturbation caused by the RF modulation. The damping
is regulated by the synchrotron frequency. Figure 3 showsa streak camera image of the synchrotron radiation and the
FEL signal.

-6time (s)Figure 2: The fundamental (660 nm) and the third harmonic (220 nm) giant pulses. The harmonic signal is abouta factor 25 above spontaneous emission.
The giant-pulse risetime provides also an estimation of
the initial FEL gain. Between each pulse the electron beamis restored and when the giant pulse starts the only negative effect is due to the optical cavity losses. This allows
to calculate the net gain of the FEL process, if the mirror
reflectivity is known.

TWO DIFFERENT EXPERIMENTALTECHNIQUES

Figure 3: Streak-camera image of the electron beam (lefttrace) and of the FEL pulse (right trace) in Q-switch operation mode.

In this section, we concentrate on the two techniques
used at Elettra for the giant pulse generation, i.e., the RF
frequency modulation and the Q-switch with the chopper.

Along the vertical axis of the picture, the evolution intime of the distribution profile is reported and one can also
see the excitation of synchrotron oscillation starting before
the laser. The analysis in Figure 4 also shows the electron
beam heating that begins before the giant pulse start.

RF frequency modulation

Q-switch with chopper

In a storage-ring FEL, in order to obtain the synchronization between the electron beam and the light stored in
the optical cavity, the mirrors are placed at inter-bunch distance. Stepper or piezo-electric motors provide the finetuning of the mirror position along the undulator axis. If
the RF frequency of the storage ring changes the revolution time of electrons changes as well, causing the loss ofsynchronization with the optical filed in the cavity. Without temporal overlap the electrons do not interact with theradiation stored in the optical cavity and then the energy
spread of the beam can decrease. The RF frequency modulation is based on a periodic detuning between the electron
beam and the radiation stored into the optical cavity. WhenIn the Elettra storage-ring FEL a mechanical gating has
been recently introduced in the optical cavity. This object,called chopper, is a molybdenum disc with a 115 mm radius with a little aperture positioned close to the border(see Figures 5). When the aperture is on-axis with the optical cavity the light stored can pass, otherwise the radiation
is intercepted by the disc. The chopper is placed near theback mirror (see Figure 6) and rotates at constant speed,
moved by a PHYTRON UHV stepper motor.
The rotating velocity determines the repetition rate of the
Q-switch.
Generally speaking, when the electron beam interacts
with the laser pulse (stored into the cavity) its longitudi-

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 7: Pictures of the chopper during the installation.

Figure 4: Analysis of the streak camera image in Figure 3.
The longitudinal distributions are obtained by means of ahorizontal cut of the picture.

the latter can be used as a clock for cross-correlation measurement in order to characterize the harmonic signal.
A summary of the peculiarities of both methods is reported in Table 1.
Table 1: Chopper versus RF modulation
chopper advantages
RF advantages
no beam perturbation
fast transition time
chopper disadvantages RF disadvantages
longer transition time
beam perturbation

Figure 5: Left: schematic design of the metallic disc.
Right: Preliminary studies in air.

nal dimensions grow up and the resulting energy spread
reduces the FEL gain. The chopper allows the giant pulse
creation because it prevents the electron-light interaction
for a suitable time so that the energy spread reduces. Thismethod does not generate beam perturbations and, as a consequence, higher power in the giant pulses is expected.
At the present the chopper technique can achieve only
a limited repetition rate if compared to the RF modulation. Nevetheless we expect in the near future to operate thechopper at frequencies of 5 Hz or more. Furthermore, since
the chopper Q-switch does not involve the RF frequency,

Measurements and results
To compare the RF frequency modulation and the chopper Q-switch techniques, a campaign of measurement has
been recently carried out using the Elettra SRFEL. Figure 8 and Figure 9 show preliminary risetime measurements for the RF modulation and the chopper case, respectively. The pictures report a train of giant pulses obtainedat the same current and repetition rate. While the RF modulation method displays a quite constant level of the signal,
the chopper exhibits an irregular behaviour. The reason isstill under investigation.

Figure 8: Sequence of 20 giant pulses, acquired by a fast
photodiode, generated using the RF modulation. The electron beam current is about 10 mA and the repetition rate is
1.5 HzFigure 6: Schematic layout of the chopper chamber (atright), near the mirror chamber (at left).

362

In Figure 10 we compare the two techniques for the 3 Hz
case: the giant pulse risetime, calculated as a mean of 20
signals, is displayed as function of the total beam current.

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH021100
98chopperrisetime (us)73 Hz
1.5 Hz
2 Hz

6
5
4
3

2

0

2

4

6

8
10
current (mA)

12

14

16

Figure 12: Efficiency of the Q-switch at different repetition
rates using chopper.
Figure 9: Sequence of 20 giant pulses, acquired by a fast
photodiode, generated using the chopper Q-switch. The
electron beam current is about 10 mA and the repetition
rate is 1.5 Hz

For high currents the chopper and RF modulation seemcomparable, while at medium-currents the chopper risetime is quite longer.

The preliminary results presented here show the capability of the chopper method to generate giant pulses. This
technique, although promising, needs more development inorder to reach, and hopefully improve, the performance of
the RF modulation method in terms of reproducibility andhigher repetition rate.

REFERENCES

100
9
8

3Hz

7

[1] J. M. J. Madey, J. Appl. Phys. 42, 1906 (1971).

chopper
RF modulation

6

risetime (us)CONCLUSIONS

54[2] G. N. Kulipanov, et al., Nucl. Instr. and Meth. A 296 (1990)
1.
[3] V. N. Litvinenko, et al., Nucl. Instr. and Meth. A 429 (1999)
151.

3

2

[4] T. Hara, et al., Nucl. Instr. and Meth. A 431 (1994) 21.
0

2

4

6

8
10
current (mA)

12

14

16

[5] G. De Ninno, et al., Nucl. Instr. and Meth. A 528 (2004) 278.
[6] I. V. Pinayev, et al., Nucl. Instr. and Meth. A 475 (2001) 222.

Figure 10: Comparison between chopper and RF modulation techniques, showing the risetime as a function of thetotal current at the same operational frequency (3Hz).

[7] G. De Ninno, et al., Elettra Internal Note.
[8] M. Amati, et al., these proceedings.
[9] V. N. Litvinenko, Nucl. Instr. and Meth. A 507 (2003) 265.

Figure 11 and Figure 12 report the risetime versus current for the RF modulation and for the chopper technique
respectively. These data do not show any strong dependence of the risetime on the repetition rate.
100
98

RF modulation

73 Hz
1.5 Hz5 Hz

risetime (us)

6
5
4
3

2

0

2

4

6

8
10
current (mA)

12

14

16

Figure 11: Efficiency of the Q-switch at different repetition
rates using RF frequency modulation.

FEL Oscillators and Long Wavelength FELs

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Proceedings of FEL 2006, BESSY, Berlin, Germany

DEVELOPMENT OF A COMPACT CHERENKOV FREE-ELECTRONLASER IN TERAHERTZ SPECTRAL RANGE
M. R. Asakawa∗1 , K. Nakao2 , N. Miyabe1 , M. Kusaba2 and Y. Tsunawaki2 ,1Kansai University, Suita, Osaka, Japan ,2
Osaka Sangyo University, Daito, Osaka, Japan .
Abstract
A Cherenkov free-electron laser (CFEL) generating terahertz radiation is now being developed under the joint research of Osaka Sangyo university and Kansai university.
The main feature of the CFEL is its compactness. Microbeamlets from Spindt-type ﬁeld emitter array are accelerated up to 50 keV and then injected into a silicon resonatorwith a path of 50 to 150 μ m spacing through which electrons propagate. Omitting the evacuation system and power
supply, the size of CFEL section, including electron gun
and resonator, is about 1 × 1 × 4 cm3 . For the generationand the transport of the electron beam few μm in diameter, we investigated characteristics of the Spindt cathode,beam focusing by electrode and the magnetic ﬁeld. A carbon nanotube ﬁeld emitter was also tested for future application.

INTRODUCTION

Figure 1: Schematic view of compact CFEL.

Cherenkov free-electron lasers (CFELs) are one of thegreat candidates for compact tunable radiation sources. A
pioneer work had demonstrated CFEL in 100 GHz frequency range using an electron beam with 35 to 75 keV
acceleration energy [1]. In order to increase the operation
frequency to terahertz frequency range, it is straightforward
to scale down the optical resonator of CFEL. Fig. 1 showsa schematic view of a compact CFEL. Electron beamlets
several μm in diameter are accelerated to 50 keV and theninjected into a dielectric resonator. Electron beamlets passing through a channel bored in the dielectric resonator excite the Cherenkov radiation and interact with the evanescent part of that radiation.
The resonant frequency is determined principally by theradius of the channel: the resonant wavelength coms toseveralfold of the channel radius. The dispersion curve of
the evanescent wave in a circular dielectric waveguide isshown in ﬁg. 2 with the dispersion of the light in vacuum
and a beam-mode for 40 keV electron [2]. Because electrons moving along the channel transfer its kinetic energy
to the radiation ﬁeld via the interaction with the longitudinal component of the radiation ﬁeld, the TM-mode which
has that ﬁeld component is important in such CFEL. Thus
the dispersion relation for the TM01 -mode is shown in theﬁgure. For the case of Rd =25 μm, the resonant frequency is
1.6THz. Note that the dispersion relations are scalable withthe channel radius, thus the resonant frequency increases

with decreasing the channel radius. CFELs are, therefore,
capable to be operated in mid-infrared to sub-millimeter
spectral range.
Our research aims a compact, more ambitiously, palmtop
CFEL that can generate the radiation over the infrared spectral area. As the ﬁrst step, we are developing the electron
beam source which can produce μm beamlets. In following
section, a CFEL test bench and experimental studies of thebeam focusing will be described.

CFEL TEST BENCH
To produce the electron beam whose radius is orderof micrometer, we used a Spindt cathode,[3] which contains 100,000 pairs of ultrasmall needles and gate electrodes in a 1 mm diameter array. Each pair of needle andelectrode generate electron beamlet with diameter around
1 μm, and these tiny electron guns are arrayed with a spacing of 10 μm. Due to the needle-gate conﬁguration and thehigh operation current density, Spindt cathode generates adiverging beam as shown in ﬁg. 3. Therefore, the beamtransport is the critical issue.
Figure 4 and ﬁg.5 show the schematic view and the picture of a developing CFEL test bench, respectively. Thissystem employs the magnetic ﬁeld for the beam focusing.
Main components, such as Spindt cathode, collector electrode and a optical resonator, are installed inside the bore

∗ asakawa@ipcku.kansai-u.ac.jp364

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Rd /c

Proceedings of FEL 2006, BESSY, Berlin, Germany

Rd kradius (0.1μm)

Figure 2: Dispersion relations of the evanescent wave for
TM01 mode. The relative dielectric constant of the medium
is 10.(red) Both axes are multiplied by the channel radius(Rd =25 μm) for the normalization. The blue solid line
shows the dispersion of 40 keV beam mode. Upper andlower dashed lines denote the dispersion of the light in vacuum and the light in the dielectric medium, respectively.

Figure 4: Schematic view of the CFEL test bench and theresonator. The left and right ﬁgures show the schematic
view of the whole system and the detailed view of the resonator, respectively.

distance (0.1μm)

Figure 3: Calculated trajectories of electrons emitted by
Spindt cathode. Red lines show the electron trajectories
and Blue lines represent the equipotential lines. E-gun code
was used for the calculation.
of a super conducting coil, which can produce magnetic
ﬂux density up to 5 T. The footprint of the whole system
including the compressor unit for super conducting magnet
is about 1 ×1 m2 .
Electron beamlets generated at the grounded Spindt
cathode needles are accelerated toward the collector electrode, which is followed by the optical resonator. The resonator consists of a pair of silicon slabs gapped by thinspacers with thickness of 50, 100 or 150 μm. The resonant frequency increases from several hundreds GHz tofew THz as decreasing the gap spacing. The end edges ofslabs facing to the cathode are coated with Al and work
as both the collector electrode and resonator mirror, while
the other edges are left uncoated to extract Cherenkov radiation. One side of the gap between the slabs facing tocathode is opened for the beam injection, while the otherside is blocked by the spacer for beam dumping and reﬂecting back of a part of radiation. The length of the laserinteraction region is 2 cm.
Figure 6 shows the time trace of the gate voltage andthe beam current. Pulsed voltage up to 100 V is applied
to the gate electrode of Spindt cathode to generate a few

FEL Oscillators and Long Wavelength FELs

Figure 5: Picture of the CFEL test bench. The high voltage
feedthrough, the 2-axis manipulator for resonator alignment and cryostat of the super conducting coil can be seen.
The height and footprint of the device are 1.9 m (including
a 0.7 m-height pedestal) and 0.7×0.7 m2 , respectively.
milli-amperes beam current. The raise time of 50 μs wasdetermined by the capacitance of the power feed cableand 100 kΩ resistance for current monitoring, and will be
shorten by reducing the resistance in the laser experimentsthat higher beam current will be required. For the operation
above the beam current shown in the ﬁgure, we sufferedfrom the serious degassing and the following brake down.
Such undesirable events were remarkable especially whenthe magnetic ﬁeld was applied. This system is under aging
process.

FOCUSING ELECTRODE
Because the magnetic focusing requires a large and expensive magnet, we also explored beam focusing using
mid-electrode. A mid-electrode was located at a distanceof 13 mm from the cathode. The spacing between the mid-365

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 6: Time trace of the gate voltage (red) and the beam
current (blue). Peak voltage is 50 V and peak current is
81 μA.
electrode and the collector electrode was set to 30 mm.
Mid-electrode had a hole 5 mm in diameter through which
the electrons pass through. The beam spot size at the collector electrode was evaluated from the ﬂuorescence image
on a phosphor screen placed at collector electrode. Figure 7 shows the beam diameters as a function of the midelectrode voltage. The collector electrode voltage was held
at 10 kV during the experiment. The gate voltage was set
to 65 V and the pulse width was 10 ms to obtain luminanceenough to observe. Note that these results show the diameter of the whole beam emitted from 100,000 tiny needles:
the ﬁne structure formed by each beamlet was smoothed
out due to poor resolution of the measurement system. It isseen that the beam diameter decreases with mid-electrodevoltage up to 30 V and then slightly increases with the voltage. It is inferred that the beam is over focused with the
mid-electrode voltage above 30 V. This result indicates thatthe beam focusing by the focusing electrode is not enoughto produce the electron beam with micrometer diameter.
We are on the way to design optimal electrode conﬁguration combined with the magnetic ﬁeld conﬁguration to ﬁnd
the reasonable focusing system.

CARBON NANOTUBE CATHODE
To develop the brighter electron beam source, we also
tested a carbon nanotube cathode. As this test is a preliminary one: powdered carbon nanotubes were smeared
over a 0.5 mm diameter plate of stainless steel and the gateelectrode was not installed. Due to the lack of the gateelectrode, the spacing between the cathode and the collector electrode was set to 0.2 mm to produce electric ﬁeld
enough for the ﬁeld emission. Figure 8 shows the beam
current vs. the collector electrode voltage. Electron emission stars at a voltage of 2.2kV and the current reaches to
2.4mA at 4.4 kV. Above 4.4 kV acceleration voltage, se-366

Figure 7: Beam diameter as a function of the mid-electrodevoltage. During experiment, the collector voltage was held
at 10 kV and pulsed 65 V voltage was applied to the gateelectrode of Spindt cathode.
rious outgassing degraded the vacuum condition, thus welimited the supply voltage to this extent. It is worth tomention that the beam current was stable for long periodof these experiment in spite of D.C. operation. Taking into
account the fact that operation of Spindt cathode with D.C.
1 mA leads serious damage on Spindt cathode, we conclude
that carbon nanotube cathodes are capable of generating
denser electron beam. Installation of the gate electrode is
the key issue for practical application.

Figure 8: V-I curve for carbon nanotube cathode. D.C. voltage up to 4.4 kV was applied to the collector electrode.

SUMMARY AND RESEARCH PLAN
A compact THz CFEL driven by 50 keV electron beam
is under development. Use of Spindt cathode and focusing of the electron beam are key technologies of this device. A CFEL test bench using super conducting coil forbeam focusing was commissioned and is under conditioning. Beam focusing by mid-electrode was also studied. To

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Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH022

ﬁnd the reasonable focusing system, we are investigating
the beam focusing by the combination of the magnetic ﬁeld
and mid-electrode. First CFEL test will be started using
high magnetic ﬁeld up to 5 T after the aging conditioningof the test bench. The output frequency will be gradually
increased from several hundreds GHz to few THz by reducing the gap spacing of the resonator. It is also planned
to study Smith-Percell FEL and Cyclotron radiator on thetest bench.

REFERENCES[1] E. E. Fisch and J. E. Walsh: ”Operation of the sapphire
Cerenkov laser”, Applied Physics Letter, Vol.60, No.11,
pp.1298-1300 (1992).
[2] H.P. Freund and A. K. Ganguly: ”Nonlinear analysis of theCherenkov maser”, Physics of Fluids B2, No.10, pp.25062515 (1990)[3] K. Mima, S. Nakai, T. Taguchi, N. Ohigashi, Y. Tsunawaki,
K. Imasaki , C. Yamanaka and M. Shiho: “ A new FEL concept driven by a vacuum microﬁelf emitter ”, Nuclear Instruments and Methods in Physics Research SectionA, vol.331,
pp.550-553 (1993).

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HIGH POWER DEEP UV LASING ON THE UVSOR-II STORAGE RING
FEL
M. Hosaka, M. Katoh, A. Mochihashi, M. Shimada, UVSOR Facility, Institute for Molecular
Science, 38 Myodaiji-cho, Okazaki, Aichi 444-8585, Japan
Y. Takashima, Graduate School of Engineering, Nagoya University,Furo-cho, Chikusa, Nagoya,
Aichi 464-8603, Japan
T. Hara, RIKEN/SPring8 1-1-1 Kouto, Mikazuki, Hyogo 679-5148, Japan
Table 1: Basic parameters of previous/present rf cavity

Abstract
Thanks to a recent upgrade of the UVSOR-II storage
ring (lower beam emittance and higher peak current), an
FEL gain has been enhanced much and we havesucceeded in high power lasing in deep UV region. The
highest extracted CW power so far is 0.25 W atwavelength of 215 nm and 1.1 W at 230 nm. Because ofits variable wavelength even in deep UV region, highpower and good coherence, the UVSOR-II FEL has cometo be recognized as a useful tool by users inside andoutside Institute for Molecular Science. Now UVSOR-II
FEL has four users groups ( solid state physics, surface
physics, bio-moleculer science). Three different kinds ofexperiments have been successfully carried out in thisyear.

INTRODUCTION
On the UVSOR storage ring, a free electron laser has
been developed as a new light source since early 1990s.
In 1996, a helical optical klystron was installed and theperformance of the FEL was improved much because of asmaller degradation of cavity mirrors and a higher FEL
gain. Then the shortest wavelength (239 nm) of thestorage ring FEL at that time was achieved [1].
Recently the storage ring was upgraded and the qualityof the electron beam was much improved. With theincreased FEL gain, a FEL lasing in shorter wavelength
was expected, where more potential users exist. Here we
report on an FEL experiment in the deep UV region at
UVSOR-II aiming users application. The FEL shouldhave enough power in addition to a good optical quality
for application experiments. We also report recent
upgrade of an rf accelerating cavity system, which plays
an important role in the short wavelength lasing.
.

Frequency
Cavity voltage
Shunt
impedance
Unloaded Q
Coupling
Structure
Inner diameter
Bore radius
Material
Tuner

Previous
90.1 MHz
55 kV
1 MΩ

Present
90.1 MHz150 kV2.45 MΩ

8370
1.75
Re-entrant ×11000 mm
50 mm
SUS + Cu
Plunge×1

20300
1.34
Re-entrant×1
964 mm55 mm
Cu (OFHC)
Plunger ×2

rf accelerating voltage (55 kV at maximum) was limited
by low shunt impedance ( 1 MΩ) of the former cavity.
Hence the new rf cavity was designed to have higher
shunt impedance. Table 1 shows basic parameters ofprevious/present rf cavity. The new cavity was installed in
the spring of 2005 and the high cavity voltage of 150 kV
was achieved. With the new cavity system, observed
Touschek beam lifetime was increased by a factor of 3.
This upgrade is also favourable to the FEL because
higher accelerating voltage leads to shorter electron bunchand higher peak current.

UPGRADE OF RF CAVITY SYSTEM
In 2003, the UVSOR storage ring was reconstructed
toward a lower emittance ring; we call it “UVSOR-II”
after the reconstruction [2]. The chief aim of this upgrade
is to provide users with brighter synchrotron radiation. We
still continue the upgrade of the ring. We replaced rf
accelerating cavity system in 2005 [3]. The aim is toimprove lifetime of the electron beam with higher
accelerating voltage. At the UVSOR, 90.1 MHz rf cavity
had been operated with a 20 kW transmitter but the368

Figure 1: Natural bunch length in various rf voltage. The
data points are measured values and the solid line iscalculated bunch length.

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 2: Typical FEL line spectra measured by changing
gap width of the optical klystron. The resolution of thespectra is limited by that of the monochrometer used in
the measurement.
Fig. 1 shows measured bunch length by using a streak
camera after installing the new rf cavity. The bunch length
at a cavity voltage of 150 kV is 67 psec; this value is
60 % of the previous one (110 psec). In this case FEL
gain increased by a factor of 1.6 is expected. This leads
the FEL lasing in the deep UV region where higher FEL
gain is needed.

LASING AROUND 215 nm
We have planned an FEL lasing around 215 nm
basically aiming to an user experiment. In the experiment,
samples of bio-molecules are irradiated by a laser with thewavelength around 215 nm, where the absorption
spectrum of the sample has a peak. The laser should haveenough power in order to proceed the irradiation
experiment quickly; otherwise the sample may be easily
effected by bacteria.
In former UV lasing experiments at the UVSOR, multilayers of HfO2/SiO2 had been employed for cavity mirrors.
In a lasing experiment around 215 nm, the multi-layer can
not be employed because the band gap energy of HfO2 isabout 5.6 eV (220 nm in a light wavelength) and a strong
absorption is expected. Then we chose multi-layers of
Al2O3/SiO2; the band gap energy of Al2O3 is well above
the laser photon energy requested. Since refraction indexof Al2O3 is smaller than HfO2, number of layers should be
increased to attain reflectivity sufficiently high for lasing.
On the other hand, transmission of a mirror becomes
smaller and a less power is extracted through the mirror
as increasing number of layers.
Compromisingreflectivity and transmission, we chose number of layer of
49 for downstream mirror and 37 for upstream mirror
from which an FEL power is extracted. The expectedround-trip reflectivity of the optical cavity is 99.3 % andthe transmission of the upstream mirror is 0.5 %.
Preparatory to the lasing experiment, we measured theround-trip reflectivity of the mirrors by ring-down methodwith a low electron beam current (~ 0.1 mA). TheFEL Oscillators and Long Wavelength FELs

TUPPH023

Figure 3: Measured extracted FEL power as a functionof beam current at energy of 600 MeV and 750 MeV. Thelines are guides to eyes.
measured value was around 97.8 %, which was muchsmaller than the expected one. We suppose that the low
reflectivity came from a degradation of the mirrors due tosynchrotron radiation during reflectivity measurement.
The mirrors degradation, however, seemed to stop after
the first irradiation by synchrotron radiation. Even after
exposure to SR of more than 1000 mA h during the lasing
experiment, we did not observe the essential change ofthe reflectivity.
The lasing experiment was started with an electronenergy of 600 MeV, with which UVSOR FEL experiment
had been made so far. The storage ring was operated in
two bunch mode with equal bunch spacing. As seen in Fig.
2. lasing from 214 nm to 218 nm was successfully
obtained changing a gap width of the helical optical
klystron. In Fig. 3, extracted laser power is plotted as afunction of a stored beam current in the storage ring. The
threshold beam current for lasing was 11 mA/bunch. The
calculated FEL gain at a beam current of 11 mA/bunch isabout 2.3 %. This value is very consistent with themeasured cavity loss of 2.2 %.
As a next step of the lasing experiment, we raised theelectron energy from 600 MeV to 750 MeV, with which
the storage ring is operated for SR use. According to theRenieri limit [4], the extracted FEL power is proportional
to the total synchrotron radiation power per turn fromelectron beam. Since the total radiation power is
proportional to the 4th power of the electron energy,
higher extracted laser power is expected at 750 MeV.
Storing a rather high beam current in the storage ring, wehave obtained successful lasing at this electron energy forthe first time on UVSOR-FEL. The measured thresholdcurrent for lasing is about 2 times higher than that in thecase of 600 MeV. But a higher laser power is extracted as
is expected. The extracted FEL power at 750 MeV isabout 1.6 times of that at 600 MeV at a beam current of
70 mA/bunch, that is well above the threshold current.
This relation is consistent with that of synchrotron
radiation power; the total synchrotron radiation power

369

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 4: Extracted FEL power and beam current as a function of time. The FEL wavelength is around 230
nm. The maximum FEL power was 1.1 W.
from an electron at 750 MeV is about 2.4 times of that at
600 MeV. The higher electron energy has anotheradvantage. The higher operating energy suppress
Touschek effect, by which electron beam lifetime of
UVSOR-II is limited. In the experiment at 750 MeV, weobserved about three times longer lifetime, which resulted
in longer lasing time for users experiment.

spectroscopy. The FEL extracted from the upstream
mirror was transported to the experimental stations byusing aluminium mirrors and was focused on samples bylenses. In the experiments, they started the measurement
after the laser became stable. The FEL power around 0.5~ 0.2 W was actually applied. Although the experiments
were made in limited machine time, the users succeededin obtaining primary results.

LASING AROUND 230 nm
Similar to the case of 215 nm-FEL, the lasing around230 nm was planned oriented to users experiments. In thelasing experiment, multi-layers of Al2O3/SiO2 were also
employed for cavity mirrors. Measured round-trip
reflectivity and transmission were 98.8 % and 0.8%,
respectively. Therefore the optical characteristics ofmirrors is advantageous for the FEL lasing as comparedwith mirror of 215 nm. The lasing experiment was carriedout with an electron energy of 750 MeV. Fig 3 shows theextracted FEL power and the stored electron beam current
as a function of time after the electron beam is stored. As
is expected, higher extracted laser power was obtained
and the observed maximum power reached 1.1 W at abeam current of 100 mA/bunch. During the experiment,
drift of the laser power was observed especially at a highbeam current as shown in the figure. The power could berecovered by adjusting the alignment with downstream
mirror once again. Therefore the power drift can be
explained by deformation of the cavity mirror due to heatload from synchrotron radiation and from the FEL. The
laser, however, became almost stable after about one hour
exposure of synchrotron radiation.
The FEL around 230 nm was applied to two
experiments on surface physics and photo-electron

370

CONCLUSION
We have succeeded in high power FEL lasing in deep
UV around 215 nm and 230 nm. Users experiments of the
FEL were carried out and primary results were obtained.
The stability of the laser at the source position and also at
the experimental station should be improved. Suppressionof the thermal deformation of the cavity mirror andstability of the laser transport system are critical issues.
We are going to lasing below 200 nm in near future. The
shorter wavelength FEL is desired for the photo-electron
spectroscopy experiment.

REFERENCES[1] H. Hama et. al., Free Electron laser and its
Applications in Asia, (1997) 17.
[2] M. Katoh et. al. Nucl. Instru. and Meth. A467 (2001)
68.
[3] A. Mochihasi et. al., UVSOR Activity Report 2004
(2005) 35. A. Mochihashi et. al., UVSOR Acitivity
Report 2005 (2006) 37.
[4] A. Renieri, Nuovo Cimento, 53 (1979) 160.

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH024

SUPER COHERENT THZ LIGHT SOURCE BASED ON AN ISOCHRONOUS
RING WITH VERY SHORT ELECTRON BUNCHES*
T. Tanaka#, T. Muto, F. Hinode, M. Kawai, K. Nanbu, K. Kasamsook, K. Akiyama, M. Yasuda and
H. Hama, Laboratory of Nuclear Science, Tohoku University, 1-2-1 Mikamine,
Taihaku-ku, Sendai, 982-0826, Japan
H. Tanaka, JASRI/Spring-8, 1-1-1 Koto, Sayo-cho Sayo-gun,
Hyogo- pref. 679-5198, Japan
Abstract
A project to develop a coherent Teraherz (THz) lightsource has been progressed at Laboratory of Nuclear
Science, Tohoku University. The coherent synchrotron
light in the THz region is emitted from electron buncheswith very short bunch less than 100 fs (rms) created by athermionic RF gun and a sophisticated bunch compressor.
The beam can circulate through the nearly complete
isochronous ring for many turns, so that the averageradiation power may be considerably enhanced. As an
injector of this ring, we have developed an independently
tunable cells (ITC) RF gun, which consists of two
independent cavities to manipulate the longitudinal phasespace. In order to generate short bunch with a significant
bunch charge, a magnetic compressor is needed atdownstream of ITC-RF gun. Two kinds of bunch
compressor have been studied. This paper presents theisochronous THz ring design and describes ITC-RF gun,the magnetic bunch compressor and results of simulations.
From simulation of the bunch compressor, we got a very
short bunch length about 42 fs (rms).

INTRODUCTION
In these years, the coherent radiation in THz region has
been observed in some 3rd generation light sources like
BESSY-II [1]. However, it seems to be difficult on thestorage ring to realize and/or maintain the short bunchwith a significant beam current against bunch lengtheningor other instabilities. On the other hand, when we focus
on the condition of an isochronous beam transport, there
is another possibility to generate the coherent radiation[2]. A very short electron bunch length around 100 fs isrequired to generate coherent THz radiation. To realize a
coherent THz source based on the isochronous ring, total
technologies of accelerators are required.
In this paper, a design study of an electron source andthe bunch compressor for a novel coherent THz radiation
source are described.

COHERENT THZ LIGHT SOURCE
Design of Isochronous Ring
The isochronous ring is the one of the candidates of thelight source of coherent THz light [3]. Since this___________________________________________*Work supported by the Grants-in-Aid of Japan Society for the
Promotion of Science, contract No. 17360035.
#
takumi@lns.tohoku.ac.jp

FEL Oscillators and Long Wavelength FELs

isochronous ring must keep a very short bunch length lessthan 100 fs (rms) from an injector in every place, it has
been designed to have very small dispersion function. To
keep bunch length for many turns at everywhere, the path
difference for one turn should be much smaller than thebunch length. So that, the momentum spread of theinjection beam must be order of 10-4 taking into accountthe momentum compaction factor which is designed as
0.0002. This ring has advantages; (1) multiple beam lines
can be utilized, (2) a high average power of THz light canbe generated since the electron beam can circulate ring formany turns. However, a betatron initial phase difference
affects on the bunch lengthening larger than the effect ofmomentum compaction factor relatively. In order toreduce this bunch lengthening, an appropriate design ofthe phase advance in arcs is required [3]. We havedesigned the lattice of isochronous THz ring, then theeffect of bunch lengthening in the bending arc has been
calculated, and it is less than 40 fs which satisfies a
condition to generate a coherent THz light. The major
designed parameters of the isochronous ring are as
follows. Tentative design parameters of this ring areshown in Table 1.
Table 1. Tentative design parameters of isochronous THz
ring.
Circumference
Beam energy
Lattice typeC
E-

Bending radiusU

45.691 m
200 MeV
Racetrack modified FODO
3 m (normal cell),
2 m (dispersion suppressor)D< 0.0002

Hrms

5 S nmrad'p/p210-4

Momentumcompaction
factorEmittance ofinjection beam
Momentumspread of
injection beam

Coherent Synchrotron Radiation
The peak power of a coherent radiation from this ringhas been calculated, and then it becomes about 100 kW
with the bunch length of 100 fs (rms). This peak power ofTHz light is larger than other THz light sources (ex. FEL,
other Lasers). This ring also has high performance in the
average power of THz light. Radiation power of THz lightsources is summarized in Table 2.

371

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Table 2. Radiation power from different THz light sources.
SourcePeak power(Micropulse length)

Average power

1 W (10 ms)
300 mW (4 ns)
10 kW (1 ps)

100 mW
60 nW
10 mW

100 kW (250 fs)

350 mW

p-Ge Laser
YAG + NOE
FEL
Isochronous
THz ring

GENERATION OF VERY SHORT BUNCH
Design of a Thermionic RF Gun
As an injector of the isochronous ring, it is required togenerate an electron beam with a very short bunch length
less than 100 fs (rms) and with a very small normalized
rms emittance less than 2 S mm mrad. To achieve highaverage power of coherent radiation, macropulse durationof the injector should be about 1.5 Ps taking into accountthe circumference of the isochronous ring. In addition, thebunch charge should be as large as possible. To gather
high bunch charge, the injector should have a large
acceptance of momentum deviation. An acceptable
momentum deviation is limited by acceptance of coherent
THz ring. The coherent THz ring requires a momentum
spread of the order of 10-4 for the injection beam. Because
the beam is accelerated from 2 MeV to 200 MeV in the
Linac, 'p/p is limited to the order of 10-2 at the injector.
To realize above parameters, a thermionic RF gun has
been adopted for the injector. As a cathode material, asmall single crystal of LaB6 with a diameter 1.75 mm has
been chosen. This cathode has a higher current density
than conventional dispenser cathode. The normalized
emittance can achieve a small value because of the small
diameter. To reduce back-bombardment effect [4], thissmall diameter may be effective. In order to control a
distribution of a longitudinal phase space at the exit ofthis RF gun, we employed independent two cells which
don't couple with each other [5]. Parameters of ITC-RF
gun are listed in Table 3.
Table 3. Design parameters of ITC-RF gun.
RF frequency
Cathode material
Current density @ cathode
Cathode diameter
Number of cells
Feeding total power
Etotal @ exit of gun
Bunch length (rms)2,856 MHz (S-band)
LaB6
100 A/cm2
1.75 mm2

simulation code [6]. This code can include effects of thebeam wakefield and of the space charge self-consistently.
We have to design an appropriate distance between thecells and the strength of the accelerating field in each cell,because the longitudinal phase space strongly depends onthese parameters. Since it is difficult for 3D FDTD code
to calculate a precise geometry because of the mesh size,a 2D code: SUPERFISH [7] has been used to decide theprecise geometry for manufacturing of ITC-RF gun.
Because the RF coupling is a very small, accelerating
fields are independent from each other. The prototype of
ITC-RF gun is shown in Fig. 1.

Figure 1. The prototype of ITC-RF gun. The RF input port
is separated each other. This is now under manufacturing.
ITC-RF gun is designed to drive at S-mode basically.
Peak accelerating fields of 1st cell E1 [MV/m], 2nd cell E2[MV/m] and relative phase between cells 'T are threedegrees of freedom to control this gun. So as to compress
the bunch length easier at the downstream of the gun, we
have searched an optimum operating point of the gun to
generate a beam with a linear dependence in thelongitudinal phase space. At the optimization, the bunchcharge from the gun should be as large as possible. The
strength of E1 was fixed around 25 MV/m in this gun,because the head of emitted electrons from a cathodemust arrive at the middle point of between cells in time ofa half RF cycle. With applying some suitable parameters(E1, E2) = (25, 50) MV/m and 'p/pmax = 2 %, longitudinal
and transverse phase spaces at exit of this gun are shownin Fig. 2 and Fig. 3 respectively.

㨪5 MW
㨪2 MeV㨪100 fs

Bunch charge

㨪several tens pC

Hnorm. rms'p/p
Macropulse duration< 2 S mm mrad
<2%
1.5 Ps3D FDTD Simulation of ITC-RF Gun
In order to study the beam dynamics in ITC-RF gun
and to design this geometry, we have used a 3D FDTD
372

Figure 2. longitudinal phase space. 'T is a variable inthis simulation. (E1, E2) = (25, 50) MV/m.

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany'L

Figure 3. transverse phase space. (E1, E2) = (25, 50)
MV/m, 'T = +18 degree.
As shown in Fig. 2, a linearity of momentum
distributions depends on the 'T. From Fig. 3, thenormalized rms emittance Hnorm. rms = 0.78 S mm mradsatisfy the design value < 2 S mm mrad. Normalized rms
emittances in other conditions also satisfy the design
value. On the other hand, the bunch charge of this beamwith momentum deviation 'p/p = 2 % is about 30 pC
which almost satisfy the design value. However the bunch
lengths of these beams are far from the design value, sothat the beams must be compressed at the downstream of
the gun.

Magnetic Bunch Compressor
To compress the rms bunch length from several ps toless than 100 fs, a magnetic bunch compressor is needed.
Magnetic bunch compression uses a difference of time offlight (TOF) for particles of different momenta p0 and p1
where these particles move from s1 to s2 along the beamaxis. For these particles, the difference of TOF can be
written as't t1  t 0
LL1
 0
cE1 cE 0
L1^ L0 ('E )  E 0 ('L)` ,(1)
cE 0 E1
where t is TOF from s1 to s2, L is a path length from s1 to
s2, E is a relative velocity, index: 0, 1 represent particles
with p0 and p1 respectively, 'E = E1 - E0 and 'L = L1 - L0.
When we assume p0 < p1 and the longitudinal distribution
in Fig. 2, a condition of the bunch compression leads 't >0. The first term of eq. (1) represents a difference of TOF
caused by a difference of each particle velocity, andbecome negligible small when E goes to unity. The
second term is caused by a difference of path lengths. In
case of ITC-RF gun, the effect of the first term can not be
negligible. When a total beam energy is 2 MeV, s2 - s1 = 1
m and p1/p0 = 1.02, the first term becomes about -5 ps. 'Lof the second term can be represented as
FEL Oscillators and Long Wavelength FELs

TUPPH024'L'p / p  'LE

xE (s)­ K ( s) ½ 'p
ds ¾
³
ds .
(2)
®³
U (s)
¯ U ( s) ¿ p
The first term of eq. (2) means a path difference produced
by an energy dispersion at bending section, and this term
can be used for bunch compression. The second term ofeq. (2) represents a path difference which comes from adifferent value of initial phase of a betatron motion, andthis term can be suppressed by reducing the beta function
and designing appropriate phase advances along lattice.
We have considered two kinds of magnetic compressor.
The first is an D-magnet [8], and the second is a triplebend achromat (TBA) lattice. An advantage of D-magnet
is that this system has a larger energy acceptance, and has
a possibility to gather larger bunch charge for a large 'p/p.
An advantage of TBA lattice is that this system has apossibility to manipulate the higher order term of 'p/p byadjusting optics. Each magnetic bunch compressor canapply different slopes of ('p/p)/'t in longitudinal phasespace. In case of TBA lattice, this system can vary the R56
by changing a dispersion function of the 2nd benging
magnet without changing its reference orbit. When the Dmagnet changes the field strength, reference orbit in it ischanged correspondingly. Each system can be an
achromat for the beam energy. At manufacturing themagnet of each system, it is easier for TBA lattice than Dmagnet to design magnets. In order to select the methodof a suitable bunch compression, studies have been
continued. In the following, basic studies are shown.
In order to estimate a bunch compression, particle
distributions in Fig. 2 and Fig. 3 have been used for bothmethods. The operating conditions of the gun are (E1, E2)= (25, 50) MV/m and 'T = +18 degree. In case of Dmagnet method, a beam tracking simulation has been
done. In case of TBA lattice method, a design of optics
and tracking simulations have been done by using SAD[9]. Since the bending angle of dipole magnets of TBA
lattice are the same angle 60 degree, TBA lattice is 180
degree bending transport system totally. In addition, TBA
lattice has four families of quadrupole which are used fortwo purposes mainly. The dispersion function in the 2nd
bending magnet is controlled by quadrupole magnets
between bending magnets to change the R56. The otherquadrupole magnets are used for matching of horizontal
and vertical Twiss parameters at exit and reducing thebeta function in bending magnets. One example of the
TBA optics is shown in Fig. 4.

373

TUPPH024

Proceedings of FEL 2006, BESSY, Berlin, Germany
0.30

Ex
Ey
Kx

2

0.20

0.10
1

0
0.0

dispersion function [m]beta functions [m]

3

0.00
0.5

1.0

Path length [m]Figure 4. TBA optics. Left axis is for beta functions. Rightaxis is for dispersion function.
In case of an D-magnet, the first term of eq. (2) can becalculated by using following equation­ K ( s ) ½ 'p
'L'p / p ®³ds ¾
¯ U (s) ¿ p

EJ 'p

KD
2

g

,

p

(3)

where KD = 191.655 Gauss1/2cm1/2 and g is the field
gradient of D-magnet in Gauss/cm. The path length in Dmagnet can be represented as K D EJ / g . In order toestimate a difference of TOF in an D-magnet, the firstterm of eq. (1) and eq. (3) should be calculated, and thenwe can find the field gradient of an D-magnet for asuitable bunch compression. After optimizations of eachbunch compressor, the longitudinal phase spaces and theparticle time distributions are shown in Fig. 5.
1.84

1.83

Total Energy [MeV]Total Energy [MeV]

1.84

(a-1)

1.82

1.81

0.0

0.1

0.2

0.3

0.4

0.5

1.83

(b-1)

1.82

1.81

0.0

0.6

0.1

0.2

500

300

400

(a-2)
Vrms = 72.2 fs

200
100
0
0.0

0.4

0.5

0.6

0.4

0.5

0.6

500

Intensity [a.u.]

Intensity [a.u.]

400

0.3
time [ps]time [ps](b-2)
Vrms = 42.7 fs

300
200
100

0.1

0.2

0.3
time [ps]

0.4

0.5

0.6

0
0.0

0.1

0.2

0.3
time [ps]As shown in Fig. 5, the compressed bunch lengths are
72.2 fs (rms) for the D-magnet system and 42.7 (rms) fs
for the TBA lattice respectively. Both bunch compressors
can achieve less than 100 (rms). TBA lattice can achieve
shorter bunch length in this case, but more studies areneeded for selecting a more suitable method.

SUMMARY
We have proposed the coherent THz light source by
employing an isochronous THz ring and an injector which
can generate a very short electron beam. From numericalcalculations and simulations, the radiation power from theisochronous THz ring may achieve higher than other lightsources of THz region. In order to generate the required
short bunch beam for this ring, we have designed theinjector which consists of ITC-RF gun and the magnetic
bunch compressor. ITC-RF gun can generate a small
normalized rms emittance value which satisfies the design
parameter. For generating very short bunch, a magnetic
compressor is needed at the downstream of ITC-RF gun.
We have studied two kinds of bunch compressor: Dmagnet transport and TBA lattice transport. Both of bunch
compressors can achieve design bunch length less than
100 fs (rms). At a glance, TBA lattice seems to be better
than D-magnet. However, we have continued to studied
more detail about them including effect of the higher
order momentum dependences and betatron initial phasedifference.

REFERENCES[1] M. Abo-Bakr, et al., Phys. Rev. Lett. 90 (2003)
94801.
[2] T. Nakazato, et al., Phys. Rev. Lett. 63 (1989) 1245.
[3] H. Hama, et al., Proc. of the 27th International FEL
Conf., Stanford, California U.S.A., pp. 1.
[4] C.B. McKee and J.M.J. Madey, Nucl. Instr. and Meth.
A 296 (1990) 716.
[5] T. Tanaka, et al., Proc. of the 27th International FEL
Conf., Stanford, California U.S.A., pp. 142.
[6] H. Hama, et al., Nucl. Instr. and Meth. A 528 (2004)371.
[7] http://laacg1.lanl.gov/laacg/services/
download_sf.phtml[8] H.A. Enge, Rev. Sci. Instr. 34 (1963) 385;
M. Borland, Ph.D. Thesis, Stanford University,
1991.
[9] http://acc-physics.kek.jp/SAD/sad.html

Figure 5. longitudinal phase space distributions and time
distributions after bunch compression. (a-1), (a-2) Dmagnet case, (b-1), (b-2) TBA lattice case.

374

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH025

RECENT EXPERIMENTS AND PROSPECT ON THE NIJI-IV VUV/IR FEL
H. Ogawa#, K. Yamada, N. Sei, M. Yasumoto, K. Yagi-Watanabe
Research Institute of Instrumentation, National Institute of Advanced Industrial Science andTechnology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan
Abstract
The NIJI-IV free electron laser (FEL) is being
developed as a compact light source with very good
optical quality and ultra-wideband tunability from the
VUV to the IR. To obtain lasing at shorter wavelengths in
the VUV region, continuous efforts to improve the cavitymirror performance have been made, so that the originalloss of mirrors was recently decreased around 195nm. A
new optical cavity system, composed of two sets of aheavy granite base and a stable mirror manipulator, wasinstalled to stabilize the lasing and also to extend thetuning range. As for the IR FEL, modification of thebeam transport system to make space for installation of
the optical cavity was completed.

29.6m. The ring has two straight sections of 7.25 m and
4.1 m in length and a 6.3-m optical klystron ETLOK-II[8] is equipped in the longer straight section for the
UV/VUV FEL experiments as shown in Fig.1. In 2004, a
3.6-m optical klystron ETLOK-III [9] was installed into
the other straight section and the construction for lasing in
the IR region is going on [10]. The optical klystronparameters are summarized in Table 1. Here we report
recent progress in the NIJI-IV FEL.
Table 1: Parameters of optical klystron ETLOK-II and III
ETLOK-IIETLOK-IIITotal length [m]

6.288

3.55

Undulator section [mm]

72

200

Dispersive section[mm]

216

720

Number of period Nu

42×2

7×2

Deflection factor K<2.29<10.04

Wavelength [μm]0.198-0.595(0.4-12)Magnetic period

INTORODUCTION
Storage ring FELs (SRFELs) are unique source andhave advantages such as good spectral resolution, highrepetition rate, and natural synchronisation withsynchrotron radiation from insertion devices or bending
magnets. These features of SRFELs are suitable forpump-probe experiments and observing a continuouschange of a phenomenon without giving sample damage.
Indeed, the use of SRFELs for the real-time surface
observation has been investigated in combination with aphotoemission electron microscopy (PEEM) at DUKE
[1,2] and AIST [3,4]. Many efforts to shorten the
wavelength in SRFELs have been made [5-7] for suchapplications. At AIST, an FEL research has been
performed using the compact storage ring NIJI-IV and the
FEL lasing down to 198nm was achieved [7]. The NIJIIV is a racetrack-type storage ring whose circumference is

ETLOK-IIIETLOK-II

Figure 1: NIJI-IV FEL system.
____________________________________________DEVELOPMENT OF THE VUV/IR FELVUV FEL Mirror
To shorten the FEL wavelength, we have been
upgrading the NIJI-IV FEL system. The replacement of
NIJI-IV vacuum chambers as well as installation of thin
sextupole magnets has been performed in order toincrease FEL gain. As for the laser cavity, Al2O3/SiO2
dielectric multilayer mirrors were adopted for the
wavelength below 220 nm. In a previous study, we tried
FEL oscillations below 195 nm with two kinds of
Al2O3/SiO2 mirrors but failed to obtain the oscillation.
The original losses of the cavity composed of two mirrors
around 195nm were small as 1.9%-2.6%, while the losses
after irradiated by the undulator radiation from ETLOK-II
were rapidly increased through degradation of dielectric
multilayer mirrors as shown in Fig.2, so that theoscillation could not be realized [10]. To improve themirror performance, the Al2O3/SiO2 mirrors were
manufactured again by tuning the dielectric coating
condition. As a result, the original loss of the cavity waspresently obtained to be down to 1.2%, which was
sufficient to realize the lasing around 195nm. Aftermeasuring an evolution of degradation of the mirrors, weare planning to perform the FEL oscillation experiments
below 195nm.

#

ogawa.h@aist.go.jp

FEL Oscillators and Long Wavelength FELs

375

TUPPH025

Proceedings of FEL 2006, BESSY, Berlin, Germany

14
exposure:58mAh

CAVITY LOSS (%)

12
exposure:23mAh

10
8
6
4
2
0

degraded mirror

original mirror
recently developed mirror

192

194

196

198

200

WAVELENGTH (nm)Figure 2: Wavelength dependence of the cavity loss of
Al2O3/SiO2 multilayer mirrors. The losses of mirrors
manufactured in the previous work are shown bysquares and circles, while the loss in the present work
is represented by triangles.

Optical cavity system
It was observed that the intensity of the NIJI-IV FEL
was modulated with a few to 10 ms period near the best
cavity tuning condition and the lasing mode was not fixed
at a stable CW mode [11]. Although its origin has neverbeen identified, it is probably caused by a mechanicalvibration of the mirror vacuum chamber, because the baseof our mirror holders had a slender structure whose
weight was only 20-30 kg. Therefore new optical cavity
system has been made for the stabilization of the FEL
oscillation, which is needed for FEL application researchsuch as a photoemission electron microscopy. Figure 3
shows a photograph of the new system which was
installed into an upstream side of ETLOK-II in this year.
We chose heavy granite stone, whose weight was about 2
ton, as the base of the cavity, so that the vibration of thebase in an optical axis was dumped below 0.1 mm, which

was measured with a vibration sensor under frequency of
200 Hz. The mirror chamber is remotely manipulated by
five-axis stage with gimbal optical mount and three linear
stages (Newport SL20AN, M-MTM100PP.1, M-ILS50PP
and M-MVN80 with precision motorized actuators LTAHL). The cavity length and mirrors can be adjustable withresolutions of 0.1 mm and 0.8 mrad, respectively. In
addition, a novel feature is that the chamber has two invacuum mirrors that are interchangeable withreproducible adjustment. This will enable us to extend
FEL tuning range restricted by a narrow reflection
bandwidth of dielectric multilayer mirrors. We willmeasure the stability of the FEL oscillation with theoptical cavity system after commissioning of new beamtransport system as described in the following subsection.

Beam transport system
In order to extend lasing range toward a longwavelength region, we have been developing the NIJI-IV
FEL in the infrared (IR) region using ETLOK-III. The
FEL gain in the visible and near-IR regions was evaluatedto be over 2% from observed spectra of a spontaneousemission from the ETLOK-III [10]. The realization of
FEL lasing can be expected in the visible and near-IR
regions since high-reflection mirrors of 99.8% or moreare available. We are preparing to make an optical cavity
system for the IR FEL and its mirror diameter would be
50mm, which is larger than that for the UV/VUV FEL of
30mm, by considering diffraction loss.
However, there was no space to install the upstream
cavity system for the IR FEL because a beam transportline was too close to the storage ring. Therefore we
decided to modify the transport system to make a space
for the cavity. The detail of design for new beam transportsystem was written in [10]. We have constructed the newtransport system, as shown in Fig.4, which is 2.48m awayfrom the former one and the beam commissioning has
been started. The beam was transported from LINAC to
Storage ring NIJI-IV

Previous beam transport

New beam transport

Figure 3: New optical cavity system.

376

Figure 4: Photograph of a part of new beamtransport system. The place where previous beamtransport located is indicated by dashed line.

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany
an entrance of the storage ring and focused into a septum
chamber of NIJI-IV. The final tuning of beam parameter
is now in progress.

DUV FEL APPLICATION
Recently, performance of the NIJI-IV FEL was
improved at the deep UV (DUV) around 200 nm by both
optimizing the transmittance of the output coupler andincreasing stored electron-beam energy [3]. Thus we canmake real-time observation of chemical reactions on atransition metal surface using a photoelectron emission
microscopy (PEEM). The metal surface was irradiated by
an FEL or spontaneous emission from ETLOK-II at awavelength of 202 nm, and the catalytic CO-oxidation(2CO + O2 → 2CO2) on a Pd(111) single crystal surface
has been investigated by introducing CO and O2 gases at apressure of ~10-5 Pa [4]. Figure 5 shows the setup for
FEL-PEEM measurement. The PEEM system (STAIB
Instrumente, type 350) is only applicable at pressures
below ~10-5 Pa, since a micro channel plate (MCP) image
intensifier equipped in the system requires a vacuum of
better than ~10-5 Pa during operation. A differential
pumping is necessary for observation of chemical reaction
under higher pressure. Therefore we prepared a turbo
molecular pump (Varian Turbo-V70LP) that is being
added to a differential pumping port close to MCP. We
are planning to observe chemical reactions on thetransition metal surfaces at higher pressure of ~10-3 Pa.

DUV FEL
MCP

Differential
pumping port
Sample chamber
Figure 5: Photograph of the FEL-PEEM system.

SUMMARYTUPPH025

IV. To shorten the lasing wavelength, Al2O3/SiO2
multilayer mirrors optimized at 195nm were improved
and the cavity loss of the original mirrors was
successfully reduced by 30%, compared with that ofprevious ones. The preparation for the lasing in the IR
region is also proceeding. The beam transport system in
NIJI-IV has been modified to make space for the opticalcavity of the IR FEL. Furthermore, in order to stabilize
the FEL oscillations in the UV/VUV regions, new opticalcavity system holding two in-vacuum interchangeable
mirrors has been installed, which was composed of heavy
granite base and five-axis manipulators. This will enable
us to carry out reproducible FEL application experiments,
such as real-time observation of surface chemical
reactions.

ACKNOWLEDGEMENTS
This study was financially supported by the Budget for
Nuclear Research of the Ministry of Education, Culture,
Sports, Science and Technology, based on the screening
and counseling by the Atomic Energy Commission ofJapan.

REFERENCES[1] W.-C. Yang et al., J. Appl. Phys. 94 (2003) 5720.
[2] W.-C. Yang et al., Phys. Rev. Lett. 90 (2003) 136102.
[3] K. Yamada et al., Proceedings of the 26th Free
Electron Laser Conference, August 2004, Trieste,
p.311.
[4] H. Ogawa et al., Proceedings of the 27th International
Free Electron Laser Conference, August 2005,
Stanford, p.467.
[5] F. Curbis et al., Proceedings of the 27th International
Free Electron Laser Conference, August 2005,
Stanford, p.473.
[6] V.N. Litvinenko et al., Nucl. Instr. and Meth. A470
(2001) 66.
[7] K. Yamada et al., Nucl. Instr. and Meth. A528 (2004)
268.
[8] T. Yamazaki et al., Nucl. Instr. and Meth. A331
(1993) 27.
[9] N. Sei et al., Jpn. J. Appl. Phys. 41 (2002) 1595.
[10] N. Sei et al., Proceedings of the 27th International
Free Electron Laser Conference, August 2005, p.469.
[11] K. Yamada et al., Nucl. Instr. and Meth. A475
(2001) 205.

An FEL with wide wavelength range from the VUV to
IR has been studied based on compact storage ring NIJI-FEL Oscillators and Long Wavelength FELs

377

TUPPH026

Proceedings of FEL 2006, BESSY, Berlin, Germany

DISPERSION EFFECTS IN SHORT PULSE WAVEGUIDE FEL
N. S. Ginzburg, E. R. Kocharovskaya, A. S. Sergeev IAP RAS, Russia.
optimal conditions are found.

Abstract
The influence of waveguide dispersion on the FEL
operation driven by short electron bunches is studied.
Under the assumption of a high quality resonator, aparabolic equation for the evolution of the profile ofelectromagnetic pulse is derived. The condition of selfexcitation are found by means of an analytical theory
describing a structure of supermodes as the sum of
resonator eigenmodes with locked phases. It isdemonstrated that due to waveguide dispersion FEL isable to generate not only for positive but also for negative
cavity detuning. The transient and nonlinear stages of thefree-electron laser operation are analyzed by the computer
simulation, and the optimal mismatches of group andcavity synchronism conditions are found.

THE MODEL AND BASIC EQUATIONS
Let us suggest that the radiation pulse propagating
through a waveguide circulates between two mirrors (withreflection coefficients R1,2 ), which are placed at somedistance, L0 . Let FEL be fed by short electron pulses ofduration U p , which is essentially less than both theround-trip of the radiation in the cavity TR = 2L0 / vgr ,and the repetition period of an electron bunch injection,
Ti . During n-the pass through a resonator, the field canbe represented asª°­ A ( z , t ) exp(i (Z0t  h0 z ))  °½º
Re « Es ( rA ) ® n
¾» ,

«¬
¯° An ( z , t ) exp(i (Z0t  h0 z )) ¿°»¼


INTRODUCTION
The mode-locking regime is typical for free-electron
lasers (FEL) driven by a train of short electron bunches.
In this regime, the electromagnetic radiation consists of
micropulses with a duration nearly equal to that of theelectron bunches. Both pulses (electron andelectromagnetic) travel together through the resonator, but
shift slightly away from each other due the difference
between the wave group velocity and the electron
velocity. Once they reach the right-hand mirror, theelectron pulse escapes from the resonator, while theelectromagnetic pulse reflects and comes back to the lefthand mirror at the time when the next current pulse
arrives.
In short wavelength (optical, infrared) FEL experiments[1-4], the group velocity of electromagnetic pulses
exceeds the velocity of electron bunches. To provide
generation under such conditions, a specific mismatch
between a period of electromagnetic pulse round trip overa resonator and a period of bunch injection was used.
However, in some experimental investigations of longwavelength FELs [5-8], a waveguide may be used, so thatthe specific waveguide dispersion allows one to realize“zero-slippage” condition, for which the group velocity ofelectromagnetic pulse is equal to the longitudinal velocityof electrons. Under such conditions, mutualsynchronization of radiation from different parts ofelectron bunches occurs due to dispersive spreading of theelectromagnetic field, whereas localization of radiationnear electron bunches is caused by its guiding properties[9,10].
In the present paper, a theoretical model of waveguide
FEL is developed which takes into account the waveguidedispersion. Under the assumption of a high quality
resonator, a parabolic equation for the evolution of the
profile of electromagnetic pulse is derived. The linear,transient and nonlinear stages of the FEL operation areinvestigated, both analytically and numerically, and the378

A

where Es is a function, describing the profile of a given
transverse waveguide eigenmode, X 0 is the reference
frequency, and h0 = h (X0 ) the longitudinal wave
number. Resonant electron-wave interaction takes place
under the synchronism condition, X 0  h 0v&  8? ,where

8? = hu v&

is

the

bouncefrequency,

hu = 2Q / Mu , Mu the undulator period. We willconsider the excitation of a resonator by a train of shortelectron bunches under the following conditions:x the reflection coefficients are close to unity,
R1,2  1 and the changes of the wave amplitude

during one pass are very small;x dispersion spreading of the electromagnetic
pulse during one pass over the resonator is small as
well.
Under these approximations, we can replace thediscrete variable n (pass number through the resonator)
by a slow time U with the period of one round trip, TR
taken as a time unit. Evolution of the pulse profile along
the resonator can be described by the parabolic equation(for details see [9]):QˆVgr w 2D
wD Z0
wD
D  Hˆ
i
2
2 wy
wWˆ 2Qwy(1)eS I 0Vgr N l³ f ( y  z / Vgr ) IZ dz ,3
2 me c J N s h0l 0
1 2S i4
where I Z
d 40 is the synchronous harmonic³ e
S 0of the beam current, Vgr wZ / wh the wave group22

velocity, Qˆ | w h / wZ | the wave dispersion parameter,

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, GermanyQ

Z0 l / Vgr (1  R1 R2 ) the resonator Q-factor, I 0 the2thepeak current of electron bunch, J 1/ 1  E
relativistic Lorentz factor, ns the norm of the operating
mode, L the electron-wave coupling coefficient, f ( y ) afunction, describing the electron pulse profile,
D eAn /( me cJ ) the dimensionless wave amplitude.
Takingintoaccount
thecavitydetuningHˆ (Ti  TR ) / TR , we use an independent time variable,yˆˆ .
t  z / Vgr  HW

and expand the field and the beam current into Fourier
series:f
D (Wˆ, y )¦ am (Wˆ ) exp(i 2S my / TR ),
m f

(3)

f

IZ

a (W , [ )a W ,[  T ,4] 0

4 0  [0, 2S ], ¨

w ·
§ w

¸4] 0 G,© w] w[ ¹

where

DNP

a

P

2

Q

wZ

2

the

functionF1
1E&  E gr

me c J and neglecting the Coulomb interaction, theelectron motion equation can be presented in the form

with the boundary conditions:
4 0  [0, 2S ],(Z0  h0V&  : A ) / V& is the initial mismatch of
2synchronism at the reference frequency, P  J
theinertial bunching parameter. With the use of normalized
variables,
Z0 y
Z0Wˆ
Z
, ] z 0 P,
[
P, W
2Q
F
c
1/ 3

§ 4S eI 0 PN 2 E gr Q ·
,
P ¨
2 ¸
J
Z
m
c
dbN
h
l
e
s
0
0
©
¹
equations (1), (4) can be transformed to the following
form:
2
wa
wa
w a L
 a H
 iQ³ F ([  ] ) I Z d ] , ( a )
2
0
wW
w[
w[

with boundary conditions:
FEL Oscillators and Long Wavelength FELs

'

c

Z0 P

.

electron-pulse

profile,is the relative value of the detuning of

2

ia

(6)

Using the expressions (3) we find all harmonics of current
Jmª i ] e ikm] ie  ikm] º« 2 » am ,
2
km
km ¼
¬ km
km

(7)

2S m / T  G .

As a result for the amplitude of each mode am from (5a)taken into account (7) we obtain
2
ªd
2S m
§ 2S m · º
1
i
H
i
Q



«
¨
¸ » amT© T ¹ »¼
«¬ dW

f

m

¦ C n an ,

(8)

n f

where
m

Cn

 ik ]
T L ª i 1e ikn]
] e n º F [ ] ei[ ( kn  km )
d] d[ .
³ ³«
»
2
T
0 0
k
k
n
n
¬
¼
m

Obviously the diagonal elements of the matrix Cn

coincide with the expression for a complex electron
permittivity found in [9, 10].
Representing the solution of Eq. 8 in the form
i:W ˆ
am e
am where 8 is a complex frequency, we get
the algebraic equations for the supermodes of theresonator excited by a train of electron bunches:fi:aˆ m(5)(b )describingw ·§ w¨ w]  w[ ¸ IZ©
¹§w §1 1 ·w·
§Z ·
i4

(4)
¨ 
¸ 4 ¨ 0 ¸ PN Re D e¨ wz ¨¨ V& Vgr ¸¸ wy ¸
© c ¹
©
¹ ¹
©

w ·
§ w
i4
¨ w]  w[ ¸ 4 Re ae ,
©
¹

F

TR

, G

Linearizing the equation of electron motion (see Eq.
5b), we obtain an equation for the electron current:22(Ti  TR ) 2QP, H

2“zero-slippage” condition. The normalized energy stored
in electromagnetic pulse is give by relation
1 T
2W³ | a | d[ .
Tc 02

where '

2

THE LINEAR THEORY

an amplitude of cavity eigenmode with the longitudinalindex m .
Assuming a small variation of electron energy§w §1 1 ·w·', 4 z 0¨  ¨¨ ¸4¨ wz V& Vgr ¸¸ wy ¸ z 0
©
¹ ¹
©

F

,

lZ0 P / c is the normalized interaction length, F [

m f

2

F

2

¦ J m (Wˆ ) exp(i 2S my / TR ).

An amplitude of each harmonic am , can be treated as

E

TRZ0 P, T

w h Vgr Z0QP

L

Under assumptions described above, we can relay upon
the periodical boundary conditions:
D (Wˆ, y ) D (Wˆ, y  TR )(2)

TUPPH026

where

m

Dn

m

¦ Dn aˆ n ,

(9)

n f
m

2

Cn  1  iH (2S m / T )  iQ (2S m / T ) .

Assumed for simplicity that the electron pulse has the379

TUPPH026

Proceedings of FEL 2006, BESSY, Berlin, Germany

rectangular
form
with
normalized
duration
Tc W cZ0 P / F , we obtain the following expression for
the elements of the matrix Dnm :emDni ( kn  km )Tc / 2e i ( kn  km )Tc / 2e ikmTc / 2(kn  km )

T

2

u

ª ieikm L ieikn L
iiLLº« 2  2  2  2   »kn
kmkn
km kn ¼
¬ km
2

2S m

§ 2S m · iQ ¨iH¸  1.
T© T ¹
The starting condition of generation corresponds to theequalityIm[:] 0.
(10)
|a|

a)

1

1
b)

0.5

0.5

-T/2

|am|

0

T/2

0

The nonlinear stage of the electron-wave interaction
was analyzed on the basis of computer simulation of Eqs.
5. The electron bunch profile has a rectangular form withnormalized duration Tc . Three basic regimes of the FEL
generation have been observed when the value of current
exceeds the generation threshold: a) stationary regime(see Fig. 3), b) periodic self-modulation (see Fig. 4a), c)chaotic self-modulation (see Fig. 4b).
At a small excess over the generation threshold, a profileof the field and its spatial spectrum are closed to thosefound from the linear analysis (see Fig.1). The dynamics
of electromagnetic pulse profile become more
complicated with increasing the dimensionless resonator
length, L (see Fig.3).

m

[

0

COMPUTER SIMULATION OF THENONLINEAR STAGE

-20

0

20

Figure 1: Normalized profile (a) and spectrum (b) of thesupermode for the dimensionless parameters: Tc 4 ,H 1 , L 2.3 , Q .3 . Resonator eigenmodes
amplitudes are shown by blue dotes.

Figure 3: Regime of the stationary generation: L 4.4 ,T=25.6 , H 0.5 , Tc 4 , Q 0.3 ,: a) time–space
evolution of an envelope of the electromagnetic pulse; b)time dependence of the electromagnetic pulse energy W :for comparison the case of the absence of dispersion isshown by curve 2.

A spatial structure of supermodes calculated via eigen
vectors of the matrix Dnm is shown in Fig. 1a; it is asuperposition of longitudinal resonator eigenmodes.
b) Lsta) Lst
2
4
5
1
2
0

0
-2

0

2

H

0

2

4

Tc

Figure 2: Dependence of the starting length, Lst a) on thecavity detuning H : 1 for dispersive parameter Q .3 , and
2 for the absence of dispersion and b) on thedimensionless electron bunch duration Tc .
Note that wave dispersion, playing a part of feedback,allows FEL to generate even in the case of negativevalues of the cavity detuning ( F < 0 , see Fig. 2a, curve1), for which the resonator can not be excited in theabsence of dispersion (see Fig. 2a, curve 2). The
increasing of the electron bunch duration leads to thedecrease of the generation threshold (see Fig. 2b). For
long electron bunch duration Tc this value as well as thecavity detuning does not practically influence thegeneration threshold.

380

Figure 4:Time–space evolutions of an envelope ofelectromagnetic pulse in the regime of periodical (a)( L 4.4 , T=25.6 , H 4 , Tc 4 , Q 1 ) and chaotic
self-modulation (b) ( L 10 , T=51.2 , H 1 , Tc 6 ,Q 1 ).
The self-modulation regime may be reached by two
ways: via increasing the dimensionless length L and/or
via enlarging the cavity detuning F . Possible quasiperiodical behavior is demonstrated in Fig. 4a.
At large excess over the generation threshold, thechaotic regime of generation takes place (see Fig. 4b). At
extremely large excess over the generation threshold, thepulse envelope evolves in a complicated stochastic
manner, so that the generated radiation is distributed
quasi-homogeneously over very wide spectral range ofthe resonator eigenmodes. According to estimates allthese regimes are reasonable for the waveguide FEL toprovide variety of applications (see Fig.5).

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

L
8

3
2

4

1

Lst
4
0
0

4

H 8

Figure 5: Zones of stationary (1), periodical (2) andchaotic (3) generation on the plane of dimensionlesslength L and cavity detuning H for Q 1 , Tc 4 ,T 51.2 . Zone (4) is absence of generation.
The stationary regime, when one supermode is
generated, has been investigated in detail for various
parameters of dispersion, the detuning of “zero-slippage”
conditions and cavity detuning. At the limit F o 0 andH o 0 the equations (5) transform into the equations forthe case of group synchronism [5, 6, 10]. Numericalsimulation of the equations (5) at small values of theparameter H , allows us to determine an optimal relation
between all FEL parameters, F , L , Tc and Q , which
gives the maximum field amplitude, i.e., provides themost effective interaction between the electromagnetic
pulse and the electron bunches.
Note also that a superradiant (nonstationary) type ofoperation regime [11] can be realized for small negative
cavity detuning H (see Fig. 6).

TUPPH026

amplitude of undulator field  6 kG, transverse sizes ofthe plane waveguide d 30 mm, b 2 mm, resonatorlosses  10% Above physical parameters corresponds todimensionless ones of length of interaction L 7 . Fromsimulations the duration of electromagnetic micropulse
is  20 ps (relative spectrum width  1.5% ) and peak
power 30kW. The value of spectrum width corresponds toexperimental date, but experimental value of peak power
is much less the theoretical limit that in particular can be
explained by the parameter spread in the real electron
bunches.
This research was supported by the grant RFBR-05-0217553.

REFERENCES[1] D.A.G. Deacon et al., Phys. Rev. Lett. 38 (1977) 892.
[2] D. Oepts et al., Phys. Rev. Lett. 68 (1992) 3543.
[3] D. C. Ngueyn et al., Nucl. Instr.&Meth. in Phys. Res.
A 358 (1995) 27.
[4] V.P. Bolotin et al., "Status of the Novosibirsk HighPower Free Electron Laser," IRMMW’2004,
Karlsruhe, September 2004, p.55.
[5] F. Ciocci et al., Phys. Rev. Lett. 70 (1993) 928.
[6] A.J. Doria et al., IEEE J. Quantum Electron. 29(1993) 1428.
[7] Y.U. Jeong et al., Nucl. Instr.&Meth. in Phys. Res.,A 483 (2002) 195.
[8] Y.U. Jeong et al., "THZ imaging by a wide-band
compact FEL", FEL’2004, Trieste, Italy 2004, p.667.
[9] N.S. Ginzburg and M.I. Petelin, Int. J. Electronics 59(1985) 291.
[10] N.S. Ginzburg et al., Nucl. Instr.&Meth. in Phys.
Res. A 407 (1998) 64.

Figure 6: Superradiant operation
regime: L 4.4 , T=51.2 , H 0.5 , Tc 16 ,Q 0.3 ,: a)time–space evolution of an envelope of theelectromagnetic pulse; b) time dependence of the fieldenergy.

[11] N. Piovella, Phys. Rev. E. 51 (1995) 5147.

CONCLUSION
In conclusion, we develop both linear and nonlinear
theory to describe regimes of operation of the waveguide
FELs with finite detuning of “zero-slippage” conditionand cavity detuning.
On the base carried out theoretical analyze it were
estimated parameters of generated radiation for KAERI
THz FEL ( O 100P m ) [7, 8]. The experiments weredone for an electron bunche of duration W p  30 ps, anelectron current  0.5 A, particle energy  6.5 MeV, theundulator period Ou 25 mm, the undulator length 2 m,

FEL Oscillators and Long Wavelength FELs

381

TUPPH027

Proceedings of FEL 2006, BESSY, Berlin, Germany

THE EXPERIMENTAL RESEARCH OF THE SR-FEL CAVITY MIRRORSAT 355nm AND 248nm*
GAO Huailin#，WANG Donglei, WANG Yong, TAN Rongqing, WU Jin, Institute of Electronics,
CAS, P.O. Box 2702-45, Beijing100080, CHINA
WANG Naiyan, China Institute of Atomic Energy, P.O. Box 275-7, Beijing 102413, CHINA.
Abstract
The cavity mirrors of the SR-FEL at 355nm and 248nm
central wavelengths are developed experimentally with
the
fused
silicasubstrateand“HfO2/SiO2+Al2O3/SiO2+M-SiO2” optical coatings.
The electron-beam evaporation and ion-beams sputtering
are used as the deposition technologies. After heating
condition at 400oC×4hrs, the absolute reflectance andwavelength-tunable range is measured with VARIANCary-5000 spectrophotometer. The experimental results
show that R=99.45% and Δλ(R≥99.00%) =75nm at
355nm for the broadband mirror. For the mirror with thedual-central wavelength at 355nm/248nm, R= 99.69%
and Δλ(R≥99.00%)=59nm at 355nm, and R=98.21%,Δλ(R≥99.00%)=9nm and Δλ (R≥98.00%) =51nm at
248nm.

INTRODUCTION
Storage-Ring Free-Electron Laser (SR-FEL) is awavelength-tunable, high power, short pulse light source.
With the optical resonator, SR-FEL will generate a laser
radiation with the best spatial and temporal coherences,
tunablewavelengthandharmonic
radiations,
simultaneously [1-3]. It is also the best seed light for
generating HGHG, X-ray laser and γ-ray laser with new
FEL schemes [1-11]. All of these light sources have apotential application in the nuclear physics, atomic
physics, molecular physics, bioscience and medicine. But
the high power UV/DUV free electron laser and thesynchrotron radiation will induce the mirror reflectancedegradation or direct damage. These will limit the laser
gain and the development of the SR-FEL toward to theshorter wavelength, shorter pulse and higher power in the
UV/DUV region [1-3,8,12-13]. Thus, it’s very important
to develop the resonator mirror with the lowest
absorption, highest absolute reflectance, needed wide
wavelength-tunable range, highest damage threshold andthe best resistance to reflectance degradation [1-13]. In
this paper, report the progress on the experimental
research of the SR-FEL resonator mirrors at 355nm and at
355nm/248nm.

PHYSICAL DESIGN TO MIRROR
COATING
The physical design of the mirror coatings is based on* Work supported by NSFC, Grant No. 10475081.
# Corresponding author, Prof. GAO Huailin, email: gao.hl@mail.china382

the experimental results in the Inertial Confinement
Fusion (ICF) driven by high energy laser and StorageRing Free Electron Laser (SR-FEL) researches from 1982
to 2006, so that it can integrate the all advantages ofdifferent physical designs, deposition technologies, filmgrowing parameters, post-deposition conditions, and soon. Here, a compound mirror coating is designed for thebroadband mirror coating at 355nm central wavelengthand the dual-band mirror coatings at 355nm and 248nm
central wavelengths. It is “HfO2/SiO2+Al2O3/SiO2+MSiO2”, where Sub is the material of the mirror substrate,
fused silica is chosen because of its stable physicalcharacteristics. HfO2/SiO2 and Al2O3/SiO2 are twocoating stacks, M=6 the layer number of the SiO2 top
layers. Because the HfO2/SiO2 coatings has the largest
bandwidth and Al2O3/SiO2 coatings has the highest
damage threshold in the UV/DUV region, as found by
LANL, LLNL, CIAE scientists in the research of ICF
driven by high-energy laser [13-18]. And the top-layer
SiO2 has an evident effect to increase the damage
threshold of the mirror coating as found by above
researchers [13-18], and to resist the reflectancedegradation induced by the synchrotron radiation and the
UV/DUV FEL as found by the ELETTRA scientists[8,12]. The theoretical design are listed in table.1, where
H is HfO2, H` is Al2O3, L and L` are SiO2. Since thedamage threshold of the Al2O3/SiO2 mirror coatings ishigher than that of the HfO2/SiO2, the absorption
coefficient of Al2O3 material is lower than that of HfO2
materials, and the laser intensity of the coherent standingwave electric field in the topmost layers of mirror coating
is higher than that in the inner. Thus, the Al2O3/SiO2
coating stack is set above the HfO2/SiO2, the top-layers
SiO2 is put on the HfO2/SiO2 coating stack. The basic
structures of the mirror coatings are “Sub.-LL-(0.5H-L0.5H)[12-pair]/
355nm-(0.5H`-L-0.5H`)[25-pair]-LL4L`/320nm” for the broadband mirror at 355nm and“Sub.-LL-(HL)[11-pair] /355nm-H-(LH)[11-pair]/248nmH`-(LH`)[20-pair]-LL-4L/212nm” for the dual-band
mirror at 355nm/248nm.

DEPOSITION TECHNOLOGY AND
PARAMETER
The past experiment research has shown that, for an
optimized mirror coating design, the deposition
technology and parameters have a strong and direct
affection to the realization of the physical design. As
found by LLNL scientists in ICF research, a mirror
coatings will have a higher damage threshold when

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany
deposited by electron-beams evaporation (EBE) than by
ion-beams sputtering (IBS) deposition [14]. But, as foundby ELETTRA scientists in the SR-FEL research [8,12],
when deposited by IBS technology, the oxide coating of
the resonator mirror will have resistance to the reflectancedegradation induced by FEL and synchrotron radiation.
Thus,
in
our
experimental
research,the“HfO2/SiO2+Al2O3/SiO2+2-SiO2” part of the mirror
coatings is deposited by EBE technology withLEYBOLD-APS-1104 machine; the rest 4-SiO2 film
layers are deposited by IBS technology with VECCOSPECTRA-IBS machine, so that these cavity mirror will
have high damage threshold to laser radiation andresistance to synchrotron radiation, simultaneously. The
deposition parameters are listed in table 2.
In Table 1, the leaked oxygen is used to re-oxide thedissociated oxygen molecular to increase the damage
threshold of coatings further, as found by IECAS
scientists in ICF and FEL researches [13]. Finally, thefresh sample is conditioned at 4 0 0 ° C× 4 hr s to decrease
the absorption of the mirror coating and increase theabsolute reflectance and damage threshold together. The
step-size of temperature increase is 70°C/1hr. After 4hour continuous treatment, the mirror sample will cool
down naturally to room temperature. Then, they aremeasured.
Table 1: deposition technology and parameters for SRFEL mirror coatings.
Dep o si tio n
tec h no lo g yV( HfO2)

0 . 5 n m/ s

V( Al2O3)

0 . 5 n m/ s

V( SiO2)

0 . 6 n m/ s

evapora tio n

T

185°C

P ( O2)

1.5×10[4 ] mb a rV( M-SiO2)

0 . 3 n m/ s

T

120°C

P ( O2)

4.0×10[4 ] mb a r

sp ut ter i n g

Hea ti n g
co nd it io nhigher than 99.00%, i.e., the top width of the reflectancespectrum.

Broadband Mirror Coatings at 355nm
In Fig.1 was shown the spectra of the absolutereflectance for the broadband mirror coatings at 355nm
before and after heating condition. The top width with thereflectance higher than 99.00% is listed in Table2. From
Fig.1 and Tab.2, it shows, after heating condition, that theabsolute reflectance at 355nm central wavelength isR(355nm)=99.45%, the wavelength-tunable range is from
406nm to 331nm, i.e., Δλ(R≥99.00%)=75nm. Relative to
the R` and Δλ` of the fresh mirror sample without heating
treatment, the average increases of the absolutereflectance and the wavelength-tunable range in the top
region are ΔR= 0.39% and Δλ*=7nm, where ΔR and Δλ*are defined asN
Δ R = 1 ∑ R ( λ j ) − R `( λ j )
N j=1

(

)

Δλ * = Δλ − Δλ `Dep o si tio n p ar a me ter

Elec tro n b e a ms

I o n -b ea ms

TUPPH027

4 0 0 ° C× 4 hr s

EXPERIMENTAL RESULT ANDDISCUSSION
The spectral performance of the SR-FEL mirror
coatings is measured with the spectrophotometer
VARIAN-Cary-5000. The parameters include theabsolute reflectance at the central wavelength and the
bandwidth corresponding to the absolute reflectance

FEL Oscillators and Long Wavelength FELs

Figure 1: The spectral performances of the broadband (a)and dual-band (b) SR-FEL mirror with heating condition
at 400°C× 4 hr s and without for the fresh samples. They
are measured with varian-cary-5000 spectrophotometer.

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Proceedings of FEL 2006, BESSY, Berlin, Germany
Δλ`(R`>99.0%)=(363-330) nm=33nm

Dual-band Mirror Coatings at 355nm/248nm
In the Figure 1 was also shown the spectra of theabsolute reflectance for the dual-central wavelength
mirror coatings at 355nm/248nm on fused silica substrate.
The absolute reflectance higher than 99.00% is listed inTable 3. From these experimental data, it can be seen that,for the mirror coatings after heating condition, all thecharacteristics of the first band at 355nm is similar to thatin Fig.1. It has a perfect shape. At the central wavelength
355nm, the absolute reflectance and wavelength-tunable
range are R=99.69% and Δλ(R>99.00%)=373nm314nm=59nm; Relative to the experimental data (R` andΔλ) in the Fig.1 for the fresh sample without heating
treatment, the average increase of the absolute reflectanceand wavelength-tunable range are ΔR= 0.73% andΔλ*=26nm, defined as above.
In the second band at 248nm for the sample withheating condition, the absolute reflectance is less than
99.00% at most of the wavelengths. The reflectance at
248nm central wavelength is only R(248nm)=98.21%.
Only in the wavelength ranges of (275-272)nm and (240234)nm, the absolute reflectance is higher than that
99.00% and Δλ(R≥99.00%)= (275-272)nm+(240-234)
nm=9nm. At most of the wavelengths, the absolutereflectance is ranged from 98.00% to 99.20%, itscorresponding
wavelength-tunablerange
isΔλ(R≥98.00%) =33nm. Relative the optical spectrum of
the fresh mirror coatings without heating treatment, its
average increase of the absolute reflectance andwavelength bandwidth are ΔR(R≥98.00%)=1.04% andΔλ*(R≥98.00%)=9nm.
Table 2: The absolute reflectance and wavelength-tunable
range of the SR-FEL broadband mirror at 355nm
λ/nm

406

405

401

400

R/%

99.02

99.10

99.55

99.67

R`/%

97.89

98.02

99.01

99.25

λ/nm

341

333

332

331

R/%

99.73

99.67

99.64

99.38

R`/%

98.65

99.02

98.53

97.73

Δλ/nm

Δλ (R>99.00%)=406nm–331nm=75nm,
Δλ`(R`>99.00%)=401nm–333nm=68nm

Table 3: The absolute reflectance and wavelength-tunable
range of the SR-FEL mirror at 355nm/248nm.
λ/nm

373

364

363

355

330

R%

99.17

99.73

99.79

99.69

99.46

R`/%

97.54

98.83

99.01

99.14

99.04

λ/nm

323

322

316

314

283

R%

99.30

98.97

99.09

99.07

98.22

R`/%

98.87

98.77

97.81

98.39

96.45

Δλ/nm

384

Δλ(R>99.0%)=(373-314) nm=59nm,

λ/nm

275

272

271

270

248

R/%

99.19

99.12

98.8 79

98.49

98.21

R`/%

98.16

98.42

98.19

97.88

97.01

λ/nm

241

240

234

233

232

R%

98.83

99.17

99.12

98.82

98.09

R`/%

93.61

98.11

98.53

97.98

96.72

Δλ/nm

Δλ (R>98.0%) = (283-259)+( 241-232)=33nm
Δλ`(R`>98.0%) = (275-271)+(240-234)=10nm

In additional, the highest reflectance is up to 99.19%
at 275nm. The shortest wavelength with reflectanceR≥99.00% is at 234nm. The shortest wavelength withreflectance R≥98.00% is at 232nm, its reflectance is
98.09%. The spectral breaking at 244nm may be inducedby the bandwidth narrowing in the DUV region. Thus, it’snecessary to improve the spectral continuity at 244nm
further.
From the experimental results for tow types of themirror coatings, we can get the following conclusion. (1)Heating condition to the fresh mirror coatings has anevident influence on increasing mirror’s absolutereflectance and expanding spectral bandwidth. It implies
that absorption coefficient of the mirror coatings have
reduced after heating treatment. It’s very important todevelop the RS-FEL mirror toward the shorter
wavelength and higher power output. (2) These resonatormirrors have get the designed absolute reflectance andspectral bandwidth. Thus, it can be used as the SR-FEL
resonator mirror.

CONCLUSION
Today’s experimental results show that it’s possible
to develop the SR-FEL cavity mirror with an absolutereflectance higher than 99.00% and wavelength-tunable
range from 10nm to 75nm in the UV/DUV region. It isvery effective to develop the SR-FEL mirror coatings
with a compound optical design, a combined deposition
technologies of electron beams evaporation and IBS,
oxygen-leaked method, and heating treatment.

ACKNOWLEDGEMENTS
The research work is supported by the naturalscience foundation of China (NSFC) with the project No.
10475081. The authors gratefully thank NSFC for her
support.

REFERENCES[1] Patrick G. O’Shea and Henry P. Freund, “FreeElectron Laser: Status and Applications”, Science,
292(2001) 1853-1858.
[2] S. V. Milton, E. Gluskin, N. D. Arnold, et al,“Exponential Gain and Staturation of a Self-

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany
Amplified Spontaneous Emission Free-electron
Laser”, Science, 292(2001) 2037-2045.
[3] L. H. Yu, M. Babzien, I. Ben-Zvi, et al, “High-Gain
Harmonic-Generation Free-Electron Laser”, Science,
289(2000) 932-934.
[4] Jialin XIE, “Current FEL Development in China”,
Proc. 2nd Asian Particle Accelerator Conf., Beijing,
China, 2001, 215-220.
[5] B. C. Zhang, K. Zhao, J. K. Hao, et al, “HighAverage Current Superconducting Accelerator At
Peking University”, Proc. 2nd Asian Particle
Accelerator Conf., Beijing, China, 2001, 97-99.
[6] CHEN Nian, HE Duohui, LI Ge, at el, “Generaldesign of coherent harmonic generation storage-ringfree-electron laser of NSRL”, Nucl. Techn., 27(2004)
405-408, (in Chinese).
[7] D. NUTARELLI, D. Garzella, E. Renault, et al,“Super ACO FEL Oscillation at 300nm”, Nucl. Instr.
And Meth.. A 445(2000) 143-148.
[8] St. Gunster, A. Gatto, M. Trovo, et al, “VUV Optics
Development for the ELETTRA Storage Ring FEL”,
Proc. 2004FEL Conf., 2004, 233-236.
[9] K. Yamada, N. Sei, H. Ohgaki, et al, “Characteristicsof the NIJI-IV UV-VUV FEL System-Toward Lasing
Down to 150nm Using a Compact Storage Ring”,
Nucl. Instr. And Meth.. A 475(2001) 205-210.
[10] Vladimir N. Litvinenko, Seong Hee Park, et al,“Operation of the OK-4/Duke Storage Ring FEL
below 200nm”, Nucl. Instr. And Meth.. A475 (2001)
195-204.

FEL Oscillators and Long Wavelength FELs

TUPPH027[11] M. Hosaka, S. Koda, M. Katoh, et al, “Recent
Progress of the UVSOR”, Proc. 2th Asian Particle
Accelerator Conf., Beijing, CHINA 2001.
[12] A Gatto, J. Heber, N. Kaiser, et al, “Highperformance UV/VUV optics for the storage ring
FEL at ELETTRA”, Nucl. Instr. And Meth.. A483
(2002) 357-362.
[13] GAO Huailin, WANG Naiyan and SHAN Yusheng,“Experimental Investigation on the Resonator mirrorof the SR-FEL and ICF KrF Laser”, High Energy
Physics and Nuclear Physics, 29(2005)99-103, (inChinese).
[14] Ralph Berggren and James D. Boyer, “Optics
Technology for KrF laser”, Inertial Confinement
Fusion at Los Alamos, Progress Since 1985, Vol.I,
Chapter VII, 1989, 1-8.
[15] F. Rainer, D. Milan and W. H. Lowdermilk, “Laser
damage thresholds of thin film optical coatings at
248nm”, NBS Special Publication, 638(1981) 339343.
[16] GAO Huailin, SHAN Yusheng and WANG Naiyan,“Research on the UV Dielectric Coatings with High
Damage Threshold”, Chinese J. Laser, B6(1997)229-237.
[17] Arthur H. Guenther, “Optical Damage: Boulder and
Beyond”, Lasers & Optronics, Oct.,1989, 57-62.
[18] Stephen R. FOLTYN and Brian NEWNAM,“Ultraviolet damage resistance of dielectric reflectors
under multiple-shot irradiation”, IEEE J. QE,
17(1981) 2092-20.

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THE RESEARCH OF FIR-FEL IN CAEP
Xingfan Yang#, Ming Li, Xiao Jin, Weihua Li, Zhou Xu
Institute of Applied Electronics, CAEP, China.
Abstract
The research of FIR-FEL has been undertaken about 10
years in CAEP (China Academy of Engineering Physics)
and first lasing at center wavelength 115 μm wasobserved in March 2005. The facility consists of RF-gun,alpha magnet, L-band SW accelerator, beam transport
line, wiggler, optical cavity and measurement system. At
present, a high brightness photo cathode RF-gun iscommissioning, the cathode material is Cs2Te and thequadruple light is used. This injector will be used in the
FIR-FEL project in the second half of this year. In thispaper, the design consideration, the system layout andexperiment results are introduced.

INTRODUCTION
The research work of FIR-FEL was started in 1997 in
CAEP. In 1999 the 30MeV RF SW electron linac wasbuilt, the linac consists three accelerating sections, theresonant frequency is about 1.3GHz, a 1+1/2cell
thermionic RF-gun was used as the injector. When doing
the FIR-FEL, only the first accelerating section(ACC1)
was used, the electron energy is about 6.5MeV∼7MeV.
The FIR-FEL facility consists of RF-gun, alpha magnet,
ACC1, beam transport line, wiggler, optical cavity andmeasurement system (shown in Fig.1). Based on thisfacility the first lasing was observed in March 2005 andthe center wavelength was 115 μm. As one important
direction of FEL the high average power FEL wasproposed. Two key technology of high average power
FEL are the high brightness photo-cathode injector andthe SRF ERL. The high brightness photo-cathode RF-gun
injector was studied in our Lab in 1999 and the first
photo-cathode injector with 2+1/2cell was operated in
2000.In order to study the SRF technology, cooperativewith the Peking University, we built a superconducting
cavity. This cavity includes a single cell (the frequency is
1.3GHz). This cavity was tested in our Lab in 2000, theenergy gain is about 0.6MeV.

B M -60

THERMIONIC CATHODE RF GUNINJECTOR
The study of FEL needs the high brightness electron
beam with small energy spread. The beam quality ismainly determined by the injector. The development ofhigh-brightness electron sources has been a challenging
project for many years. RF gun is one kind of highbrightness electron source which developed for the
purpose of FEL research in 1984[1]. It has high electricfield. The electron was accelerated to the light speed ina short distance, so the space charge effect has been
reduced efficiently and easy to get the small emittance.
There are two kinds of RF guns, one is the thermioniccathode RF-gun, the other is photo-cathode RF gun.
The work of thermionic RF gun in our Lab isintroduced in this section and the photo-cathode RF gun
will be introduced in the next section. The advantagesof thermionic cathode RF gun are the simple
construction, operating reliability and low cost, it acts
as an important role in the research of FEL especially atthe beginning and it has been studied in detail. We built
thermionic RF-gun as the injector for the 30MeV linac.
The drawback of this kind of injector is the relativelarger energy spread aroused by the wide capture phaseand electron back bombardment. In order to decrease
the electron back bombardment and obtain good quality
electron beam, several guns with different structure
have been built and experimented in our Lab. The
SUPERFISH and PARMELA codes were used for theaccelerating structure design. The ring cathode RF gun
was tested also, but the experiment result was not good.
Finally the 1+1/4cell gun was selected (shown in Fig.2),
the electric field on the axis was measured using
network analyser (shown in Fig.3). It was built in2004(shown in Fig.4), the cathode material is LaB6, thediameter is 5mm and the electron energy of this injector
is about 1.5MeV. Using this injector, the FIR-FEL
stimulated emission was observed.

ACC1

a-M
BM P
QT
BCT
S
R F G unFig.1: the schematic of the FIR-FEL facility.
___________________________________________#

xingfan_y@caep.ac.cn

386

Fig.2: the schematic of the thermionic cathode injector.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH028

Fig.3: the electric field on the axis.
Fig.6: the electric field on the axis.

Fig.4: the thermionic cathode injector.

PHOTO-CATHODE RF GUN INJECTOR
The photo-cathode RF gun injector developed from1985[2], comparing with the thermionic cathode RF-gun
injector, the photo-cathode RF-gun is more adaptive to thetresearch of FEL, it is easy to get the short pulse with highcurrent and small energy spread. We started to study thephoto-cathode RF-gun in 1999, and the first one was builin 2000, the electron energy is about 3MeV. In order toldevelop the 3μm∼8μm FEL, the second photo-cathodeRF-gun with 4+1/2cell was studied in 2004(schematicwas shown in Fig.5, the frequency is 1.3GHz), so the tota
electron energy(including the injector and three
accelerating sections) is about 37MeV. The electric field.
on the axis was measured using network analyser (shownin Fig.6). It was built in 2005(shown in Fig.7), thefocusing solenoid and compensated solenoid were used
This injector is commissioning at present.

Fig.7: the 4+1/2cell photo-cathode injector.
The cathode material is Cs2Te and the quadruple lightis used. The quantum efficiency is about 1%, the electronenergy is 7MeV. The cathode-driving laser system(shownin Fig.8) of the RF photoinjector include the mode-locked
oscillator(fromTime-Bandwidth),
diode-pumned
amplifier and FHG (fourth harmonic generation). The
average power of the oscillator is 10W , the timing jitteris 0.56ps, the width is 11.9ps at a repetition rate
54.167MHz . Micropulse energies is 3 J of 266nm light.

μFig.8: Optical Schematic of the cathode-driving laser
system F, the Flady isolator.P, pockel .HR, high reflector.

THE WIGGLER

Fig.5: the schematic of the photo-cathode injector.

FEL Oscillators and Long Wavelength FELs

The Wiggler is one of the most important components
for FEL and it is the region where the relative electron
and the radiation field will interact. It’s performance, suchas the peak field, good field aperture etc. will determine

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Proceedings of FEL 2006, BESSY, Berlin, Germany

the FEL gain when we calculate the relative electron
performance. A NdFeB-FeCoV hybrid wiggler has been
designed and built for CFEL. More than 10mm good
aperture and as high as 3235 Gs peak field were achieved
with a 18 mm gap (shown in Fig.9). The trace simulation
for a single electron showed that the center offset was lessthan 0.1 mm, the electron trajectory was simulated(shownin Fig.10), and the ratio of the small signal gain versus theideal small signal gain was more than 98 percent.
Recently, we’ve observed the resonance light in the 115
um FIR-FEL experimental study which used this wiggler.

Fig.9: the wiggler.

THE FIR FEL EXPERIMENTThe parameters of the FIR-FEL facility is shown intable 1.The macro-pulse current is measured by BCT andthe beam currents are measured at the different position of
the beam line, shown in Fig.12. The width of the micropulse is measured by the streak camera. The microwave
power of the injector and ACC1 are provided by a
klystron with 10MW. The stimulated signal is obtained in
the March 2005, shown in Fig.13 and the spectrum of thestimulated signal is measured using grating analyser,
shown in Fig.14, the center of the spectrum is 115μm, thewidth of spectrum is about 1%.
Table 1: parameters of the FIR-FEL facility
Energy6.5MeV
Normalized
emittance
20πmm⋅mrad
Macro-pulse
current Number of wiggler periods
130mA
44
Period length 32mm
Macro-pulse width 4μs
Micro-pulse current 4A
Wiggler gap 18mm
Micro-pulse width 25ps
Magnetic field 3250Gs
Energy spread
1%
Opticalcavitylength2536mm

Fig.12: the beam current at the different position on the
beam line, measured with BCT.

Fig.10: simulation trajectory of the electron in the wiggler.

THE STUDY OF SRF TECHNOLOGY
In order to get the high average FEL power, the highaverage electron beam power should be provided first,
and the machine should be operated in the CW condition
thus the SRF is required. SRF ERL technology is thepractical way to obtain the high average power FEL andproved by JLAB[3]. Cooperate with the Peking
University, we built a facility to study the SRF technology,(shown in Fig.11), at this facility the 2+1/2cell photocathode injector was used. The high average power FEL
was proposed and we will begin to build the SRF ERL
machine in the next years.
Helium Liquefier

CryostatPhoto-Cathode2+1/2 RF Gun

Superconducting Cavity

Mode-Locked Laser

KL-28

500W CW

Control System

Beam Diagnosis

Vacuum System

Fig.11: the schematic of the SRF test facility.

388

Fig.13: the FEL stimulated emission signal.

Fig.14: the spectrum of the stimulated signal.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH028

CONCLUSIONREFERENCES

We have made great efforts in the research of FIRFEL, and obtained the stimulated emission in 2005. The
thermionic-cathode and photo-cathode RF gun injectors
have been built. The high power FEL project was
proposed and a single cell superconducting facility wasbuilt and tested. The next step we will build the SRF
energy recovery Linac.

[1] A. Westenshop, J.M.J. Madey, “Microwave ElectronGun”, Laser and Particle Beam, 1984, 2(2), p223.

FEL Oscillators and Long Wavelength FELs

[2] C.H. Lee etc IEEE Trans Nucl Sci NS-225 1985,
p3045.
[3] S. Benson, D. Douglas, M. Shinn, etc, “High Power
Lasing in the IR Upgrade FEL at JEFFERSON LAB”
Proceeding of FEL2004, p229-232.

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DEVELOPMENT OF POWERFUL FEMS OF X, KA AND W BANDSFOR PHYSICAL AND INDUSTRIAL APPLICATIONS*
N. Ginzburg, N. Peskov, M. Petelin, Institute of Applied Physics RAS, N.Novgorod, Russia
A. Kaminsky, S. Sedykh, Joint Institute for Nuclear Research, Dubna, Russia
M. Einat, The College of Judea and Samaria, Ariel, Israel
A. Gover, Y. Socol, Tel-Aviv University, Israel
J. Lucas, The University of Liverpool, UK.
Abstract
The possibility to develop powerful FEMs capable forphysical and industrial applications is being studied at
Tel-Aviv University, IAP RAS, JINR and The Universityof Liverpool within the framework of the INTAS
collaboration project. Present paper summarizes the
progress in three successful FEM experiments: (1)Electrostatic-accelerator driven 70-130 GHz TandemFEM with kW-level pulse power (Tel-Aviv University);(2) Linac-driven 30-GHz FEM with pulse RF power of~ 20 MW (JINR + IAP RAS); (3) Sub-relativistic e-beamindustrial FEM tunable over X-band with output power
up 1 kW (The University of Liverpool).

INTRODUCTION
Free electron masers (FEMs) are among the main
sources of powerful microwave pulses from X to Wbands. Interest to such sources is caused by the large
number of potential physical and industrial applications,requiring a wide variety of the radiation parameters. For
example a new generation of the accelerators (SLAC,CERN etc.) requires sources of ~100 MW pulse power at30-38 GHz with a narrow spectrum. Material processing
stations require kW-level average power. Spectroscopic
and imaging experiments as well as biologicalexperiments, require lower power but fine control andtuning of the radiation spectrum.
Presently there are no ready industrial RF sources withparameters necessary for the applications mentioned
above. Investigations carrying out in collaboration
between aforementioned Institutes are aimed to partiallyfill up the gap with FEMs from X to W bands fordifferent applications including testing components ofhigh gradient accelerators and material processing.
Present paper is devoted to the progress in thedevelopment of FEMs and their applications.

70-130 GHz TANDEM FEM
The Israeli FEM [1] resonator was re-designed in orderto reduce the overall round-trip losses and achieve control
on the radiation output-coupling. In its new configuration,
the resonator consists of overmoded corrugatedrectangular waveguide and two radiation mode splitters,*This work is partially supported by INTAS (grant # 03-51-5319) andRussian RFBR (grants # 04-02-17118, # 05-02-16833, # 05-02-17036)

390

separating the high-energy e-beam from the laser
radiation. The electron input splitter is based on Talbot
effect in an overmoded rectangular waveguide. The
radiation out-coupling is done in the output splitter. It isbased on novel design and it combines Talbot effectbetween two parallel plates with free space propagation,and focusing by two curved cylindrical mirrors in a
confocal imaging scheme. The waveguide and thesplitters were tested experimentally, showing improved
performance in comparison with the former resonator.
The measured unloaded Q-factor of the new version isincreased by a factor of ~ 3, attaining up to Q = 25 000.
Accordingly, the round-trip losses are ~ 23%. Rotating
grids control the radiation out-coupling allowing wide
variation for maximization of the radiation output powerand extraction efficiency.
Additional R&D work was aimed on increasing
FEM power by boosting the electron beam energy after
the radiation build-up. A fine control of the electron beamenergy during the radiation pulse is designed tocompensate the small energy degradation during thepulse. Also, a controlled ramp (up or down) in theelectron energy during the pulse will be applicable aswell. We compared the theoretical estimations of theoutput power in the presence of electron energy change
during the pulse, to the obtained experimental results.
Two models, showing good agreement between them andwith the existing data, were compared: low-gain
analytical model based on the pendulum equation, andrigorous 3D FEM interaction model solved numerically.
Another expected result of the design is to further extend
the pulse duration with stable conditions and to obtain
improved coherency.

30 GHz JINR-IAP FEM
The FEM-oscillator has been developed in Ka-band
during last few years in a collaboration between JINR
(Dubna) and IAP RAS (Nizhny Novgorod) [2]. Theseexperiments aim to develop a pulsed power microwave
source for testing behaviour of materials in high-Q
structures under the influence of RF-pulses. Information
about the life-time of different metals in strong RF-fields
would be beneficial, in particular, when designing highgradient accelerating structures for future linear colliders[3]. Such application requires a high power RF-sourcewith a narrow frequency bandwidth. In addition, the

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH032

solenoid with reversed guide field orientation

helical wiggler

linac focusing coils

FEM output section based on Talbot effectelectron beam

Bragg resonator with step of phase of corrugation

Figure 1: Schematic diagram of the JINR-IAP FEM.
radiation frequency should be exactly matched to theoperating frequency of the accelerating structure, andtherefore precise frequency tuning is essential for such agenerator.
A schematic diagram of the JINR-IAP FEM
experiments is shown in Fig.1. The induction linac LIU3000 (JINR), which generates a 0.8 MeV / 200 A / 250 ns
electron beam with a repetition rate of 1 Hz, drives the
FEM-oscillator. Transverse velocity in the magneticallyguided beam is pumped in a helical wiggler of 6 cm
period. The main advantages of developed FEM is the useof a reversed guide field, which provides high-quality
beam formation in the tapered wiggler section with a low
sensitivity to the initial beam spread, alongside with
Bragg resonator having a step of phase of corrugation,
which possesses high electrodynamical mode selection.
As a result, stabile single-mode operation with highelectron efficiency was achieved in the FEM. At thepresent stage, the FEM generates 20 MW / 200 ns pulses

at 30 GHz with the spectrum width of 6 - 10 MHz (Fig.2).
Precise tuning of the oscillation frequency of the FEM
was performed by inserting short sections of smooth
waveguide between the two Bragg structures. If the phaseshift between the Bragg structures is varied from 0 to 2π
the frequency of the fundamental eigenmode moves fromthe lower to the higher edge of the Bragg zone. It is
important to note that only one high-Q eigenmode exists
inside the Bragg zone at any value of phase shift, i.e. thehigh selective properties of the resonator are maintained
over a sufficiently wide frequency band. For a phase shiftequal to π the frequency of nearly 30 GHz was measured.
In the experiments frequency tuning was achieved over arange of 6%, the spectrum width in all regimes ofoscillations did not exceed 0.1% (Fig.3).
The test facility to study surface heating effects at
30 GHz, which was constructed based on the FEM source[4], is shown in Fig.4. The experimental set-up includes a
two-mirror confocal transmission line and mode

heterodyne beating signal

frequency spectrum (50 MHz/div)

30,5Frequency, GHz

RF-power detector (100 ns/div)

30,0central mode

29,5
29,0

side mode

28,50,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8Corrugation phase shift, in π units
Figure 2: Typical oscilloscope traces of the RF-pulse
generated by 30 GHz JINR-IAP FEM.

FEL Oscillators and Long Wavelength FELs

Figure 3: Measured dependence of the FEM oscillation
frequency on the value of the phase shift ofcorrugation between the Bragg structures.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

FEM output section

two-mirror transmission line

copper test cavity
directional coupler

RF detector

TE1,1 to TE0,1 mode converter

Figure 4: Schematic diagram of the test facility for studying surface heating effects based on JINR-IAP FEM.
W_averag.(MW)800

durat_level(ns)

800

700

Number of pulses

Number of pulses

700
600
500
400
300
200
100
0
0

20

40

60

80 100 120 140 160

Pulse duration (FWHM), ns

600
500
400
300
200
100
0
0

1

2

3

4

5

6

Average power, MW

Figure 5: Statistic distributions of pulse duration and RF-power after the test cavity in the series of 104 pulses.
converters to transport the RF-power from the FEM to thetest cavity. A special copper cavity operating with TE0,1,1
mode and having Q-factor ~ 1500 was designed to model
temperature regime in a high-Q accelerating structure of
the CLIC project. The profile of the cavity surface was
optimized to enhance the RF magnetic field in a certain
zone and provide needed temperature rise during eachRF-pulse. The resonant frequency of the cavities is alsomechanically tuned to coincide with the frequency of the
FEM source. A directional coupler is included to control
both the incident and reflected powers. After a certain
number of pulses the Q-factor of the cavity would bemonitored using a network analyzer to detect early signsof surface damage. “Cold” tests of all components of theexperimental set up were carried out and demonstrated
good agreement with designed parameters.
Simulations carried out demonstrate principal ability of
the FEM to be used for the aforementioned application.
Results of the first experiments also proved possibility of
the FEM to operate at the high-Q load. When frequencyof the test-cavity was tuned to the FEM generation
frequency it was observed that during the RF-pulse the392

reflected signal decreased and the test-cavity became
transparent. As a result, accumulation of the RF-power inthe load was achieved. At the present stage the effect of
the copper surface degradation at 30 GHz was studied in
the statistics of 105 pulses (Fig.5) at the temperature riseof 50 °C during each RF-pulse. The test cavity providing
temperature rise at the certain zone up to 150 °C wasdesigned and the experiments with the statistics of 106
pulses, which are important for design of CLIC collider
components (CERN), are in progress currently.

REFERENCES[1] A.Abramovich, M.Canter, A.Gover, e.a., Phys. Rev.
Lett. 82 (1999) 5257.
[2] N.S.Ginzburg, A.К.Kaminsky, N.Yu.Peskov, e.a.,Phys. Rev. Lett. 84 (2000) 3574.
[3] I.Wilson, CLIC Note 52, Oct. 1987.
[4] A.К.Kaminsky, A.V.Elzhov, I.N.Ivanov, e.a., Proc.
of the 22nd Int. FEL Conf., Durham, USA, 2000,
p.II-41.

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH033

A FEL AMPLIFIER BASED ON PLANAR BRAGG WAVEGUIDES*
Ginzburg N.S. #, Malkin A.M., Rozental R.M., IAP RAS, Nizhny Novgorod, Russia,
Dorfman K.E., Department of Physics, Texas A&M University, College Station, USA

Abstract
We study a new version of FEL amplifier on the baseof wide sheet electron beams. We suggest using atransverse open Bragg structures which can provide
radiation waveguiding with simultaneous effective mode
selection (filtration). Theory of transverse current FEL
amplifier based on planar Bragg waveguides is
considered.

INTRODUCTION
A planar periodic Bragg structure can be used not only
as resonant elements of FEL oscillators [1-3] but asselective waveguides in different new schemes of FEL
amplifiers. Open Bragg waveguide where wave
propagates in the direction transverse to the lattice vector(Fig.1) can provide high selectivity over the transverse
coordinate when its size essentially exceeds wavelength.
In a transverse current amplifier scheme it is beneficial touse a grating with a step of corrugation, which results inthe existence of a single low dissipative mode locatednear defect. The sheet electron beam moves across the
waveguide to be resonant to one of partial waves forming
the operating mode. Another way is a traditional
travelling wave amplifier scheme where electron beam
moves along waveguide axis. To increase effective size ofoperating mode one ca use a structure with regularlongitudinal corrugation that couples two partial waves
propagating at some angle to the axis to the wave
propagating directly along the axis. This wave, which inmoving reference frame is transformed into a cut off
mode, is excited by the electrons. Analysis shows rather
high gain and efficiency of the novel schemes withsimultaneous discrimination of parasitic modes.
This paper is organized as follows: in the Sect.1 westudy wave propagation in the Bragg waveguide with astep of corrugation to find the mode spectrum of thisstructure. In the Sect.2 we investigate the model of thetransverse current FEL amplifier. In Conclusion webriefly overview another scheme of Bragg amplifier basedon coupling of some higher mode of the planar waveguideand two TEM modes.

EIGENMODES OF THE OPEN PLANAR
BRAGG WAVEGUIDE WITH A STEP OF
CORRUGATION
We consider a planar waveguide (Fig.4) with weakly
corrugated walls(1)
l = l0 cos(h x )where 2 l 0 is the depth of corrugation. Assuming thatlattice vector h = 2π , (d is the period of corrugation) isddirected in x direction. The coupling exists for TEM
waves with x- and z- wavenumbers satisfying Bragg
resonance condition (see Fig.1)

hz1 = hz 2 = h; hx1 = −hx 2 = h / 2
We assume that the deflection of the waveguide surface

l (x) is much less than the wavelength λ and thecorrugation period d : l 0 << λ , d . In this caseperturbation of waveguide plates can be treated by using
the equivalent surface magnetic current [4]. We seek theelectric and magnetic fields as the linear combination of
two TEM modes of a corresponding regular waveguide(Fig.5):

(
)
,
r
r
r
H = Re ( A ( x, z ) H e + A ( x, z ) H e ) exp(iω t − ihz )rrr−i h x

E = Re ⎡ A1 ( x, z ) E10 e 2 + A2 ( x, z ) E2 0 e 2 exp(iω t − ihz ) ⎤
ih x

⎢
⎣

Figure 1: The diagram showing thecoupling of waves on the Bragg lattice.
____________________________________________*Work supported by RFBR grants 06-02-17129-а and 05-02-17036-а
and the Dynasty foundation.
#
ginzburg@appl.sci-nnov.ru

FEL Oscillators and Long Wavelength FELs

⎡
⎢
⎣

⎥
⎦

1

0 i h2 x1

20 − i h2 x
2

⎤
⎥
⎦

Slowly varying (in the wavelength scale) partial waves
amplitudes, A1,2 ( x, z ) satisfy the coupling equations:h ∂A1,2h ∂A1,2+ iα A2,1 = 0
m
k ∂z
2k ∂x

(2)

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Proceedings of FEL 2006, BESSY, Berlin, Germany

where
l h2
α= 0
4a0 2kis the coupling parameter ( a0 is the distance between
plates), h =k 2 − ( h / 2) 2 , k = 2π / λ . If we introduce

an angle

between the partial wave propagation

ϕdirections ( sin ϕ = h ), the coupling parameter can be
2krepresented aslα=h sin ϕ .
4 a0
The maximum value of the coupling parameter takes
place when the frequency tends to the cutoff frequency
and the wave vectors of the two partial waves are counter
directional

π ⎞.
⎛⎜ϕ = ⎟
2⎠⎝

The coupling parameter and theangle ϕ tend to zero while the frequency shift from thecutoff increases. By seeking seek the solution of theeqs.(2) as A1,2 exp(igx + iГz ) , we have the dispersion
h
2

2

2

2

(5)

⎧
πN
πN h
⎪gN = 2− i2
L
Lx 2 2kα⎪x⎪2⎛πN h ⎞ ⎞
k N ⎛
⎪
⎜
1+ 2⎜
⎨Re Г N = α⎟ ⎟α Lx 2k ⎠ ⎟
h N ⎜
⎝
⎪
⎝
⎠
⎪
3
2
⎪
k (π N ) ⎛ h ⎞⎪Im Г N = −α h 4 (α L )3 ⎜ 2k ⎟
⎝ ⎠
x
⎩

(6)

where N = ±1, ±2, ±3... are the mode numbers.
Fig. 2 demonstrates the dispersion diagrams for thedifferent mode numbers and the diffraction losses curves
via the frequency shift from the cutoff Ω =

2k
−1.
h

It should be noted that expressions (5,6) diverge at

h → 0 , while the frequency tends to the cutoff. Theseequation for the unbounded grating( g ) = ( kГ ) − ( kα )⎧2k⎪ g 0 = ±iαh⎪⎪⎨Re Г 0 = 0⎪⎪Im Г 0 = −2α k exp ⎛⎜ −α 2k Lx ⎞⎟
h
h
⎪⎩
⎝
⎠
and a set of higher modes:(3)

where g and Г are small amendment to the transverseand longitudinal wavenumbers g << h / 2, Г << h0 .
The defect of corrugation in the middle of the
waveguide can be entered as a π/2 phase step of the
waveguide corrugation (1) which leads to the change ofthe sign of α in (2) at the point x = Lx / 2 :⎧+ | α |, x < Lx / 2⎩− | α |, x > Lx / 2
Using the coupled waves equations (2) one can find theeigenmodes of an open in x direction planar Bragg
waveguide with width Lx . In this case the boundary
conditions for partial waves correspond to the absence ofreflections and can be presented as follows:
A1 (0) = A 2 ( Lx ) = 0 .
Taking (2) into account and using the fields continuity
condition on the step of corrugation, the characteristic
equation for the bounded grating can be presented in aform similar to the theory of Bragg resonators [2]:2α 2 = ⎡⎣ Г 2 − Г ( g 2hk ) ⎤⎦ exp(igLx ) +(4)+ ⎣⎡ Г 2 + Г ( g 2hk ) ⎦⎤ exp(−igLx )α = α ( x) = ⎨formally infinite diffraction losses appear when theapplicability conditions of perturbation theory fail tofulfill. Nevertheless for practical use of Bragg
waveguides it is interesting situation of rather large wave
group velocities corresponding to large detuning ofradiation frequency from the cutoff (Bragg frequency)
where expressions (5),6) are non-divergent.
th

For N>0 the transverse structure of the N
waveguide mode represents the distribution close to a
standing wave with sine wave envelope having N halfperiods on the length Lx (Fig.3a), while the lowest mode
distribution is localized near the defect and has the
exponential transverse structure (Fig.3b).

Equations (3),(4) can be solved approximately in theassumption of strong wave coupling ( α Lx >> 1 ). The
spectrum of longitudinal wavenumbers consists of thesingle mode at the exact Bragg resonance ( Re Г = 0 )(which would be treated as “0”th mode):

394

Figure 2: Dispersion diagrams for different mode
numbers (left) and diffraction losses curves via thefrequency shift (right).

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germanya)

TUPPH033b)ξζ

Input wave

Figure 3: Transverse structure of modes with N=0(a) and N=1 (b).

Diffraction losses of this mode ( Im Г ) are proportional
to exp(− 2kα Lx / h ) and are very small at large Lx ,while the high order modes have significantly greater
decrements (they decrease as 1 3 ) than the dominantLxmode decrement. Thus, such wide structures can be used
for highly selective waveguiding.

TRANSVERSE CURRENT FELAMPLIFIER
Transverse current amplifier schemes are well known
in microwave electronics. In case of a rectilinear electron
beams such type of interaction can be realized by meansof oblique corrugation of slow wave structure [5]. In caseof curves beams the synchronous interaction can berealized in smooth electrodynamical systems. One of the
problems arising in such systems is distortion of thetransverse field structure by the electron beam [6, 7]. This
problem can be solved by means of using the open
waveguides based on Bragg structures which provides
high selectivity over the transverse mode index.
We consider a thin over the y coordinate sheet electron
beam moving in the undulator field and in the uniformrr
guiding magnet field H 0 = H 0 ξ 0 (the directions of thecoordinates and ξ are shown in the Fig.4). The beam is
injected into the waveguide in the direction corresponding
to the direction of propagation of the one of the coupled
TEM waves in the waveguide described in the previous
section and it is synchronous to this mode.
We consider the electron-wave interaction in the caseof the undulator synchronism assuming the bounce
frequency Ω is far from cyclotron synchronism withelectrons:ω − hvII − ωH T >> 2π , Ω − ωH T >> 2π ,where ω

H0

=

eH 0

m0 cγ 0is a cyclotron frequency, vII is

the longitudinal velocity of electrons, γ 0 = (1 − v / c )2

2 −1/ 2is relativistic factor, T is characteristic time ofinteraction. We also consider the ultra relativistic case
γ 0 >> 1 .

FEL Oscillators and Long Wavelength FELs

Figure 4: The scheme of a FEL amplifier withtransverse current.
The process of monochromatic signal amplification in
the transverse current FEL scheme can be described by
the equations similar to the nonstationary equations of
traditional FEL with 1D Bragg resonator [2] with time
variable replaced by spatial one. These equations describe
the formation of transverse structure of the fields together
with their longitudinal structure2π⎧ h ∂a1 h ∂a1
1
− iθ
+
−
+
=
i
δ
a
i
α
a
)
⎪
)
1
2
∫0 e dθ 0
2
∂
∂
k
z
k
x
π
⎪
⎪⎪ h ∂a
(7)
h ∂a2
2
⎨
) − iδ a2 + iα a1 = 0) −⎪ k ∂z 2k ∂x
2⎪⎛ h ∂
h ∂ ⎞
iθ
⎪⎜
+
) ⎟ θ = Re a1e
)
2
∂
∂
k
z
k
x
⎠
⎩⎪⎝
Here the normalizations, variables and parameters are)) )definedasfollows: x , z = Ckx, Ckz , α = α /(Ck ) ,()

a1, 2 = eKμA1, 2 / C 2 , θ is electron phase, C is Pierce
parameter, μ is bunching parameter, K is electron-wave
coupling parameter, δ is normalized synchronism
detuning.
If the input signal is a TEM wave packet entering thesystem under the angle corresponding to the direction of
propagation of the partial wave A1 , then the boundary
conditions for (7) take the formdθ
| X = 0 = 0, θ | X = 0 = θ 0 ∈ [0, 2π ),dX
a1 |Z = 0 = a0 , a1 |X =0 = 0, a2 | X = Lx = 0(8)Results of direct numerical simulation of (7-8) arepresented in Fig.5. In the Fig 5a the dependence of theamplification coefficientLxГ=∫ ( A ( X ) + A ( X ) ) dX
2

1

2

2

0

Lx

∫ A ( X ) dX
2

вх

0

on the longitudinal coordinate is depicted.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

We can estimate the parameters of such system for an
8mm FEL basing that can be realized on the base of U2high current accelerator at BINP RAS, Novosibirsk(width of the beam is ~150 cm, energy of electrons
1 MeV, γ 0 = 3 , current density j0 = 1kA / cm ). We

corrugation with the following Bragg resonanceconditions h = 2hx , where hx is the transverse
wavenumber of TEM modes. This interaction is describedby the following equations.
∂A± ∂A±
±
= iαB
∂Z
∂X

∂B i ∂ 2 B+= −iα ( A+ + A− ) + J∂Z 2 ∂Z 2

Γ(dB)These equations are similar to those describing theexcitation of the FEL oscillator based on coupling of the
propagating and the trapped waves (see [10]) withexcitation factor removed into the equations for the higher
mode. Preliminary estimations show that in this casemultiplication coefficient also should be rather high.
It should be noted in conclusion that the considered in
section 1 system with defect of periodicity can be treatedas a simple realization of photonic bandgap structures[8, 9]. Advantage of these Bragg waveguides is theircompatibility with powerful sheet electron beamtransportation system.

a)b)

REFERENCES[1] A. Yariv, Introduction to optical electronics (1976)[2] V.L. Bratman , G.G. Denisov, N.S. Ginzburg, M.I.
Petelin IEEE J. оf Quant. Electr., v.9 E-19, N3, p.282(1983)
Figure 5: a) Dependence of the gain on the longitudinalcoordinate, b) transverse structure of the fields.

[3] N.S. Ginzburg, A.S. Sergeev, N.Yu. Peskov, et al.,IEEE Transactons on Plasma Scienсe, Vol. 24, No. 3, pp.
770-780. (1996)

assume the undulator period d u = 8cm , undulator field[4] N.F. Kovalev, I.M. Orlova, M.I. Petelin, Izv.Vuzov
Radiofizika Vol.11 N.5 1968, p. 783.

H u = 2kOe , guiding magnetic field
H 0 = 10kOe , a0 = 1cm (the Pierce parameter is
C = 0.01 ). At the following parameters of Bragg
waveguidel0 = 0.4mm , d = 1mm , Lx = 50cm ,amplitude[5] D.A.Dann, W.A.Harman, L.M.Field, G.S.Kino, Proc.
IRE, 1956, p.879.
[6] Zhurahovsky A.V., Radiotehnika i electronika, 1969,
p.8 (in Russian)Lz = 160cm , ϕ = 180 one can get the gain up to 40 dB.

[7] Bykov Yu.V., Gaponov A.V., Petelin M.I., Izv.
Vuzov Radiofizika, 1974, p.1219 (in Russian).

CONCLUSION[8] R.J. Temkin, J.R. Sirigiri, K.E. Kreischer, et al.,Phys. Rev. Lett., Vol. 86, p.5628 (2001)

Another variant of using of an open Bragg structure forprovision of higher selectivity in a FEL amplifier can bebased on coupling between two TEM waves A±
propagating at some angle to the axis and the wave B witha higher y-index propagating directly along the systemaxis. The latter wave is synchronous to the beam
propagating directly along the axis, while the former
waves provide the synchronization of radiation over the xcoordinate. The coupling is provided by the regular396[9] E. Yablonovitch, T.J.Gmitter, and K.M. Leung, Phys.
Rev. Lett. Vol. 67, p.2295 (1991)[10] N.S.Ginzburg, A.M.Malkin, N.Yu.Peskov, et al.,Phys. Rev. ST Accel. Beams 8, 040705 (2005)

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH034

GENERATION OF NARROW BAND SHORT MM WAVESUPERRADIANCE PULSES IN A NON-UNIFORM PLANAR WAVEGUIDE*
N. Ginzburg, R. Rozental#, A. Sergeev, I. Zotova, IAP RAS, N. Novgorod, Russia.
Abstract
A method for suppressing of spurious transverse modes
excitation in the process of supperradiance from intenseelectron bunch is described. Such method based on theuse of the waveguide with variable geometry (in the caseof planar waveguide it is distance between plates). In suchwaveguide phase velocities of the different modes varied
over longitudinal coordinate. For given waveguide profile
variations are increased with increasing transverse mode
indexes. As a result modes with large Brillouin angles(including near cut-off modes) which are responsible forlow frequency radiation suppress more effectively thanmodes with small Brillouin angles. For the case of planar
geometry this effect demonstrated both in the frame of theaveraged equations and the full PIC-simulations.

150 GHz and with the fundamental TEM mode at thefrequency of about 200 GHz.
To suppress spurious interaction we suggest using thenon-uniform waveguide with tapered radius (cylindricalgeometry) or distance between plates (planar geometry).
In such a waveguide the phase velocities of the different
modes varied over longitudinal coordinate. For given
waveguide profile variations are increased with increasingtransverse mode indexes. As a result modes with large
Brillouin angles (including near cut-off modes) which areresponsible for low frequency radiation suppress more
effectively than modes with small Brillouin angles. In
planar waveguide situation is even more preferable
because phase velocity of fundamental TEM mode istotally independent on the distance between plates.

INTRODUCTION

BASIC MODEL

Recently significant progress was achieved in
production of ultrashort pulses in millimeter wave band
based on supperradiance from intense electron bunch [13]. One of the problems for advance generators based onsuch mechanisms in shorter (first of all sub-mm) wave
bands is the spectrum broadening caused by thesimultaneous excitation by an electron bunch several
waveguide modes in oversized waveguide. For example
at the fig.1 the dispersion diagram of the 1 MeV electron
beam propagating through the planar waveguide with
1 cm gap is shown. Electron beam interacts
simultaneously with three propagating modes (theinteraction at the cut-off frequency with the TE1 mode
could be neglected): with TE2 mode at the frequency of
about 50 GHz, with TE1 mode at the frequency of about

Let us assume, that a sheet electron beam with initialrvelocity v0 = v0 zr passes through a planar undulator with

250

100

electron beam

50

k||
-10

0

10

20

30

40

50

Figure 1: Dispersion diagram of the 1 MeV electron beamand planar waveguide with 1 cm gap.
___________________________________________*Work supported by Russian Fund for Fundamental Researches,
grant 05-02-17553#
rrz@appl.sci-nnov.ru
Pr

As = Re{As ( x, z ) exp(iωt − ik|| z )x}r

where As ( x, z ) is the slowly-varying amplitude of thesynchronous wave, ku = 2π d . The reference frequency ωk ⊥ = nπ b , Ω = k u v|| is the bounce-frequency.

TEM
TE1
TE2
TE3

150

(Fig.2). We also assume that the system is infinite over
the y-axis and the electron beam excites the TEn-mode ofa planar waveguide with n variations over the transverse
coordinate x. Vector-potentials of the periodic undulator
field (subscript u) and operating mode (subscript s) may
be presented asrr
Au = Re{Au ch (k u x )exp (ik u z ) y},

was chosen to be the frequency at exact undulator
synchronism ω − k|| v|| ≈ Ω , where k|| 2 = k 2 − k ⊥ 2 , k = ω c ,f, GHz200

period d and homogeneous magnetic field with strengthr
H 0 in a planar waveguide with gap between plates b

Using the independent variables
kC (t − z v|| )kCZ
ζ = 3 2 ,τ= 3 2
β || γ 0
β || γ 0 (1 v|| − 1 v gr )superradiance process can be described by the following
equations:
2π
∂a ∂a
+
= f (τ ) ∫ e −iθ dθ 0
∂ζ ∂τ
0
(1)
∂u
∂θ
iθ
= Re{ae }
=u−Δ
∂ζ
∂ζ
with the boundary conditionsa= a0 , a
=0, u
=0,
τ =0

ζ =0

ζ =0

θ ζ =0 = θ 0 + r cos(θ 0 ), θ 0 ∈ [0,2π )P

FEL Oscillators and Long Wavelength FELs

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Proceedings of FEL 2006, BESSY, Berlin, Germany
TEM mode) and wave with dispersion ( Δ 0 = −1 , whiche–bcorresponds to excitation TE1 mode). In the first case we
see formation of powerful superradaince spike. In thesecond case output radiation is practically suppressed.

d

x

r
H0

z

Figure 2: Scheme of the basic model.
The following dimensionless variables have been used:3
eAs eAu β || k u c ⎛ 1
1 ⎞
⎜
⎟
a=
−
2
2
2
⎜
2mc 2mc C ⎝ Ω − ω H Ω + ω H ⎟⎠is the wave amplitude, θ = ωt − (k|| + ku )z is the electron

PIC-SIMULATIONS
The 2-D version of the PIC-code KARAT was used for
additional simulations. The 110 cm length planar
waveguide was excited by the 1 MeV, 100 A/cm, 600 ps
electron bunch which was transported through theperiodic undulator with period 2 cm and 2 kOe strengthand guiding magnetic field with strength of 22 kOe(Fig.4a). For regular waveguide simulation showed thatthe spectrum of the output signal includes three mainfrequencies (Fig.4c), which correspond to thesimultaneous excitation of the TEM, TE1 and TE2 modes.

phase with the respect to the synchronous wave,
u = C −1 (1 − γ γ 0 ) is the relative electron energy,
C=

⎛
1
1 ⎞⎤
eI cγ 0 ⎡ eAu⎟⎥
β || 3 k u c⎜⎜−⎢32
Ω + ω H ⎟⎠⎦mc 4πN s ⎣ 2mc⎝ Ω − ωH

is the Pierce parameter, ωΗ is the cyclotron frequency, I
is the electron beam current, Ns is the norm of theoperating wave,
β 3γ 2 ⎛ k + k1⎞
Δ = || 0 ⎜ || u − ⎟⎜C ⎝ kβ|| ⎟⎠
is the mismatch from the undulator synchronism,f (τ ) = 1 , τ ∈ [0, T ] , where T is the normalized duration of
the electron bunch.
Let is consider the influence of the variation of themismatch of the undulator synchronism over thelongitudinal coordinate on the superradiance process. We
choosethesimplest
lineardependence:.
Fig.3
demonstrates
theresultsof theΔ(ζ ) = Δ 0 ζ L − Δ 0
simulation of Eqs. (1) for L = T = 30 in the case of nondispersive wave ( Δ 0 = 0 , which corresponds to excitation

30

|a|2

Δ0 = 0Δ0 = -1

20

20

40

(b)

2
0

t, ns
3.5

4

4.5

5

Sf

0

τ
0

4 P, MW5.5(c)f, GHz

10
0

(a)

2

60

100

200

Figure 4: PIC-simulations of superradiance in the uniform
oversized waveguide: (a) is the geometry of interaction
space (solid lines denotes the ideal conductor, dash lines
marked the boundary of the microwave absorption
layers); (b) is the output signal and (c) is the spectrum of
output radiation.

Figure 3: Simulation of averaged equations: output signal
in case of uniform (Δ0 = 0) and non-uniform waveguide(Δ0 = -1).

398

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH034[2] N.S.Ginzburg, et al., Opt.Comm., 2000, 175(1-3),
139.

(a)

[3] A.G.Reutova, et al. , JETP Lett., 2005, 82(5), 263.

4

P, MW

(b)

2
0

t, ns
3.5

4

4.5

5

5.5

Sf

(c)

f, GHz0100

200

Figure 5: PIC-simulations of superradiance in the uniform
oversized waveguide: (a) is the geometry of interaction
space; (b) is the output signal and (c) is the spectrum of
output radiation.
Fig.5 demonstrated the results of simulation ofsuperradiance in the waveguide with linearly increased
gap between plates from 0.2 to 1 cm (fig.5a). In this caseall spurious modes were suppressed and the output
radiation includes one powerful spike (fig.5b). As a result
the spectrum of output radiation is concentrated near theoperating frequency of 200 GHz corresponding to
excitation fundamental TEM mode (fig.5c).

CONCLUSION
A method of suppressing excitation of spurious modesin the process of supperradiance from intense electron
bunch in the planar oversized waveguide is considered.
The simulations of the averaged equations and PICsimulations were carried out and it was shown that in theplanar waveguide with linearly increasing gap between
plates the SR pulse associated with excitation of single
transverse mode could be obtained.

REFERENCES[1] Ginzburg N.S, et al., Nucl.Instr.Meth.Phys.Res.,
1999, A429(1), 94.

FEL Oscillators and Long Wavelength FELs

399

TUPPH035

Proceedings of FEL 2006, BESSY, Berlin, Germany

GENERATION OF SUPERRADIANT PULSES BY BACKSCATTERING OF
PUMPING WAVE ON THE INTENSE ELECTRON BUNCH*
V. Belousov, G. Denisov, N. Ginzburg, A. Sergeev, I. Zotova#, IAP RAS, N.Novgorod, Russia
A. Reutova, M. Ulmaskulov, A. Sharypov, V. Shpak, S. Shunailov, M. Yalandin, IEP RAS,
Ekaterinburg, Russia.
Abstract
At the first time the generation of superradiance pulses
in the process of stimulated backscattering of powerfulpump wave by intense electron bunch (250 keV, 1 ɤȺ,
600 ps) has been observed experimentally. Using a
relativistic 38 GHz BWO as a pump wave source, theshort 200 ps superradiance pulses of scattered radiation
with peak power ~1 MW were obtained. Due to the
Doppler up-shift, in the spectrum of scattered radiationhigh frequency 150 GHz component was presented

guiding magnetic field H 0 H 0 z 0 . Under assumption of
the fixed pump wave amplitude, the generation of short
single pulse of scattered radiation (SR pulse) can be
described by the nonstationary equation for scattering
signal amplitude As and the averaged equations forelectrons’ motion in the field of combination wave:
wa s wa s
I 2S
if W ai g ³ e iT dT 0
w]
wW
S 0
w 2T
w] 2

INTRODUCTION
Recently a significant progress was achieved in thegeneration of subnanosecond pulses in the millimeter andcentimeter wave bands utilizing the cyclotron and
Cherenkov mechanisms of superradiance (SR) of electron
bunches [1-3]. The maximal peak power in the case of
Cherenkov SR exceeded gigawatt level [3]. This paper isdevoted to the novel mechanism of superradiance in thecase of the stimulated backscattering of powerful pumpwave by intense electron bunch. In this situation, due tothe Doppler up-shift effect the radiation frequency cansignificantly exceed the frequency of the pump wave:
1  V|| V ph .i
Z s Zi,(1)
1  V|| V ph .s

where V|| is the translational electron velocity, V ph.i ,s are
the phase velocities of the pump wave (index i) and thescattered wave (index s). If the radiation of powerful laser
undergoes backscattering at the electron beam withenergy about 1-2 MeV the frequency of scatteredradiation will belong to ultraviolet band. In the case when
the pump wave is generated by relativistic microwave
generator (for example BWO) it is possible to produce
radiation at the short millimeter and submillimeter wave
bands. In this paper we present a basic theoreticaldescription of the superradiance regime of stimulated
backscattering. The results of theoretical consideration are
confirmed by the first experimental observation of above
SR mechanism.

BASIC MODEL
Let us consider the backscattering of the powerfulpump wave by the hollow electron bunch with injection
radius Rb and duration 't b that moves through acylindrical waveguide with radius R along homogeneous*Work supported by Russian Fund for Fundamental Researches,
grant 05-02-17553#
zotova@appl.sci-nnov.ru

400

Here

]

^

P Im a s ai ge

Zc z c ,

iT

`

.

(2)

W Zc c t  z V|| 1 Vgr  1 V|| 1 ,eAi ,s 2m0 Jc 2 are the dimensionless amplitudes of

ai ,spump and scattered waves, T Zɫ t  k c z is the electrons
phase with respect to the combination wave,
Zc Z s  Zi , k c hs  hi , hi ,s are the longitudinal
pump

I

and

scatteredwave

eJ 0 mc 3  2J 0 hs k c R 2 N s1numbers,P

J 02E||3 ,, J0 is the electron

current, Ns is the norm of the scattered wave. Factor
g J ni 1 k Ai Rb J ns 1 k A s Rb : :  Z H(3)describes the increase of oscillation velocity of electrons
near the cyclotron resonance, Z H eH 0 m0 cJ 0 is the
gyrofrequency, :Zi  hiV|| is the bounce frequency,k Ai ,s is the transverse wave number, J n x is the Bessel

function, ni,s are the azimuth indices of the waveguidemodes. Function f ( W ) defines the profile of electron
current
withnormalized
durationWb't b Zc c 1 V gr  1 V|| 1 .

Equations (2) describe the joint combinational action of
the pump and the scattered waves on the electrons. Suchan action leads to selfbunching that starts from small
initial density perturbations. As a result the amplitude of
scattered wave grows. In the absence of external feedback
the synchronization of radiation from different parts ofextended electron bunch is provided by slippage of thescattered wave with respect to electrons due to adifference between the electron velocity and theelectromagnetic wave group velocity. As a result the
scattered wave radiates in the form of a single short pulse,
as is shown in Fig.1. The parameters of simulation arechosen in accordance with the performed experiment. The
pump wave with 100 MW power and 38 GHz frequency
has the transverse structure of the TE11 mode. This wave

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

undergoes the backscattering by the 250 keV, 1 kA,
200 ps electron bunch guided in 24 kG magnetic field.
According to the simulation the duration of the scattered
SR pulse is about 50 ps with peak power ~25 MW.
According to waveguide dispersion the scattered wave
frequency should be about 150 GHz.

TUPPH035

EXPERIMENTAL SET-UP
Experiments on the observation of the stimulated
backscattering in the superradiance regime were carriedout at Institute of Electrophysics (Ekaterinburg, Russia)
based on two synchronized nanosecond andsubnanosecond high-current RADAN-303 accelerators[4-5]. The 4 ns electron beam from the first accelerator
was used to drive the low frequency pump wave
generator. The pump wave undergoes backscattering withfrequency up-conversion on the subnanosecond electron
bunch produced by the second accelerator. The generalview of experimental set-up is shown in Fig.3.

Figure 1: Superradiance pulse of scattered radiation.

KARAT PIC-CODE SIMULATIONS
The possibility of the observation SR in the process ofbackscattering has been tested also using the particle-incell (PIC) code KARAT. In simulation we used thesimplified two-dimensional axial symmetric model of thescattering. The pump wave with frequency 38 GHz andpower 100 MW represents the TE01 wave in contrast to
the experimental situation. The guiding magnetic field
was 28 kG.
As it is seen from Fig.2 scattered radiation has the formof the short pulse with the duration less than 100-200 ps
and peak power about 3 MW. The radiation spectrum has
a component with frequency about 150 GHz.
Nevertheless the spectrum of radiation is rather wide. It
may be explained by the dispersion of electron velocities
as well as by excitation of several waveguide modes.
Above factors also may result to the reduction of the peak
power in comparison with the model described above.

Figure 2: Results of KARAT PIC code simulations: (a)scattered SR pulse, (b) spectrum of SR pulse

FEL Oscillators and Long Wavelength FELs

Figure 3: Experimental set-up
In experiments the pump wave was generated byrelativistic BWO with operating frequency 38 GHz. For
transmission of the pump wave to the scattering section a
specially designed quasioptical mirror has been used. The
mirror possessed the high reflectivity 95% at the pumpwave frequency 38 GHz. The partial transparency of themirror for the scattered radiation at frequencies above
60 GHz was provided by the mesh of holes with diameterof 3 mm having a step of 4 mm.

EXPERIMENTAL RESULTS
Oscilloscope trace of the 4 ns, 100 MW pump wave
pulse with duration is shown in Fig.4a. In absence ofsubnanosecond electron bunch, the signal from BWO
registered by detector installed after quasioptical mirror isshown in Fig.4b. This signal is caused by parasitic highfrequency radiation from the pump wave generator at theharmonics of operating frequency. Presence of suchharmonics in a spectrum of the pump wave is confirmedby the direct simulation based on PIC-code KARAT.
In the scattering section with 30 cm length the low
frequencypump
wave
underwent
stimulated
backscattering by the high current relativistic
subnanosecond bunch (250 keV, 1 ɤȺ, 600 ps). It is
important to note that in absence of the pump wave thebackground noise radiation of electron bunch was below
the threshold sensitivity of a microwave detector. Whenthe pump wave generator was switched on, the short
powerful pulse could be observed, as is shown in Fig.4c.
This pulse has rather short duration (about 200 ps) andcan be interpreted as a superradiance pulse. SR pulses
were observed in a large area of magnetic field detuning.

401

TUPPH035

Proceedings of FEL 2006, BESSY, Berlin, Germany

The maximal peak power was obtained for field strength20-25 kG when the magnetic field strongly affects theamplitude of electron oscillations.

a

b

c

Figure 4: (a) Pulse of the pump wave. (b) High frequency
component of BWO radiation in the absence of electron
e-bunch registered by detector after quasioptical mirror.
(c) Superradiance pulse caused by backscattering of pumpwave by electron bunch.

calculated one. However it should be noted that detector
sensitivity decreases with frequency. So the real fall ofintensity of high frequency components should be lessthan detector indications shown in Fig.4. A rather wide
spectrum of scattered radiation can be explained by the
spread of electron velocities in the real electron bunch aswell as by excitation of several waveguide modes.
Integral (over frequency spectrum) peak power of SR
pulse amounts up to 1 MW. It was estimated basing on
the power level indicated by microwave detector taking
into account the aperture of the reception antenna, thedistance from a radiator and the width of the radiation
pattern.

CONCLUSION
As a result of the experiments the effect of generationof short electromagnetic pulses was observed in theprocess of stimulated backscattering of the powerfulpump wave by the intense electron bunch. Scatteredradiation had the form of ultrashort pulse with peak powerof 1 MW and duration of 200 ps. Due to the Doppler
frequency up-conversion the spectrum of scatteredradiation included the frequencies up to 150 GHz thatexceeded the pump wave frequency in several times. This
process can be interpreted as a superradiance of electron
bunch since the radiation of the short pulse occurs in theabsence of external high frequency signal and in theabsence of external cavity and correspondingly cannot be
attributed to traditional amplification or oscillation
regimes. Due to the development of selfbunching inside
the extended electron bunch the peak power of scatteredsignal significantly exceeds the power of the spontaneousradiation of electrons in the pump wave and the durationof scattered pulse was essentially shorter than the durationof the background noise.

REFERENCES

Figure 5: Spectrum measurements. Relative amplitudes ofdetector signal after filters with different cut-off
frequencies.
To analyze the radiation spectrum a set of cut-off
waveguides was used. Amplitudes of detector signals
after filters with different cut-off frequencies are shown in
Fig.5. Locations of vertical lines correspond to the cut-off
wavelengths of different filters and the lengths of lines areproportional to the signals registered by the detector.
Obviously the jumps of dashed line characterize thecontent of different spectrum components in the scatteredradiation. The main components of radiation concentrateat the interval within wavelength 3.5 y 4.2 mm. But at thesame time there are high frequency components withwavelength around 2 mm, which is rather close to the402[1] N. Ginzburg, I. Zotova, A. Sergeev, I. Konoplev, A.
Phelps, A. Cross, S. Cook, V. Shpak, M. Yalandin, S.
Shunailov and M. Ulmaskulov, Phys. Rev. Letters,
78(12) (1997) 2365.
[2] N. Ginzburg, Yu. Novozhilova, I. Zotova, A.
Sergeev, N. Peskov, A. Phelps, A. Cross, V. Shpak,
M. Yalandin, S. Shunailov and M. Ulmaskulov,
Phys.Rev.E, 60(3) (1999) 3297.
[3] S. Korovin, G. Mesyats, V. Rostov, M. Ulmaskulov,
K. Sharypov, V. Shpak, S. Shunailov and M.
Yalandin, Technical Phys. Lett., 30 (2) (2004) 117.
[4] V. Shpak, S. Shunailov., M. Ulmasculov and M.
Yalandin In Digest of the 12th IEEE Int. PulsedPower Conf., USA,1999, 2, 1472
[5] G. Mesyats, S. Korovin, V. Rostov, V. Shpak and M.
Yalandin. Proc. of the IEEE, 92 (7) (2004) 1166.

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH036

OPTIMIZATION OF THE INJECTION SYSTEM FOR MICROTRONBASED TERAHERTZ FEL*
Grigory M. Kazakevich#, Viatcheslav M. Pavlov##, Gennady I. Kuznetsov, BINP, Novosibirsk,
630090, Russia,
Young Uk Jeong, Seong Hee Park, and Byung Cheol Lee, KAERI, Taejon, 305-600, South Korea.
Abstract
A compact widely-tunable microtron-based terahertz
Free Electron Laser (FEL) has been developed and during
last few years operates for users. The laboratory-size,
stable facility at the macro-pulse power of tens of W is
attractive for application in research laboratories anduniversities. Reliability in operation and stability of suchmicrotron-based FEL is determined generally by the
microtron injection system. Main parameters of theinjection system were studied on the base of 2-D tracking
considering the frequency drift of the accelerating cavity
as a result of variation of the beam loading caused bycathode overheating due to back bombardment with nonresonance electrons. The obtained results show that the
injection system based on a thermionic single crystal LaB6
2.5 mm-in diameter emitter provides operation of the
microtron-based FEL with standard deviation of themacro-pulse lasing power less than 10% during long-timework. Experimental check of the FEL during more than
five years confirmed stable and reliable operation of the
microtron-based FEL with the macro-pulse power of tensof W in the terahertz range.

INTRODUCTION
The injection system of the accelerator intended to drive
the terahertz FEL has to provide a suitable bunch current
with appropriate transverse parameters of the beam. The
qualities are well matched in the system using theclassical high-current microtron with an internal injection.
In this case the acceleration starts in a high-gradientelectric field that allows getting small beam emittance; themulti-turn motion of the electrons through theaccelerating gap in the cavity provides good bunching of
the beam. Worth to note that such system is simple andinexpensive in manufacturing but some drift of the beamloading during the macro-pulse is inherent to the system.
The drift makes worse the intrapulse bunch repetition ratestability and the FEL operation as well because of theeffective fluctuation of the FEL optical resonator length,
detuning the resonator. The primordial source of the drift
is a pulse overheating of the cathode emitting surface
caused by back-streaming electrons.
___________________________________________*

Work was supported in frames of the BINP-KAERI scientificcollaboration and with Korea Research Foundation Grant (KRF-2004042-C00053)#
Corresponding author. Current affiliation:
FNAL, Batavia, IL 60510, U.S.A.
E-mail: gkazakevitch@yahoo.com (G.M. Kazakevich)##
Current affiliation: University of Strathclyde, Glasgow, G4 0NG,UK.

FEL Oscillators and Long Wavelength FELs

To minimize the effect we optimized design andparameters of the microtron injecting system to operatewith minimal acceptable cathode diameter. In this case thesimplest and cheapest RF system employing themagnetron generator stabilized through the backward
wave reflected from the accelerating cavity provides
stable operation of the widely-tunable terahertz FEL
based on the classical S-band microtron, [1]. For the
optimization we calculated the accelerating cavity
frequency drift caused by intrapulse variation of the beamloading as a function of the cathode diameter. The
calculation was done for I-type injection, [2], basing on 2D tracking in the microtron median plane. Comparison of
the calculation with measured detuning curves of the FEL
optical resonator showed that a single crystal LaB6 emitterwith diameter of 2.5 mm at a minimal acceptable detuningof the magnetron and the accelerating cavity can provide
operation of the widely-tunable terahertz FEL withradiated macro-pulse power tens of W at a suitablestability and life time. Operation of the terahertz FEL
during more than five years demonstrates that the
optimized microtron injection system employing thethermionic cathode operating at the temperature of 19000
K at the strength of the electric field of > 10 MV/mprovides reliable operation of the terahertz FEL. Resultsof simulations and measurements are presented anddiscussed in the article.

ANALYSIS OF THE EMISSION CURRENT
IN THE MICROTRON WITH INTERNALINJECTION
At operation of the high-current microtron with theinternal injection the main part of electrons is emitted in
non-resonance phases. The electrons could not reach theextracting channel, but they are participating in theprocess of acceleration and mainly hitting the cavity
walls; a number of them hit the emitting surface making
the back bombardment of the cathode. As was shown in[3], the back bombardment results in the pulse
overheating of the emitting surface. This causes anadditional emission including emission in resonancephases, thus the electron beam loading the cavity becomesincreasing in time domain due to enhancement of numberof synchronous electrons and non- synchronous as well.
To consider the effect of the back-streaming electrons
hitting the cathode and increasing because of that theloading of the accelerating cavity we calculated thecathode overheats using 1-D analytic expression of theheat conduction along the emitter axis, [4]:403

TUPPH036

Proceedings of FEL 2006, BESSY, Berlin, Germany

Pbs 0 14χ ⋅ tm
,
(1)
⋅
⋅
2
π
π ⋅ rC k C
where: kC is thermal conductivity, χ is thermal
ΔT 0 (t m ) =diffusivity coefficient, rC is the cathode radius, and t m is
the pulse duration of the emission current in the
microtron. The average power of the electrons heating theemitter per the RF period, Pbs(T), was calculated using
expression:

Pbs (T ) =

rC
⎤
⎡
1
⋅ ∫ ⎢2π ⋅ ∫ iC (T , r, ϕ) ⋅ ε (r, ϕ ) ⋅ r dr⎥ dϕ , (2)2π ϕbs ⎢⎣⎥⎦0

where: ε (r , ϕ ) is the energy of back-streaming electron
emitted in point with a coordinate r and with an initial
phase ϕ , the average value of ε is approximately of 8.9
keV; iC (T , r , ϕ ) is the emission current density of LaB6
single crystal emitter depending on emitting radius r andinitial phase ϕ ; the term was calculated considering
Schottky effect through the expression:⎡ − eφ + 3.79 ⋅ 10 − 4 ⋅ E (r , ϕ ) ⋅ 10 4 ⎤ , (3)C
CS⎥
iC (T , r , ϕ ) = AT 2 ⋅ exp ⎢
k ⋅T
⎥⎦
⎢⎣

where A = 73 A / grad2·cm2 and eφ C = 2.66 eV are theRichardson constant and the work function for LaB6,
respectively, k is the Boltzmann constant and T is theemitter temperature in Kelvin deg; ECS(r,ϕ) is theelectric field strength at the emitting surface with an
initial phase ϕ. For cylindrical accelerating cavity
employed in the microtron the E010 mode electric fieldstrength was calculated for the emitting surface deepened
relatively the cavity cover surface by dC = 0.5 mm andemitter located in the center of the cathode hole, made in
the cavity cover. The hole radius rH is 2 mm; coordinateof the emitter center RC is 30 mm. The ECS(r,ϕ) values
were calculated using the expression:

J (k ⋅ r ). (4)ECS (r , ϕ ) = E0 ⋅ J 0 (k0 ⋅ RC ) ⋅ cos (ϕ ) ⋅ 0 r
ch (k z ⋅ d C )Here: E 0 ≈ 35.53 MV/m is maximal field on the cavity
axis corresponding to the microtron optimal regime,
k 0 = 2π / λ0 , k r = χ 01 / rH , J 0 is the first kind Bessel
function, χ 01 = 2.405 is the first square of Bessel function
and k Z = kr 2 − k02 .
Calculated maximal value of the current density at theemittertemperature
of
19000
K
is:
0
2
iC max = iC (1900 K ,0,0) ≈ 49.5 A / cm . At thistemperature the developed thermionic cathode with asingle-crystal LaB6 emitter, [3], has a life time
approximately of 1000 h. The initial value of the emission
cathode current was calculated using following
expression, [3], for several values of the cathodediameter:404

I C (T ) =

rC
2π
⎡
⎤
1
⋅ ∫ ⎢2π ⋅ ∫ iC (T , r, ϕ ) ⋅ r dr ⎥ dϕ .
2π 0 ⎣⎢
0⎦⎥(5)

To calculate the loading current of the accelerating
cavity we performed tracking of the electrons in the
microtron using 2-D Lorentz equation in the medianplane. The E010 mode electric and magnetic components ofthe cavity accelerating field and the permanent microtron
magnetic field were considered. The electrons hitting thecavity walls (inside or outside the cavity) were nonparticipating in the tracking. The 2-D Lorentz equations
were integrated up to last (12-th) orbit. The tracking in the
microtron was done for several values of cathodediameter and the microtron parameter Eps = E 0 / cB ,where: B - is the value of the microtron permanent
magnetic field (for our microtron the optimal value of
B = 0.1065 T).
Results of calculation of the cathode overheats vs. thecathode diameter for the microtron operating condition at
the initial emitter temperature of 19000 K for several
values of Eps parameter and the emission macro-pulse
current having duration of 6 μs are presented in Fig 1. The
values of kC and of χ for LaB6 at the high temperature
were taken from [5].
0Δ T , d eg

140

E ps = 1 ,1 1120
100
E ps = 1 ,0 58060

Δ t = 6 μ s, E ps = 1 .0 5 - 1 .1 1

40
1 .5

2.0

2 .5

3 .0

3 .5

4 .0

C a th od e d ia m e te r, m m

Fig. 1. Cathode overheats caused by back-streaming
electrons during 6 μs macro-pulse vs. cathode diameter at
the initial temperature of 19000 K. The arrow shows
variation of the parameter Eps .
Note that we did not consider the heat losses caused bythermo-conductivity of the emitter holder and radiation ofheat from the emitter. Because of that the ΔT° values andthe overheating effects are overestimated.
Calculated values of the initial emission current at theinitial temperature of 19000 K vs. the cathode diameter areplotted in Fig. 2.
Calculated values of the final emission current increased
because of the overheating through the electron backstream during the 6 μs- macro-pulse are plotted in thisfigure as well.

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

Here: R sh = 1.08 MOhm is the effective shunt impedance

6of the accelerating cavity, I - is the averaged emission
macro-pulse current, W and ϕ W are dimensionless firstE m ission cu rren t, A

E p s = 1 ,1 1

5
F in a l v a lu e o f th ee m iss io n c u rre n t

4harmonic current amplitude and the harmonic phase,respectively, depending on the cavity voltage amplitude,
VC . ( VC is equal to 0.586 MV for Eps = 1.08 ). The

E p s = 1 ,0 5

32value of

1

1 .5

2 .0

2 .5

3 .0

3 .5

4 .0

C a th od e d ia m e te r [m m ]Fig. 2. Initial and final values of the emission current vs.
cathode diameter at the initial emitter temperature of
19000 K and the macro-pulse duration of 6 μs. The arrowshows variation of the parameter Eps.

ESTIMATIONS OF THE FREQUENCYDRIFT IN A HIGH-CURRENTMICROTRON WITH INTERNALINJECTION
Obtained data allow calculating the intrapulse variation of
the accelerating cavity beam loading; that results infrequency drift of the cavity. Performing 2-D tracking of
the electrons we calculated velocities of the electrons as
well. That allowed us to determine the amplitude and phaseof the fist harmonic cavity loading current. Note that theused method allows considering the cavity loading throughall accelerated particles, synchronous and non-synchronous
as well.
The highest possible frequency drift of the accelerating
cavity caused by variation of the beam loading was
calculated using following expression, [6]:

ΔF ≈

⎛ I ⎞
1 η e0 ⋅ ω 0C
⋅ tan ϕW ⋅ ⎜⎜1 − F ⎟⎟ ,
⋅
2π
2Q0C
I0 ⎠
⎝

(6)

where: I 0 - initial emission current at the temperature of
19000 K, I F - final value of the emission current
increased because of additional heating of emitting
surface through back-streaming electrons during 6 μs
macro-pulse, Q0C = 9800 is the accelerating cavity wall
quality factor (measured value), ω 0C is the circular eigen
frequency of the cavity, η e 0 is the initial beam loading
coefficient, and ϕW is the phase of the cavity loading
current.
The value of η e is determined as a ratio of the beam
power Pe and the cavity wall loss power PC :Pe [I ⋅ VC ⋅ W ⋅ cos(ϕW )] Rsh ⋅ I
. (7)
=
=
⋅ W ⋅ cos(ϕW )2PC
VC⎡ VC ⎤⎢⎥⎣ Rsh ⎦FEL Oscillators and Long Wavelength FELs

VC is a constant (in steady-state); the values of

W and ϕW are constants as well.

In itia l va lu e o f th ee m is sio n cu rre n t

0

ηe =

TUPPH036

Note that using 2-D tracking without consideration of
the vertical motion of the electrons causes overestimationof the contribution of the synchronous electrons in the
beam loading; for the contribution of the nonsynchronous electrons the 2-D tracking gives someunderestimation.
From the tracking we determined the values of W and

ϕW for various values of Eps parameter. For optimalvalue of Eps =1.08, W =2.607, ϕ W =20.9º, and forI ≈1.07 A the calculated beam loading coefficient η e ≈4.8. The value is higher by 10-20% than obtained fromthe measurements because of overestimation of theaccelerated current as was noted above. Fig. 3 shows
calculated maximal estimation for the frequency driftcaused by overheating of the emitting surface with theelectron back-stream vs. the cathode diameter.
ΔF, M Hz
1 .0

E p s = 1 .0 8

0 .8

0 .6

0 .4

0 .2

0 .0
1 .5

2 .0

2 .5

3 .0

3 .5

4 .0

C a th o d e d ia m e t e r , m m

Fig. 3. The cavity frequency drift caused by overheatingof the electron emitter with the electron back stream vs.
cathode diameters at the initial emitter temperature of
19000 K and the value of Eps parameter of 1.08.

EFFECT OF THE FREQUENCY DRIFTON THE TERAHERTZ FEL OPERATION
The described drift of the frequency of the accelerating
cavity makes worse stability of the bunch repetition rate
because of the stabilizing feedback through reflectedwave coming to magnetron. Additional contribution in thebunch repetition rate instability causes increase of themagnetron current during the macro-pulse at a finite valueof the frequency stabilization coefficient. The intrapulse
increase of the magnetron current and the magnetron

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Proceedings of FEL 2006, BESSY, Berlin, Germany

power, respectively, is used to keep constant accelerating
voltage and accelerated current at increase of the cavity
loading, [1]. Both contributions result in the bunch
repetition rate deviation during the macro-pulse; that
effectively leads to intrapulse detuning of the FEL opticalresonator.
Our terahertz FEL optical resonator, confocal free-spacemode in horizontal plane and waveguide mode in verticalplane, was formed with two cylindrical mirrors mounted
on the ends of a rectangular waveguide; one of the mirrors
has a coupling hole to extract the FEL radiation.
The distance D between the mirrors was chosen using
the expression:

D = 52 ⋅λb
2= 52 ⋅c,2 ⋅ Fb(8)

were: λb is the wavelength of the accelerating voltage, c
is light velocity, Fb is the bunch repetition rate equal tothe accelerating cavity frequency. For Fb ≈ 2.801 GHz,c≈ 10 .703 cm. From expression (8) follows:
Fb
ΔF
ΔD = 26λb ⋅ b . I.e. for the optical resonator
Fb

λb =

FIR m acro-pulse en ergy, rel. unit

variation of the bunch repetition rate by 1 MHz
approximately corresponds (in a signal level) to thedetuning by 1 mm. Measured FEL optical resonator
detuning curve at the lasing wavelengths of 113 μm isshown in Fig. 4.

SUMMARY
Effect of the back-streaming electrons bombarding theemitting surface of the thermionic cathode in a classicalmicrotron with the internal injection on the lasing of the
microtron-based FEL was analyzed. The results allow
choosing the optimal size of the microtron thermioniccathode to provide stable and reliable operation of the
microtron-based widely-tunable terahertz FEL with themacro-pulse lasing power few tens of W.

1.0
0.8
0.6
0.4
0.2

REFERENCES
0.0-1400 -1200 -1000

-800

-600

-400

-200

0

S hift of the o utcou pling m irro r, μ m ,Fig. 4. Detuning curve of the FEL optical resonatormeasured at the wavelengths of 113 μm.
The measurements were done employing developed
cathode assembly based on 2.5 mm-in diameter single
crystal, face (100), LaB6 emitter, operating at the initial
temperature of ≈ 19000 K. The microtron operating
parameters were chosen to provide the intrapulse bunch
repetition rate deviations ≤ 0.25 MHz; that was measured
using heterodyne method, [7]. At the measurements the
microtron provided the beam current of 40 mA at theundulator entrance. The detuning of the FEL opticalresonator was done by precise motion of the outcoupling
mirror through a stepping motor.

406

The Fig. 4 curve shows that detuning by 0.2-0.25 mm,corresponding to variation in bunch repetition rate by 0.20.25 MHz, decreases the FEL macro-pulse energy by few
tens of percents. The value can be used as an upper limitof the intrapulse bunch repetition rate deviations for the
microtron intended driving the terahertz FEL. Considering
curve plotted in Fig. 3, this points to a necessity inlimitation of the emitter size though the emitter withlarger diameter provides higher accelerated current at thesame life time of the cathode.
Optimal diameter of 2.5 mm of the single crystal LaB6
emitter for the microtron-terahertz FEL injector waschosen as a compromise considering requirements ofreliable operation of the microtron and stable operation of
the terahertz FEL. With the emitter at the microtron
regime optimized for long-life operation of the cathodewe obtained radiated macro-pulse lasing power of 40-50
W in the wavelength range of 100-200 μm. The
measurements were done using calibrated pyro-electricdetector measuring the lasing macro-pulse energy and thewide-band Schottky barrier detector measuring the lasing
macro-pulse shape and the pulse width.
The thermionic cathodes with such emitters at
optimized regime of the microtron have life time
approximately of 1000 h, providing operation of thewidely-tunable terahertz FEL with standard deviation of
the lasing macro-pulse energy less than 10% during longtime work, [3].

[1]. G. M. Kazakevitch, Y. U. Jeong, V. M. Pavlov,
B. C. Lee, NIM A 528 (2004) 115-119.
[2]. S. P. Kapitza and V. N. Melekhin, The Microtron
London. Harwood, 1978.
[3]. G. M. Kazakevich, G. I. Kuznetsov, V. M. Pavlov,
Y. U. Jeong, S. H. Park, and B. C. Lee “Injection
system for microtron-based Terahertz FEL”
Proceedings of the 27th International FEL
Conference, JACoW / eConf C0508213.
[4] L. D. Landau and E. M. Lifshitz, in Course of
Theoretical Physics ("Nauka" (In Russian), Moscow,(1986), Vol. 6, Fluid Mechanics, p. 288-289.
[5] Takaho Tanaka, J. Phys. C 7, L177-L180 (1974).
[6] E. L. Kosarev. Ph.D. Thesis, Inst. of Phys. Problems,
Moscow, 1971, (in Russian).
[7] G. M. Kazakevitch, Y. U. Jeong,
B. C. Lee, J. Lee, NIM A 483 (2002), 331-335.

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH037

FEL-OSCILLATOR SIMULATIONS WITH GENESIS 1.3
J.G. Karssenberg, P.J.M. van der Slot∗ , J.W.J. Verschuur, I.V. Volokhine † K.-J. Boller
Laser Physics and Non-Linear Optics Group, University of Twente
PO Box 217, 7500 AE Enschede, The Netherlands
Abstract
Modeling free-electron laser (FEL) oscillators requires
calculation of both the light-beam interaction within the undulator and the propagation of the light outside the undulator. We present a paraxial Optical Propagation Code (OPC)
based on the Spectral Method and Fresnel Diffraction Integral, which in combination with Genesis 1.3 can be used toperform either steady-state or time-dependent FEL oscillator simulations. A flexible scripting interface is used bothto describe the optical resonator and to control the codesfor propagation and amplification. OPC enables modelingof complex resonator designs that may include hard-edge
elements (apertures) or hole-coupled mirrors with arbitrary
shapes. Some capabilities of OPC are illustrated using the
FELIX system as an example.

INTRODUCTION
Free-electron laser (FEL) oscillators are complex devices. They require simulation of both the amplificationof the radiation field within the undulator and the propagation of the radiation field through the resonator, to correctlypredict the spectral and spatial properties of the output of
the laser. These properties are very important for the designof user experiments.
To date, several codes exist that can simulate an FEL
amplifier or oscillator (see, e.g., [1]). However, the wellestablished Genesis 1.3 FEL code [2] is primarily used
for FEL amplifier or SASE simulations. In this paper we
present an optical propagation code (OPC) that works together with Genesis 1.3 to simulate FEL resonators. The
full functionality of Genesis 1.3 is maintained and simulation of FEL oscillators can be done both in steady-state andtime-dependent modes.
To propagate the radiation field between optical andgain elements, we have implemented three related paraxial
methods: the Spectral Method [3], the Fresnel Diffraction
Integral Method [4] and a modified Fresnel Diffraction Integral Method. The latter is based on the normal Fresnel
Diffraction Integral, however, it includes the ABCD matrix of the optical system between input and output plane[5]. The radiation field produced by Genesis 1.3 at the undulator’s exit is propagated using one of these methods tothe first optical element. Then the action of that particular optical element is applied to the wave and one of the∗ p.j.m.vanderslot@tnw.utwente.nl† Current address: Philips Research, High Tech Campus 34, 5656 AE
Eindhoven, The Netherlands

FEL Oscillators and Long Wavelength FELs

propagation methods is again used to propagate the wave tothe next optical element. This procedure is repeated until
the undulator’s entrance is reached. Note that propagation
through a cascaded set of optical elements can be done in asingle step if this set can be represented by a single overall
ABCD matrix and using the Modified Fresnel Diffraction
Integral for the propagation.
We have chosen to separate the optical propagation
model from the FEL simulation model for two main reasons. First, the optical propagation model can be used withdifferent gain models and is, in principle, not limited to
FELs. Second, the propagation model can then also be
used to propagate the field outside the resonator and determine the field distribution, for example, in the far field orin a user area that can be located at a considerable distancefrom the laser in the case of FELs. The optical propagation
code is available for download [10].
In the remainder of this paper, we first describe briefly
the different propagation methods, then the OPC code andend with an example illustrating the capabilities of the combination of the OPC code with Genesis 1.3.

PARAXIAL OPTICAL PROPAGATION
By applying a Fourier transform over the transverse coordinates, the paraxial wave equation can be written as [5]:
∂ ũ
= 0,
∂z

(1)

u(x, y, z)e−i(kx x+ky y) dxdy(2)

(kx2 + ky2 )ũ − 2ikwhereũ(kx , ky , z) =
 ∞ ∞−∞−∞

is the Fourier transform of the complex wave amplitude
u(x, y, z). Given a known optical field u 0 (x, y) at z = 0,
the optical field after a propagation over a distance z can beobtained from eq. 1:ũ(kx , ky , z) = ũ0 (kx , ky )e−i k (kx +ky ) .
2z

2

2

(3)

The propagation method described by eq. 3 is known
as the Spectral Method and consists of applying the spatial
Fourier transform eq. (2) to the input plane, propagate thefield over a distance z (eq. 3) and applying the Inverse
Fourier Transform to ũ(k x , ky , z). This Inverse Fourier
Transform is similar to eq. 2 with the roles of ũ, k x andky interchanged with those of u, x and y, respectively, anda factor 1/4π 2 added.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

It can be shown that paraxial wave propagation over a
distance z = L through a cascaded optical system can berealized in a single step using the elements of the overall
ABCD matrix in Huygens’ Integral for propagation [5]. If
we use the following transform to remove the spherical portion of the wave at the input plane [5]:v0 (ξ  , η  ) ≡π(Ay −My )η2
π(Ax −Mx )ξ 2
√
−i
By λ
Bx λ
a1 a3 u0 (ξ, η)e−ie(4)
Figure 1: Flowchart of the simulation loop.

and at the output plane:

IMPLEMENTATIONv(x , y  ) ≡−1−1 )x2π(Dy −My )yπ(Dx −Mx
√
+i
By λ
Bx λ
a2 a4 u(x, y, L)e+i
e
, (5)
2

where x = a1 x, ξ  = a2 ξ, y  = a3 x, η  = a4 η, andAx(y) . . . Dx(y) are the ABCD matrix coefficients for thex- and y direction respectively, then Huygens’ Integral canbe written as a modified Fresnel Diffraction Integral:v(x , y  ) = i Nc,x Nc,y × 1 1K(x , y  , ξ  , η  )v0 (ξ  , η  )dξ  dη  , (6)−1−1where the kernel K is given by


 2



 2

K(x , y  , ξ  , η  ) = e−iπNc,x (x −ξ ) e−iπNc,y (y −η ) , (7)and the equivalent collimated Fresnel numbers N c,x(y) are
given byMx(y) a21(3).
(8)
Nc,x(y) =Bx(y) λThe arbitrary scaling factors a 1..4 in eqs. 4-5 define two
magnification factors M x(y) = a2(4) /a1(3) , if they correspond to either the size of a hard aperture or a size sufficiently large that the field is just negligible outside thearea covered by that size. Note that for free-space propagation A = D =1, C =0 and B = L = z, and using
Mx = My =1, reduces eqs. 6-8 to the normal Fresnel
Diffraction Integral.
Both the Spectral and the Modified Fresnel propagation
methods are implemented using Fast Fourier Transforms
and therefor their computation time scales as N 2 log2 (N 2 )for a N × N grid. For an equal grid, the Spectral method isthe faster of the two because it requires less operations [6].
However, care has to be taken with the Spectral Methodthat the field remains zero at the border of the grid to avoid
artificial reflections. The Modified Fresnel Diffraction Integral has the advantage that propagation through an opticalsystem, described be a single overall ABCD matrix, is obtained in a single step. Another advantage is that the scaling
applied to this method allows a magnification factor for thegrid so that the mesh size in the input plane does not haveto be the same as the mesh size in the output plane.

408

Simulation of an FEL oscillator requires simulation ofboth the gain within the undulator and the propagation of
the radiation through the remaining part of the resonator,that may contain multiple optical components. Genesis 1.3[2] is used to propagate the optical wave through the undulator and calculate the amplification of the wave. The OPC
receives the optical output from Genesis 1.3, and propagates it from optical element to optical element using oneof the methods described above, until the undulator’s entrance is reached and the next round trip can start. If acascaded set of optical elements can be described by a single ABCD matrix, then propagation through the cascaded
set can be done in a single step using the Modified Fresnel
Diffraction Integral. Output can be produced at various positions, and by the optical elements, which is of advantage
for beam diagnostics and for designing suitable optics for afurther propagation of the output beam.
While the actual simulation algorithms are written in
FORTRAN, the Perl scripting language is used to both control the program flow and define the resonator geometry.
Fig. 1 shows schematically the program flow. The advantage of using a script to control the program instead of aconfig file is that it gives the user a lot of freedom to create
complex models. Table 1 gives an example of a script for
simulation of the FELIX system [7].
This example script contains all essential elements
needed to simulate the FELIX system. The first three lines
are headers needed to load a library. Then two objects are
created, one that corresponds to the genesis program (l.5)
and one that corresponds to the optical propagation code(l.6). The genesis object requires the standard configuration file for Genesis 1.3 as input. A Perl script function isprovided that gives the user complete control over the parameters in the configuration file. This allows, for example,
the use of a Gaussian seed for Genesis 1.3 in the first roundtrip and the resonator feedback as input for Genesis 1.3 inconsecutive round trips.
To define the optical propagation through the resonator,
the optics object (l.6) accepts a simple script that describes the propagation methods and optical components
used (l.7-16). The available propagation methods are described above, and the optical components so far include
diaphragms, square apertures, curved mirrors and thin

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH037

Intensity (a.u.)

Table 1: Example script for simulating the FELIX FEL oscillator.

20000

A

15000

01:
02:
03:
04:
05:
06:
07:
08:
09:
10:
11:
12:
13:
14:
15:
16:
17:
18:
19:
20:
21:
22:
23:
24:
25:

#!/usr/bin/perl
use lib ’./lib’;
use Physics::OPC;

10000
5000
0

$genesis = genesis(’./felix.itdp.in’);$optics = optics( ”fresnel z=1.062
mirror r=3 R=98% # Downstream mirror
fresnel z=5.89
hole r=0.0015 ( # Out-coupling
dump var=output
fresnel z=1# Far field distance
dump var=far )mirror r=4 R=98% # Upstream mirror
dump var=reflected
fresnel z=2.358 ” );22.5

s (mm)

3

30

20

10

0

-10

lenses. Each optical component is defined by a set ofparameters, for example the downstream mirror (l.8) for
FELIX has a curvature (’r’) of 3 m and a reflectivity (’R’)
of 98 %. Other possible parameters for a mirror are absorption (’A’), transmittance (’T’), offset (’xoff’ and ’yoff’),
and a small tilt (’xr’ and ’yr’). The optical propagation
starts with propagation over a distance z=1.062 m from theundulator’s exit to the downstream mirror using the Fresnel Diffraction Integral (l.7). Then the downstream mirror
is defined (l.8). After the downstream mirror the wave is
propagated to the upstream mirror, again using the Fresnel Diffraction Integral (l.9). In FELIX, the output beam
is extracted through a hole in the upstream mirror. In themodel the ”hole” component (l.10) is processed before theactual mirror component (l.14). The hole component creates two waves, one that is transmitted through the hole,and one that corresponds to the part outside the hole thatremains within the resonator. In this case, the transmitted beam corresponds to the radiation extracted from theresonator. The output beam is propagated over a distancesufficiently large to be in the far field (l.11-13). At l.14 thescript continues with the part outside the hole and this isreflected by the upstream mirror. The combination of the”hole” and ”mirror” commands represent the upstream mirror with the hole. The resonator is closed by propagationfrom the upstream mirror to the undulator’s entrance (l.16).

FEL Oscillators and Long Wavelength FELs

-30

x (mm)

Intensity (a.u.)
10000

B
5000

0
2

for $i (1 .. 75) {run $genesis;
run $optics;
move $output => "output.$i.dfl";
move $far=> "far.$i.dfl";
move $reflected => "reflected.$i.dfl";
move $field => "entrance.$i.dfl";}-20

s (mm)

2.5
3

30

20

10

0

-10

-20

-30

x (mm)

Figure 2: Radiation intensity just after reflection on the upstream mirror (A) and just before the undulator’s entrance(B) as a function of the horizontal cross-section (at y=0)
and the position within the optical micro pulse s after 75
round trips and for ΔL=-1.5λ.
The ”dump” commands indicate positions where output isproduced for further analysis.
The last part of the Perl script is the actual simulation
loop where we run the two programs consecutively andsave binary dumps (l.21-34) for each round trip at varies
positions defined in the optical configuration. The binary
files used by the propagation code have the same format as
the field files produced by Genesis 1.3, so existing analysis
tools can be re-used. Utilities to extract plain text data fromthese files are included with the OPC code. Using plotting
tools such as Gnuplot, the user can create all kinds of views
to analyze the optical pulse.
In steady-state mode Genesis 1.3 produces one field distribution, i.e., a single slice, as output, which is then processed by the propagation code. Genesis 1.3 can also run intime-dependent mode, which includes slippage effects. In
this mode Genesis 1.3 produces a set of slices representing
the radiation pulse as output. In time-dependent mode, thepropagation code will process all slices produced by Genesis 1.3 consecutively. Each slice is propagated using thecenter wavelength of the optical pulse, which is valid only
for a narrow bandwidth of the optical pulse. The slowly
varying amplitude and phase approximation used by Genesis 1.3 limits the maximum bandwidth of the pulse. Furthermore, an analysis by Dattoli et.al. showed that the relative bandwidth is limit to about 10 −3 to 10−2 for typicalparameters of VUV, UV and IR FELs [8].

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Proceedings of FEL 2006, BESSY, Berlin, Germany

EXAMPLECONCLUSION
We have developed an Optical Propagation Code that
propagates an arbitrary radiation wave, in the paraxial approximation, through a complex optical system. In combination with a code to simulate the gain medium, such as
Genesis 1.3 in case of FELs, this optical code can be used
to model the output of a laser oscillator. The use of a flexible scripting interface allows a user to create both simple
and complex resonator configurations. The OPC package
is available for download at our website[10].

REFERENCES[1] S. Biedron, Y. Chae, R. Dejus, B. Faatz, H. Freund, S. Milton, H.-D. Nuhn, and S. Reiche, Nucl. Instrum. Methods

410

Output power (W)
1.5e+08
1e+08
5e+07
0
0
0.5
1
1.5

s (mm)

40

2
2.5

10

3

60

50

70

30
20 Round trips (#)

Figure 3: Micro pulse optical power as a function of boththe position s within the pulse and the round trip number
for a detuning ΔL=-1.5λ.
12Micro pulse energy (μJ)

The script shown in Table 1 is used to illustrate some of
the capabilities of the OPC code. The script describes theresonator for the FELIX system [7]. The script produces
four binary dump files for each iteration (that is, for eachround trip). The first gives the field distribution just outside
the outcouple mirror (l.21), l.23 gives the field distribution
just after reflection at the upstream mirror containing thehole for extraction of the radiation, and l.24 gives the distribution at the entrance of the undulator. The far-field distribution (l.22) will not be used here. It should be notedthat the same script is used for both steady-state and timedependent simulations, the only changes required are madein the genesis configuration file.
We performed a time-dependent simulation of the
FELIX system. The horizontal cross-section (at y=0) of
the radiation intensity just after reflection on the upstream
mirror and just before the undulator’s entrance are shown in
Fig. 2 as a function the horizontal position x and the position s within the optical micro pulse after 75 round trips andfor a cavity detuning ΔL=-1.5λ. This figure clearly showsthe effect of the hole in the mirror (Fig. 2A) on the radiation profile and how this profile has changed when propagated to the undulator’s entrance (Fig. 2B), that shows anear maximum on-axis intensity. Note that the broad radiation profile at the undulator’s entrance may be clippedby the electron beam transport tube. Although not present
in the current script, this can be included by adding a diaphragm component just after propagation to the undulator’s entrance (l.16) in Table 1.
If we integrate the intensity over the cross-section of the
optical pulse, we obtain the micro-pulse optical power asa function of the position s within the micro-pulse. Thisis shown in Fig. 3 as a function of the round-trip number. The oscillation in the micro-pulse optical power as afunction of time (=round trip #) is known as the so called
limit-cycle oscillations [9]. It is more clearly visible in the
total micro-pulse energy that is shown in Fig. 4 for threedifferent values of the cavity detuning ΔL.

10

ΔL = -0.5λ
ΔL = -1.0λ
ΔL = -1.5λ

8
6
4
2
0
10

20

30

40

50

60

70

Round trips (#)

Figure 4: Total energy of the micro pulse as a function ofround-trip number for a detuning ΔL of -0.5λ, -1λ and 1.5λ respectively.
Phys. Res. A, Accel. Spectrom. Detect. Assoc. Equip. A445,
110 (2000).
[2] S. Reiche, pbpl.physics.ucla.edu/ reiche.
[3] E. Sziklas and A. Siegman, Appl. Opt. 14, 1874 (1975).
[4] H.A. Hause, “Waves and fields in optoelectronics,” 1984,
Prentice-Hall, Englewood Cliffs.
[5] A.E. Siegman, “Lasers,” 1986, University Science Books,
Mill Valley.
[6] I.V. Volokhine, “Design and Numerical Analysis of TUEFEL II”, Ph.D. thesis, 2003 University of Twente.
[7] D. Oepts, A. van der Meer, and P. van Amersfoort, Infrared
Phys. Technol. 36, 297 (1995).
[8] G. Dattoli, H. Fang, L. Giannessi, M. Richetta, A. Torre,
and R. Caloi, Nucl. Instrum. Methods Phys. Res. A, Accel.
Spectrom. Detect. Assoc. Equip. A285, 108 (1989).
[9] D. Jaroszynski, R.J. Bakker, D. Oepts, A.F.G. van der Meer,and P.W. van Amersfoort, Nucl. Instrum. Methods Phys.
Res. A, Accel. Spectrom. Detect. Assoc. Equip. A331, 52(1993).
[10] OPC design team, lf.tnw.utwente.nl/opc.html.

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH038

COMMISSIONING OF S-BAND RF GUN AND LINAC
FOR THE MARK-III FEL FACILITY AT DUKE UNIVERSITY
Y. Kim∗ , J. Gustavsson, P. Wang, G. Swift, M. Emamian, S. Hartman, P. Wallace, and G. Edwards
Free Electron Laser Laboratory, Duke University, Durham, NC 27708-0319, USA
Abstract
At the Free Electron Laser (FEL) Laboratory of Duke
University, there is an S-band linac based Mark III FEL
facility which can supply coherent FEL photon in the infrared wavelength range. To supply high quality electron
beams and to have excellent pulse structure, we installed an
S-band RF gun with a Lanthanum Hexaboride (LaB 6 ) single crystal cathode for the Mark III FEL facility in 2005.
Its longest macropulse length is about 6 μs, and maximum repetition rates of a macropulse and a micropulse are
15 Hz and 2856 MHz, respectively. Therefore we can generate about 17142 bunches within a bunch train and about
257142 bunches within one second by the S-band gun. In
this paper, we describe recent commissioning experiencesof our newly installed S-band RF gun and linac for theMark III FEL facility.

Figure 1: Photograph around the newly installed gun.

INTRODUCTION
The Mark III FEL is a wavelength-tunable light source
facility which can generate coherent and ultra-bright FEL
photon beams in the infrared wavelength range. Originally,
the Mark III FEL facility was operated at Stanford University, then it was moved to Duke University in 1989 [1].
After relocating to Duke University, we had upgraded several machine components of the Mark III FEL facility [2],[3]. Recently, many FEL facilities started to use the laser
driven RF photoinjector to generate high quality electron
beams with a high peak current and a low transverse emittance. However, the laser driven RF photoinjector has alimitation to generate a good micropulse structure due toa low repetition rate of the gun driving laser. Since manyusers working for biophysical and biomedical science request high repetition rate of FEL photon beams, we haveused an S-band thermionic RF gun with a LaB 6 cathode to
supply excellent micropulse and macropulse structures [4].
After successful operation for several years, in 2003, we
had met a strong back bombardment problem which caused
malfunction of our gun [2], [5]. Therefore we re-installed a
new S-band thermionic RF gun in 2005 to generate stable
FEL photon beams continuously. In this paper, we describe
our commissioning experiences of the new S-band RF gun
and linac for the Mark III FEL facility.

LAYOUT OF GUN AND LINAC
The geometry and parameters of the newly installed gun
are almost the same as those of our original gun. Its original∗ E-Mail : yjkim@FEL.DUKE.edu

FEL Oscillators and Long Wavelength FELs

shape and parameters can be found in reference [6] and [7].
In our new gun, we modified geometry of a deflection magnet and shifted its core position to backward by 3.175 mm
for easy fabrication. Photograph around the new gun andlayout of the Mark III FEL facility are shown in Figs. 1 and2. And its main accelerator parameters are summarized inTable 1 where all emittances are estimated from ASTRA
and ELEGANT simulations. As shown in Figs. 1 and 2,
at the upstream of the gun cavity, there is the deflection
magnet which bends electron beam orbit vertically to reduce the back bombardment on the LaB 6 cathode surface.
At the downstream of the gun cavity, there are two vertical correctors to compensate vertically bended beam orbit
which is intentionally generated by the deflection magnet.
After those correctors, there is a quadrupole doublet (GQ1
and GQ2) and the first gun toroid (T1) to measure electron
beam current in a macropulse or bunch train. Then electron
beams are transferred to an α-magnet [8]. Since horizontal dispersion is not zero in the α-magnet, electron with ahigher energy takes an outer or longer path, and electronwith a lower energy takes an inner or shorter path in the αmagnet. In that manner, bunch length is compressed by the
combined function of the nonzero momentum compaction
factor R56 and nonzero energy spread in the α-magnet [6].
Since horizontal beam size becomes larger in the α-magnet
due to nonzero dispersion as shown in Fig. 2, we chop tailor head part of electron beams by lower and higher energy
filters to control beam energy spread, beam energy, andtransverse emittance. Only electron beams which can go
through two energy filters are transferred to linac [6]. Additionally, to supply macropulse with a frequency of 1 Hz,

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Figure 2: Layout of Mark III FEL Facility.

Table 1: Accelerator parameters of the Mark III FEL.
Parameter
RF frequency of gun and linac
number of gun cell
cathode diametercathode operation temperature
cathode energy spreadcathode work function
cathode heater power
operating vacuum in gun
single bunch chargemacropulse current at gun exit
macropulse current at α-magnet exit
klystron power
gun forward RF powermax gradient on cathodecavity cooling water temperature
total beam energy at gun exit
total beam energy at linac exit
beam energy spread at linac exit
peak current at linac exit
thermal emittance at cathodeprojected emittance at linac exit
slice emittance at linac exit
macropulse length at linac exit
max macropulse rate
micropulse length at linac exit
micropulse rate

Unit
MHz
cell
mm
K
eV
eV
W
Torr
nC
mA
mA
MW
MW
MV/m
deg
MeV
MeV
%
A
μm
μm
μm
μs
Hz
ps
MHz

Value
2856
1
1.75
∼ 1800
∼ 0.4
2.69
∼ 11
< 10−7
0.14
∼ 400
∼ 180
30
∼ 1.8
∼ 30
32.2
∼ 1.6
25 − 450.3
15 − 45∼ 0.35∼5∼12−6
15
0.5 − 32856

there is a 11.5 kV kicker in the α-magnet. In this case,only one macropulse is transferred to linac in one second,
and all other macropulses are dumped in the α-magnet by
the kicker [6].
After the α-magnet, beams are focused by the second
quadrupole doublet (GQ3 and GQ4). There are two toroids(T2 and T3) to measure beam current at the downstream ofthe α-magnet and linac. By accelerating electron beams
with a 3 m long S-band accelerator, beam energy is in-412

creased up to about 45 MeV, and bunch length is morecompressed to about 0.5 ps by the bunch compressor (CHICANE1). By optimizing two quadrupole doublets (LQ12and LQ34) and steerers at the downstream of linac, we canget a beam waist in undulator which is helpful to increaseinteraction between electron beams and spontaneous emitted photon beams. After making the interaction to induce
the microbunching in electron beams and lasing, electron
beams are sent to the beam dump.

COMMISSIONING EXPERIENCES
To reduce space charge effects which increase transverse
emittance and bunch length, we have to accelerate electron beams quickly in the gun cavity. By sending about
2 MW RF power to the gun cavity, electron beams can be
accelerated to about 1.6 MeV in the gun. However, we
could not send such a high power at the beginning stageof our commissioning due to too strong waveguide bangs,
arcs, and poor vacuum at the gun region. Hence, first ofall, we had to reduce gun reflected RF power by matching
the resonance frequency of gun cavity with a driving RF
frequency. By optimizing temperature of cavity coolingwater, position of a gun cavity tuner, and position of the
LaB6 cathode, we could change volume of the gun cavity slightly, and we could get a best matched point which
gives a minimum reflected RF power and the best beamemittance as shown in Fig. 3 [6]. Here the left means thehead region of macropulse, and a large reflected RF powerat the tail region was generated by a resonance frequency
shift which was induced by the increased back bombardment and beam loading effect along the macropulse [5].
After reducing reflected power, by increasing gun forward
power and macropulse length gently, we performed continuous gun cavity RF conditioning until we could get a stablevacuum status in gun region. Since gun reflected power ischanged as forward RF power and macropulse length are
increased, we had to re-optimize gun reflected RF power
at a higher power and a longer macropulse. After performing continuous RF conditioning for three months, we

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany
could obtain required basic beam parameters for the MarkIII FEL operation, and vacuum at gun region was also stabilized as shown in Fig. 5. Here macropulse length is about
6 μs, the maximum beam current in the macropulse is about
400 mA at T1, and its maximum beam current at T2 isabout 180 mA as shown in Figs. 3 and 4.
Although we optimized the deflection magnet to reducethe back bombardment on the cathode surface, we could
not avoid the problem completely when macropulse length
was longer than about 2 μs and beam current at T1 washigher than about 200 mA. Therefore, as shown in Figs. 3
and 4, beam current at T1 was continuously increased
along the macropulse, and a large spike was generated at
the tail region of the reflected power due to the resonancefrequency shift. Generally, electron emission rate from athermionic cathode becomes higher as the gradient on thecathode surface is increased. This increased current density
Js can be described by the well-known Schottky equation
which is given byJs = A · T 2 exp −(Φ − e eEc /(4π0 ) )/kT , (1)where A = 120 A/(cm2 ·K2 ) is the Richardson constant, T
is the cathode temperature, Φ = 2.69 eV is the work function of the LaB6 cathode, k = 8.62 × 10−5 eV/K is theBoltzmann constant, and E c is the external electric fieldon the cathode surface [6], [9]. Therefore there are two
ways to obtain a higher beam current at T1. One way isincreasing RF forward power while keeping cathode temperature at a low value. The other way is increasing cathode temperature while keeping RF forward power at a low
value. According to our experience, the latter way was useful to reduce the back bombardment along the macropulse.
Hence during commissioning, we operated our gun with ahigh cathode temperature of about 1800 K.
After considering beam loading effect and the higher
beam current at the tail region, we had to send more higher
RF forward power along the macropulse to get a uniform
energy distribution. If gun reflected power is close to unbalanced shape as shown Fig. 3(top left), head and tail partsin the macropulse are chopped by two energy filters in
the α-magnet, and pulse length after the magnet became
shorter. Therefore we optimized reflected and forward
power signals to have a good linearity along the macropulse
as shown in Fig. 3(bottom left) and (bottom right). Fromthe information on position of the lower energy filter andmagnetic field of the α-magnet, we could estimate total
electron beam energy E at the gun exit which is given by
E [MeV]  0.511 1 + (0.205 · Iα [A])2 ,(2)
where Iα is the current of a power supply for the α-magnet,
and the lower energy filter is located at 16 mm. By scanning Iα and monitoring T2 signal, we could estimate thelowest and the highest beam energies as well as energy
spread in the macropulse, which are useful for us to keep
reproducibility of gun RF amplitude and phase. Since peakcurrent and beam loss along linac were sensitive to I α , a

FEL Oscillators and Long Wavelength FELs

TUPPH038

Figure 3: Signal of gun reflected RF power when reflected
power are unbalanced at head and tail parts (top left), whenhead part has a high reflected power (top right), when reflected power is minimum and its slope along macropulse
is optimized (bottom left), and signal of forward RF power
when reflected power is optimized (bottom right).

Figure 4: (left) signals of the first gun toroid (yellow), thesecond gun toroid (cyan), and linac toroid (magenta) whenbeam transmission from gun to linac and back bombardment along macropulse are optimized, (right) signal of thefirst gun toroid when there is no transmission in the αmagnet. Here calibration factors for T1, T2, and T3 are
0.4 A/V, 0.4 A/V, and 1.0 A/V, respectively.
fine tuning of Iα was also needed to get a lasing. After optimizing gun reflected power, quadrupoles, correctors, andthe α-magnet properly, we could get about 45% transmission and a flat current distribution at the downstream of the
α-magnet as shown in Fig. 4(left). If beam energy is too
low or Iα is too high, we could not get any beam transmission at the α-magnet as shown in Fig. 4(right).
To optimize beam orbit and optics at gun and linac regions, we used signals from three radiation monitors which
are distributed along linac. Although those signals were
low during 1 Hz operation, they were significantly increased during 10 Hz operation as shown in Fig. 6. Dueto the excellent pulse structures, those loss level were very
high when beam orbit and optics at gun and linac region
were slightly changed from a golden orbit and optics whichgive the minimum radiation loss and the best emittancefor lasing. Therefore, we had to optimize all quadrupoles,
steerers, and the α-magnet carefully to reduce those loss.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 5: (top) spiky vacuum status on January 19, 2006
when gun generated 400 mA at T1 for the first time, (bottom) stabilized vacuum status on January 31, 2006 whengun generated 400 mA at T1 without any vacuum interlock
for about 80 minutes.

pulse length is about 4.4 ps, energy per a micropulse isabout 1 μJ, and the maximum micropulse repetition rate is
9 MHz [11], [12]. This photoemission mode operation will
be certainly helpful to increase the peak power of our MarkIII FEL facility. Normally, electron beam quality and FEL
performance are significantly changed even though RF amplitude and phase of gun and linac are slightly changed.
Therefore we would like to develop a real time RF monitoring system to get a stable and reproducible FEL operation. And we want to develop an optical fiber based on-line
beam loss monitor to stabilize beam orbit around undulator, which is certainly helpful to keep continuous and stableinteraction between electron beams and spontaneous emitted photon beams in undulator. At the moment, we do nothave a direct diagnostic tool to measure bunch length ofabout 0.5 ps long electron beam. To measure bunch length
directly and to optimize FEL performance, we would liketo install a small S-band deflection cavity in the near future. To control bunch length or peak current easily andto reduce geometrical wakefields and coherent synchrotron
radiation, we are under developing a new bunch compressor with four electromagnetic dipoles. Now we are also
under developing an emittance measurement system with a
Flea digital camera of the Point Grey Research [13].

SUMMARY

Figure 6: Signals of three radiation monitors along linac
during 1 Hz and 10 Hz operations.

FUTURE UPGRADE PLANS
We are under developing and considering following upgrade plans to improve performance of the Mark III gun
and linac. First of all, to keep electron beam current constant and to reduce the strong back bombardment problem,
we need a real time cathode temperature monitoring system. By installing an infrared temperature detector andby giving a feedback to the power supply of a cathodeheater, we can keep cathode temperature and beam current constant. And to remove the back bombardment problem completely, we are also under operating the other RF
gun with the photoemission mode by shooting a Continuum
Minilite-II Nd:YAG laser on the LaB 6 cathode surface [10].
Since the thermal emittance of the LaB 6 cathode is about
0.35 μm for a diameter of 1.75 mm, and quantum efficiency
is about 0.05% at 266 nm, to improve transverse emittance,
peak current, and energy spread more, we would like to
use a high-class laser such an Nd:YLF laser whose the rms

414

By performing gun cavity RF conditioning for threemonths, we could get a stable vacuum status and required
basic beam parameters. After optimizing reflected power,
toroid signals, radiation loss along linac, and focusing
around undulator, in January, 2006, we could send electron
beams to the beam dump successfully. Since we could geta strong signal from a power meter in April, 2006, it is certain that our new gun and linac were optimized properly togenerate FEL photon beams from our undulator. Authors
thank to M. Pentico, O. Oakley, V. Rathbone, S. Huang, V.
Popov, S. Mikhailov, and Y. Wu for their helpful comments
and contributions for Mark III recommissioning project.

REFERENCES[1] S. V. Benson et al., Nucl. Instr. and Meth. A 296 (1990) 110.
[2] G.A. Barnett et al., Nucl. Instr. and Meth. A 375 (1996) 97.
[3] I. Pinayev et al., in Proc. PAC2001, 2001.
[4] G. S. Edwards et al., Rev. Sci. Instrum. 74 (2003) 3207.
[5] Toshiteru Kii et al., Nucl. Instr. and Meth. A 475 (2001) 588.
[6] G. A. Westenskow et al., HEPL Tech. Note TN-86-1, 1986.
[7] C. B. McKee, Ph.D. dissertation, Duke University, 1994.
[8] Harald A. Enge, Rev. Sci. Instrum. 34 (1963) 385.
[9] Yu Song, IEEE J. Quantum Electronics 27 (1991) 898.
[10] J. G. Neumann et al., Rev. Sci. Instrum. 76 (2005) 033303.
[11] J. M. Lafferty, J. Appl. Phys. 22 (1951) 299.
[12] S. Schreiber, in Proc. FEL2005, 2005.
[13] http://www.ptgrey.com/products/flea/.

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH039

BRIGHT ELECTRON BEAMS AND SMITH-PURCELL FREE-ELECTRONLASERSCharles H. Boulware#, Heather L. Andrews, Jonathan D. Jarvis, Charles A. Brau
Department of Physics & Astronomy, Vanderbilt University, Nashville, TN 37235, U.S.A.
Abstract

SPFEL THEORY
Smith-Purcell (SP) radiation is generated when an
electron beam passes close to a grating. The virtualphotons of the field of the electrons are scattered by thegrating, and the wavelength λSP observed at an angle θ
is
⎞
L ⎛1
λSP =
− cosθ ⎟
(1)
⎜
m ⎝β
⎠
where L is the grating period, m is the diffraction order,
β c is the electron velocity, and c is the speed of light.
The angular spectral fluence of this radiation is describedby several authors [4,5,6]. The intensity of the SPradiation falls off exponentially with the distance between
the beam and the grating, with a characteristic length

βγλSP
(2)
4π
where γ is the Lorentz factor for the electron beam [6].
When the electron beam current over the grating issufficiently high, the interaction between the electrons
and the fields above the grating becomes nonlinear, andthe electrons become bunched. Periodic bunching of theelectron beam intensifies the SP spectrum coherently [7].
Nonlinear emission with increasing beam current has been
observed at Dartmouth College using a modified scanningelectron microscope as a beam source [8,9].
The interaction between the electron beam and the
h=

#

0.40
normalized frequency

We present further developments to the theory ofSmith-Purcell free-electron lasers [1] (SPFELs) andcharacterization of a blunt needle cathode electron sourcein use to test the theory. The theory of SPFELs has beenrefined to include the effects of resistive losses on theevanescent surface wave supported by the grating andreflections of the wave from the ends of the grating.
Losses are included directly in the grating dispersion
relation and the reflections appear in the boundary
conditions for the growing wave. Based on earlier workin sharp needle cathodes [2,3], an yttrium metal blunt
needle cathode has been developed for the purpose ofdriving a SPFEL device. Space charge expansion of thebeam in the transverse direction and aberration in theelectron optics place limitations on the useful beam thatcan be generated.
Both experimental and simple
analytical characterizations of these limitations arepresented and considered in light of the requirements of
the SPFEL.

grating dispersion relation
0.30
operating
point

0.20
0.10

electron beam (30 keV)
0.00
0

0.5
normalized wavenumber

Figure 1. Grating
synchronous solution

dispersion

relation1
showingfields above the grating is significant only for a grating
surface wave whose phase velocity is equal to the electron
velocity. The dispersion relation for a lamellar grating
without external mirrors has been calculated by matching
the boundary conditions for fields inside the grooves of
the grating to a set of Floquet modes above the grating[10].
The electron beam is synchronous with a single
evanescent mode of the grating, as shown in Fig. 1. The
evanescent mode does not itself radiate except by
scattering at the ends of the grating, and the wavelength ofthe mode is always longer than the lowest-order SP band.
The SP radiation spectrum is coherently enhanced,
however, at harmonics of the bunching frequency dictatedby the wavelength of the synchronous evanescent wave.
The group velocity (the slope of the dispersion relation)at the synchronous point can be positive or negative,
depending on the electron beam energy. The energy flowin the evanescent wave, therefore, can be copropagatingor counterpropagating with respect to the electron beam.
At high electron energy, the energy flow is copropagating,and the device operates on a convective instability as doesa traveling wave tube amplifier. At low electron energy,
the energy flow is counterpropagating and the device
operates on an absolute instability in the manner of a
backward wave oscillator. In the oscillator case, feedback
is provided by the backward moving wave even in theabsence of mirrors. At some intermediate energy, thesynchronous point on the dispersion relation coincides
with the Bragg point, where the group velocity vg
vanishes.

charles.h.boulware@vanderbilt.edu

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Proceedings of FEL 2006, BESSY, Berlin, Germany

The gain coefficient for the evanescent wave in either
the amplifier or oscillator regime can be calculated byexpanding the grating dispersion relation around thesynchronous point. A dimensionless expression for thisexpansion (without losses) is(δω − v δ k ) (δω − β cδ k ) = Δ
2

(3)

g

where δω is the frequency deviation from thesynchronous point, vg is the group velocity, δ k is thewavenumber deviation, andω 2p GΔ= 3(4)γ
where G is a constant that depends on the grating profile.
The gain coefficient of the device varies as v g−1 3, whichdiverges near the Bragg point. However, the resistive
losses in the grating have an attenuation coefficient thatvaries as v g−1, which diverges at the same point [1].

Resistive losses also introduce a real phase change. To
see this, we consider a short section of grating as aresonant cavity by imagining perfect reflectors at eachend. Small resistive losses in the grating surface thenintroduce a frequency shift given byQδω = −(5)(1 + i )2 U⎞(1 + i ) ⎟ (δω − β cδ k )2 = Δ

j =1

j

3

j =1

416

iδ k j Z

j

20

30
40
Voltage (kV)50

Figure 2. Effect of reflections on the start current as afunction of beam voltage
where the index j represents the three different solutionsof the dispersion relation expansion, Aj is the relative
amplitude of the three waves, and Z is the length of thegrating [1].
These boundary conditions can be refined to include
reflections from the ends of the grating and losses in thereflected wave. When this is done, the last boundary
condition becomes∑(e3− iδ j Z

j =1)− Reiδ 0 Z = 0

(10)

where

length of the evanescent wave, and k is the wavenumber
at the operating point. This width is much greater than∑jNo loss, reflection
No loss, no reflection(9)

EFFECT OF REFLECTIONS
Equation 6 admits three solutions: a grating structure
wave and so-called fast and slow space-charge waves.
The three waves are locked together in frequency to forma single mode, but have slightly different wavenumbers
and correspond to very different plasma dielectricsusceptibilities. Interference allows the waves to satisfy
boundary conditions at the ends of the grating. At the
upstream end of the grating, the electron beam enters withuniform distributions of both density and velocity. In theabsence of reflections, the electric field vanishes at thedownstream end. These three boundary conditions are
3
Aj
=0
(7)
2
j =1 ( δω − β cδ k )j
3

Loss, reflection
Loss, no reflection

(8)

(6)

⎠

∑ δω −Aβ cδ k = 0∑Ae =0

1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

δω
−δ kj ,(11)βc
β + βgβ + βgδ0 =δω +ν (1 + i ) ,(12)
ββ g cβ − βg
R is the (complex) round-trip reflection coefficient, andν = U 2vg Q is the empty grating loss coefficient.
The boundary conditions are solved with the dispersion
relation as a constraint. The effect of the reflection
coefficient is to increase or decrease the computed growthrate according to whether the phase shift on reflection
leads to constructive or deconstructive interference withthe backward waves. The start condition for oscillation isthat the growth rate, the imaginary part of the frequency,
be positive. Details on the calculation of reflection at thegrating ends and the inclusion of losses in the grating
dispersion relation can be found elsewhere [12].
The condition for oscillation can be expressed as a start
current. Figure 2 shows start current as a function ofvoltage for the parameters of the Dartmouth experiments[8]. The interference effects resulting from a nonzero
reflection coefficient are clearly observed. The observed
start current is on the order of 1 mA, in agreement withthe experiments. However, the two-dimensional theory
described here should underestimate the start current. We
expect the diffraction width of the mode on the grating to
be on the order of Ζ g / k ≈ 1 mm , where Z g is the gain

where i = −1 , Q is the power loss into the grating
resistance, U the energy density in the surface wave, andthe angled brackets represent averages over one period of
the grating and one cycle of the wave [11]. The correct
dispersion relation with losses is therefore⎛ω0⎜ δω − vg δ k +2Qc⎝

Start current (mA)

EFFECT OF LOSSESδj =FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH039

screen current (mA)

6
5
4
3
2

40.0 kV1

46.6 kV

0

Figure 3. Schematic offocusing/steering magnets

electronsourceandthe transverse size of the electron beam, thus reducing theeffective interaction and raising the start current.

BLUNT NEEDLE CATHODES
The short vertical coupling length h between theelectron beam and the grating makes necessary a highbrightness electron source for a SPFEL device. Sharp
needle cathodes made of tungsten have been investigatedas high-brightness electron sources [2,3].
Thephotoelectric quantum efficiency of photoemission fromthe tungsten metal is enhanced by several orders ofmagnitude at the high surface electric fields (up to 1010
V/m) that can be obtained at the 1 μm-radius tip of achemically etched tungsten needle. At these fields, theSchottky effect reduces the barrier for electron emission
by as much as 2.5 eV. The electron beams created fromthese sharp tips are highly divergent and difficult to focus.
A less divergent electron beam can be obtained from ablunt needle cathode with a tip radius on the order of 1
mm. The surface field is reduced to 107 V/m, but the loss
in quantum efficiency can be mitigated by changing theneedle material from tungsten to yttrium. Yttrium has alower work function than tungsten (2.9 eV compared to
4.5 eV), so a reduction of the barrier by the Schottky
effect is not necessary to enhance the quantum efficiency.
At 107 V/m, for example, the Schottky effect is only 0.1
eV, but the effective work function of an yttrium cathodeis similar to a tungsten cathode at 109 V/m.
The needle-cathode device at Vanderbilt University
uses an yttrium cathode with a ≈ 700 μm radius spherical
tip at the end of a 10 mm long square rod. Removal ofadsorbate molecules from the yttrium surface is criticallyimportant to the quantum efficiency of the cathode. We
use electron bombardment to raise the surface of the metal
to its melting point (1800 K) for several seconds to
produce a clean, smooth surface. The partially-covered
cathode is held at a positive potential of 2-3 kV, andbombarding electrons are provided by a tungsten ion
gauge filament positioned close to the cathode. The
heating process is unstable when both the filament and thecathode tip are hot. Yttrium deposited on the tungsten
filament lowers its work function, increasing thethermionic emission.

FEL Oscillators and Long Wavelength FELs

0

20

40

60

total needle current (mA)

Figure 4. Current detected at the phosphor screen as afunction of total needle current
After cleaning, the cathode is illuminated with aquintupled Nd:YAG laser (4-ns pulses at 20 Hz, <1 μJ per
pulse, 5.9 eV per photon). Peak currents of 50 mA are
produced reliably, corresponding to a QE of ~10-3. The
laser is focused on the cathode with a spot radius of 20
μm to give a current density at the source ofJ e ≈ 107 A/m 2 . For an electron temperature Te ≈ 1 eV ,the normalized brightness of the source ism c2 J(13)
BN = e e ≈ 1012 A/m 2 -steradian
2π k B Te
where me is the electron mass and k B is the Boltzmann
constant [13].
A schematic of the experiment is shown in Fig. 3. A
conical anode allows the ultraviolet laser light to enter thechamber from the side and be reflected by a mirror to theneedle tip. The electron beam is focused by a 500-turnsolenoid in an iron yoke designed to minimize theeffective needle-lens distance, and therefore, the size ofthe beam in the lens. Steering coils direct the beam pastan aluminum grating to a phosphor screen, which also
serves as a Faraday cup. A fused quartz window above
the grating allows millimeter-wave radiation to becollected by a He-cooled InSb bolometer. SP radiation
above the bolometer noise level has yet to be detected.
The usable beam current from the needle cathode islimited by the fraction of the beam that can be collected
and focused. Space-charge forces play a significant rolein the divergence of the beam at the source, and the usable
beam current increases sublinearly with total needle
current at high laser intensities, as shown in Fig. 4. The
importance of the space-charge effect is somewhat less at
higher accelerating voltages. At 60 kV, with laser powerat the needle damage threshold, 5 mA (about 10%) of thetotal beam current reaches the phosphor screen.
The spot size of the electron beam at the grating can beaffected by aberration in the solenoid focusing magnet,
beam emittance, and space charge at the beam focus [13].
The generalized perveance for a uniform round beam is2I
K= 3 3(14)
β γ I0417

normalized camera intensity

TUPPH039

Proceedings of FEL 2006, BESSY, Berlin, Germany

with a CCD camera and provide differential current
density across the beam. By changing the solenoid fieldstrength, the beam is scanned through its focus. The
effects of spherical aberration are observed clearly as anintense beam edge upstream of the electron focus.
Several transverse current profiles at different lens
strengths appear in Fig. 5. The measured radius at thebeam waist is 200 μm, dominated by spherical aberration.

500 µmincreasing solenoid
current

CONCLUSIONS

Figure 5. Transverse beam profiles show the effect ofspherical aberration upstream of the electron focus
where I is the current in the beam, I 0 = 4πε 0 me c 3 qe , ε 0
is the vacuum permittivity, and qe is the electron charge.
In terms of the generalized perveance, the space-charge
dominated beam radius is−α 2
2K

r = Ae(15)
where A is the beam aperture at the lens and α is theconvergence angle. The space-charge limitation on the
focal spot for the Vanderbilt device is less than 1 μm.
The calculated brightness of the yttrium blunt needle
source corresponds to an emittance of ε ≈ 10 −7 m for 5
mA current at the grating. The limitation posed by theemittance on the spot size at the focal point is

ε
(16)
α
which corresponds to a 10 μm spot above the grating.
The limitation on the spot size resulting from sphericalaberration in the focusing solenoid is independent of thebeam current. Expanding the magnetic field near the axis
and keeping terms up to third order in the transverse
distance from the axis gives a radial dependence on the
focal length of the solenoid (spherical aberration)
r=

∞
⎡∞
qe2
1
5r 2 ⎛ dBz ⎞ ⎤=Bz2 dz +⎟ dz ⎥∫⎜
2 2 2 ⎢∫
8 −∞f 4me β c ⎣⎢ −∞⎝ dz ⎠⎥⎦
2(17)

where Bz is the axial magnetic field and r is thetransverse distance from the axis. The dependence of
focal length on the transverse position of electrons
entering the solenoid produces a spot size (at the circle of
least confusion) of2∞
5qe2⎛ dBz ⎞
3
r=
f
A
(18)
0
⎟ dz
∫⎜
128me2 β 2 c 2−∞ ⎝ dz ⎠where f 0 is the paraxial focus of the lens. The
aberration-limited spot size varies with the cube of theaperture size at the final lens. For the Vanderbilt
experiment, this spot size is 125 μm at 60 kV andrepresents the dominant contribution to the radius of thebeam at the circle of least confusion.
The size of the electron beam is measured by scanningthe beam across a knife edge or by analyzing images ofthe phosphor screen. Images of the screen are captured

418

Detailed effects of losses and reflections have been
incorporated into the theory of SPFELs. The modified
dispersion relation for the grating evanescent wave gives
both the attenuation and phase shift due to resistive losses.
The effects of reflection at the grating ends are accounted
for in the boundary conditions on the three waves thatcomprise the grating mode. The start current calculated inthis way agrees with the Dartmouth experiments, though
the two-dimensional treatment neglects diffraction of theevanescent mode in the transverse direction, which should
increase the start current.
Experiments are underway using the yttrium cathodedevice at Vanderbilt to drive the oscillator-regime
operation of a SPFEL. Spherical aberration limits the
spot size of the electron beam in the Vanderbilt device,
reducing the effective current interacting with theevanescent wave.
Aperturing the beam to reduce
spherical aberration also reduces the fraction of total
needle current to the grating.

REFERENCES[1] H. L. Andrews, C. H. Boulware, C. A. Brau, and J. D.
Jarvis, Phys. Rev. ST-AB 8, 050703 (2005).
[2] C. Hernandez Garcia and C .A. Brau, Nucl. Inst. Meth.
Phys. A483, 273 (2002).
[3] C.H. Boulware and C.A. Brau, Free Electron Lasers
2002, K.-J. Kim, S.V. Milton, E. Gluskin (eds.),
Elsevier Science B.V., II-47 (2003).
[4] P.M. van den Berg and T.H. Tan, J. Opt. Soc. Am. 64,
325 (1974).
[5] L. Schaechter, Beam-Wave Interaction in Periodic andQuasi-Periodic Structures (Springer-Verlag, Berlin,
1996).
[6] Y. Shibata et al., Phys. Rev. E 57, 1061 (1998).
[7] H. L. Andrews, C. H. Boulware, C. A. Brau, and J. D.
Jarvis, Phys. Rev. ST-AB 8, 110702 (2005).
[8] J. Urata et al., Phys. Rev. Lett. 80, 516 (1998).
[9] A. Bakhtyari, J.E. Walsh, and J.H. Brownell, Phys.
Rev. E 65, 066503 (2002).
[10] H. L. Andrews and C. A. Brau, Phys. Rev. ST-AB 7,070701 (2004).
[11] J. D. Jackson, Classical Electrodynamics, 3rd edition(Wiley, New York, 1999), p. 374.
[12] H. L. Andrews, C. H. Boulware, C. A. Brau, J. T.
Donohue, J. Gardelle, and J. D. Jarvis, submitted
manuscript.
[13] J. D. Lawson, The Physics of Charged Particle
Beams, Clarendon Press, Oxford, 1988.

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH040

EMITTANCE COMPENSATION OF SUPERCONDUCTING GUN AND
LINAC SYSTEM FOR BEAMS WITH LARGE CHROMATIC VARIANCE
B. Buckley, Cornell University, Ithaca, NY 14853, USA
D. Kayran, V. N. Litvinenko,
Collider Accelerator Department, Brookhaven National Laboratory, Upton, NY 11973, USA*
Abstract
Among the methods of emittance compensation for a
superconducting rf gun and linac system include utilizing
a solenoid and drift space after the gun to achieve a
specific beam envelope with zero beam divergence before
entrance into the linac. Studies on this method haveassumed minimal energy spread in the beam. However, incases where chromatic effects cannot be ignored this one
solenoid emittance compensation technique is inadequate.
Proposed is a new method of emittance compensation
utilizing two solenoids in order to minimize emittance inbeams with large energy spread. We present a theoreticalbasis for the new technique along with a computer
optimized configuration. The results are compared withprevious methods of emittance compensation.

INTRODUCTIONFirst introduced by Carlsen [1] and expanded
upon theoretically by Serafini and Rosenzweig [2] is ascheme for emittance compensation for an rf gun andlinac system that uses a solenoid magnetic field tocompensate for space charge defocusing. Chang et al. [3]extended the method for systems with a superconducting
gun for which the solenoid must be placed outside thegun. Such studies and further experiments have achieved
good emittance compensation results for beams with little
energy spread [4].
Touched upon by Chang et al. are the effects on
emittance caused by varying energy along the bunch.
Energy dependence in solenoid focusing, space charge
defocusing and linac ponderomotive focusing leads toemittance increases when large energy spread in thebunch is present. Previous studies have laid thefoundation for cancelling out chromatic effects at the
linac entrance [3]. However, there are other important
chromatic effects that should be looked into.
In this paper we study the chromatic effects ofthe solenoid focusing and space charge defocusing. We
introduce a method for compensating for emittanceincreases caused by these effects by adding a second
solenoid. The mechanism of this emittance compensation
scheme is studied with analysis of the beam through thesystem. The relationship between the placement andstrengths of the two solenoids is studied theoretically andcompared to a computer optimized setup. Finally, this twosolenoid method is compared to the one solenoid method*

Work performed under the auspices of the U.S. Department of Energy

FEL Oscillators and Long Wavelength FELs

by running Parmela [5] simulations with both setups andcomparing final normalized emittance values. We findthat the two solenoid method is superior to the one
solenoid method at minimizing emittance at the exit of thelinac.

EMITTANCE COMPENSATIONThe essence of the emittance compensation method
described in detail in Ref [2] involves focusing thediverging beam immediately after the gun with a solenoid
and reaching a point of zero convergence after a drift
space at which point the beam enters the linac. The
solenoid field must be of a certain strength in order tohave the beam enter the linac at the invariant envelope ofthe linac. This envelope is given by:

ˆ =

2
  



I
3IA 

(1)

where IA= 17,054 A is the Alfven current, I is the current
in the beam, and  is the average accelerating gradient of
the linac. Entering at this envelope with zero divergence,
the beam will exit the linac with zero divergence and withan envelope satisfying Eq. (1).

Chromatic Effects
Chromaticity comes into play in the energy dependenceof the solenoid, space charge and linac focusing. As
previously stated, we will not focus on the latter in thispaper.
The envelope equation for a cylindrical space charge
dominated beam through a focusing element, in this casea solenoid, is given by [2]:  =  S +

Qc
n2
+
3
2
2IA z ( )  ( )  3(2)

where n is the normalized emittance and  S is thesolenoid focusing strength eB  2
S = 
 2mc 

(3)

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Proceedings of FEL 2006, BESSY, Berlin, Germany

where e is the charge of electron and B is the magnetic
field of the solenoid. From the dependence on  in each ofthese terms one can see that slices along the bunch withdifferent energies will transform differently through thesolenoid-drift space element.

spread of 3% and a total charge of 5nC, one of thepossibilities for the RHIC e-cooling project at
Brookhaven National Laboratory [6]. (a) Slices aligned
before solenoid, immediately after gun. (b) Slices
misaligned after solenoid focusing.

ANALYSIS OF PHASE SPACE ANGLE

From Eq. (3) the dependence on energy is clear.
Figures 1(a) and 1(b) illustrate the effect on the phasespace distributions of three slices of varying energy. Afterthe solenoid the phase space slices are no longer aligned
leading to a rise in projected emittance.

To illustrate these chromatic effects on the emittance
we take a look at the transformation of the phase space
angle

=




(4)

Through Drift SpaceFor beam parameters typical for BNL’s ERL injector(Q ~ 1 nC,  ~ 5,  z ~  ~ 1cm, and a normalized slice
emittance of n ~1 mm.mrad) the ratio between third andsecond terms on the right of Eq. 2 is very low:

through the solenoid and drift space elements.

Through Solenoid
In this analysis we will assume a small solenoid length
in which no change in  occurs, focusing only on the firstterm on the right hand side of Eq. (2). Taking the integral
and dividing by  we achieve

I A z n2 /Qc 2 ~ 5105 . Hence, only the second
term on the right side of the envelope equation isnecessary:  =

 =  sL(5)with L the length of the solenoid.

P=

50

(a)

40

(6)

Qc
3
2IA z ( )(7)with P being the perveance, a function of energy. Near the
waist, the envelope can be approximated by a parabola
[7]:

30
20
10

X' (mrad)P;P ( z  zw )  w +
2 w

0
-10
-20

2

(8)

-30

with divergence of

-40
-50
-60
-25

-20

-15

-10

-5

0

5

10

15

20

25

X, mm

 

P ( z  zw )
.
w

(9)

20

(b)

Dividing the two we obtain a phase space angle of15

X' (mrad)

10



5

2P ( z  zw )22 w + P ( z  zw )

2

.

(10)

0

The envelope at the waist is given by integrating thedifferential equation of Eq. 6 to obtain the equivalent firstorder differential equation and rearranging to achieve

-5
-10
-15
-20
-25

-20

-15

-10

-5

0

5

10

15

20

25

X, mm

w = i e

 2
 i
2P

.

(11)

Figure 1: Phase space plots of three different slices ofvarying energy. Average energy of 2.5 MeV, energy420

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany
The position at the waist is found by taking the equivalent
integral equation of Eq. 6 and using a polynomial
approximate solution [3]:

zw 

i 
 i
 2 i .009165+.95449+.21824. (12)P PPFrom these equations we are able to analyze how the
spread in the phase space angle varies through thesolenoid and drift space. In Fig. 2 we plot the differencein angle between the head and tail slices of the same
bunch from Fig. 1, the head having a higher energy than
the tail.

Figure 2: Difference between higher energy and lower
energy slices in bunch immediately after solenoid. The
beam waist occurs at z = 0 meters. The calculations andplots were done with Mathcad [8].
The plot begins after the solenoid at the maximum
spread in angle and continues through drift space. We seethat the slices align before z=0, the waist position, and arethus misaligned at the waist. This leads to a nonoptimized emittance before entrance into the linac.
What one notices is that since the lower energy slices
rotate past the higher energy slices it would be possible touse a second solenoid to realign the slices in phase space.
The above equations allow one to calculate the spread in after an arbitrary distance and thus the relationshipbetween the solenoid strengths of the first and second
solenoids and the distance between them, which would
result in realignment of the phase space slices.

OPTIMIZATION
A two solenoid, rf gun and linac system was optimized
for lowest normalized emittance by optimizing position
and field strengths of the two solenoids and position of
the linac. Plots of normalized emittance and envelope can

FEL Oscillators and Long Wavelength FELs

TUPPH040

be found in Fig. 3 where they are compared to the sameplots for a non-optimized one solenoid setup. The one
solenoid configuration is set up following the invariant
envelope method [2]. Since it is not optimized, looking at
final emittances does not make for a definitive
comparison. Instead, the plots serve to illustrate theoverall advantage the two solenoid method has over theinvariant envelope one solenoid method when dealing
with large energy variation.
The optimized magnetic fields of the first and second
solenoids and drift length between them are respectively
854 Gauss, 607 Gauss and 333.9 cm. To test the accuracyof the above equations describing the alignment of phasespace slices we use them to calculate the magnetic field of
the second solenoid, which would realign the phase spaceslices with all other optimized parameters unchanged. We
obtain a theoretical magnetic field strength of roughly 520
Gauss for the second solenoid. This is significantly lower
than the optimized value above. However, whencomparing standard deviations in  with 500 slices wefind that the theoretical value has a lower spread in ,.0846 inverse meters, than does the optimized value,.0897 inverse meters. This should not come as a surpriseas the theoretical calculation minimized spread in  after
the second solenoid while the optimized value minimized
normalized emittance after the linac, not necessarily
minimizing spread in . What the comparison of spread in does is validate the accuracy of our theoretical
approach, even if it should not be used as the exact value
when attempting to minimize emittance.

DISCUSSION AND CONCLUSION
We have introduced a new method of emittancecompensation that has advantages compared withprevious methods using one solenoid in minimizing
emittance of beams with significant energy spread. Our
theoretical analysis of the transformations of phase space
angle due to solenoid focusing and space charge
defocusing has proven to be accurate and may serve as abasis for future analysis into this new emittancecompensation scheme.
Further studies however must be undertaken inorder to gain a better understanding of this new method.
Firstly, alignment of sliced phase space angles is not the
only parameter affecting total normalized emittance.
Individual sliced emittances must also be minimized
along with spread in slices and the two might not be
simultaneously minimized. Studies into optimizing spreadin  after the linac have resulted in increases innormalized emittance.
Another aspect that should be looked into further
are the chromatic effects of the linac focusing. As seen in
Fig. 3, for the optimized two solenoid set up the beam
does not enter the linac at the waist as is deemednecessary in previous one solenoid methods. Instead thebeam enters at a significant convergence. Non-linearities

421

TUPPH040

Proceedings of FEL 2006, BESSY, Berlin, Germanyin the linac focusing due to this convergent entrance
perhaps might be playing a large role in minimizing
individual sliced emittances. Efforts at moving the linac

further from the second solenoid have not resulted inlower values of normalized emittance.
12

(a)

8
6
4
2

0

1

2
3
Distance (m)

30

4

6
4

(c)

20
15
10
5

0

1

2

3

4

0

5

25

0

8

2

Normalized Emittance (mm.rmrad)

Normalized Emittance (mm.rmrad)

0

(b)

10

Envelope (mm)Envelope (mm)105Final Normalized Emittance: 7.5 μm-rad

0

1

2

3

4
5
Distance (m)

6

30

7

8

(d)

25
20
15
10
5
0

0

1

2

3

4

5

6

7

8

Final Normalized Emittance: 2.8 μm-rad

Figure 3: Comparison of one solenoid and two solenoid methods: Electron beam envelope with one solenoid (a) andtwo solenoids (b). (c) Normalized projected emittance with one solenoid (c) and two solenoids (d).

REFERENCES[1] B. Carlsen, “New Photoelectric Injector Design for theLos Alamos National Laboratory XUV FEL
Accelerator”, NIM A285 (1989) 313-319.
[2] L. Serafini and J. B. Rosenzweig, “Envelope Analysis
of Intense Relativistic Quasilaminar Beams in RF
Photoinjectors: A Theory of EmittanceCompensation”, Phys. Rev. E 47, 2031 (1993).
[3] X. Chang, I. Ben Zvi, and J. Kewisch, “EmittanceCompensation of Compact Superconducting Guns
and Booster Linac System”, PRST-AB 9, 044201(2006).

422[4] X. Qui, K Batchelor, I Ben-Zvi, and X-J Wang,“Demonstration of Emittance Compensation throughthe Measurement of the Slice Emittance of a 10-ps
Electron Bunch”, Phys. Rev. Lett. 76, 3723-3726(1996).
[5] L. M. Young, Los Alamos National Laboratory
Report No. LA-UR-96-1835 (revised 2001).
[6] V. Parkhomchuk and I. Ben-Zvi, Brookhaven
National Laboratory Report No. C-A/AP/47, 2001.
[7] M. Reisner, Theory and Design of Charged Particle
Beams (John Wiley and Sons, New York, 1994), p.
201[8] Mathcad 2000, Reference Manual, MathSoft Inc., 101
Main Street Cambridge, Ma 02142, USA

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH044

FREE ELECTRON LASER STUDY OF FREE CARBON CLUSTERS
C. Spezzani*, E. Allaria, M. Coreno, F. Curbis, B. Diviacco, G. De Ninno, L. Romanzin, S. Tileva,
M. Trovò, Sincrotrone Trieste, Strada Statale 14 - km 163.5, 34012 Basovizza, Trieste ITALY
M. Amati, G. Bongiorno, C. Lenardi, T. Mazza, P. Milani, T.A. Mostefaoui, P. Piseri, L. Ravagnan,
Dipartimento di Fisica and CIMAINA, Università degli Studi di Milano, I-20133 Milano, ITALY.

Abstract
UV absorption from carbon nanoparticles is a very
interesting astrophysical topic. The prominent humpcentred at 217.5 nm is the most dominant feature in theinterstellar extinction curve and also the mostcontroversial and a long-standing problem inastrophysics. At the University of Milano an experimental
set-up based on a Pulsed Microplasma Cluster Source has
been developed for the investigation of free clusters at the
Elettra Gas Phase beamline. The cluster source producesvery intense cluster beams with tunable size distribution.
The design of the apparatus is extended with a chamber
for gas phase reaction (water vapour, CO, H2...) providing
a unique opportunity to study the gas phase properties ofcarbonaceous particles in different environments.
We plan to investigate Resonant Raman scattering offree carbon particles tuning the high brilliance UV/VIS
storage ring FEL of ELETTRA across the region of
217.5 nm where the UV absorption hump in astrophysicaldata is observed and where a number of electronictransitions exist for variable size linear carbon chains.

INTRODUCTION
Since its discovery by Stecher (1965), the ultraviolet
extinction curve feature observed at 217.5 nm has been
attributed to π-electron plasmon absorption or π-π * bandtransitions in small graphite particles or amorphous
carbon grains. Despite the early assignment tocarbonaceous material, the exact physical nature of thecarrier is still unknown and strongly debated. One
peculiar behaviour of the 217.5 hump is the constancy ofits spectral position regardless of the choice of theastronomical object under observation [1]. On the other
hand, the peak position of the bump predicted for graphite
particles is quite sensitive to grain size, shape andadsorbate coatings, which is inconsistent with theobservations.
Many different models have been proposed to explain
the experimental observation and many different attempts
have been made to reproduce in laboratory an adequate
prototype for cosmic dust [2,3,4]. Experiments conductedon hydrogenated carbon nanoparticles isolated in noble
gas matrix pointed out the relevance not only of particle
shape and size but also of their chemical environment [1].

Other observations indicate that the presence of an ice
mantel surrounding the carbon particles strongly
influence their UV optical response [3]. Other authors
have succeeded in synthesizing carbon aggregates thatshow optical constants fitting quite well the extinction
curve [4, 5], but, the adopted methods don't match very
well with the environment conditions where carbon grainsin the intergalactic medium are expected to form.
Actual models of dust astrophysics lack ofexperimental data about carbon dust in gas phase, their
optical proprieties, mass distribution, reactivity and ofcourse their absorption of the UV light in the 217 nm
region. In order to attempt a meaningful reproduction, atthe laboratory scale, of this astrophysical system it isimportant to study carbon clusters in isolated condition, asa function of their dimension and chemical environment.
Recently the potential of optical spectroscopy in free jet
expansion for experiments on astrophysically relevant
species has been demonstrated [6].
Resonant Raman Scattering (RRS) is a powerful
technique for the characterization of such a system. It
combines the sensitivity to vibrational properties ofcarbon structures relevant for astrophysics like carbyne[7, 8] with a selective transfer of energy when the exciting
photons are tuned at the energy corresponding to a given
resonance, increasing in this way the scattering crosssection.
We present here an experimental setup for a RRS studyof free carbon clusters which make use of the storage ring
Free Electron Laser (SRFEL) radiation.

EXPERIMENTAL SETUPThis section quickly reviews the experimental setupthat we are developing at ELETTRA in the framework of
the collaboration between the CIMAINA of Milan
University and the SRFEL group of ELETTRA, Trieste.

CESyRA
CESyRA (Cluster Experiments with Synchrotron
RAdiation) [9] is a research project of the CIMAINA
focused on free cluster spectroscopy with the highintensity UV and soft X-ray light from the ELETTRA
synchrotron radiation facility.

___________________________________________* e-mail: carlo.spezzani@elettra.trieste.it

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TUPPH044

Proceedings of FEL 2006, BESSY, Berlin, Germany

Fig. 1: Main elements of CESyRA apparatus: (Ch1) expansion chamber, (Ch2) deposition and gas exposure
chamber, (Ch3) TOF, (1) PMCS, (2) manipulator, (3) gas line, (4) TOF, (5) to dumping chamber and quartz
microbalance.
The experiments are implemented in a UHV
compatible supersonic cluster beams apparatus. The main
constituents of the system are sketched in figure 1.
Briefly, it consists of three differentially pumped, highvacuum chambers (Ch1, Ch2 and Ch3) separated by twoskimmers (S). Heart of CESyRA apparatus is the Pulsed
Microplasma Cluster Source (PMCS) [10,11], developed
at the Molecular Beam and Nanocrystalline Materials
Laboratory in Milano, which is able to deliver highly
collimated and intense seeded beams of clusters fromrefractory materials (typical deposition rate for carbon:
100 µm/h at 500 mm source-substrate distance, ~ 0.8 cm2
covered area). The PMCS is based on target ablation
obtained by He plasma sputtering: a pulse of He flux is
directed against a target by means of a valve driven by anelectromagnet (opening time of about 300 μs). The gas isthen ionized by a pulsed discharge fired between thetarget rod (cathode) and the anode. The sputtered particles
are carried through an aerodynamic lens system by the Heflow and the mixture eventually undergoes a supersonic
expansion into a high vacuum chamber. In order toprevent the formation of holes on the cathode rod and to
reduce the need for source maintenance, since the ablation
is extremely localized, the target rod is maintained inrotation during source operation (see figure 2). The
clusters are emitted in pulses that propagate at a speed ofabout 1000 m/s and that last typically 15 ms. Lighter
aggregates are mostly located at the head of the pulse
while the heavier ones at the tail.
The PMCS is located outside vacuum andcommunicates through the nozzle with the expansion
chamber (Ch1). The beam passes through a skimmer that,
due to particle focusing on the beam axis [12], efficiently
separates the clusters from the carrier gas. In the second
chamber a gas cell is installed to allow gas exposure of
the free particles in the beam (3). A diaphragm separates
the second from the third chamber (2) to produce
differential vacuum and finally the beam is directed into
an interaction chamber where a short linear time of flight(TOF) mass spectrometer is mounted perpendicularly tothe plane formed by the intersection of the light andcluster beams (4). A sample manipulator is mounted, inorder to intercept the beam and thus to allow cluster
deposition onto a substrate. Finally, the beam is dumped
onto a quartz microbalance (5) that monitors the cluster
flux.

424

The SRFEL of ELETTRAThe CESyRA setup has primarily been thought for
application with synchrotron radiation on refractorymaterials in gas phase, demonstrating for the first time thepossibility of performing XAS measurements on free Ti
nanoparticles [13]. However, for this particularapplication on carbon clusters, the requirements on thelight source that has to be used make the SRFEL of
Elettra [14] the best candidate for our objective. To probe
the cluster beam in gas phase, we need a very high flux ofphoton with a wavelength that can be precisely tuned
around 217.5 nm (5.7 eV). In this respect, the Elettra
SRFEL can produce a very bright monochromatic beamthat can be directed into the interaction volume by meansof few optical elements, minimizing the photon flux
losses due to radiation transport.
The maximum average lasing power that can beachieved using a SRFEL is limited by the heating of theelectron beam induced by the laser onset [15, 16]. The
increase of the electron-beam energy spread is indeed
responsible for the diminution of the optical gain while, atFig. 2: a) schematic diagram of the PMCS source;b) pressure contour plot of He jet inside the PMCS
cavity (see ref [11]); c) scanning electron microscope
micrographs of the cathode region eroded by theplasma. The cathode is continuously rotated in orderto prevent the formation of holes. A very smooth andprecise trace formed by plasma erosion is clearly
distinguishable.

New Science at FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany
saturation, the latter reaches the level of the optical cavity
losses. However, for applications requiring a high peak
power, the FEL power can be ‘‘concentrated’’ into a seriesof giant pulses, applying the so-called Q-switching
regime. In this case, the peak power is considerablyenhanced (one to few orders of magnitude) while theaverage power is only slightly reduced [17]. To operate
the SRFEL in Q-switching, we apply a modulation on theradiofrequency (RF) that drives the electron bunches inthe storage ring (figure 3a) [18]. The giant pulses that we
obtain are typically 100 μs long (figure 3c). The
development of a giant pulse introduce a quite big energy
spread that implies a recovery time for the dumping of theelectron beam of the order of 10~100 ms. For this reason
Q-switching is normally operated at a repetition rate offew Hz (figure 3a and 3b). In RRS experiment setup, theRF modulation is triggered after a variable delay by the
opening of the He valve in the clusters source. Adjusting
the delay we are able to probe, with the highest power
available, different parts of the cluster pulse and therefore
sample cluster populations with different average size.
In order to probe the clusters with the Raman scatteringin the spectral region of interest, we use mirrors for the
FEL optical cavity especially designed for thatwavelength. The interferential coating has been preparedat the Laser Zentrum Hannover.

Fig. 3. Q-switching of the SRFEL: a) the RF modulation
can be triggered by the opening of the He valve of theclusters source, b) development of a sequence of giant
pulses, c) detail of a giant pulse: typical duration is
100 μs.

New Science at FELs

TUPPH044

PRELIMINARY TESTS AND FUTURE
DEVELOPMENT
The CESyRA system is in the experimental hall of
ELETTRA since May 2006 for the long term projectapproved on the Gas Phase beamline [9,13,19]. When thechamber is not in use for this project it is available for the
preparation of the RRS experiment.
In Raman spectroscopy, one of the most frequently
encountered problems is related to the presence of theelastic background. Since the Raman cross section istypically 4-5 orders of magnitude smaller then the elastic
one (Thomson scattering), the Raman signal risks to besubmerged by the tails of the elastic peak. Moreover, in
our setup, the interaction volume is in vacuum, separated
from the spectrometer and the SRFEL by quartz
view-ports. This introduces an additional source of
scattered light that further decreases the "peak tobackground" ratio. The first step in the preparation of theRaman experiment has been the measurement of a total
scattering yield, i.e. the collected light signal regardless of
its spectral distribution, in order to evaluate the relevanceof the background and to assess the interaction between
the clusters and the radiation. For this purpose, we used a
photomultiplier tube (PMT) to detect the photons that arecollected by a small quartz lens focusing in the interaction
volume about 5 mm far from the PMCS nozzle, where thecluster density is close to the maximum. When the setup
will be optimized, the PMT will be replaced with aspectrometer.
Since now, few hours have been dedicated to optimize
the experimental setup. FEL light at 217.5 nm has been
generated with a very good stability. We expect to extract
a power of few tenth of mW in free-run mode that should
correspond to a flux of 1017~1018 ph/s in the Q-switching
regime. The FEL light has been used to perform thealignment of the chamber as well as some preliminary
tests aimed at optimizing the Raman setup. The light was
focused on the cluster beam by means of a lens locatedoutside the chamber and one mirror in vacuum at 45º that
deflect the light in the vertical direction. A second mirror
at 45º was used to extract the light from the chamber. The
focus of the collecting lens was placed at the intersectionof the laser and clusters beams, so that the collection was
done in the direction perpendicular to both of them. A
multichannel time to digital conversion board has beenused to record the detected events keeping track of theirdelay with respect to the opening of the valve. The fullrange temporal window of detection is 20 ms, with a time
resolution of 82 ps. The acquisition software allows
integration over an undefined number of consecutive
pulses. To obtain a good background subtraction despite
the possible drifts in laser and cluster source operation,
the measurements have been done alternating acquisitionof pulses with and without clusters; this was obtained byfiring the vaporization discharge in the PMCS every
second gas pulse only. Typical integration time was 5 min
at a repetition rate of 5 Hz that corresponds to acquisition

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Fig. 4: Acquisition with PMT of the scattered intensity.
Black line (circles) SRFEL pulse plus clusters pulse. Redline (square) SRFEL pulse with only the carrier gas(notice the absence of the HV discharge noise).
of about 750 laser pulses with clusters in the beam and
750 without clusters.
Figure 4 shows an example of detected events for an
acquisition obtained setting a nominal delay of 1.2 ms
between the He valve and the RF modulation. The peak at
1.45 ms corresponds to the photon counts collected under
the giant pulses of the SRFEL. The black line with circles
is associated to the pulses with clusters and the red one(squares) without clusters. The sharp spike at 0.73 ms isdue to electrical noise introduced by the HV discharge in
the PMCS and thus occurs only in the pulses where thegeneration of clusters is on; excluding this instrumental
effect, no significant differences were measurable
between the two curves at any delay. An expanded viewof the peak at 1.45 ms (figure 5) shows that photon counts
are detected with a time structure that closely follows the
microtemporal structure of the FEL radiation. The factthat the detection rate is of the order of one photon countper micropulse indicates that the intensity of lightscattered inside the chamber by the optical elements ishindering the signal of interest as the detector is probably
saturated by background counts.
Those preliminary results show the importance ofscreening the detector from the intensity scattered by the
optical elements. At present, we are developing a new
optical scheme to minimize this source of backgroundthat certainly would prevent the detection of the weak
Raman signal. We are also implementing a Nd:YAG table
top laser that, even if not tunable at the proper
wavelength, will be helpful for off-line preparation of theexperiment with the SRFEL.
Considering the small number of shifts that for the
moment have been dedicated to the experiment, we canbe optimistic for the future developments. The CESyRA
apparatus and the SRFEL reveal to be stable enough forthe acquisition of data with good statistic.
We acknowledge the storage ring control group of
Elettra for collaboration and Stefan Günster of LZH(Hanover) for the realization of FEL optics.

426

Figure 5: Expanded view of the microtemporal
structure of photon count peak under FEL giant pulsein the Q-switch mode.

REFERENCES[1] M. Schnaiter, et al., Astr. J. 498:486-496, 1998.
[2] W. Kraetschmer, Astrophysics and Space Science
128:93-99, 1986.
[3] D.C.B. Whittet, et al. Astr. J. 602:291-297, 2004.
[4] W.W. Duley and S. Lazarev, Astr. J., 612:L33-L35,
2004.
[5] Manish Chhowalla, et al., Phys. Rev. Lett. 90:155505,
2003.
[6] T. Motylewsky, et at., Astrophys. J. 531:312-320,
2000.
[7] L. Ravagnan, et al., Phys. Rev. Lett. 89:285506, 2002.
[8] L. Ravagnan, "Synthesis and Characterization of
Carbynoid Structures in Cluster Assembled Carbon
Films", PhD thesis (2005).
[9] C. Lenardi, et al., Elettra Highlights 2003-2004, 92.
[10] E. Barborini, et al., J. Phys. D 32:L105-L109, 1999.
[11] H. Vahedi Tafreshi, et al. J. Nanosci. Nanotechnol.
6:1140-1149, 2006.
[12] P. Piseri, H. Vahedi Tafreshi, P. Milani Curr. Op.
Solid St. Mater. Sci. 8:195-202, 2004.
[13] P Piseri, et al., New J. Phys. 8:136, 2006.
[14] R.P. Walker, et al., Nuclear Instruments and Methods
in Physics Research A, 429: 179–184, 1999.
[15]

N.A. Vinokurov, et al., preprint
Novosibirsk, (unpublished) 1977.

INP77.59[16] A. Renieri, Il Nuovo Cimento 35:161, 1979.
[17] I.V. Pinayev, et al., Nucl. Instr. and Meth. A 475:222,
2001. proceedings.
[18] G. De Ninno, et al., Nuclear Instruments andMethods in Physics Research A, 528:278–282, 2004.
[19] K.C. Prince, et al., J. Sync. Rad. 5:565, 1998.

New Science at FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH046

FREE ELECTRON LASER PULSE CONTROL BY ACOUSTO- OPTIC
MODULATORS
Taizou Kanai*, Sachiko Yoshihashi-Suzuki, Kunio Awazu, Institute of Free Electron Laser,
Graduate School of Engineering, Osaka University, Japan
Abstract
The free electron laser (FEL) at Osaka University canbe continuously varied over a range from 5.0 to 20.0 μm
when using the 30 MeV electron beam. The FEL has adouble pulse structure. The structure consists of a train ofmacropulses with a pulse width of 15 μs, and eachmacropulse contains a train of 330 micropulses with apulse width of 5 ps. The FEL’s tunability and short pulse
make possible new medical applications, such as
investigating protein dynamics and ablating soft tissues.
Precise control of the micropulse train is essential for FEL
medical applications because macropulses of long pulse
duration lead to undesirable thermal effects. An FEL
pulse control system, using an acousto-optic modulator(AOM), was developed to investigate the non-thermal
effects of FEL on living tissues. This system provides
efficiency (~ 65%) and a fast switching speed (> 200 ns),
and we predict that FEL will serve as a novel tool inmany new applications.

(3) High efficiency;(4) Easy pulse duration adjustment; and(5) Portability between different experimental stations.
An acousto-optic modulator (AOM) has therefore beenchosen as the best solution for the Osaka University FEL
system. Section 2 describes the principles of AOMs andpulse control systems. Section 3 details the performance
evaluations of the pulse control system, and Section 4reports the results of these evaluations.

＜M acropulse＞ 0.1 s
15 us＜M icropulse＞

45 ns

5 ps

Figure 1: Pulse structure of FEL.

INTRODUCTION
The free electron laser (FEL) at Osaka University is apulsed, tunable infrared source. It is designed to work in
the region from 5 to 20 μm at an average power of up to
50 mW. The FEL applications research is broadlyinterdisciplinary, including measurements of investigationof protein dynamics, the ablation of soft tissues andnarrow band-gap materials [1-4].
An electron beam of 30 MeV energy is the laser gain
medium for the FEL. It is accelerated with a linear, pulsed
RF accelerator. This leads to the pulsed beam current andcomplex temporal intensity profile of the emitted IR lightas shown in Fig.1. The accelerated electron pulses haveup to 20 μs duration and each of them generates one
optical “macropulse” have duration of 15 μs. The mode
locked pulse or “micropulse” have duration of
approximately 5 ps with 44.8 ns spacing between pulses.
For many FEL application 15 μs duration of themacropulse leads to undesirable thermal effects or
obscures signals from fast optical process. The FEL user
community has identified the need for selecting thenumber of micropulse. The switching device to achieve
this should have the following properties;(1) Operating wavelength of 5 to 12 μm;(2) Variable pulse duration between 500 nanoseconds
and the full macropulse length, with fast rise and falltimes;* kanai@fel.eng.osaka-u.ac.jp

New Science at FELs

MATERIALS AND METHODS
The principle of an Acousto Optic Modulator
An AOM is a device that allows control of the power,
frequency, or spatial direction of a laser beam using anelectrical drive signal. It is based on the acousto-optic
effect, i.e., refractive index modification by the oscillating
mechanical pressure of a sound wave. The geometry of
the input and output laser beams relative to the acoustic
column is shown in Figure 2. An AOM’s key element is atransparent crystal (or a piece of glass) through which thelight propagates. A piezoelectric transducer attached tothe crystal is used to excite a high-frequency sound wave.
Light can then be diffracted at the periodic refractive
index grating generated by the sound wave. The scattered
beam has a slightly modified optical frequency (increased
or decreased by the frequency of the sound wave) and aslightly different direction. The frequency and directionof the scattered beam can be controlled via the frequencyof the sound wave, while the acoustic power allows
control of the optical power. For sufficiently high acoustic
power and to align the input laser beam for a true Bragg
input angle, more than 70% of the optical power can bediffracted as the first order beam. When a supersonicwave intercepts the incident beam, the AOM generates afirst order beam. Therefore, the rise time of first orderbeam depends on the diameter of the incident beam andthe speed of the supersonic wave. The rise time of thefirst order beam is given by equation (1). The following

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equation describes the time required before the primarylight output rises from 10% to 90% [5].
TR = S/ (v*1.56),(1)

where:
TR = Rise time of first order beam,
S = Diameter of incident beam,
V = Speed of supersonic wave,
1.56 = correction factor.

PERFORMANCE EVALUATIONS
The laser damage threshold for Ge was determined
empirically for the FEL. Surface damage occurred at 20mW of average power, less than 1.5 mm Φ beam
diameter, and 6.3 μm wavelength. The absorption by Ge
does not change significantly between 6 and 12 μm. Our
experimental setup is shown in Figure 5. The FEL enters
the AOM at a diameter of 1.5 mm Φ and the pulse
duration is controlled by adding a supersonic wave pulse
to the AOM. First order beam is detected by infrared
detector (MCT; VIGO Systems, R005). MCT signal isrecorded by an oscilloscope (LeCroy, WaveMaster 8000).

RESULTS 1
Wavelength-dependence of pulse control system
Figure 2: Principles of an AOM.

The wavelength dependence of the pulse control
system is shown in Figure 4, Input/picked FEL average
power vs. wavelength in the range from 5.4 to 12 μm.

Pulse control system design

145
Input FEL average power

40

0.9

Picked FEL average power (max)

0.8

35

0.7

30

0.6

25

0.5

20

0.4

15

0.3

10

Pulse control efficiency

Modulation index

FEL average power (mW)

The diameter of the original FEL is about 50 mm Φ. To
control the high efficiency/high speed pulse, it isnecessary to incident para-parallel/diameter of very small
beam into AOM. A schematic diagram of an FEL pulse
control system is shown in Figure 4. The FEL beam (50mm Φ) diameter was reduced in size to 1.5 mm Φ by two
mirrors with either long (radius of curvature = 385 mm)or short (radius of curvature =50.0 mm) focal lengths.
Table 1 shows the specifications of a standard AOM(AGM-402A1, IntraAction Corp).

0.2

5

0.1
0

0
5

5.5

6

6.5

7

7.5 8 8.5 9 9.5 10 10.5 11 11.5 12
Wavelength (um)Figure 4:Wavelength-dependance of pulse control system.

Measurement of first order FEL

Table 1: Specifications of Ge-AOM
Optical Wavelength
Acousto-optic Material
Acoustic Velocity
RF Center Frequency *Optical Insertion Loss
Optical Power Capability
Laser Polarization
Rise Time (diameter)
Bragg Angle
Beam Separation
Diffraction Efficiency

428@10.6 μm
Single Crystal Germanium
5.5 mm/μsec
40 MHz<7 %25 Watts
Parallel to Base
116 nsec (1 mm)
38.5 mrad
77 mrad<70 %*Other frequency available

P u ls e g e n e r a to r o u tp u t s ig n a l
F E L 1 s t O rd e r o u tp u t s ig n a l

M a c r o p u ls e tr a in

Output (mV)

Figure 3: Experimental setup for pulse control.

The MCT signal of the FEL first order beam is shown in
Figure5. This pulse control system can control the FEL
pulse width in the range of 10 micropulses (>200 ns) to
the full macropulse (15 μs). A 630 ns first order FEL is
produced by a control signal of 500 ns, a 360 ns firstorder FEL is produced by a control signal of 200 ns.
Based on these results, the rise/fall time of this pulse
control system is about 100 ns. This result aligns closelywith the theoretical value derived from equation (1).

0

0 .5

0 .8
0 .6
0 .4
0 .2
0

1 .0

1 .5

2 .0

2 .5

3 .0

P u ls e g e n e ra to r S ig n a l
500 ns
630 nsF E L 1 s t o r d e r p u ls e S ig n a l

1 .5 4 u s

0 .8
0 .6
0 .4
0 .2
0

0

0 .5

1 .0

1 .5

2 .0

2 .5

3 .0

2 .0

2 .5

3 .0

200 ns360 ns

0

0 .5

1 .0

1 .5
T im e ( u s )Figure 5: The pulse structure of the picked FEL.

New Science at FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

EXPEREMENTTUPPH046

FEL macropulse structure

Photo penetration depth = 3 um

Irradiation stop
~2000 um

Shock wave intensity level (a.u.)

Pulse width = 15.0 us ( original pulse )In case of FEL irradiation to gelatin, interaction arrives
at depth of 2mm, at the maximum. However, Photo
penetration depth = 3 μm. Interaction extends to much
deeper from the region where light can arrive at. It isthought that this reaction depends on a shock wave.

Pulse width = 7.0 us ( x 1 pulse)

Pulse width = 1.0 us ( x 7 pulses )Pulse width = 500 ns ( x 14 pulses )Pulse width = 300 ns ( x 25 pulses )Pulse width = 200 ns ( x 35 pulses )

0

20

40

60

100

80

Time (us)BubbleGelatin

Shock wave ?

Figure 8: A difference of a level of shock wave by adifference of pulse structure.

Photo excitation region

1000

1400

500 umPhoto induced shock wave
regionFigure 6: The process of gratin cut.

Experiment setup
Experiment setup for proof experiment of pulse control
effect is shown in Fig 7. In this experiment, change of ashock wave is estimated by an image analysis and wave
pattern analysis.

Gelatin(Gelatin concentration=(20%, 1 mm thick)Camera(x450)
MonitorOscilloscope
Shock wave detector(transducer, WAT18, 10 MHz)

Evaluate with shock wave level

Figure 7: Experiment setup for proof experiment of pulse
control effect.

RESULTS 2
A difference of a level of shock wave by a difference ofpulse structure is shown in Figure8. Figure 9 illustrates
the maximum shock wave level (peak to peak)/ maximum
shock wave arrival depth (image analysis) vs. FEL pulse
width. From these results, the same tendency was seen inan analysis result by an image and an analysis result by awave pattern. A shock wave grows up to 1-2 μs andreaches saturation afterwards.

New Science at FELs

1200

800
1000

700
600

800

500

系列2
系列1

400

600

Shock wave arrival depth
Shock wave intensity level

300

400

200
200

100
0

0
0

1

2

3

4

5

6

7

8

Pulse width (us)Figure 9: A difference of shock wave by a difference ofpulse structure.

FEL pulse control system

Evaluate with images

Shock wave arrival depth (um)900

Shock wave intensity level (a.u.)

Irradiation start

CONCLUSIONSFEL pulse control system using an AOM was developedin order to investigate of non-thermal effect between the
FEL and living tissue. With a time scale of 200 ns ~ 15
μs, this system provides the efficiency of ~65 % and afast switching speed.
From results of pulse control effect proof experiment,
the same tendency was seen in an analysis result by animage and an analysis result by a wave pattern. A shock
wave grows up to 1-2 μs and reaches saturation
afterwards. This system made it possible to control ashock wave by controlling a thing of pulse structure.
Picking out a single micropulse is impossible using thisdevice with a time scale from 200 ns to 15 μs; it is,however, a very successful pulse control technique.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Thermal intensity

Shock wave intensity

Controllable region

10ns 100ns 1us 10us 100usTime

Photo excitation
Photo induced shock wave
ThermalREFERENCES[1] GS. Edwards, D. Evertson, W. Gabella, TL. King, J.
Kozub, M. Memdenhall, J. Shen, RH. Traeger: IEEE J.
Sel. Top. Quantum Elec. Vol.2 (1998), p.810[2] K. Awazu, A. Nagai, K. Aizawa, The Reveiew ofLaser Engineering. Vol.26, No.5 (1998), p.369[3] K. Awazu, The Reveiew of Laser Engineering.Vol.28,
No.5 (2000), p.291[4] Klaus Becker, J. Bruce Johnson, Gleen Edwards, Rev.
Sci. Instrum. Vol.26, No.5 (1998), p.1496[5] Mike Hillier: Acousto Optic Tuneable Filters Basic
Theory And Design Considerations, Isomet corporation(1998)

Figure 10: Controllable region by pulse control system.
100
Pulse width (us)50
Laser knife

10

Excavation(Dentistry, Cartilage )

5
1
0.5
0.1

Bimolecularanalysis/control

Shock wave knife

Surface modification(Dentistry )vital function control(Biodynamics )5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0

Wavelength (um)Figure 11: New regions that FEL can apply.

DISCUSSIONS
Using this system, the pulse width becomes the thirdparameter of the FEL system, in addition to the twoconventional irradiation parameters of wavelength andpower density. This system allows more precise FELbiomolecular interactions, and was thereby able toproduce a new irradiation effect of FEL that was notpreviously available (Figure 11). Improvement of thepulse control system (higher speed, higher power density)affords more selective excitation of biomolecules on apico- and nanosecond time scale. In addition, by using
FEL as the excitation light, we can introduce thepicosecond time resolution vibration minute light method
to the field of chemistry and biology.

430

New Science at FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH047

ABSOLUTE AND CONVECTIVE INSTABILITY OF SMITH-PURCELL
FREE ELECTRON LASER
D. Li#, K. Imasaki, ILT, 2-6 yamada-oka, suita, Osaka 565-0871, JapanZ. Yang, UEST, Chengdu, 610054, P.R.China
Gun-Sik Park, SNU, Seoul 151-747, Korea
S. Miyamoto, S. Amano, T. Mochizuki, LASTI, 3-1-2 Koto, Kamigori, Hyogo 678-1205, Japan.
Abstract
The effect of dissipative loss in the grating surface
on the Smith-Purcell free-electron laser is investigatedwith the help of a two-dimensional particle-in-cellsimulation. The simulation model supposes an open
aluminium grating driven by a continuous electron beam.
With the present parameters, it has been shown that sucha device can oscillate on both the convective and absoluteinstability when ignoring the surface-loss. The growthrate is found to be dependent of the beam energy, and it
decreases when the surface-loss is involved. The results
are compared with the recent theory.

INTRODUCTION
As a promising alternative in the development of acompact, tuneable and powerful THz source, the SmithPurcell free-electron laser (SP-FEL) has attracted many
attentions in recent years [1-5]. The SP-FEL can berealized on the configuration of an open grating [6-10],
which is different from the conventional configuration,“orotron” or “ledatron” [11,12].
When an electron passes close to the surface of thegrating, it not only emits Smith-Purcell radiation, but also
excites the evanescent wave [13,14]. The evanescentwave, with the frequency below the lowest frequency of
the Smith-Purcell radiation, travels along the grating andundergoes partial diffraction and partial reflection at bothends of the grating. The diffraction potion is radiative inthe free space and can be utilized. The dispersion relationof the evanescent wave, as shown in Fig. 1, is similar tothe backward-wave oscillators (BWOs) and travelingwave tubes (TWTs), since the grating could be regarded
as a kind of slow-wave structure. The frequency of theevanescent wave is determined from the intersection pointof the dispersion curve and the beam line, as shown in Fig.
1, meaning that the beam velocity is synchronous with thephase velocity of the wave. The group velocity can bepositive, negative or zero. When the interaction happensin the positive group velocity, the wave and the beam
moves in the same direction. Such an interaction induces
convective instability, and the device operates in themanner of TWTs [15]. When the group velocity is
negative, the wave and the beam moves in the opposite
direction. In this case, the interaction leads to absoluteinstability, and the device can operate without external
feedback, like BWOs [15].
The case of absolute instability has been much#dazhi_li@hotmail.com

New Science at FELs

Figure 1: Dispersion relation for our grating.
addressed [6-9]. Andrews and co-workers predicated that
there is possibility for device to start oscillation based on
the convective instability, since the wave reflects at bothends of the grating, playing the role of external feedback[15]. In this paper, we address on the oscillation induced
by absolute and convective instability, respectively, withthe help of a two-dimensional particle-in-cell code,
MAGIC [16], a code for simulating processes involving
interactions between space charge and electromagnetic
fields. The simulation is performed with and without
involving the surface-loss of the grating, respectively, todemonstrate the effect of the loss on the operation of thedevice.

SIMULATION DESCRIPTION
The simulation geometry is shown in Fig. 2. A
grating with rectangular form is set in the centre of thebottom of the simulation box. The surface of the grating isassumed to consist of conductor whose grooves are

Figure 2: Simulation geometry.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

parallel and uniform in the z direction. We use a sheet
electron beam with thickness of 24 Ǵm, and place itsedge 34Ǵm above the top of the grating. It is a perfectlaminar beam produced by the MAGIC algorithm and isgenerated from a cathode located at the left boundary of
the simulation box. The electron-wave interaction andradiation propagation happen in the vacuum area, whichis enclosed by a special region (called free-space in
MAGIC language), where the incident electromagnetic
waves and electrons can be absorbed. The wholesimulation area is divided into a mesh with rectangle cellsof small size (Ǭx=17.3Ǵm, Ǭy=17.3Ǵm) in the regionof beam propagation and grating, and large size ( Ǭ
x=17.3Ǵm, Ǭy=51.9Ǵm) in the rest of the region. The
Cartesian coordinate system is adopted with the origin at
the centre of the grating. Since it is a two-dimensional
simulation, it assumes that all fields and currents are
independent of the z coordinate. And it should be notedthat the current value mentioned in this paper represents
the current per meter in the z direction.
The main parameters of the grating and electron
beam are summarized in table 1. The electron beam
Table 1 Main parameters for simulation
Grating period   L=173 Ǵm
Groove width   w=62 Ǵm
Groove depth   d=100 Ǵm
Period number
N=50
Electron beam energy   E=40 ~140 KeV
Beam current
I=648A/m
Beam thickness ǻ=24 Ǵm
Beam-grating distance  Ǭ=34Ǵm
External magnetic field  Bx=2T
energy will be varied in the following simulation. The
external magnetic field is used in order to ensure stablebeam propagation above the grating. It should be notedthat some parameters of the grating and electrons, such as
period length, groove depth and width, and electron’senergy, used in our simulation are the same as those in
Dartmouth experiment [1]. Consequently the radiation
occurs in the THz regime. However, the grating length inour simulation is shorter than the one used in Dartmouth

experiment because of the limited capacity of ourcomputers. In addition, the form of the beam is different,
since we use a sheet beam and the experiment used around beam.
As to the diagnostics, MAGIC allows us to observe avariety of physical quantities such as electromagnetic
fields as functions of time and space, power outflow, andelectron phase-space trajectories [16]. We can set therelevant detectors anywhere in the simulation area.

SIMULATION RESULTS
Ignoring Surface-loss
We first perform the simulation at the ignorance ofthe surface loss, i.e., the grating is supposed to be perfectconductor. The choice of beam energy spans the regionsof absolute and convective instability. According to thetheory of Andrews and Brau, the beam line intersects thepoint of zero group velocity, called Bragg condition, withthe energy of 125 keV[15]. Fig.3 and 4 show the contour
plot of Bz and energy modulation for the beam energy of
50 keV, at the time of 4.703 ns. In this case, the device
operates on the absolute instability, and the energy
modulation tells that the oscillation happens. If the beamenergy is 140 keV, the device operates on the convective
instability. From Fig. 5 we understand that the ends of thegrating reflect the wave, and therefore provide feedback.

Figure 4: Energy modulation for the case of 50
keV eelectron beam.

Figure 5: Contour plot of Bz for the case of 140
KeV electron beam.
Figure 3: Contour plot of Bz for the case of 50
KeV electron beam.
432

The reflected waves form the interference pattern. Fig. 6
illustrates the modulation of the energy, meaning that the
New Science at FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

device oscillates. The electric field component of theevanescent wave is observed near the grating surface, as
examples, simulation results for some chosen energies are
given in Fig.7. It is seen that the evolution of the

TUPPH047

means the effect of surface loss strongly depends on the
beam energy.

Figure 8: Evolution of amplitude of Ex withrespect to time.
Figure 6: Energy modulation for the case of 140
keV electron beam.
amplitude of the electric field component in the x
direction shows the exponential growth for all chosenenergy, which means the device can oscillate by bothabsolute and convective instability, even at the Bragg
condition. We noticed that when the beam energy is 125
KeV or more, the curves illustrate several sharp decreases
as the amplitude growing.

Figure 7: Evolution of amplitude of Ex withrespect to time.

Growth rate
The growth rate of the evanescent wave can bederived from the simulation data. From the plot of
amplitude of Ex(t) vs t we can extract the slope of thelinear envelop, which is the imaginary part of thefrequency, Im(ȁ) [9]. Plenty of simulations are carriedout with the variation of electron beam energy, and thegrowth rate for the particular energy is acquired by theway described above. The dependency of growth rate on
beam energy is illustrated in Fig.9, for the cases of withand without surface loss, respectively. It has been shown
that, the growth rate decreases when the surface-loss isinvolved. With the present parameters, the maximum
growth rate appears at the energy of ~65 KeV for the caseof with surface loss, then it goes down quickly to zero
before the Bragg condition. That is the reason that thedevice can only operate on the absolute instability. If we
expect the device oscillate at the convective instability,
much higher current of electron beam is required to get
the net gain. Also plotted in Fig.9 are the theoreticalresults from the recent theory [17], which show about two
times larger than the simulation results.

Involving Surface-loss
To be more practical, the grating should not be
perfect conductor and it has loss in the surface. In thispaper, we consider aluminium grating, which has the7

conductivity of 3.72 u 10 mhos/m. With involving thesurface-loss, the evolution of the electric field amplitude
corresponding to Fig.7 is as shown in Fig.8. It is
understood that only the curves for 50KeV, 100KeV and
115KeV (operating on absolute instability) demonstrate
the exponential growth, while for the case of 140KeV
electron beam (operating on convective instability) the
oscillation refuses starting. Further analysis of thesimulation data shows that with the present parameters
the device can only oscillate on the absolute instability.
Comparing with Fig.7, the curve of 50KeV comes tosaturation ahead of the curve of 100KeV in Fig. 8, which

New Science at FELs

Figure 9: Growth rate with respect to beamenergy.
CONCLUSION
The operation of a SP-FEL on absolute and convective
instability is discussed in this paper. We demonstrate thatthe ends of the grating can provide the external feedback,which is possible to make the device oscillate at the433

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Proceedings of FEL 2006, BESSY, Berlin, Germany

convective instability. The surface-loss will decrease thegrowth rate, especially in the region of convective
instability. The growth rate drops down to zero before theBragg condition with the present parameters. Higher
beam current is predicted to provide the net gain if we
expect the device to oscillate on the convective instability
when the practical metal, such as aluminium, is used tomake the grating.
ACKNOWLEDGMENTS
The authors gratefully acknowledge helpful
discussions with Charles Brau and Heather Andrews.

[1]
[2]
[3]
[4]
[5]

434

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J. Urata, M. Goldstein, M. F. Kimmitt, A. Naumov,
C. Platt, and J. E. Walsh, Phys. Rev. Lett. 80, 516(1998).
A. Bakhtyari, J. E. Walsh and J. H. Brownell, Phys.
Rev. E 65, 066503 (2002).
L. Schachter and A. Ron, Phys. Rev. A 40, 876(1989).
S.E.Korbly, A.S. Kesar, J.R.Sirigiri and R.J.Temkin,Phys. Rev. Lett. 94, 054803, (2005).
K. –J. Kim and S. –B. Song, Nucl. Instrum.
Methods Phys. Res., sect. A 475, 158 (2001).

[6]

H. L. Andrews and C. A. Brau, Phys. Rev. ST Accel.
Beams 7, 070701 (2004).
[7] H.L.Andrews, C.H.Boulware, C.A.Brau and
J.D.Jarvis, Phys. Rev. ST Accel. Beams 8, 110720(2005).
[8] V. Kumar and K.-J. Kim, Phys. Rev. E 73, 026501(2006).
[9] J.T.Donohue and J.Gardelle, Phys. Rev. ST-AB, 8,060702 (2005).
[10] J.T.Donohue and J.Gardelle, Phys. Rev. ST-AB, 9,060701 (2006).
[11] R. P. Leavitt, D. E. Wortman, and C. A. Morrison,
Appl. Phys. Lett. 35, 363(1979)[12] K. Mizuno, S. Ono and Y. Shibata, IEEE Trans.
Electron devices, ED-20, 749 (1973)[13] D.Li, Z. Yang,K.Imasaki and Gun-sik Park, Phys.
Rev. ST-AB 9, 040701 (2006)[14] D.Li, K.Imasaki , Z. Yang and Gun-sik Park, Appl.
Phys. Lett. 88, 201501 (2006)[15] H.L.Andrews, C.H.Boulware, , and J.D.Jarvis, Phys.
Rev. ST Accel. Beams 8, 050703 (2005).
[16] L. Ludeking, The MAGIC user’s manual.
[17] C.A.Brau (private communication).

New Science at FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH048

SUPERRADIANT SMITH-PURCELL RADIATION IN THE TERAHERTZWAVE REGION FROM BUNCHED ELECTRON BEAMS*
Zongjun Shi#, Ziqiang Yang, Zheng Liang, Institute of High Energy Electronic, University ofElectronic Science and Technology of China, Sichuan, Chengdu, 610054, P. R. China
D.Li, K.Imasaki, Institute for Laser Technology, 2-6 Yamada-oka, Suita, Osaka 565-0871, Japan

Abstract
This paper presents an analysis of a possible methodof producing the bunches and obtaining the coherent THz
radiation. With the help of a two-dimensional particle-incell (PIC) simulation, the simulation proposes a modelwith two sections consisting of a square-toothed gratingwith a flat conducting roof above it and an open grating.
In the first section, an initially continuous beaminteracting with TM modes is bunched by using an
external signal. In the second section, the coherent THz
radiation is produced by the well bunched beaminteracting with the open grating. The strongest radiation
is at 1200 and at frequency 266.5GHz.

INTRODUCTION
In recent years, there is a substantial interest in
development of coherent radiation sources, especially tothe coherent THz radiation. An important source ofradiation in the THz region is Smith-Purcell(SP)radiation[1].
It is well known that the SP radiation may occur atangles θ measured from the direction of the electron
beam and order n such that λ = L(1 β − cosθ ) n , where L
is the grating period, βc the electron velocity, and c the
speed of light. The coherent SP radiation has been
observed in the THz region from experiments. One
example is the Dartmouth experiments [2] with an
initially continuous beam. The other is the MIT
experiments [3] using the beam already bunched when it
reaches the grating. The bunched beam from a linac
operating at 17.14Ghz delivers pulses of duration 1ps.
Quite recently, the PIC code simulations related to thecoherent and superradiant SP radiation are performed by
Li et al [4], Donohue and Gardelle, respectively [5,6]. In
their simulations, the Dartmouth experiment and MIT
experiment have been presented. These simulations areable to clearly observe coherent SP radiation at harmonics
of imposed bunching frequency. Those results support
the viewpoint of Andrews and Brau [7]. In the theoreticalside, Kumar and Kim have performed a detailed 2D
analysis in which the SP free-electron laser is treated as a
BWO [8]. And a thorough discussion of the radiation
emitted by prebunched beams has been given recently by
Gover [9].
We know it is necessary for generating coherent SP

radiation that the bunches are short comparing with theradiation wavelength. However, for the short electron
bunches high quality electron accelerator which is
expensive is needed. The bunches are unstable both intime and along the grating for the bunching of the initiallycontinuous beam by an evanescent wave that is operatingin backward wave region.
In this paper, with the help of a two-dimensional PIC
simulation we discuss and analyze a new method ofmaking the bunches and obtaining the coherent THz
radiation. The simulation proposes a model with two
sections consisting of a square-toothed grating with a flat
conducting roof above it and an open grating. In the firstsection, an initially continuous beam interacting with TM
modes is bunched by using an outer incoming signal. The
electron-wave interaction is operating in the travellingwave region, which resembles a Cerenkov amplifier. Dueto the Mechanism for TWT, the bunches are relative
stable compared with what is operating in backward wave
region. In the second section, the coherent THz radiation
is produced by the well bunched beam interacting withthe open grating.

DETAILS OF THE NUMBER ANALYSIS
Geometry and parameters of the simulation
The simulations are carried out using the PIC code
CHIPIC[10]. It is a finite-difference, time-domain codefor simulating plasma physics process. Our simulations
use a 2D PIC code in this paper. The geometry is given in
Fig. 1. The basic structure consists of a grating bounded
above by a roof and an open grating .The surface of thegrating and the roof are assumed to consist of a perfectconductor whose rectangular groove are parallel anduniform in the z direction. A sheet electron beam
propagates along the x-direction. It is a perfect beam
produced from a small cathode located at the left
boundary of the simulation. The drive signal is also___________________________________________*Work supported by National Nature Science Foundation of
P.R.China (60571020),#shizongjun@163.com

New Science at FELs

Figure 1. Simulation geometry.

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Table 1. Parameters of the simulations
Parameters
First section Second section
Beam energy
120 kV
Current
200 A
Beam thick
0.4 mm 0.4mm
Beam -grating distance 0.1 mm 0.1mm
Grating period
0.5mm
0.5mm
Grating groove depth 0.625mm 0.2mm
Grating groove width 0.25mm 0.3mm
Number of period
135
20
External magnetic field 2T
Drive signal
2kW
Mesh size(50um)2 (50um)2
250

beam lineP'f (Ghz)200

light line
L=0.5mmh=0.2mmd=0.3mm

150
P

100

L=0.5mmh=0.625m m
d=0.25mm

50
0
0.0

0.2

0.4

k/k 0

0.6

0.8

1.0

Figure 2.Dispersion relation for the grating

period L=500um, a width of slots d=0.25mm, and a depth
h=0.625 mm. The distance from the tops of the teeth to
the roof is 0.75 mm. We assume a beam voltage of
120kV, a current of 200A, a beam thickness of 0.4mm,
and beam-grating distance 0.1mm, external magnetic field
Bx=2T. The main parameters of the grating and electron
beam are summarized in Table 1.

Description of our idea
In fig. 2, the solid line shows the lowest order TM
mode dispersion relation for the grating with a roof, andthe dash line for open grating. Due to the choice ofparameters, the lowest-order TM mode will be resonantwith the beam in the neighborhood of 90-100GHz. At theoperating point P, the group velocity is positive, whichmeans electron-wave interacts at the traveling-wave
region, as in the traveling-wave tube (TWT). The working
process of the device is explained as follows. By using an
initial injected signal with frequency 88.5GHz, theelectron beam interacts with TM mode electromagnetic
wave through the first section, and gets density bunching.
The bunching wavelength will be the same as the spatial
wavelength of the operating point P .In the second sectionin order to clearly observe coherent SP radiation at
harmonics of the bunching frequency, we varied theparameters of the grating. In fig.2, the point P is theoperating point. Then the operating point frequency of theevanescent wave is different from the bunchingfrequency.
Through the second passage, which also acts a drift tube,
the well bunched beam interacts with the grating, and thecoherent radiation is produced.
'

(a)

(b)

(a)

Figure 3. Phase-space distribution (a) density of electrons
in the x-y plane at 1.15ns.Bunching is evident.(b) kinetic
energy-x density at the same time

(b )
0 .8
t= 1 .1 5 n s

436

I (A*m)0 .6

imposed on the left, which provides a 2kW power to thedevice. The beam-wave interaction and radiation
propagation happen in the vacuum box. The boundary is
enclosed with absorbers. At the end of the first section,
there is an attenuator, which prevents most of theelectromagnetic wave reaching the second section fromperturbing the bunching and interpreting the coherent
radiation. The grating parameters we choose have a

0 .4
0 .2
0 .0

0

2

-1

4

λ (m m

6
)

-1

8

10

12

14

Figure 4. Space dependence of current (a) current
I(x), (b) corresponding FFT.

New Science at FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany(b)

the simulation are given in fig.6, and three radiations areclearly observation. It has be shown that the dominantradiation is with the frequency of third harmonic ofbunching wave, 88.5GHz peaked at the angle of about
120 deg which corresponds to the SP radiation angle.
While the other two radiation are with the frequency of
the fourth and fifth harmonics ,respectively, and also
corresponds to the SP radiation angle. From the contour
plot of fig.7 we can observe that the dominant third
harmonic radiates at the angle of about 1200, in agreementwith that shown in fig.6.Of course, due to theinteracting of the beam-wave which reduces the value ofthe particle velocity, the discrepancy appears somehow
for the simulation data for the radiation angle compared tothe theoretical value.
harmonic #3

SP order #1

0.8

-5

3x10

-5

3x10

Figure 5. (Color ) Current as a function of time: (a) at end of
the first section .(b) at the center of the open grating .
f (THz)

0.6

-5

2x10

0.4

-5

-5

1x10

0.2

SIMULATIONS RESULTS
In this simulation, the main goal of the first section is
not gaining the maximum output power of the beam-wave
interaction, but obtaining the well stable bunches. Hence,by using of an outer injected wave, choosing a reasonable
period numbers, an initial continuous beam travels
through the first section and gets velocity modulation anddensity bunching, then passes through the open grating
and the stable bunches are generated. The bunching can
be clearly observed as a function of both space and time.
In fig.3, we observe the beam bunching: phase-spaceplots at time 1.15ns and energy modulation of the electron.We note that the mean energy loss is about 5keV of thebeam energy. The spatial modulation of the current
displayed in fig.4 increases with x, and the period of themodulation is 1.94mm. The beam is well bunched at thedownstream of the first of passage. We note that thebunching is relative stable along the open grating. In fig.4(b) shows the bunching is nonlinear when it becomesstrong. In fig.5 the beam current is a function of time, forlocations at the end of the first of the passage and thecenter of the open grating. One clearly sees the bunchingcurrent is stable in time after time about 1ns. This is anadvantage compared to the bunching of the initiallycontinuous beam by an evanescent wave that is operatingin backward wave region. In fig.5(b), the bunchingcurrent shows the beam is well bunched at the center ofthe open grating compared with that at the downstream of
the grating with roof displayed in fig.5(a). It shows thatthe open grating also resembles a drift tube.

Coherent terahertz radiation
Here we analyze the radiation from the periodic
bunching interacting with the open grating. The results of

New Science at FELs

-6

5x10

harmonic #5

0.0

Electron bunching

2x10

harmonic #4

0

30

60

SP FFT amplitude(a)

TUPPH04890θ (deg)

120

150

0
180

Figure 6. Radiation frequency and the peak of FFT
amplitude of Bz as a function of angle, detected at the
distance 10.58mm from the grating center.

Figure 7. (Color ) Contour plot of Bz for coherent
radiation

CONCLUSIONS
We have presented results of the coherent THz
radiation through the simulations of electron bunching ofcontinuous beam interacting with an open grating. The
results show that the bunching is stable in time and along
the grating. The strongest radiation is at 1200 and at
frequency 266.5GHz at the simulation parameters. The
coherent radiations are emitted at frequencies that are
integer multiples of the bunching frequency, and at thecorresponding SP angle.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

REFERENCES[1] S.J.Smith,E.M.Purcell. “Visible light from localized
surface charges moving across a grating”.Phys. Rev.
1953 92 15 :1069[2] J. Urata M.Goldstein ,M.F. Kimmitt et al.. “Super
radiation Smith-Purcell emission” .Phys. Rev. Lett.,
1998,80(3): 516~519[3] S.E.Korbly,A.S.Kesar,J.R.Sirigiri et al.. “Observationof frequency-Locked coherent terahertz SmithPurcell radiation”. Phys.Rev.Lett.2005,94(5):0548031~4.
[4] D. Li, Z. Yang, K. Imasaki, and Gun-sik Park.
“Particle-in-cell simulation of coherent andsuperradiant SP radiation” .Phys. Rev. ST Accel.
Beams 9 040701 (2006). [5] J.T. Donohue and J.
Gardelle. “Simulation of Smith-Purcell radiation

， （ ）
，

438

using a particle-in-cell code”.Phys.Rev. ST Accel.
Beams 8,060702 (2005).
[6] J.T. Donohue and J. Gardelle.“Simulation of SmithPurcell terahertz radiation using a particle-in-cellcode”.Phys.Rev. ST Accel. Beams 9,060701 (2006).
[7] H.L. Andrews, et al.. “superradiant emission of Smith-Purcell radiation”. Phys. Rev. ST Accel. Beams
8,110702 (2005).
[8] Vinit Kumar and Kwang-Je Kim. “Analysis of SmithPurcell
free-electron
lasers”Phys.
Rev.
E
73.020501(2006)[9]A.Gover and Dyunin. “Superradiant and stimulated
superradiant emission in prebunched electron-beamradiators”. Phys. Rev. ST Accel. Beams I
2005,8(3):030701-1~15[10]Di Jun ,Zhu Da-jun ,and Liu Sheng-gang ,et al..
“Electronmagnetic field Algorith of the chipic code”.

New Science at FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH049

STUDY ON SUPERRADIANT SMITH-PURCELL RADIATION
D. Li#, K. Imasaki, ILT, 2-6 yamada-oka, suita, Osaka 565-0871, JapanZ. Yang, UESTC, Chengdu, 610054, P.R.China
Gun-Sik Park, SNU, Seoul 151-747, Korea
S. Miyamoto, S. Amano, T. Mochizuki, LASTI, 3-1-2 Koto, Kamigori, Hyogo 678-1205, Japan.
Abstract
An analysis of superradiant Smith-Purcell radiation
is carried out with the help of performing a threedimensional simulation in GHz regime using a particle-incell code. The simulation model supposes a rectangulargrating with limited length and width, to be driven by asingle electron bunch, a train of periodic bunches and acontinuous beam, respectively. Besides the Smith-Purcell
radiation, the evanescent wave is clearly observed, whichholds the frequency lower than the allowed minimum
Smith-Purcell frequency. It is also shown that thesuperradiant radiations excited by periodic bunches are
emitted at higher harmonics of the bunching frequency
and at the corresponding Smith-Purcell angles. The
distributions of the radiation intensity are presented andcompared with a recently proposed theory. The “start
current” for a continuous beam to make the device start
oscillation is addressed as well.

In this paper, we perform a three-dimensional
particle-in-cell simulation for the coherent andsuperradiant SP radiation using MAGIC [14], a code forsimulating processes involving interactions between spacecharge and electromagnetic fields.
SIMULATION MODEL
The simulation model involving a rectangular grating
and a cylindrical electron beam is shown in Fig. 1, whered is the periodic length, s the groove width, h the groove
depth and w the width of the grating. The main
parameters are summarized in table 1, and we note thatthe grating period, groove width and depth and initial
electron’s energy are same as those in Ref. [15]. The
length of the grating is set differently for particularsimulation case, which will be mentioned lately. The
grating, assumed to be a perfect conductor, is set in the

INTRODUCTION
The superradiant Smith-Purcell (SP) radiation has
attracted many attentions since Urata and co-workers
observed this phenomenon in their experiments [1,2]. It isa promising alternative in the development of a compact,tuneable and high power THz sources. To better
understand the physics of the superradiant SP radiation isnecessary for improving the performance of such kinds ofdevices.
It is known that the SP radiation is emitted as anelectron passes close to the surface of a periodic metallic
grating [3]. The wavelength O of the radiation observedat the angle T measured from the direction of electron
beam is given by1 1(1)(  cos T ) ,dn E
where d is the grating period, Ec the electron velocity,c the speed of light, and n the order of the reflection

Ofrom the grating. The incoherent SP radiation has been
analysed in many ways, such as diffraction theory,
integral equation method and induced surface current
model [4-8]. The experimentally observed superradianteffect is regarded as the result of the appearance of
periodic electron bunches. Several theories have been
proposed to reveal the physics of the superradiantphenomenon [9-13], and a three-dimensional simulation
is supposed to be necessary.
#dazhi_li@hotmail.com

New Science at FELs

Figure 1: Three-dimensional simulation model ofgrating and electron beam.
centre of the bottom of a vacuum box, which is boundedby an absorption region. A perfect laminar beam
produced from a cathode moves in the z-axis. The
simulation area is divided into mesh with rectangular cell
Table I: Main Parameters for Simulation
Electron beam energy (injection) E=100 keV
Beam radius
r=2.5 mm
Beam-grating distance
a=2 mmGrating period
d=2 cmGrating groove depth
h=1 cmGrating groove width
s=1 cmGrating width
w=10 cmof very small size in the region of beam propagation andlarge in the rest.
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Proceedings of FEL 2006, BESSY, Berlin, Germany

SIMULATION RESULTS
Single Bunch
We first perform the simulation of a single electron
bunch. The grating is arranged to be 10 periods. The
bunch length is chosen as 0.1 ps with the current of 1A. It
is short compared to the radiation wavelength, so theradiation is coherent. In our simulation we focus on thefirst order SP radiation since the high orders are notevident. Fig. 2(a) illustrates the temporal behaviour of By,
detected at the point of ǰ=120o, Ǿ=0o. We notice that
the SP radiation pulse consists of 10 periods and isseparated in time from the evanescent wave. The
corresponding FFT is given in Fig. 2(b), where one canFigure 2: Time signal of By (a), and its
corresponding FFT (b).

find two clear peaks. The one peaked at 6.5 GHz is the SPradiation, while the other at 4.5 GHz is the evanescentwave. Not like the SP radiation, the evanescent wave
frequency is angle independent. The dependency of the
SP frequency and the amplitude of By on the angleǰis asshown in Fig. 3, observed at the same distance 36.35 cm
to the centre of the grating. For comparison, we also plot
the analytical result calculated from the theory ofAndrews and co-workers [16]. It is seen that thesimulation data for the SP radiation frequency agrees wellto the theoretical curve as ǰ over 90o, somehow thediscrepancy appears for the rest. Our best guess is that thedetector is not far enough for far-field detection. We also
see that the maximum amplitude of By appears at 125o.
There are slight differences between the analytical andsimulation results, which might be due to the fact that we
use a broad electron beam that nearly reaches the grating,whereas they use a narrow electron beam model. In Fig.4,
we give the distribution of field amplitude with respect tothe azimuthal angle Ǿ . The observation angle cannot
vary in a large range due to the limit of the simulationgeometry. The distribution shows maximum at the centre
pointǾ=0 for cases ofǰ=130o and ǰ=80o, but minimum
forǰ=50o.

Figure 4: The dependency of By amplitude on
azimuthal angle.

Periodic Bunches

Figure 3: Distribution of SP frequency and its By
amplitude.

440

In all radiation sources using an intense electron
beam, the mechanism leading to superradiance is beam
bunching. The spectral intensity of the radiation isenhanced at the bunching frequency and its harmonics.
Recently Korbly and co-workers have carried out a SP
experiment at MIT with using a pre-bunched electron
beam [17]. When certain conditions are satisfied, acontinuous beam can be bunched by the interaction withthe evanescent wave, which has been discussed by
Donohue and Gardelle [15]. In order to demonstrate theproperties of superradiant radiation more clearly, we
avoid the problem of bunching from an initiallycontinuous beam. Instead, we generate a train of bunches
to drive the grating.

New Science at FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

The repetition frequency of bunches is chosen as 3
GHz, and the parameters for grating length and eachsingle bunch are same to those mentioned earlier. Within
the time of code running, 30 bunches are generated andenter the simulation area. From the FFT of the temporal
behaviour observed by By detectors we know that theradiation focused on three frequencies, the second, thirdand forth harmonic of bunching frequency, as shown in

Figure 5: Distribution of superradiant SP radiation
frequency and its By amplitude. The dotted blueline is the simulation results, and the red line theanalytical result multiplied by 10.

TUPPH049

originally continuous beam is high enough to get the net
gain, the beam will be bunched by the enhanced
evanescent wave and the oscillation starts. The bunchedbeam consequently excites the superradiant SP radiation
as discussed early. The value of the current starting theoscillation is called “start current”, which needs carefulanalysis. In this section, we concentrate on determining
the “start current” by three-dimensional simulation.
Considering the limit of the capacity of ourcomputers, a grating consisting of 46 periods was
employed in this simulation. The electron beam from thecathode is continuously generated, and an external
magnetic field of 2T is introduced to prevent the beamfrom diverging. We vary the beam current and observe
the amplitude of Ex of the evanescent wave. The
appearance of exponential growth of Ex means that theoscillation happens.
The simulation results are given in Fig. 7. It is shown
that, the electric field shows no growth when the current
is lower than 0.4 A, while it shows evident growth as thecurrent is above 0.5 A. And the radiation can reachsaturation if the current is higher that 0.6 A. From Fig. 7,
we can roughly estimate that the “start current” is ~0.5 A.
The precise value can be reached if more simulations are
performed.

Fig. 5. The dominant radiation is the second harmonic
peaked at the angle 134o, which corresponds to Eq. 1.
Also plotted In Fig. 5, is the analytical result according toRef. [16], and we find the differences are smaller than one
order of magnitude. Another evidence to show the factthat the radiations emit only at certain angles can befound in the contour plot of By, as shown in Fig. 6, where
the second harmonic radiation is observed to radiate at theangle of about 134o, corresponding to what is shown in
Fig. 5. These results strongly support the viewpoint ofAndrews and co-workers.
Figure 7: Evolution of amplitude of Ex.

Figure 6: Contour plots of By.

Continuous beam
From the theoretical analysis in Ref. [15], we knowthat the beam line intersects the dispersion curve at apoint representing a backward wave, which means thedevice operates in the mode of backward-wave oscillator(BWOs). Such a device is possible to start to oscillate
without external feedback. When the beam current of an

New Science at FELs

CONCLUSION
In conclusion, we have studied the coherent andsuperradiant SP radiation through the three-dimensional
simulation of an open grating system driven by different
modes of electron beam. The single bunch simulation
helps us to distinguish the true SP radiation from theevanescent wave. They are different in both frequency
characteristics and generation mechanism. The amplitudeof the SP radiation is angle dependent. The strongest
radiation appears at 125o at the present parameters. The
supperandiant effect is demonstrated with the simulationof a pre-bunched beam. We provide powerful evidence
showing that the superradiant radiations are emitted at
frequencies that are integer multiples of the bunchingfrequency, and at the corresponding SP direction. The
simulation of an originally continuous beam determinesthe “start current” for the present parameters.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

ACKNOLOWEDGEMENTS
The authors gratefully acknowledge helpful
discussions with Charles Brau, John Donohue, andHeather Andrews.

[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]

442

REFERENCES
J. Urata, M. Goldstein, M. F. Kimmitt, A. Naumov,
C. Platt, and J. E. Walsh, Phys. Rev. Lett. 80, 516(1998).
A. Bakhtyari, J. E. Walsh and J. H. Brownell, Phys.
Rev. E 65, 066503 (2002).
S. J. Smith and E. M. Purcell, Phys. Rev. 92, 1069
(1953).
P. M. van den Berg, J. Opt. Soc. Am. 63, 689 (1973).
P. M. van den Berg and T. H. Tan, J. Opt. Soc. Am.
64, 325 (1974).
Y. Takaura and O. Haeberle, Phys. Rev. E 61,4441(2000).
J. Walsh, K. Woods and S.Yeager, Nucl. Instrum.
Methods Phys. Res. A 341, 277 (1994).
Y. Shibata, S. Hasebe, K. Ishi, S. Ono, M. Ikezawa,T. Nakazato, M. Oyamada, S. Urasawa, T.
Takahashi, T. Matsuyama, K. Kobayashi, and Y.
Fujita, Phys. Rev. E 57, 1061 (1998).

[9]

L. Schachter and A. Ron, Phys. Rev. A 40, 876(1989).
[10] K. –J. Kim and S. –B. Song, Nucl. Instrum.
Methods Phys. Res., sect. A 475, 158 (2001).
[11] H. L. Andrews and C. A. Brau, Phys. Rev. ST Accel.
Beams 7, 070701 (2004).
[12] H.L.Andrews, C.H.Boulware, C.A.Brau and
J.D.Jarvis, Phys. Rev. ST Accel. Beams 8, 050703(2005).
[13] V. Kumar and K.-J. Kim, Phys. Rev. E 73, 026501(2006).
[14] D. Smithe and T.M. Abu-Elfadi, Comput. Phys.
Commun. 106, 95 (1997).
[15] J.T.Donohue and J.Gardelle, Phys. Rev. ST-AB, 8,060702 (2005).
[16] H.L.Andrews, C.H.Boulware, C.A.Brau and
J.D.Jarvis, Phys. Rev. ST Accel. Beams 8, 110720(2005).
[17] S.E.Korbly, A.S. Kesar, J.R.Sirigiri and R.J.Temkin,Phys. Rev. Lett. 94, 054803, (2005).

New Science at FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH052

FUTURE FEL STUDIES AT THE VISA EXPERIMENT
IN THE SASE AND SEEDED MODES*
G. Andonian, M. Dunning, A. Murokh, C. Pellegrini, S. Reiche, J. Rosenzweig,
UCLA, Los Angeles, CA 90095, USA
M. Babzien, I. Ben-Zvi, V. Yakimenko, BNL, Upton, NY 11973, USA.
THE VISA EXPERIMENTAL PROGRAM

Abstract
The VISA (Visible to Infrared SASE Amplifier) experiment at BNL (Brookhaven National Laboratory) has previously demonstrated saturation at 840 nm in 2001. Further
SASE studies, in 2003, have demonstrated an anomalously
large bandwidth spread of the FEL spectrum due to offangle emissions. This paper disseminates the current andfuture program of the VISA experiments at BNL. This includes a study of a seeded FEL, using a 1 micron YAG laser
as a seed, and the accompanying diagnostics to characterize the radiation. Diagnostics include the double differential spectrometer, a mode converter to investigate the orbital angular momentum of light in the FEL, and an optical
pepper-pot for coherence measurements. Start-to-end simulations, which are reliabily used for experimental modeling, are presented.

INTRODUCTION
The advent of the X-ray free electron laser (FEL) is on
the horizon [1, 2]. The creation and diagnosis of ultra-shortpulses is of great importance to the FEL community. The
generation of femtosecond long, Ångstrom wavelength radiation will open doors to a myriad of scientific endeavors
at ultra-short time scales [3].
The VISA program was developed to investigate properties of a high gain self amplified spontaneoous emission(SASE) free electron laser. A proposal to obtain ultrashort pulses [4], by manipulating frequency chirped FEL
output, is the inspiration for the VISA II experiment. The
frequency chirped radiation produced from an undulator ismonochromatized and is used to seed a second undulator.
The ultimate goal of the VISA II project is to operate thehigh gain SASE FEL with a large electron beam chirp.
The current mode of operations expands on this goalby utilizing the optimized capabilities of the facilities employed. Under these conditions, the VISA FEL operates inthe seeded mode, using a 1 micron YAG laser as the seed.
The experimental mission of the seeded FEL is to investigate high gain radiation properties with studies focusing
on the far-field angular distribution and coherence of theradiation.
*This work supported by Dept. of Energy Contract no.
DE-FG-98ER45693, and Office of Naval Research no.
N000140210911

New Science at FELs

VISA IThe VISA project is hosted by the Accelerator Test Facility (ATF) of Brookhaven National Laboratory (BNL).
The experimental layout is described in detail in Ref. [5](Fig. 1 shows a schematic). The VISA I project succesfully demonstrated saturation of a SASE FEL within a 4
meter undulator at 840 nm. The high peak current, a resultof nonlinear electron bunch compressoin along the dispersive line of the transport, was ultimately responsible for theobserved high gain lasing. A start-to-end simulation suiteof codes, PARMELA [6], ELEGANT [7], and GENESIS
1.3 [8], modeled the beam dynamics in the gun, transport
and undulator, respectively. SASE FEL properties, such as
pulse energy, profile, and angular distribution were computed with GENESIS. The complete characterization of the
SASE FEL properties included gain lengths, spectra, energies, angular distributions and observation of nonlinear
harmonics, and was successfully benchmarked against thesimulation suite [9].
Beamline 3

F-LineH-LineGun

DipoleOpticsLinac Sections

FEL Diagnostics
HES
e-beam direction

OpticsUndulator

Optics

DipoleFigure 1: Layout of the ATF beam transport (not to scale).
The VISA undulator is located along Beamline 3 after the
20 degree dogleg.

VISA IB
Subsequent measurements at VISA, informally referred
to as VISA IB, also took place at the ATF in 2003. An
anomolously large bandwidth, up to 15% full width, wasobserved at high gain (Fig. 2), accompanied by atypicalfar-field angular radiation patterns.
The electron beam (330 pC, 1.7% energy spread) was
subjected to the same nonlinear bunch compression mechanism as in VISA I, except with a much higher degree ofcompression and thus a higher peak current. The SASE

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Power Spectrum (a.u.)

1200
1000
800
600
400
200
0
820

840

860 880 900
Wavelength (nm)

920

940

960

and is a direct study of the intensity of the beam presented
d2 I.
in the familiar form, dωdθyRaw data from a preliminary prototype of this diagnostic
is presented in Fig. 4. The overall parabolic structure of thebeam, from red shifting, in (θ, ω) space is evident, witheven richer multi-mode patterns also present. Upgraded
GENESIS post-processing tools were used to further understand this data and indeed displayed the parabolic structures along with the presence of higher order modes.

Figure 2: Sample shot of observed SASE FEL spectrum
displays an anomalously large bandwidth.
FEL output (2 μJ average energy), was extremely stable
and insensitive to RF and laser timing jitter. The spectrum is notable for a characteristic double peak structure,accompanied by a mean bandwidth value of 12% full width(greater than 100 nm), as seen in Fig. 2.
GENESIS simulations reproduced the features of the radiation (large bandwidth and double spiked structure). After transport, the electron beam displayed a highly nonlinear longitudinal phase space. The secondary spike was due
to amplification of an off-axis mode. The mode was excited by the non-ideal centroid and envelope motion of thebeam through the undulator’s quadrupole focusing lattice.
The lasing core of the beam was mismatched to the undulator focusing lattice yielding significant excursions inbeam size in both transverse planes. Additional transverse
motion causes a red-shift in the radiated wavelength andamplification of the off-axis modes [10].

Figure 4: The parabolic structure (left) is evident in the images from the double differential spectrometer, where theangle is represented along the horizontal axis and the frequency along the vertical. Richer structures have also been
observed (right).
Far-field Angular Distribution This far-field angular distribution measurement was made by propagating theoutput radiation, without optical focusing, to a screen located 3 m (10 Z R ) downstream. Observed patterns werehollow in nature, like previous VISA results, except more
pronounced in angle (with spiral shaped patterns accompanying the hollow modes). The helicity of this patterns will
be studied via a mode converter.

Power Spectrum (a.u.)

40
30
20

(a)

860

900
940
Wavelength (nm)980

Figure 3: SASE FEL power spectrum obtained from GENESIS. The large bandwidth and the double hump featureobserved in measurements were reproduced with simulations.
Double Differential Spectrometer The double differential spectrometer is diagnostic developed to unfold therelationships between frequency and angle of the FEL radiation. A slice of the FEL ouput is passed through graduated slits, then focused onto a set gratings (1200 in −1 ). The
resulting image displays the photon beam with frequency
along one axis, and transverse angle along the other axis,

444

(c)

Figure 5: Far-field angular distribution profiles display an
atypical spirality and helicity (a,b); superimposed with areference alignment laser (c).

10
0

(b)

Chirped Beam FEL
The goal of the VISA II experiment is to inject a linearly
chirped electron beam into the undulator to produce frequency chirped SASE FEL radiation. The bunch compression mechanism facilitates high-gain lasing, however, it restricts the management of beam properties through transport. Preservation of the electron beam chirp applied at the
linac will be accomplished by the manipulation of nonlinear longitudinal compression by the addition of sextupole
magnets placed at high horizontal dispersion points. The
sextupoles will mitigate second order effects, particularly
by diminishing the T 566 element, of the transport matrix,
to a negligible value [11]. Three sextupoles have been installed and commissioned at the ATF.

New Science at FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany
Frequency Resolved Optical Gating A frequency resolved optical gating (FROG) [12] system will be used tomeasure the frequency chirped, short pulse radiation. Thismethod was successfully used elsewhere, to measure boththe amplitude and phase of the radiation [13].
The frequency resolution of the FROG spectrogram is aconcern at the VISA experiment. The diagnostic system isconstrained by the doubling crystal and can not adequately
resolve the radiation expected from the VISA II FEL. The
thick lens must be replaced by a thin lens to increase theresolution; a dedicated spectrometer must be added to compensate for the loss of functionality of the thin lens. The
CCD camera (several megapixel) must be able to cover alarge range of wavelengths to resolve the observed bandwidth.
GENESIS outputs for the chirped beam case show aclear effect for idealized beam shapes and have been analyzed for varying degrees of chirp. Indeed, the inversion algorithm is robust enough to handle other exotic shapes andpatterns which have been simulated and reconstructed via
the commercial FROG software (Femtosoft) for the VISA
II experiment. Fig. 6 shows an example of a spectrogram
obtained from GENESIS for the running conditions of the
VISA II FEL. This structure shows the complex nature of
the FEL pulse, which is expected to contain several spikes.
This longitudinal pulse profile was retrieved when the spectrogram was analyzed with the FROG reconstruction algorithm.

Figure 6: Spectrogram (with frequency along the verticalaxis and time delay along the horizontal) of the expectedradiation from the VISA II experiment. Further processingof this spectrogram has yielded the longitudinal profile ofthe pulse used in simulations.

Mode Converter The investigation of hollow modeand spiral shaped far-field angular radiation patterns at
VISA is conducted with the introduction of a diagnostic mode converter. The mode converter is designed totransform light with planar polarization to circular polar-

New Science at FELs

TUPPH052

ization, and vice versa [14]. The π/2 mode converter isconstructed of√two cylindrical lenses, separated by a distance of d = 2f , and the resultant light will have distinct
observable properties. This data will yield insight into theunderpinnings of the unusual angular distribution patterns
observed throughout the tenure of the VISA program. The
cylindrical lenses for the mode converter have been setup
and will be placed in the diagnostic station downstream of
the undulator.
Polarizer The VISA project will also examine thestudy of coherent transition undulator radiation [15], theradiation emitted by the electron bunch as it passes throughthe entrance and exit of the undulator, due to the change inlongitudinal velocity. Theoretically, the radiation is radially polarized, describing yet another possible explanation
for the helicity of the observed far-field patterns from theplanar undulator at VISA. The quantization of this effectrequires minimal alteration of already existing diagnostics
with the addition of grid polarizers to determine the polarization of the radiation. The effects of coherent transition
radiation, from the electron beam striking a metal mirror,
will have to be addressed (by the placement of a kicker
magnet) before useful data is recovered from this measurement.

SEEDED FEL MEASUREMENTS
The results of the far-field angular distribution patterns at
the VISA experiment have motivated further studies of the
FEL in the seeded regime. The seeding pulse (a 1 micron
YAG laser) will establish transverse and longitudinal coherence of the FEL (low bandwidth, high brightness). Such aradiation source will provide a short Rayleigh length FEL
beam.
Further motivation for seeded FEL studies arises fromcontrolling and managing the high power FEL in the farfield. Increasing the emission angles will decrease the intensity in the far-field (hollow modes) which will be technically useful in delivering high power radiation with minimal damage to sensitive optical elements.
The proposed experiment involves the VISA undulator with the ATF YAG laser as a seed. The YAG laser(1064 nm) serves as the drive laser for the photoelectron
beam at the ATF and some its energy is transported to theexperimental hall for deposition into the VISA undulator.
A longitudinal delay line is currently being used to ensure
adequate timing overlap with the electron beam and seedlaser. The electron beam energy for the seeded FEL operations is lowered to 61 MeV to account for the higher
wavelength operations
The experiments that will be carried out revolve aroundthe detuning parameter of the FEL. Start-to-end simulations have been conducted for ideal and virtual particle sets.
The results of the far-field angular distribution patters arepresented in Fig. 7. It is apparent that detuning the electron beam indeed changes the angles and produces hollow

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modes in the far-field. The power gain curves derived from
GENESIS simulations (Fig. 8) have also been studied.

1054 nm

1064 nm

1074 nm

REFERENCES[1] M. Cornacchia et al., Linac Coherent Light Source Design
Study Report no. SLAC-521 (1998)[2] TESLA-FEL, Deutsches Elektronen Synchrotron 2001-05(2001)[3] R. Neutze et al., Nature 406, 752 (2000)[4] C. Schroeder et al., J. Opt. Soc. Am. B 19, 1782 (2002)[5] A. Murokh et al., Phys. Rev. E 67, 066501 (2003)[6] L.M. Young, J.H. Billen, Los Alamos National Laboratory
Report No. LA-UR-96-1835 (rev. 2000)

15 mrad[7] M. Borland, Advanced Photon Source LS-287 (2000)

Figure 7: GENESIS simulation of the far-field angular distribution patterns of the seeded FEL for different values ofdetuning (1064 nm is the nominal wavelength).

[8] S. Reiche, Nucl. Instrum. Methods A 429, 243 (1999)[9] A. Tremaine et al., Phys. Rev. Lett. 88, 204801 (2002)[10] G. Andonian et al., Phys. Rev. Lett. 95, 054801 (2005)[11] J. England et al., Phys. Rev. ST Accel. Beams 8, 012801(2005)

10 71054 nm
1064 nm
1074 nm< P > [W]10 6[12] R. Trebino, Frequency Resolved Optical Gating, Kluwer
Academic Publishers (2000)[13] Y. Li et al., Phys. Rev. Lett. 89, 234801 (2002)

10 5[14] M.W. Beijersbergen et al., Optics Comm. 96, 123-132(1993)

10 4[15] S. Reiche et al., Procedings of the 2004 FEL Conference,
193-196, Trieste, Italy.

10 3[16] R. Ischebeck, et al., Nuc. Inst. and Meth. in Phys. Res. A
507, 175, 2003.

10 2
0

1

2
z [m]

3

Figure 8: Power gain curves (GENESIS simulations) for
varying detuning parameters.

Transverse Coherence
Transverse, or spatial coherence is an important figure of
merit of any FEL. The transverse coherence for the seeded
FEL will be verified with an arrangement of slits, by performing variations on the classical Young double-slit experiment. The FEL radiation diffracts at the slits, and thetransverse coherence is calculated by measuring the ratio of
the sum and difference of the maximum and minimum observed intensities [16]. Since the transverse coherence is afunction of longitudinal position, it is measured at different
positions downstream of the undulator exit. Several variations of slits have been fabricated for the transverse coherence study, including double-slits of various widths andspacings, crossed-slits, circular apertures of differing diameter, and a pepper-pot pattern of circular apertures. The useof these slits will be expanded after the seeded FEL experiment to also encompass SASE coherence measurements.
The pepper-pot pattern is of particular interest because theemitted radiation from the uncorrected chirped-beam FEL
experiments yielded intensity distributions with radial (helical) characteristics that provoke further investigation.

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TUPPH053

MAGNETIC CHICANE RADIATION STUDIES AT THE BNL ATF∗
M. Dunning, G. Andonian, A.M. Cook, E. Hemsing, A. Murokh, S. Reiche, J. Rosenzweig,
D. Schiller, Particle Beam Physics Laboratory, Department of Physics and Astronomy, UCLA,
Los Angeles, CA 90095, USA
M. Babzien, K. Kusche, V. Yakimenko, Accelerator Test Facility, Brookhaven National Laboratory
Upton, NY 11973, USA.

Abstract

EXPERIMENT DESCRIPTION

Radiation emitted by relativistic electrons traversing themagnetic eld gradients of a chicane bunch compressor has
been studied in an attempt to characterize coherent edge
radiation (CER). The studies performed at the Accelerator Test Facility (ATF) at Brookhaven National Laboratory (BNL) include frequency spectrum, angular distribution, and polarization measurements. A reconstruction of
the longitudinal charge pro le from the measured spectrum shows that the bunch has been compressed to approximately 30 μm FWHM, with a peak current exceeding
1.5 kA. Measurements of radiation from the short pulses
are compared to predictions from QUINDI, a new simulation code developed at UCLA to model the radiation.

Chicane Compressor
The chicane compressor is currently installed along thehigh-energy line (H-line) of the ATF. The operating beamenergy is 60-61 MeV for the present chicane radiation studies. The compressor consists of four dipole magnets oriented in a chicane layout, as in Fig. 1.

INTRODUCTION
The chicane compressor studies are a collaboration with
the Particle Beam Physics Laboratory (PBPL) at UCLA
and the ATF, the user facility which hosts the experiment.
The chicane was designed to compress the electron beam
to yield the high peak current necessary to drive a selfampli ed spontaneous emission free electron laser (SASE
FEL) to saturation [1] and to expand the ATF core capabilities. Recent experiments have focused on the creation ofvery short electron beam pulses (∼30 μm), and measurements of CER and coherent synchrotron radiation (CSR)
emitted by such short bunches. The correlation between
these radiative effects and microbunching instabilities areunder investigation, as are other parasitic effects of the radiation. These are signi cant issues for larger projects, suchas the Linac Coherent Light Source (LCLS), which will
employ similar devices and diagnostics for the productionof short duration pulses. CER has also been shown to bea bright source of infrared radiation, which makes it wellsuited for certain types of microscopy and spectroscopy [2].
∗ Work supported by DOE grant DE-FG02-98ER45693 and NSF grant
PHY-0355048.

New Science at FELs

Figure 1: A rendering of the four dipole chicane compressor. The cutaway view shows the approximate radiation
source between the third and fourth dipoles (A) and the radiation extraction port (B).
The chicane features a dedicated radiation extraction
port that enables viewing of the region (Fig. 1A) which
extends through the downstream edge of the third magnet to the upstream edge of the fourth magnet. The rectangular exit port (Fig. 1B) has transverse dimensions of
26 mm × 11 mm, with the longer dimension in the bendplane [3].
Table 1: Chicane design parameters
Parameter
B-Field
Bend Angle
Geometric Length
Magnet Gap

Value
2015
20
41
2.1

Units
Gauss
deg
cm
cm

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Terahertz Radiation Transport
Radiation exits the chicane compressor through a fusedsilica vacuum window located on the extraction port
(Fig. 1B). The radiation is guided with three adjustable mirrors (gold-coated) and a translatable Picarin lens, throughmetallic pipes (56 mm diameter) to an external diagnostic
station. The entire length of the radiation transport line isapproximately 7 m. The Picarin lens is positioned one focal length (1.25 m) from the approximate radiation source(between the third and fourth dipoles) to achieve a pointto-parallel transport con guration.

Diagnostic Station
The diagnostic station located at the end of the radiation transport is designed to be modular for versatility.
It consists of focusing/turning mirrors, two individual lter wheels containing room temperature and cryogenicallycooled lters, a wire grid polarizer, an iris on a twodimensional translation stage, a silicon bolometer, and aMichelson-type interferometer.
Silicon Bolometer
In order to characterize the chicane radiation, a cryogenically cooled silicon bolometer (IR Labs model HDL-5) is
employed. The bolometer is cooled with liquid helium andhas a built in lter wheel, loaded with cut-on lters (longpass) with wavelengths of 13, 27, 45, 103, and 285 μm.
The detector element incorporates a Winston Cone collector, protected by a wedged polyethylene window (that provides an additional cut-on wavelength of 13 μm) [4].
Interferometer
The radiation spectrum is measured at the output of aMichelson-type interferometer as a function of bolometer
voltage. The interferometer is optimized for the 15 μm to1 mm wavelength range, and has a translatable mirror along
one orthogonal leg with 1 μm spatial resolution [5].

CHICANE RADIATION OVERVIEW
Radiation exiting the chicane contains features of bothsynchrotron and edge radiation due to the measurement position and the magnet geometry. For electrons emitting under the same radiation process, the far- eld intensity distribution is expressed as
I (ω) = I0 (ω)[Ne + Ne (Ne − 1)F (ω)],(1)

where I0 (ω) is the single electron intensity distribution
and F (ω) is the bunch form factor. For wavelengths longer
than the bunch length (∼ 30 μm), each type of radiationis coherently enhanced by a factor of N e , the number ofelectrons in a bunch. Typically, N e ∼ 109 for the present
ATF running parameters.
The edge radiation emitted from electrons entering andexiting the edges of bend magnets is expected to havegreater intensity at longer wavelengths than synchrotron

448

radiation [6]. The characteristics of CER also depend on
the topology of the eld gradient. In the zero-edge length
model [7], the eld of the bending magnet is approximatedby a step function. The resultant radiation is radially polarized, with a cylindrically symmetric spatial distribution
characterized by a null on the straight section axis and maxima at θ ∼ 1/γ, analogous to transition radiation. Analytic
nite edge length models result in complicated expressions,requiring numerical calculations [8].

Simulations
Start-to-end simulations for the experiment were conducted with PARMELA [9] for the electron beam dynamics
in the accelerating modules. The code QUINDI was used
for the beam transport and radiation studies.
QUINDI is a parallel-computing code speci cally developed to model the emitted radiation from electron bunches
within the ATF chicane. The program avoids the sequential approach of a magnetic lattice, relying instead on an
object-driven description of magnetic elements. The observed radiation eld is calculated on a user-de ned plane
based on the acceleration eld of the Liénard-Wiechert potentials.

MEASUREMENTS AND ANALYSIS
Frequency Spectrum
Spectral measurements of the emitted chicane radiation
were conducted at the ATF. Interferograms were obtained
from scans with the Michelson-type interferometer to provide information about the spectral content. This data wasused to reconstruct the longitudinal charge distribution of
the beam.
Interferometer signal amplitudes from the output of thesilicon bolometer were recorded for N shots per mirror
position. An averaged, normalized interferogram with thecorresponding measured electron beam charge is shown in
Fig. 2(a). Each point on the interferogram records the meanvalue and the error bars depict the standard deviation.
b

a
1

Intensity
Neq [nC]

0.8
0.6
0.4
0.2
13
14
15
16
Absolute Mirror Position [mm]

1
0.75
0.5
0.25
0
-0.25
-0.5

Signal
HM(x)

-2

-1
0
1
2
Relative Mirror Position [mm]Figure 2: (a) Normalized, averaged signal amplitudes frominterferometer scans of chicane radiation. (b) Apodized
signal via a Hamming function.
For an accurate spectral reconstruction with a Discrete Inverse Fourier Transform (DIFT), the non-zero
offset of the interferogram is removed and the signal
is multiplied by an apodization function. Fig. 2(b)New Science at FELs

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TUPPH053

shows the results of apodization by a Hamming function
HM(x) = 0.54 + 0.46 cos( πxa ), where 2a = 4 mm is thelength of the interferometer scan centered on the maximum peak. This standard procedure removes arti cial lowfrequency components and corrects for the spurious tails
that arise from the nite sum in the DIFT [10],n1
Ij e2πi(k−1)(j−1)/n ,I˜k = Re
n j=1

(2)

where n is the number of equally spaced interferometer mirror positions recorded over a nite distance[ctmin , ctmax ]. This yields n/2 non-repeating intensity
values, Ik , up to the maximum frequency, where I j is thej th intensity point in the modi ed interferogram.
Fig. 3(a) displays the resulting spectrum of the apodized
signal. The peak at f peak ≈ 0.5 THz coincides with thedominant frequency given by results from QUINDI simulations.
Kramers-Kronig Reconstruction
The forward far- eld radiation intensity spectrum produced by the bunch is given by Eq. 1, where the longitudinal form factor F (ω) is
⏐2
⏐
⏐
⏐
⏐
⏐
iωz/c
dz ⏐ ,F (ω) = ⏐ ρ̂(z)e
⏐
⏐

(3)

with ρ̂(z) = ρ(z)/Ne q, the normalized longitudinal charge
density. Following a minimal-phase reconstruction technique, a discretized Kramers-Kronig relation is used to extract ρ̂(z) [11].
The minimal phase is
max
2ωi 
ln[ξ(ωj )/ξ(ωi )]Δω,πωj2 − ωi2Nψ(ωi ) =

(4)

j=i

where ξ 2 (ωi ) = F (ωi ), and Δω is the resolution from thespectrum. The normalized pro le ρ̂(z) then has the formρ̂(z) =Nmax
1 
ωi z Δω.
ξ(ωi ) cos ψ(ωi ) −πc i=0c(5)

The bunch distribution is calculated from the form factor,
determined by tting well-behaved asymptotes to the measured normalized spectrum. Results of this reconstruction
are shown in Fig. 3(b). The values for current are scaled
to the average measured charge of N e q ≈ 330 pC. Dueto experimental limitations (discussed below) and numerical tting of the form factor, this reconstruction technique
is useful as an approximation of the true bunch distribution. Nevertheless, the reconstructed pro le shows generalagreement with predictions from PARMELA simulations in
the overall structure of the asymmetric bunch and the compressed head of ∼ 30 μm FWHM.

New Science at FELs

Figure 3: (a) Spectra from apodized interferogram andfrom simulation. Prominent water absorption frequencies
are shown as vertical dotted lines. (b) Minimal phase
Kramers-Kronig bunch reconstruction for the measured
spectrum.
Limitations on Spectral Analysis
The simulated and measured spectra show that the radiation is dominated by frequencies below 1.5 THz, however, several experimental factors contribute to spectral ltering which affect the measured frequency distribution andthe longitudinal bunch reconstruction. The primary experimental artifact near the dominant frequency band is theselective ltering from water absorption (due to high levels of humidity encountered through the radiation transport
on the dates of data acquisition). This effect is exempli ed
by strong absorption troughs located near f = 0.57 and0.75 THz. Signi cant absorption frequencies are plotted inFig. 3(a) for a 7 m travel path [12]. The spectrum is also
affected by the radiation transport line, which acts as a highpass lter due to its inherent nite apertures and acceptanceangles. Further, the fused silica vacuum port window maintains a transmission coef cient that slowly decreases forfrequencies greater than 0.3 THz, but rapidly approaches
zero for frequencies greater than 6 THz.

Polarization
The transverse radiation pro le and polarization were
measured in an effort to observe the distinctions between
CER and CSR. Fig. 4 shows the measured intensity (normalized to maximum) as a function of polarizer rotation
angle. The wire grid polarizer was mounted at the end of
the transport and rotated in 15 ◦ increments, and the focusedsignal intensity was measured with the bolometer. The linearly polarized component of radiation (sinusoidal) is consistent with that expected from synchrotron radiation. The
non-linearly polarized component, which introduces a vertical offset, is a clear signature of edge radiation. Analytic
studies show that pure synchrotron radiation would give a
ratio of approximately 7:1 between the maximum and minimum signal [13], while the observed ratio is approximately
4:1. QUINDI results are consistent with the measured data
(Fig. 4).

Transverse Spatial Distribution
The transverse far- eld spatial intensity distribution of
the emitted radiation was measured by scanning a small iris

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ef ciently resolve the chicane radiation spectrum.

Intensity (a.u.)

1

REFERENCES

0.8[1] G. Andonian, et al., Proceedings of the 2003 Particle Accelerator Conference, 944, 2003.

0.6
0.4

[2] T. E. May, R. A. Bosch, and R. L. Julian, Proceedings of the1999 Particle Accelerator Conference, 2394, 1999.

0.2
0[3] R. Agustsson, UCLA M.S. Thesis (2003).

50 100 150 200 250 300 350[4] http://www.irlabs.com/.

θ°[5] http://www.radiabeam.com/.

Figure 4: Normalized polarization intensity of the chicane
radiation. Solid line is from QUINDI, dots are measured at
the bolometer. The zero angle is arbitrary.
(3 mm diameter) in a 19 mm × 23 mm rectangular array of
discrete points (Δd =3.8 mm). The iris was scanned acrossthe transport tube exit and the signal was focused into thebolometer. Iris scans were performed for varying radiation
polarizations with the aforementioned wire-grid polarizer(Fig. 5).

[6] O. V. Chubar and N. V. Smolyakov, J. Optics (Paris) 24, 117(1993).
[7] R. A. Bosch, Il Nuovo Cimento 20D, 483 (1998).
[8] O. V. Chubar and N. V. Smolyakov, Proceedings of the 1993
Particle Accelerator Conference, 1626, 1993.
[9] E. Colby, UCLA PhD Thesis, FERMILAB-THESIS-199703 (FNAL, 1997).
[10] J. F. Rabolt and R. Bellar, Applied Spectroscopy 35, 132,
1981.
[11] R. Lai and A.J. Sievers, Phys. Rev. E 50, 5 (1994).
[12] P.U. Jepsen, private communication.

Θ  40°10510

Θ  60°5

010

Θ  80°50Θ  100°

10
5

0

10

0

5

5

5

5

10

10

10

10

105 05 10

Θ  140°510

105 05 10

Θ  160°510

105 05 10

Θ  180°5

105 05 10

Θ  200°

10
5

10

0

0

0

0

5

5

5

5

10

10

10

10

10

5 10

105 05 10

105 05 10

105 05 10

Θ  220°50
5
105 0[13] J.D. Jackson, Classical Electrodynamics, John Wiley andSons, New York, 1999.

0

5
10
10

Θ  120°5

105 05 10

105 0

5 10

Figure 5: Interpolated far- eld radiation intensity distributions for 20 degree polarizer angle increments, with resultsfrom QUINDI simulations (contours) overlayed for comparison. The x and y scales have units of mm.

CONCLUSION
The chicane radiation studies at the ATF display telling
signatures of edge radiation. The transverse spatial distributions show patterns consistent with simulations, namely
strong peaks shifting into multiple peaks for varying degrees of polarization with identi able nulls in the distribution on-axis. The non linearly polarized component ofradiation observed as an offset to the sinusoidal signal in
the overall polarization curve is a clear indication of theactuality of prominent edge radiation.
Future plans to improve the measurements include radiation transport modi cations such as replacement of the
fused silica chicane radiation port window with a diamondor z-cut crystalline quartz window; this will greatly improve the spectral range of the measurements. In addition, enclosing and ushing the transport line with dry nitrogen will mitigate the effects of water absorption lines
in the measured spectrum. Also, a Czerny-Turner type
monochromator is currently being built in order to more

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BEAM PICKUP DESIGNS SUITED FOR AN OPTICAL SAMPLINGTECHNIQUE
K. Hacker, F. Loehl, H. Schlarb DESY, Hamburg, Germany
Abstract
The beam arrival-time monitor and large horizontal
aperture chicane BPM at FLASH are important tools tostabilize the arrival-time of the beam at the end of thelinac. The pickups for these monitors will be paired with afront-end that samples the zero-crossing of the transientthrough the use of electro-optical modulators (EOMs) and
sub-picosecond-long laser pulses delivered by the masterlaser oscillator (MLO). The design of pickups for thisfront-end requires the consideration of the transient shape
as well as the amplitude. Simulations and oscilloscope
traces for pickups that use or will use the EOM based
phase measurement and the expected limitations of eachpickup are presented. In particular, a method to reduce thebeam position sensitivity of the beam arrival-time pickup,
the potential resolution of a button pickup arrival-timemeasurement, and the design for a 5 μm resolution BPM
with a 10 cm horizontal aperture are described.

INTRODUCTION
A beam arrival-time stability of 30 fs (~10 μm at v=c)
is desired for pump-probe experiments and is mandatory
for laser-based electron beam manipulation at FLASHand the XFEL [1]. With the accelerating LLRF goalenergy stability of 10-4 at FLASH, the transverse position
jitter in the dispersive section of the first chicane becomes
34.5 μm and results in a longitudinal position jitter of 18
μm. A monitor for a feedback system should be able tomeasure the beam energy by a factor of three better thanthe desired energy stability of 5*10-5 and this means thatthe resolution for a beam position measurement in the
chicane must be better than 6 μm and a longitudinal timeof-flight path-length measurement should resolve 3 μm.
A longitudinal time-of-flight energy measurement canbe made with two beam arrival-time monitors: one before
and one after the chicane, but a chicane BPM energy
measurement has an advantage given by the ratio of the
R16 to the R56 terms. In the case of the first bunch
compressor for the XFEL, this advantage in the required
sensitivity of the monitor is a factor of six.
The arrival-time monitor and the chicane BPM candistinguish the energy jitter that results from injector
timing jitter from the energy jitter caused by theacceleration RF phase and amplitude jitter. A bunch
length monitor and the chicane BPM can distinguish the
RF amplitude jitter from the RF phase jitter. BPMs before
the chicane can be used to remove incoming orbit jitterfrom the chicane BPM’s energy measurement.
The pickup transients for these energy measurements
will be paired with the sub-picosecond pulses from themaster laser oscillator (MLO) from the timing and
The Challenge of fs Pulses and Synchronisationsynchronization system to sample the zero crossing of thebeam transient through an electro-optical modulator(EOM). The beam arrival-time monitor installed in thetunnel, a perpendicularly mounted stripline to be installedin the dispersive section of the chicane in October 2006,
and button-style pickups are analyzed with Microwave
Studio simulations and compared to measured
oscilloscope traces with regard to their suitability for theEOM phase measurement technique. The front-ends forbeam transient pickups typically filter the transient down
to 2 GHz or less and utilize the ringing or amplitude of
the signal to get the desired beam information, but thisEOM front-end works at 10 GHz or more and samples thezero-crossing, so attention must be paid to the transient
shape.

EOM PHASE MEASUREMENT
Test BenchTo date, 30 fs resolution has been achieved with the
EOM phase measurement and a limited but not combined
output of the ring shaped arrival-time monitor pickup [2].
It utilizes a short optical pulse (< 1 ps) from a master laser
oscillator that is locked to the 1.3 GHz reference of themachine. The light pulse travels via fiber optics throughan electro-optical modulator (EOM) which encodes theamplitude information of an RF pulse into the laser pulse
energy. Essentially, the laser pulse samples the beamtransient. The modulated laser pulse is then detected witha 50 MHz bandwidth photo diode and read out by a 100
MHz, 12bit ADC that is clocked with the laser pulse at
twice the repetition rate of the laser.
Since changes in the RF pulse arrival-time produce achange in laser intensity, the measurement is limited by
the steepness of the RF signal slope and the precision of
the laser amplitude detection. Slope changes can distort
the measurement, so a feedback is used to maintain themeasurement at the zero-crossing. The slope at the zerocrossing for the 30 femtosecond resolution measurement
was 250 mV/ps and the single-shot noise with which thelaser pulse intensity was detected was 0.3%. Shot-noise of
spontaneous emission from the laser is a suspected noise
source, but as of yet there is no conclusion.

Future Applications
It is anticipated that for each pickup output, thetransient signal will be split for a low-resolution (large
range) phase measurement and a high-resolution (small
range) phase measurement. A delay-line will use the lowresolution measurement to put the high-resolution
measurement in range. The phase measurement is givenby the position of this delay-line plus the fine451

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Proceedings of FEL 2006, BESSY, Berlin, Germany

measurement given by the laser amplitude. This delay line
must have sub-micrometer resolution over 10 cm and be
adjusted between macro-pulses (10 Hz) in order to keep
the system measuring the beam transient at the zerocrossing, thereby reducing the systematic errors of slope
variation.
The EOM setup will be standardized and duplicatedseveral times for use with two or more beam arrival-time
pickups and two large horizontal aperture chicane BPMs.

PICKUP DESIGN
Beam transient pickups for the EOM phasemeasurement must produce a steep slope for sampling of
the zero-crossing with a picosecond-long laser pulse togive maximum resolution. They must also have aminimum of ringing so that the transient of a bunch thatcomes earlier is not detected. The bunch spacing will be
200 ns for the XFEL. A steep slope requires the highbandwidth and voltage that are produced by short bunches
and pickups with a large area exposed to the beam.
Bunches that are longer than ~25 ps (RMS) will have
reduced resolution because the slope of the transient
becomes less steep (e.g. 50% for 25 ps) for longer
bunches. Minimal ringing can be achieved throughtapering from the pickup to the feedthrough.

150
100

Volts

The design utilizes a cylindrical pickup within acylindrically shaped vacuum chamber channel that lies
over and perpendicular to the path of the electron beam(see Fig. 1) [3]. It was originally proposed by [4]. Whenthe electron beam travels beneath this pickup, shortelectrical pulses travel to opposite ends. The arrival-timesof the pulses are then measured with the EOM techniqueand used to determine the position of the electron beam.
In Fig. 1, the perpendicularly mounted stripline isdepicted in 3-D as well as in cross-section.

RF
PulsesRF

SMA output
SMA output

pulsesTapering
tapering

beam
Beam

Vacuumvacuumbeam
Beam

Figure 1: Perpendicularly-mounted stripline BPM pickup.

452

Simulated Stripline Output

50

Position Monitor

Stripline
stripline

In the 3-D depiction, only the upper-half of the BPM isshown, since the lower-half is identical. The beam isrepresented by a thick line underneath the stripline. The
central piece of the stripline is tapered on both ends froma 3 mm diameter to an SMA sized connector pin. The
vacuum feedthroughs to SMA connectors are at the endsof the stripline.
Standard stripline designs do not have tapering from the
pickup to the feedthrough, but instead have a larger radius
pickup connected at a sharp angle to a smaller SMA
connector sized feedthrough. The tapered design waschosen because in simulation it transmits 20% moresignal amplitude and has 80% less ringing amplitude
compared to the non-tapered design.
In a Microwave Studio simulation, a 50 GHz
bandwidth (FWHM) Gaussian pulse was applied to themonopole mode of a waveguide port in order to simulate
the electron beam. The output signals of the SMA
connector ports were scaled according to a 1 nC electron
bunch charge (Fig. 2).

0
-50
-100
-150

-100

0

100
200
Time (ps)

300

400

Figure 4: Simulated stripline output with a marker at the
sampling location. The slope at the marker is 10 V/ps.
A similar simulation for an existing pickup also
predicted such a high voltage, and when the pickup output
was measured in the tunnel, the results matched thesimulation within a few volts. The transient without along cable is most interesting because the EOM front-end
will be installed in the tunnel within a temperaturestabilized enclosure, thus minimizing cable lengths andtemperature dependent signal drifts.
The BPM’s horizontal response is linear over the entire
horizontal aperture and is insensitive to small changes inthe beam shape. Vertical position changes and chargechanges influence the amplitude of the signal but not thephase. The average of two outputs’ phase measurements
can also be used to measure the beam arrival-time, as longas the energy spread is constant. Alternatively, if theelectron beam arrival-time is known, the energy spreadcan be measured through changes in the sum of the BPM
outputs’ phase measurements with a projected sensitivityof 1.5 fs/μm (Fig. 3), but this is only possible when the
beam width is larger than the length.

The Challenge of fs Pulses and Synchronisation

Proceedings of FEL 2006, BESSY, Berlin, Germany

phase monitor with and without cold combiner

BPM beam width dependence

800
slope at zero crossing (mV/ps)0arrival time (ps)

-5
-10
-15
-20
-25
-30
0

1

2
beam width (cm)3

4

Figure 3: Energy spread measurement with BPM.
An important thing to note about pickup transients isthat a measurement of the zero-crossing gives the RMS
value of the beam position, in the case of the transverse
stripline, or, in the case of the beam arrival-time monitor,
it gives the RMS value of the arrival-time. This isdifferent from measurements with devices that canmeasure the peak intensity of an electron distribution,such as synchrotron light monitors and electro-opticalsampling. For non-linear, inhomogeneous compression
schemes the RMS value and the peak value can differ, but
for linear, homogeneous compression, they should be one
and the same. About 30 fs difference between the peak
and RMS values has been measured for the current
compression scheme. The 3rd harmonic cavity will be
installed in summer 2007 to linearize the compression.

Arrival-time Monitor
The arrival-time monitor pickup is a ring electrode in a
thick flange with two SMA feedthrough sized pins
attached to the ring in the horizontal plane. The frequency
response of the ring shows a notch at 5 GHz whichcorresponds to a quarter-length of the ring circumference,
implying that the beam does not couple strongly to thesecond harmonic of the ring. A position dependence of theoutput signals is therefore seen through a beat between
the fundamental and third harmonic of the ring. This
problem reflects the original intended use of the pickup ina lower-resolution RF down-mixing phase measurementthat was not affected by the transient shape. For the EOMphase measurement the two outputs were combined toremove this effect (Fig. 3). The, so called, cold-combinerthat was designed for a toroid-based charge measurement
crossed the output pins of the SMA connectors in acircular void and terminated one of the arms of the crosswith 50 Ohms [4].

The Challenge of fs Pulses and Synchronisation

TUPPH054

700
600
500
400
300
200
100
0
-4

-2

0
2
4
horizontal position (mm)68Figure 3: Slope at zero-crossing of arrival-time pickup
with (star) and without (diamond) combiner. Simulation(red) and oscilloscope (blue) results are shown.
The output from the monitor was measured with an 8
GHz bandwidth oscilloscope and simulated with aGaussian ‘beam’ in Microwave Studio. Simulation andoscilloscope results agree well when cable, bandwidth,and combiner attenuation are taken into account (Figs. 3
and 4).

Button Pickups
Button pickups are installed in a few locations in the
FLASH linac. Their output amplitude is proportional tothe button size and distance from the beam and it can becomparable to that observed from the ring shaped pickup.
Buttons can be more desirable than the ring electrode dueto the lack of a notch in the frequency response thatcauses zero crossing changes with beam position changes.
No detectable change of the transient zero crossing occurs
for beam position changes. Buttons also produce a
steeper, very linear slope with a lower peak-to-peakvoltage.
Measurements of the beam transient with button
pickups at FLASH were conducted with an 8 GHz
bandwidth oscilloscope inside the tunnel and steep slopesof 1-2 V/ps were observed. The large changes in the slope
due to beam position changes make the challenge ofmeasuring on the zero crossing more critical. If the slopechanges prove to be unworkable, a combiner could again
be used.
The main problem with the pickups that were measured
was that the signal was still ringing 200 ns after thetransient with an amplitude that was 0.7% of the peakvoltage. This would be a problem for the 200 ns XFEL
bunch spacing because 10 fs resolution requires almost 10
times less ringing amplitude (Fig. 5).

453

TUPPH054

Proceedings of FEL 2006, BESSY, Berlin, Germany
ringing button pickup

3

15

2

10

1

0.8 V

no limiter
limitersimulation

5

0

Volts

Volts

arrival-time monitor with and without limiter

-1

0
-5

-2
-3

-10
XFEL bunch spacing

-4

-15
0

0.2

0.4
0.6
time (us)0.81Figure 5: Ringing of button pickup with 120 Volt peak topeak transient. The ringing must be smaller than 10 mVby the time a new bunch comes for a 10 fs resolution
phase measurement.
A few button pickup designs were simulated to look forways to reduce or characterize the sources of the ringing.
It was noted that for a large amplitude output, the pickup
pin needed to be long or have a large button attached to it.
For a long pin or a large cylindrical button, the transient
amplitude was good, but the ratio between the transient
amplitude and the ringing was bad. For a short pin
without a button, there was practically no ringing, but thetransient amplitude was insufficient (Fig. 6). More workneeds to be done to understand and optimize the design.
Simulated Button Output
short pinlong pin
50

-0.2

Volts

0

0.1 0.2
time (ns)

0.3

0.4

Figure 7: Limited and combined ring output fromoscilloscope measurement and simulation including
attenuation and dispersion from the cable, splitter, andcombiner.
rendered opaque to the laser light. No limiter was in place
and the damage occurred over less than a minute.
The Agilent N9355C 26.5 GHz bandwidth limiter thatwas in place throughout most tests of the EOM setup (Fig.
7) appeared to protect the EOM crystal from standard
beam operation. With the limiter in place, even extreme
off axis kicks from the transverse deflecting cavity
upstream did not appear to damage the EOM. A
conclusive study of the long-term effects of high voltage
with the limiter has not, however, been done. The
temperature dependent drifts of the limiter have also notbeen studied and are of interest even though thecomponent will be used in a temperature controlled
enclosure in the tunnel. It has also not bee used, longterm, in the tunnel, where 120 Volts peak to peak havebeen measured from the combined ring pickup.

0

SUMMARY
•

-50

•

-100
1

2
Time (ns)3

4Figure 5: Button pickup with a long or short pickup pin.
The long pin is more like a pickup in a cavity BPM.

EOM DAMAGE
The EOMs in the front-end are damaged by highvoltages and care must be taken to preserve the steep
slope of the transient while protecting the electronics
from high voltage. Following a voltage surge through thearrival-time pickup caused by electron beam spray or
incidence, the EOM’s Lithium Niobate crystal was

454

-0.1

•

EOM technique makes high resolution phasemeasurements possible.
Optimal pickups for the EOM technique must
maximize the slope and minimize ringing andtransient distortions.
EOMs must be protected from high voltage.

REFERENCES[1] X-FEL Technical Design Report Sect. 4.8 2006.
[2] F. Loehl et. al., “Beam Arrival-time Monitor”,
EPAC’06, Edinburgh, June 2006.
[3] K. Hacker et. al., “BPM with Large Horizontal
Aperture”, EPAC’06, Edinburgh, June 2006.
[4] Manfred Wendt, personal communication.

The Challenge of fs Pulses and Synchronisation

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH055

DESIGN OF AN XUV FEL DRIVEN BY THE LASER-PLASMAACCELERATOR AT THE LBNL LOASIS FACILITY∗
C. B. Schroeder, W. M. Fawley, E. Esarey, W. P. Leemans
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
Abstract

SIS laser facility at LBNL.

We present a design for a compact FEL source of ultrafast, high-peak flux, soft x-ray pulses employing a highcurrent, GeV-energy electron beam from the existing laserplasma accelerator at the LBNL LOASIS laser facility. The
proposed ultra-fast source would be intrinsically temporally synchronized to the drive laser pulse, enabling pumpprobe studies in ultra-fast science with pulse lengths oftens of fs. Owing both to the high current (∼10 kA) andreasonable charge/pulse (∼0.1–0.5 nC) of the laser-plasmaaccelerated electron beams, saturated output fluxes are potentially 1013 − 1014 photons/pulse. We examine devices
based both on SASE and high-harmonic generated input
seeds to give improved coherence and reduced undulator length, presenting both analytic scalings and numerical simulation results for expected FEL performance. A
successful source would result in a new class of compact
laser-driven FELs in which a conventional RF accelerator
is replaced by a GeV-class laser-plasma accelerator whose
active acceleration region is only a few cm in length.

INTRODUCTION
Recent advances in laser-plasma-based accelerators havedemonstrated generation of low energy spread, ∼100 MeV
electron beams [1]. These experiments used an ultraintense ∼1019 W/cm2 laser pulse focused on a gas jet, withtypical length of a few millimeters, to generate plasma
waves with accelerating fields on the order of 100 GV/m.
By using a gas-filled discharge capillary for creating aplasma channel, the laser-plasma interaction length can beextended to a few centimeters, resulting in high-quality
GeV electron beams [2]. In addition, the electron bunches
emerging from a laser-plasma accelerator have naturally
short durations (tens of fs) [3], and are intrinsically synchronized to the short-pulse laser driver, making such asource ideal for ultra-fast pump-probe applications. Theselaser-plasma accelerator experimental results [1, 2] open
the possibility of a new class of compact, high-peak flux,
x-ray free-electron laser (FEL) in which the conventional
radio-frequency (RF) accelerator (10–100 m length) is replaced by a GeV-class laser-plasma accelerator (several cm
length), in principle greatly reducing the size and cost ofsuch light sources [4].
In this paper we discuss the design of an XUV FEL
driven by the existing laser-plasma accelerator at the LOA∗ Work supported by the U.S. Department of Energy under Contract
No. DE-AC02-05CH11231.

The Challenge of fs Pulses and Synchronisation

LASER-PLASMA ACCELERATOR
The LOASIS Laboratory at LBNL presently produces
ultra-short (<50 fs), relativistic electron bunches with highcharge (100 pC/bunch) via a laser-plasma interaction.
The bunches are generated by a laser wakefield accelerator (LWFA): radiation pressure from a short pulse, intenselaser excites high-field plasma waves (wakefields) that accelerate electrons [5]. The LWFA at LBNL uses a 10 Hz,
Ti:Sapphire laser system to focus ultra-short (∼30 fs)
laser pulses of relativistic intensity (>10 18 W/cm2 ) into a
plasma channel. GeV-energy electron beams have been
demonstrated [2] using the LBNL 100 TW-class laser system and a gas-filled capillary discharge waveguide [6] forplasma channel production, which allows for low plasma
densities (∼1018 cm−3 ) and long (∼cm) laser-plasma interaction lengths. These LWFA-produced electron beams arehigh current (∼10 kA) and ultra-short (<50 fs), properties
which are attractive as an input beam for an FEL generating
ultra-short x-rays.
In recent experiments using the plasma-channel-guided
LWFA at LBNL, a 18-TW, 72-fs laser (25 μm focused spotsize) is guided in capillary waveguide (which generates aplasma channel via a discharge in the hydrogen filled capillary), producing 0.5 GeV with 5% RMS projected relative energy spread, 2.0 mrad RMS divergence, and 50 pC of
charge [2]. Experimental results using 2 J of laser energy
have produced 1-nC electron beams at 0.5 GeV. At present,slice energy spread σ γ measurements of the electron beam
have not been performed, but simulation results [7] predict that the slice energy spread is an order of magnitude
smaller than the projected value.

FEL DESIGN
We consider interaction of the LWFA-generated 0.5GeV electron beam in a conventional magnetostatic undulator. For this study we will consider the LWFA electron
beam and undulator parameters listed in Table 1; the latter correspond to the existing “THUNDER” device (seeRef. [8] for a detailed description), which provisionallywill be transferred to LBNL from Boeing in late 2006.
THUNDER contains 220 periods divided into ten 50-cm
sections, each separated by a 4-cm diagnostic and steering space. The maximum
RMS undulator strength param√
eter is au = K/ 2  1.31 (≈1.0 T peak magnetic field)
which may be tapered section by section. Wiggle-plane455

Proceedings of FEL 2006, BESSY, Berlin, Germany

focusing is provided by a canted pole configuration withthe expected matched beta-function k β−1 ≈ 3.6 m for the
peak field and 0.5-GeV beam. Conventional magnetic optics will transport the electron beam from the laser-plasma
accelerator to the undulator. Note that there could be nontrivial beam transport issues concerning the required degreeof achromaticity and preservation of pulse duration (i.e.,peak current). At 0.5 GeV, the beam is sufficiently “stiff”
that pulse lengthening via drift will be small; for example,
a 5% energy chirp results in less than 1 fs of pulse lengthening over a transport distance of a few meters.

1
0.8

L g (m)TUPPH055

0.6
2.5 kA

0.4

5 kA
7.5 kA
10 kA

0.2
0

0.002

0.004

0.006

0.008

0.01

σγ /γ

Table 1: Electron Beam, Undulator and HHG
Source Parameters
LWFA electron beam:
Beam energy, γmc 2
Peak current, I
Charge, Q
Bunch duration (FWHM), τ b
Energy spread (RMS, slice), σ γ /γNormalized transverse emittance
Undulator:
Undulator type
Undulator period, λ u
Peak magnetic field
Undulator parameter (peak), K
Magnetic gap
Beta-function, kβ−1
HHG seed:
HHG radiation wavelength
Coherent HHG radiation power
HHG pulse duration

0.5 GeV
5 kA
0.1 nC
20 fs
0.25%
1 mm mrad
planar
2.18 cm
1.02 T
1.85
4.8 mm
3.6 m
31 nm
15 MW
20 fs

FEL PERFORMANCE
We consider two modes of FEL operation: self-amplified
spontaneous emission (SASE) and seeding by a highharmonic generation (HHG) source. Results from FLASHat DESY [9] and SSCS at Spring-8 [10], operating in the
XUV wavelength regime, have confirmed the applicabilityof the basic SASE physics at XUV wavelengths. Existing laboratory HHG sources have demonstrated productionof ultra-short (tens of fs) coherent soft x-ray (e.g., 31 nm,
26th harmonic of a 0.8 μm drive laser) pulses with 0.3 μJof energy (see, e.g., Ref. [11]). HHG seeding has significant advantages over the simpler SASE mode of operation
as it will provide improved temporal coherence and a much
reduced power saturation length.
The resonant wavelength for the beam and undulator
parameters of Table 1 is λ = λ u (1 + K 2 /2)/(2γ 2) 
31 nm (40-eV photons), while the matched electron beam
size in the undulator is 60 μm. The FEL parameter isρ ≈ 5 × 10−3 and the ideal 1D (i.e., no emittance, energy spread, or diffraction effects) exponential power gain

456

Figure 1: Exponential gain length as a function of incoherent energy spread for various electron beam currents asdetermined from the Xie [12] empirical fitting function.
√
length is L1D = λu /(4π 3ρ)  0.19 m. Including these
non-ideal effects via the Xie gain length formula [12] canincrease the gain length (L g ) 1.5–3 fold compared to theideal 1D gain length, depending upon the assumed value ofσγ . For the parameters of Table 1, the 3D gain length is
Lg ≈ 0.3 m. Figure 1 displays contours of gain length as afunction of peak current I and relative energy spread σ γ /γ.
If one presumes empirically that the product Iσ γ remains
constant, one sees that it is best to operate at relatively large
currents. However, consideration of slippage effects overthe full THUNDER undulator (τ s = λNu /c ≈ 24 fs) suggests that reducing the electron beam pulse duration τ b below τs will have diminishing returns. Hence, we believe
peak currents of I ∼ 2.5–10 kA for a bunch charge ofQ ≈ 100 pC is the likely region of interest. Space charge
effects will not degrade the FEL performance in this highcurrent regime provided (λ u /λp )2 /γ 3  (2ρ)2 (i.e., thecharacteristic wavelength of the space charge oscillation in
the lab frame is much greater than the FEL gain length),where λp is the plasma wavelength of the electron beam.
This condition is satisfied for the parameters of Table 1.
We performed a series of time-independent GINGER [13]simulations to examine in detail the predicted FEL output
from such a device, examining both the SASE and HHGseeded cases. We adopted electron beam and undulator
parameters as given in Table 1 with the exception that we
also considered 7.5-kA peak current (150 pC charge) SASE
and HHG-seeded cases and a 10-kA peak current (200 pC
charge) SASE case, in addition to the nominal 5-kA HHGseeded FEL. The simulations used a parabolic temporalprofile for the electron beam; the details (i.e., the sub-20 fs
structure) of the actual experimental electron beam profile
have not been measured. All the SASE results presented
here are from one single simulation run for each of the twocurrents. Note that an ensemble average over many different runs, each with a different initial shot noise presentation
would give smoother profiles for P (t) and P (ω).
Figure 2 shows the maximum power for the HHG-seededcase (FEL in amplifier mode with 15 MW initial HHG

The Challenge of fs Pulses and Synchronisation

Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 2: Predicted (GINGER calculations) maximum
power in amplifier mode (with 15 MW initial HHG seed)over the THUNDER undulator (5 m) as a function of initialincoherent energy spread for various beam currents.

TUPPH055

Figure 4: Predicted (GINGER calculations) output power
temporal profiles for the cases associated with Fig. 3. The
electron beam center is at t = 0.

Figure 3: Predicted (GINGER calculations) radiation pulse
energies as a function of undulator length z for both SASE
and HHG-seeded cases.

Figure 5: Predicted (GINGER calculations) output spectraat the 31-nm wavelength fundamental for the various SASE
and seeded cases. Each bin is 64.6 meV wide while 1 GW
is equivalent to 1.0 × 10 13 photons.

seed) versus initial incoherent RMS energy spread for several beam currents. As the figure shows, for the nominal
beam current (5 kA), greater than 10 GW of power can beachieved provided the RMS energy spread is 1.25 MeV(σγ /γ  0.25%).
Figure 3 displays time-integrated radiation pulse energies as a function of undulator length z; for reference,
1 μJ of energy corresponds to 1.5 × 10 11 photons at 40 eV.
The SASE results show a strong current dependence thatis attributable to the sensitivity of L g to current in thisshort-pulse regime with normalized σ γ comparable to ρ.
One sees in Fig. 3 that the 7.5-kA SASE case is about again length away from saturation, while the 10-kA SASE
case reaches saturation. Given that we presumed idealized Gaussian transverse distributions with no offsets, tilts,
etc., additional current and charge might be required toreach full saturation with the assumed energy spread of
1.25 MeV. Earlier saturation in z might also be achievedby employing additional focusing (by adding focusing optics between the THUNDER undulator sections) thereby
reducing the beta-function. Saturation is achieved in <3-m
distance for the HHG-seeded cases.
Figure 4 shows output power temporal radiation profiles;
one sees that the radiation pulse remains temporally close
to the electron beam (whose center is at t = 0) when com-pared with slippage (τ s ≈ 24 fs). Since the electron beam
duration τb is only a few times the steady-state coherence
length cτc ≡ λ/(4πρ3D ), the output profile is dominatedby a single longitudinal mode, which results in spectral purity (at the price of reduced gain). This is apparent also in
Fig 5 which shows quite clean power spectra for all cases
except the 10-kA SASE run where there appear to be weak“sidebands” to either side of the central line; we expect ensemble average over many shots would likely show a simple Gaussian shape whose width would be slightly wider
than this specific run.
For the HHG-seeded cases shown in Figs. 3, 4, and 5
we presumed an input seed with a 20-fs FWHM Gaussian
temporal profile and peak power of 15 MW. The results
indicate significantly improved performance of the HHGseeded FEL, compared to the SASE cases (e.g., compare
the 7.5-kA cases). As seen in Fig. 3, saturation occurs
before 3 m in the undulator, and peak powers exceeding 10 GW appear possible with FWHM durations ∼15 fs(Fig. 4). Despite the early saturation, both HHG-seededcases (5 kA and 7.5 kA) show essentially single mode spectral output with inverse normalized bandwidths (RMS) for
the on-axis far field of ω/Δω ≈ 500 and autocorrelation
times ∼ 12 fs. Predicted third harmonic power (due to

The Challenge of fs Pulses and Synchronisation

457

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Proceedings of FEL 2006, BESSY, Berlin, Germany
Table 2: FEL Performance

Radiation wavelength, λResonant photon energy
FEL parameter, ρ
3D Gain length
Slippage length
Spontaneous radiation power
Steady-state saturation power
Photon/pulse (at saturation)
Peak brightnessa (at saturation)
Saturation length (HHG-seeded, 5 kA)
Saturation length (SASE, 10 kA)
a

31 nm
40 eV
5 × 10 −3
0.3 m
7.2 μm
4 kW
12 GW
3 × 10 13
2 × 10 16
2.4 m
5m

photons/pulse/mm 2/mrad2 /0.1%BW

the nonlinear harmonic microbunching associated with thestrong fundamental bunching) is about 0.4% and 0.8% of
the fundamental for the 5-kA and 7.5-kA cases, respectively. The normalized spectral bandwidths for the third
harmonic are narrower than the fundamental by slightly
more than a factor of two; one expects less than the theoretical maximum of three due to the variation in temporalmicrobunching fraction [i.e., the third-harmonic bunchingparameter b3 (t) has a narrower pulse shape than the fundamental b1 (t)]. Despite the much lower photon/pulse valueof the third harmonic radiation, it may, nonetheless, be ofinterest for certain experiments.

DISCUSSION AND CONCLUSIONS
Recent advances in laser-plasma-based accelerator experiments [1, 2], and, in particular, the demonstration ofhigh quality GeV electron beams [2], have enabled thepossibility of a new class of compact laser-driven FELs
in which the conventional RF accelerator is replaced by a
cm-scale laser-plasma accelerator, greatly reducing the sizeand cost of the FEL. The natural short bunch length of thelaser-plasma accelerator (tens of fs), and the intrinsic temporal synchronization between the short-pulse laser generating the electron beam and the FEL radiation, make thelaser-driven FEL an ideal source for ultra-fast pump-probe
applications. As discussed above, seeding of the FEL by an
HHG source (generated from the same LWFA drive laser,and, therefore, temporally synchronized with the electronbeam) has significant advantages over the simpler SASE
mode of operation. The coherent amplification of the HHG
source in the FEL leads to reduced undulator length andimproved longitudinal coherence.
In this paper we have discussed the design of a XUVFEL employing the 0.5 GeV laser-plasma-generated electron beam produced at the LOASIS laser facility at LBNL.
Table 2 shows the expected FEL performance employinga 31-nm HHG seed assuming the input parameters given
in Table 1. Presuming a reasonably small incoherent energy spread of 1.25 MeV, a 15 MW HHG input seed pro-458

vides sufficient initial power for the FEL to reach saturation in a few meters using the THUNDER undulator. For
SASE, higher currents (e.g., 10 kA) are needed to reach saturation in the 5 m undulator distance. The proposed HHGseeded FEL, using the existing 0.5 GeV-LWFA at LBNL
and the THUNDER undulator would capable of producing
ultra-short (∼15 fs) XUV (40 eV) pulses with >10 13 photons/pulse. The predicted third harmonic emission wouldbe ∼ 2.5 orders of magnitude less. A key beam parameteris the actual incoherent (i.e., slice) energy spread. Values
much above 1.25 MeV (0.25%) would require peak currents ≥ 10 kA for saturation to occur within the THUNDER undulator.

REFERENCES[1] S. P. D. Mangles et al., Nature 431 (2004) 535; C. G. R.
Geddes et al., ibid. 431 (2004) 538; J. Faure et al., ibid. 431(2004) 541.
[2] W. P. Leemans et al., Nature Phys. 2 (2006) 696.
[3] J. van Tilborg et al., Phys. Rev. Lett. 96 (2006) 014801.
[4] D. A. Jaroszynski et al., Phil. Trans. R. Soc. A 364 (2006)
689.
[5] E. Esarey et al., IEEE Trans. Plasma Sci. 24 (1996) 252.
[6] D. J. Spence and S. M. Hooker, Phys. Rev. E 63 (2001)
015401.
[7] C. G. R. Geddes et al., Phys. Plasmas 12 (2005) 056709.
[8] K. E. Robinson, D. C. Quimby and J. M. Slater, IEEE J.
Quantum Electron. QE-23, (1987) 1497.
[9] V. Ayvazyan et al., Eur. Phys. J. D 37 (2006) 297.
[10] T. Shintake, “First Lasing at SCSS”, Paper MOAAU04,
these proceedings.
[11] E. Takahashi et al., Phys. Rev. E 66 (2002) 021802(R).
[12] M. Xie, Nucl. Instrum. Methods Phys. Res. A445 (2000) 59.
[13] W. M. Fawley, LBNL Technical Report No. LBNL-49625(2002); see also paper MOPPH073, these proceedings.

The Challenge of fs Pulses and Synchronisation

Proceedings of FEL 2006, BESSY, Berlin, Germany

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COMPARATIVE STUDY OF DIGITAL AND ANALOGSYNCHRONIZATION TECHNIQUES FOR LASERS IN ACCELERATORS
Axel Winter, Universität Hamburg, Hamburg, Germany,
Wojtek Jalmuzna, Warsaw University, Warsaw, Poland.

Abstract
Pulsed laser systems play an important role in present
and future light sources. These lasers need to be synchronized very precisely to the accelerator RF. One approachis using an analog controller, which offers low-noise performance and has been demonstrated to achieve sub-50 fs
stability. A digital controller based on a high-performance
FPGA offers more flexibility, for instance the possibility
to implement notch filters to evade the limitations by resonances of the piezo crystal used to adjust the laser cavity
length. This paper presents results obtained with both approaches.

INTRODUCTION
A mode-locked laser serves as an ultra-stable laser master oscillator (LMO) for the proposed optical synchronization system for the European XFEL, which will be tested at
the FEL facility FLASH [1]. Fiber lasers are well suited torealize such an optical master oscillator, because of the easeof coupling to the fiber distribution system, their excellent long-term stability, and the well-developed and maturecomponents that are available at the optical communications wavelength of 1550 nm. A detailed description of thelaser master oscillator can be found elsewhere [3]. Erbiumdoped fiber lasers exhibit an extremely low phase noise
at high offset frequencies making these lasers competitive
with the best low-noise microwave oscillators around. Environmental effects like microphonics and vibrations cause
excessive low-frequency phase noise, which can be significantly reduced by phase-locking the fiber laser to a ultralow noise reference oscillator. Due to the extremely highupper state life time of erbium (1 ms), noise for frequencies above 1 kHz, due to for instance the pump laser, issuppressed.

SETUP OF THE LMO SYSTEM
A schematic of the setup of the LMO system is shownin Figure 1. Two fiber lasers run at a repetition rate of 54
MHz, which is the 24th subharmonic of the accelerator RF
frequency of 1.3 GHz. Part of the laser pulse train is detected using a high-bandwidth photodiode. In frequency
domain, the ultrashort pulses consist of harmonics of therepetition rate with equal energy and a spacing of the repetition frequency. Using a bandpass filter of appropriate

The Challenge of fs Pulses and Synchronisation

PZT-driver

pump
diode

FPGA
from Microwave MO
OSA

AC

27 MHzexception handlingfrom Microwave MO

1.3 GHz

PhotodiodeEDFA

diagnostics
AOM

to links
diagnostics

redundant laser system

Figure 1: Schematic of the proposed FLASH LMO system.

bandwidth, the 23rd harmonic is selected and amplified
to a level of around 5 dbm. The reference signal comesfrom a low phase noise RF oscillator at 1.3 GHz. Both signals are fed to a analog double-balanced diode ring mixer.
The resulting error signal is now amplified by the loop filter, which is either a digital or analog proportional-integral
controller. The proportional and integral part are in parallel, so the advantages of an integrator at low frequencies
can be obtained without compromising the phase margin at
higher frequencies. After being amplified to higher voltage
levels to fit the range of piezo crystals, the signal is fed to apiezo-based fiber stretcher, onto which a substantial part ofthe optical fiber making up the laser cavity is wound. Thisadjusts the repetition rate of the LMO.
To achieve the required uptime of the LMO system, it isbuilt redundant. Both lasers run continuously and should
one of the lasers fail, the backup unit will take over. To
enable an ultra-low residual jitter performance, the highest possible comparison frequency is selected which is 1.3
GHz in our case. This however leaves 24 possible positions where the PLL can catch. If the phase-lock of a failed
unit is reestablished, it cannot be guaranteed that the laser
pulse position is identical to the one of the backup laser
which is now seeding the synchronization system. The solution to this problem is the introduction of a second PLL
into the system. It runs at a comparison frequency which459

Proceedings of FEL 2006, BESSY, Berlin, Germany

DIGITAL CONTROLLER

Figure 2: Schematic of the digital controller architecture.
The digital PI controller was implemented using an inhouse developed controller board for the low-level RF control, called SIMCON 3.1[5]. The application utilizes the
Virtex 2 Pro FPGA, located on the controller. The internal structure of the controller is shown on Figure 2. The
digital controller offers the same functionality as its analog pendant, namely a parallel PI-controller with an optional second order infinite impulse response low-pass filter. The error signal from the double balanced mixer issampled with a sampling frequency of 50 MHz. Then thedata is decimated to provide one valid sample every 1 μs.
Optionally averaging of 50 samples of the error signal canbe used to reduce the ADC noise. The controller transfer
function is applied to the resulting digital signal which isthen converted with a DAC and fed to the piezo driver. For
diagnostic purposes, a flexible data acquisition system wasused. It saves 16 signals over 64 ms (64000 samples ofeach signal) to the external SRAM memory of the SIMCON controller. Two forms of communication were were
implemented: a VME interface and an RS232 serial link.

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Phase (deg)is equal to the repetition rate of the LMO. This leaves only
one zero-crossings where the PLL can catch per revolutionof the laser pulse inside the cavity. The lower frequency
PLL catches first and thus selects the phase of the laser
pulse. Once the lock is established, the second PLL running at 1.3 GHz will take over.
There are two fundamental approaches which can beconsidered for the controller of this system. One choice
is to use a conventional analog controller. It has beenshown, that excellent synchronization performance can beachieved using such a system [4]. The limits of an analog
controller lie in the flexibility it can offer. It is very difficult to realize more complex transfer functions than that ofa simple PI controller. One aspect of where this is helpful is the implementation of a notch-filter to counteract theeffects of the resonance of the piezo crystal in the fiber
stretcher to obtain a higher gain in the PLL. Furthermore
the switching of two PLL’s is significantly easier using a
digital controller which will be described in the next section.

Magnitude (dB)

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Frequency (Hz)Figure 3: Bode Plot of the open loop transfer function(magnitude - blue, phase - red).
All the controller’s parameters can be set with MATLAB
software using a channel independent interface [6].

CONTROLLER TYPE AND SIMULATION
The feedback acts on the cavity length through the piezo
which stretches the optical fiber. Care has to be taken not
to disrupt the laser dynamics through introduced birefringence which occurs if the fiber is bent. The fiber stretcher
is constructed such that bending is avoided and only thelength of the fiber is varied by the piezo. Hence laser dynamics will to first order not be influenced and the laser
will in terms of phase act as an integrator with the transfer
function Gl = ksl , where kl is the gain of the piezo inside the laser cavity (in our case is 0.35 Hz
V ). Mechanicalresonances of the piezo have to be considered (∼ 40 kHz),
which can be modeled by a harmonic oscillator. This yields(2·π·fres )2
a transfer function of G piezo = s2 +4πγf2res ·s+(2πfres )which ultimately limits the achievable gain of the PLL. A
linear response is assumed for the phase detector aroundthe locking point, which is valid for analog mixers aroundthe zerocrossing, i.e. Δφ = 0, π, 2π . . .. The controller
consists of a PI-controller (G P I = KP + KsI ) and an
optional low pass filter with a corner frequency of f lp =10 kHz.
The simulated open loop transfer function is shown in figure 3. The unity gain bandwidth is at 1 kHz which is ingood agreement with the experimental results. It can beseen from Figure 5, that the phase noise spectra of thelocked laser and reference oscillator start deviating justabove 3 kHz which is the point of unity gain.

RESULTSThe first step to compare the performance of the two systems was to lock one LMO to a 1.3 GHz reference andevaluate the residual jitter. Figure 4 shows the power spectral density of the error signal when the system is locked
for both analog and digital controller. The integration ofthese signal yields the respective residual jitter for either
the analog or the digital controller. It amounts to 74 fs forthe analog controller and 107 fs for the digital controller,
both in a bandwidth from 1 Hz to 112 kHz. The differencein performance of the two controllers is almost entirely due

The Challenge of fs Pulses and Synchronisation

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH056

reducing the sampling rate to 1 MHz. This reduces the uncorrelated noise of the ADC by a factor of almost 8.
It is important, that the activated PLL does not increase
the phase noise at higher offset frequencies. The measured
phase noise with and without feedbacks is depicted in figure 5. There is no significant increase in the high frequency
phase noise when locking with either system.
A further important issue is the possible change of the optical properties of the laser pulses due to the phase locking.
The insert to Figure 5 shows the optical spectrum of thefiber laser without any feedback and with either controller.
No significant change was observed for either feedback option.
Figure 4: Power spectral density of the closed-loop error
signal for both analog (black) and digital (red) controllers.

CONCLUSION AND OUTLOOKAn optical master oscillator system requires a precise
phase-lock of the fiber lasers to an external RF clock. Thiscan be achieved by either using a digital or an analog controller. The measured performance for either system wascomparable. No significant differences in the high frequency phase noise or the optical spectrum could be observed. This indicates that the more flexible approach using
an FPGA as a digital loop filter is feasible without compromising the locking performance.

REFERENCES[1] J. W. Kim et. al., “Large scale timing distribution and RFsynchronization for FEL facilities,” FEL Conference 2004,
Trieste, Italy, 2004.
[2] J. Kim, F. X. Kärtner, and M. H. Perrott, “Femtosecond synchronization of radio frequency signals with optical pulse
trains,” Opt. Lett. 29, 2076-2078 (2004).

Figure 5: Phase noise for the locked fiber laser with both
analog (red) and digital (green) controllers and the reference (black). Insert: Optical spectrum of the fiber laser
without feedback (black), with digital controller (red) andanalog controller (green).

to the PLL peaking of the digital controller. This is due toa slightly higher proportional gain which limits the phasemargin of the system and leads to the power spectral density increase around 2 kHz. Reducing the proportional gain
will yield a comparable result to the analog controller. It
should be noted, that a significant part of the jitter in thedigital controller is due to the 50 Hz line. The magnitudeof this perturbation does not change with proportional andintegral gain settings of the controller, making a crosstalkfrom the power supply to the DAC a likely candidate forthe cause. It can possibly be improved in the next redesignof the digital controller board. An advantage of the digital controller is the possibility to average the ADC data.
The sampling rate of the ADC is a lot higher than needed
for the regulation (60 MHz), so an average was employed

The Challenge of fs Pulses and Synchronisation[3] A. Winter et. al., “Towards high-performance optical master
oscillators for energy recovery linacs,” Nucl. Inst. Meth. A
557, 299-304 (2006).
[4] A. Winter et. al., “Femtosecond Synchronisation of Ultrashort Pulse Lasers to a Microwave RF Clock,” Proceedingsof the PAC 2005, Knoxville, TN.
[5] W. Giergusiewicz et. al., “Low latency control board for
LLRF system SIMCON 3.1,” Proc. of SPIE Vol. 5948,(2005).
[6] J. Szewinski et. al., “Software for Development and Communication with FPGA Based Hardware”, TESLA Report
2005-16.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

FIRST TOLERANCE STUDIES FOR THE 4GLS FEL SOURCES
D.J. Dunning, N.R. Thompson, J.A. Clarke and D.J. Scott, ASTeC, CCLRC Daresbury Laboratory
B.W.J. McNeil, SUPA, Department of Physics, University of Strathclyde, Glasgow, UK.

INTRODUCTION
4GLS is a 4th Generation Light Source proposed by
CCLRC Daresbury Laboratory in the United Kingdom tomeet the needs of the ‘low photon energy’ community.
The 4GLS facility will combine energy recovery linac(ERL) and FEL technologies. This paper summarises theresults of first tolerance studies for the XUV-FEL and the
VUV-FEL. For the XUV-FEL, Genesis 1.3 [2] has beenused to simulate the effects of a temporal offset between
the electron bunch and the seed. For the VUV-FEL
simulations, a one-dimensional, time-dependent FEL
oscillator code which includes the effects of electron
bunch arrival time jitter has been used.
The XUV-FEL design [3] consists of an undulator
system directly seeded by a tuneable HHG laser source. It
is capable of generating short, tuneable, high-brightness
pulses of 8-100 eV photons with peak output powers of~2-8 GW and typical FWHM pulse length < 50 fs. The
FEL undulator consists of a lattice of undulator modules
separated by beam focusing elements and diagnostics.
The first eight undulator modules of the FEL will beplanar, while the final five will be of APPLE-II design inorder to produce variably elliptical polarised radiation.

XUV-FEL SIMULATIONS
100 eV Pulse Amplifier Lasing
A simulation of the XUV-FEL operating at 100 eV isperformed, using the CDR parameters for the case of
seed/electron bunch synchronism. The full set of planar
and variable undulator modules are used with the APPLEII undulators set to helical mode so that circularly
polarised radiation is generated. Figure 1 shows the seedpulse of peak power P = 30kW and duration 30 fs
FWHM. Also plotted is the electron beam current of peakcurrent Ipk = 1.5kA and duration 626 fs (18812) FWHM.
At the end of the FEL a peak saturated power of Ppk 3
2.4 GW is shown in Figure 2. A ‘clean’ central seeded
region upon a noisier pedestal is seen. The pedestal is the
pre-saturation SASE - as the shot noise power is only a
few tens of watts, the seed power of 30 kW saturates first.
2000

35

HHG Seed Pulse PowerElectron Bunch Current

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Current (A)The Conceptual Design Report for the 4th Generation
Light Source (4GLS) at Daresbury Laboratory in the UK
was published in Spring 2006 [1]. 4GLS features three
distinct FEL designs, each operating in a different
wavelength range: an externally seeded amplifier
operating in the photon energy range 8-100eV (XUVFEL); a regenerative amplifier FEL operating over 310eV (VUV-FEL); an FEL oscillator operating from 2.5200µm (IR-FEL). Preliminary results of tolerance studies
for the FEL designs are presented. In particular, theeffects of the relative timing offset between the seed pulseof the XUV-FEL and the electron bunch, as well as theeffects of electron bunch timing jitter in the VUV-FEL,
are presented.

To enable variable polarisation, APPLE-II typeundulator sections are employed throughout with a strong
FODO focussing lattice and beam diagnostics distributed
between sections.

Power (kW)

Abstract

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12345678539 2 56523 Figure 1. Input HHG seed power and electron bunch
current as a function of longitudinal position.
1.0E+101.0E+09462

Power (W)

1.0E+08

The VUV-FEL [4] is a regenerative-amplifier-type FEL(RAFEL) [5] designed to deliver intense sub-ps pulses oftuneable coherent radiation in the photon energy range 3–
10eV. A hole-outcoupled low-Q cavity using robust low
reflectivity optics provides sufficient feedback to allow
high gain type FEL saturation after only a few cavity
round-trips. In its standard operating mode the VUV-FEL
will generate temporally coherent photon beams withpeak power ~500 MW and FWHM pulse lengths of~170 fs. Cavity length adjustment may allow superradiantoperation with enhanced peak powers of ~3 GW and
FWHM pulse lengths of ~25 fs. These figures are themaximum values across the full wavelength range.

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12345678539 2 56523 Figure 2. Radiation power at the exit of the XUV-FEL
showing peak power Ppk 34567489.

The Challenge of fs Pulses and Synchronisation

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH057

100eV Pulse Amplifier Lasing with Offset Seed

2.5E+09

The above results are for synchronism between the peak
HHG power and the peak of the electron bunch current.
However, there may be an inherent noise associated withthe arrival time of each bunch which results in a relative
timing offset of magnitude 12. Simulations have been
carried out in which312 is varied, as in Figure 3 (top). Also
shown (bottom) is the radiation power at the end of the
FEL, with the synchronous seed case for comparison. For
seed offset of 12 = 100 fs, the peak power is reduced from
2.4 GW to 1.7 GW.

2.0E+09

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Figure 4. The effect of an offset 12 from electron/seedpulse synchronism upon the peak output power at the endof the FEL, for 100 eV operation.

1600

Comparison with FEL design formulae

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25

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The Xie design formulae [6] have been used to estimate
the effects of timing offset on the saturation power. Thishas been done by correlating the timing offset 12 with thebeam current via the relation:

400
5⎛ (Δt ) 2 ⎞2 ⎟⎝ 2σ e ⎠ .

I ( Δt ) = I pk exp ⎜ −

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12345678539

2 56523 

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This was carried out for the planar modules only. In
Figure 5 these results are compared with the results ofGenesis simulations which are seen to yield a slightly
more stringent restriction on 12.

2.5E+09
30um offset
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Synchronous

Xie
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12345678539 2 56523 Figure 3. (Top) Seed offset by 100 fs (30 1m) behind theelectron pulse and (bottom) radiation power at the end of
the FEL for the offset case (red) and synchronous case(blue).
The offset, 12, was varied between ± 250 fs and resultsof peak power against offset plotted in Figure 4. These
results suggest that electron bunch offset should be
limited to approximately ± 45 fs for peak output power tolie within 90% of the synchronous peak power Ppk.
From Figure 4, it is noted that the peak output power atthe end of the FEL is higher for a negative 12 (seed pulse
arriving behind the electron bunch) than for a positive
offset of the same magnitude.

The Challenge of fs Pulses and Synchronisation

0.0-250 -200 -150 -100

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1234567

Figure 5. Simulations of the effect of an offset3 12 fromelectron/seed pulse synchronism upon the peak power atthe end of the FEL. The results are scaled with respect totheir synchronous values at 12 = 0.

VUV-FEL SIMULATIONS
A one-dimensional, time-dependent FEL oscillator code
(FELO [7]) has been used. The code includes the ability
to model a temporal jitter in the electron bunch arrival
into the FEL cavity (this effect is simulated by adding ajitter to the cavity length).
The simulated output power and pulse width variation
with cavity length detuning is shown in Figure 6 for 10eV
operation in planar mode. For cavity length detuning of181234 5674 89 74 564 4 t a maximum. Typical pulse
shape evolution with cavity pass number is shown in
Figure 7. These simulations replicate start-up from shot-

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Proceedings of FEL 2006, BESSY, Berlin, Germany

noise, with the output pulse typically developing tosaturation over 10-15 passes.

350
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Figure 6. Plots of peak power and pulse width against
1234567 89 5 7 95 4 7 c) for simulations of the VUVFEL operating at 10eV in planar mode.

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Figure 7. FELO simulation of the VUV-FEL at 10eV and
123456789 5 7 95 4 77745 79798915 7 1 7
arrival time jitter. The red points show the peak intensityof the pulse at each pass.

P [MW]

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t [ps]

Simulations with Electron Bunch Time Jitter
In Figure 8 the variation of pulse shapes for different
cavity pass numbers are plotted for three different
electron bunch arrival time jitter values. Increasing jittershows increasing variation of the pulse shape with pass
number. The pulse shape remains approximately Gaussian
for the cases where jitter  ± 80 fs. For the greater jitter
value of ± 120 fs, the output pulse is seen to have a lessstable shape.

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Figure 8. Variation of pulse shape with cavity pass
number for electron bunch arrival time jitters of ± 40 fs(top), ± 80fs (middle) and ± 120 fs (bottom). Only passes
13 to 30 are shown. Increasing the temporal jitter showsincreasing variation of the pulse shape.

Analysis of output power
Due to shot noise, repeat runs from the same input data
yield slight variations in output. For jitter = 0, five runs
were carried out and an average peak power was plotted
as shown in Figure 9.

The Challenge of fs Pulses and Synchronisation

Proceedings of FEL 2006, BESSY, Berlin, Germany
400

Short-pulse operation of the VUV-FEL

350

For a cavity length detuning of 1.7 92tion is insuperradiant mode, peak output power is near maximum
and the pulse width is at a minimum (see Figure 6).
Simulations using the FELO code show that at this cavity
length detuning, it is possible for the side-spikes todevelop into the peak with maximum power [8]. The
evolution of the pulse where electron bunch arrival time
jitter = ± 40 fs is shown in Figure 11.

300
Peak Power [MW]TUPPH057

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average

Figure 9. Peak power of pulse with pass for repeated runs
at jitter = 0. The variation between different runs is due tothe effect of shot noise only.
Repeated runs were carried out for different jitter values
and the RMS variations from this average (at saturation)
were calculated and are presented in Table 1.
Table 1. Variation of saturation power for different valuesof electron bunch arrival time jitter.
Jitter (fs)Saturation Power (MW)± 0.0

300 ± 2.5%± 20

300 ± 4.1%

± 40

300 ± 6.0%

± 80

300 ± 8.0%

± 120

300 ± 18.8%

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Figure 11. Pulse shape evolution for short-pulse operation
with electron bunch arrival time jitter of ± 40 fs.

CONCLUSION

For the case of maximum jitter where the pulse shaperemains approximately Gaussian (jitter = ± 80 fs), theoutput power at saturation is ~300MW ± 8%. The
evolution of pulse shape with pass is shown for jitter of ±80 fs in Figure 10.

First tolerance studies for the 4GLS XUV-FEL and VUVFEL have been carried out. For the XUV-FEL, increased
offset between seed and electron pulse has been shown todecrease saturation power. For the VUV-FEL electron
bunch arrival time jitter has been shown to result inincreased instability in the shape of the output opticalpulse. It has been concluded that for the XUV-FEL,
temporal electron bunch offset should be limited toapproximately ± 45 fs for output power to be within 90%
of optimum. For the VUV-FEL, jitter should be limited toapproximately ± 80 fs for approximate Gaussian output
with peak power within ± 8 % of optimum.

500

REFERENCES

P [MW]

400
300
200
100
0
0
0.2
t [ps]

30

0.4

20
0.6

10

pass

0

Figure 10. FELO simulation of the VUV-FEL at 10eV for
123456789 5 7 95 4 77745 7jitter of ±80 fs. The
red points show the peak intensity of the pulse at eachpass.

The Challenge of fs Pulses and Synchronisation[1] 4GLS Conceptual Design Report, Council for the Central
Laboratory of the Research Councils, UK (2006), available
from: http://www.4gls.ac.uk/documents.htm#CDR[2] S. Reiche, Nucl. Inst. Meth. Phys. Res. A, 429, 243, (1999)[3] B.W.J. McNeil et al, ‘The Conceptual Design of the 4GLSXUV-FEL’, these proc.
[4] N.R. Thompson et al, ‘A 3D Model of the 4GLS VUV-FEL
Conceptual Design Including Improved Modelling of the
Optical Feedback Cavity’, these proc.
[5] B. W. J. McNeil, IEEE J. of Quantum Electron., 26, 1124
(1990)[6] Ming Xie, Proc of 1995 Part. Accel. Conf., (1996) p183.
[7] B.W.J. McNeil et al, ‘FELO, a one dimensional timedependent FEL oscillator code’, these proc.
[8] D.J. Dunning, ‘Results of simulations varying the electron
bunch arrival time jitter for the 4GLS VUV-FEL’, Internal
Report fgls-upcdr-rpt-0013, 2006.

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PHASE NOISE COMPARISON OF SHORT PULSE LASER SYSTEMS
S. Zhang, S. Benson, J. Hansknecht, D. Hardy, G. Neil, and M. Shinn
TJNAF, Newport News, VA23606, USA.
Abstract
This paper describes phase noise measurements of several
different laser systems that have completely different gain
media and configurations including a multi-kW freeelectron laser. We will focus on state-of-the-art shortpulse lasers, especially drive lasers for photocathodeinjectors. Phase noise comparison of the FEL drive laser,
electron beam and FEL laser output also will bepresented.

RF Signal
Generator
Reference
RF signal

Phase
Detector

METHOD AND SETUP
Phase noise is a drive laser quantity that is often
discussed. Phase noise is a direct representation of thetiming jitter of a mode-locked laser system. Timing jittercan be quantified by measuring the phase noise. There
are two basic methods widely used to measure the phasenoise (and timing jitter) of optical pulse trains; a) the
Phase Detector Technique (PDT) and, b) the PowerSpectral Density Technique (PSDT) [1]. The PSDT
provides better precision and was used for all of themeasurements described below. The measurement
requires a fast photodiode and a spectrum analyzer. In thiscase the timing jitter of the mode-locked or gain-switched
optical pulse train is determined by measuring the phasenoise spectral density.

466

Motor
control

PZTControl

ML Laser
Oscillator

photodiode

INTRODUCTION
The stability of the drive laser plays a very importantrole in the performance of photogun-based acceleratorsand free-electron lasers (FELs). With the increasing
demand for shorter wavelengths (including XFEL) andshorter pulse duration (sub-50 fs), phase noise and timing
jitter issues are drawing more and more attention. Overthe past decade, short pulse lasers technology has seen
dramatic advancement due to the rapid development ofsolid-state materials and high power semiconductor laser
diodes. Some state-of-the-art femtosecond lasers haveshown superior performance in terms of both amplitude
and phase stability. These lasers provide a unique
opportunity to overcome challenges in the development of
the next generation accelerator light sources.
The photogun drive laser is used to extract the electron
beam that provides the gain medium for numerous FELs
worldwide. Drive laser instabilities will limit high power
FEL operation. Of all the instabilities associated withshort pulse high repetition rate lasers, timing jitter appears
to be the most important and most difficult to control. In
this paper, we present phase noise and timing jittermeasurements of several different lasers that can be used
to drive photoguns. We believe a comparison of theselasers provides valuable information about the pros andcons of each system in their specific applications.

Loop gain& filter

Laser beam

Fig.1. Schematic of a generic phase locking system.
PD

BS

L

F
ATN
AMP

Laser beam

SSA
E5052

Fig.2. Schematic of the timing jitter measurement
setup. BS, beam splitter. ATN, attenuator. L, lens. PD,
photo-diode. F, RF filter. AMP, RF amplifier.
Fig.1 shows the basic principle of a generic phaselocking system used by many lasers. The laser phase error
is detected and corrected by the RF feedback loop. The
measurement setup is shown in Fig.2. The detectors usedin the experiment were fast photo-diodes with bandwidth
between 2 to 20 GHz. A Signal Source Analyzer (SSA,
Agilent E5052A) was used for the phase noise and timing
jitter data acquisition. This instrument presents faster
speed and better precision compared with some otherspectrum analyzers. The phase noise is usually measured
at 1.497 GHz, the 20th harmonic of the 74.85 MHz laser
pulse frequency in order to minimize the laser amplitude
noise. The 1.497GHz signal was filtered out using an RF
filter and amplified by a low noise RF amplifier before
being fed into the SSA. For higher repetition rates, it was
sometimes difficult to perform the measurement at the20th harmonic. The noise added to the measurement fromthe RF amplifiers and filters was determined to be
negligible.

DIFFERENT LASER SYSTEMS
Flash-lamp-pumped Active Mode-locked Laser
The first laser system tested was a frequency doubled
CW mode-locked Nd:YLF laser pumped by flash lamps

The Challenge of fs Pulses and Synchronisation

Proceedings of FEL 2006, BESSY, Berlin, Germany(Coherent Antares laser made in early 90’s). It has served
as the drive laser for the photocathode injector at the JLab
FEL facility for more than ten years. We studied thestability of this laser in the past [2]. Here we will focus on
the phase noise characteristics. The laser has a folded
cavity design and intracavity acousto-optic modulator(AOM) for mode-locking. The AOM can be driven with
RF supplied by the laser power supply (internal RF) orwith RF from the accelerator (external RF). The laser
phase is monitored and controlled by the RF control
module. A fast photodiode detects the optical pulses
signal from the infrared light leaking through the highreflector. Unlike most other laser systems that use active
laser cavity length adjustment to minimize the phasenoise, the RF to the acoustic mode-locker on this laser istuned to compensate the phase change. To detect thephase error and complete the phase loop, the 20th
harmonic of the laser frequency (74.85 MHz) is filteredout, amplified and sent to an RF control module.

TUPPH061

From the results shown in Fig.3, the excellent
performance is primarily due to the fact that the laser
cavity was designed to have a particularly stable length:
all components are mounted to an Invar rod to reduce
temperature dependence. In addition, the phase control
loop associated with the RF reference signal is very
important, as can be seen by comparing the two RF
sources, internal and external. The laser performs
significantly better when using RF supplied by theaccelerator, with timing jitter five times less compared tothat obtained with RF supplied by the power supply.
Most of the phase noise comes from the lower frequency
band below a few hundred Hz. There are always morenoises below 10Hz and the feedback loop does little toreduce them (Fig.3(c)). Usually a flash-lamp pumped
laser tends to have noticeably higher phase noise thanthose pumped by diodes. But this measurement clearly
indicates that the phase noise of a flash-lamp pumped
system can be controlled to a very low level.

Phase noise (dBc/Hz)-40
Timing jitter-60

SESAM Mode-locked Laser

Ext RF 239fs
Int RF 1.49ps

-80
-100
-120
-140
1

10

2

3

10

4

5

10
10
Frequency (Hz)

6

10

10

Timing jitter-100

Ext RF 101fs
Int RF 87fs

-120
-140

Phase noise (dBc/Hz)

Phase noise (dBc/Hz)

(a)

-160
3

4

10

5

10

10
10
Frequency (Hz)

6

7

10

(b)
-40
Phase noise (dBc/Hz)

The SESAM mode-locked Nd:YVO4 laser serves as
the master oscillator, providing seed pulses for a multistage amplifier that provides over 50 W average power at
1.064 um and 25 W at 532 nm. This Maser-OscillatorPower-Amplifier (MOPA) system will be used to drive a
100mA photoinjector. A detailed system description canbe found in another paper [3]. The passively mode-locked
Nd:YVO4 laser is diode-pumped and produces over 500
mW at 1064 nm with 74.85 MHz pulse repetition rate and25 ps pulses (Time-Bandwidth Product, GE100). It uses a
semiconductor saturable-absorber mirror (SESAM) toinitiate mode-locking. The laser cavity length is actively
stabilized and the phase of the optical pulse train can belocked to an external RF reference signal.

Timing jitter

370fs
-80
-100
-120
-140

Ext RF 1.8ps
Int RF 2.1ps-60

Timing Jitter

-60

1

10

-80

2

10

3

4

10
10
Frequency (Hz)

10

5

10

6

-100
-120
-140
0

10

10

1

2

10

3

4

10
10
Frequency (Hz)

10

5

6

10

(c)
Fig.3. Phase noise spectral density plots of flash-lamped
pumped Antares Nd:YLF laser at different offset
frequency. (a)10 Hz~1 MHz. (b)1 kHz~40 MHz, and (c)1
Hz~1 MHz. As explained in the text, Ext and Int refer toexternal RF and internal RF, respectively.

The Challenge of fs Pulses and Synchronisation

Fig.4. GE100 laser phase noise spectral density plotsobtained over few minute time period. Mostly, the timing
jitter is less than 400 fs but occasionally larger values are
obtained.
When the laser cavity is optimized, it runs very wellwith timing jitter around 300 fs. Random fluctuations canbe seen from time to time, which may be caused byenvironmental disturbances. Phase noise spectral density
plots for this laser are shown in Figure 4. These plots
were obtained over a few minutes and mostly timing jitter

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Proceedings of FEL 2006, BESSY, Berlin, Germany

is less than 400 fs but occasionally values surge over
500fs. We also intentionally unlocked the cavity length
feedback loop. This has a profound affect, with timing
jitter increasing to 4 ps (Fig.5). The overall timing jitter
also depends highly on the laser cavity alignment andoptimization. Timing jitter values can exceed 1ps in thecase of poorly aligned cavity.
Phase noise measurements were also made downstreamof the power amplifier section of this laser system. The
Master oscillator (MO) seed light from the passively
mode-locked Nd:YVO4 laser passes through four
Nd:YVO4 amplifiers, with total output power at 1.064 um
greater than 50 W. As expected, the diode-pumped
amplifiers do not add much noise to the system (Fig.6).
The added noises are most likely from the environment.
Phase noise (dBc/Hz)-20

cavity length with a pico-motor and PZT attached to thehigh reflector (HR) end mirror. A photodiode picks up thelaser signal from a beam splitter and the phase iscompared to the reference RF to create a phase error
signal. The pulse repetition rate is 74.85 MHz, the same
as for measurements with other laser systems. Phase noise
spectral density plots are shown in Fig.7 formeasurements at two different times. As with the
SESAM mode-locked laser, phase noise was closely
related to cavity alignment and optimization. The timing
jitter was observed to jump up and down, but mostly
values stay within a range between 200 and 400 fs (Fig.
8). When the feedback loop was turned OFF, timing jitter
values surge upward by a factor of ten.

Timing Jitter-40

Locked 320fs
Unlocked 4ps

-60
-80
-100
-120
-140
1

10

2

10

3

4

10
10
Frequency (Hz)

10

5

10

6

Timing Jitter

-60

380

Oscillator 320fs
Amplifer 390fs

-80
-100
-120
-140

Case 1Case 2

360
340
320
300

1

10

2

10

3

4

10
10
Frequency (Hz)

10

5

6

10

Fig.6. MOPA laser: GE100 laser and multistage power
amplifier. Phase noise spectral density plots comparing
MO and MOPA signals.

KLM Ti:sapphire Laser
Widely used fs-pulse Ti:sapphire lasers rely on selfmode-locking (KLM), a passive technique that relies on
Kerr lensing within the Ti-sapphire crystal and a gain
aperture effect that provides more gain for shorter pulses.
These lasers are broadly tunable and can generate
extremely short pulses because of the exceptionally broadgain bandwidth of the lasing medium.
Phase noise measurements were carried out using a
Spectra Physics Kerr mode-locked Ti:sapphire laser(Tsunami, 100fs, 1W at 800nm) pumped by a frequencydoubled and diode pumped Nd:YVO4 laser (Millennia,
CW 10 W at 532 nm). The laser has a phase-locking unitthat detects and corrects the laser phase by adjusting the468

Fig.7. Tsunami laser phase noise spectral density plots
at two different times.

Timing Jitter (fs)Phase noise (dBc/Hz)

Fig.5. GE100 laser phase noise spectral density plots withlaser cavity length feedback loop open and closed.

280
0

20

40

60

80

Time (minutes)

Fig.8. Tsunami laser. Timing jitter versus time. The
square and the triangle stand for the data taken at two
separate times.
The Tsunami laser uses an intracavity AOM to initiate
and stabilize mode-locking. We investigated the influenceof the AOM on timing jitter by making phase noise
measurements with the AOM on and off. Measurements
indicate that the AOM does not introduce additional
instability. This confirms that AOM only helps to start
the KLM process and set the fundamental frequency forthe feedback loop to lock the cavity length. Once thecavity is optimized and loop is closed, AOM is notneeded.

Gain-switched Diode Laser
Gain-switched diode lasers have a number ofadvantages over mode-locked lasers such as simplicity,

The Challenge of fs Pulses and Synchronisation

Proceedings of FEL 2006, BESSY, Berlin, Germany
good stability and low cost. They also provide a wide
range of pulse repetition rates independent of laser cavity
length. While there is no doubt about amplitude stability,
we did an investigation of phase noise performance. The
laser system consists of a sub-milli-watt gain-switched
InGaAs laser at 1.56 um and a fiber amplifier to boost thepower to a level suitable for the measurement. Gainswitching at frequencies below 100 MHz produces longer
optical pulses with tails, so a step-recovery diode (SRD)
was used to improve the temporal profiles of the laser
pulses. There is no cavity length adjustment for thissystem.

stabilization. The phase noise rises dramatically at all offset frequencies, especially at the higher bands. If we lookat the electron bunches in the wiggler region, they
actually appear to be very quiet (timing jitter less than 60fs). The phase noise actually gets suppressed compared tothe drive laser. The two curves in Fig.10 for FEL weretaken at two different times to show the random
fluctuation during the same machine operation. In view ofthe exceptionally long FEL laser cavity length, the FEL
output is remarkably stable. However, this measurement
suggests that the FEL phase noise could be reduced using
feedback mentioned in earlier sections.
-40-60
Timing jitter-70

Phase noise (dBc/Hz)

Phase noise (dBc/Hz)

TUPPH061

50MHz/662fs
300MHz/484fs
750MHz/228fs

-80
-90
-100
-110

DL 319fs
FEL 3.368ps
FEL 2.364ps
E-bunch 56fs

-60
-80
-100
-120
-140

-120
10

1

10

2

3

4

10
10
Frequency (Hz)

10

5

10

6

1

10

2

10

3

4

10
10
Frequency (Hz)

5

10

6

10

Fig.9. Phase noise spectral density plot and timing jittersof gain-switched diode laser and fiber amplifier at threedifferent repetition rates.

Fig.10. FEL phase noise spectra. The carrier
frequency is 1.49 GHz. Laser frequency is 9.37 MHz.
Lasing wavelength is 1.6 um. DL, drive laser. Ebunch, electron bunches.

Phase noise spectral density plots for the gain-switched
diode laser at three pulse repetition rates are shown in
Figure 9. The timing jitter increases inversely with thepulse frequency. At the lowest frequency 50 MHz, thetiming jitter is larger than lasers mentioned previously.
Note for the 50 MHz case, the phase noise at frequencies> 1 kHz is noticeably higher. The RF generator used hereis the same as the previous lasers. The possible
contribution to the noise is poor impedance matching at
the SRD and driving circuits. The signal from the SRD
shows different waveforms as the RF frequency andpower changes. It requires a good balance between theseparameters including the near threshold DC bias. Further
work is needed to improve the performance before they
can be adapted into the FELs.

We have presented the phase noise characteristics ofseveral lasers that can be used to drive GaAs photoguns.
The performance of each laser depends on the phaselocking mechanism. Active cavity length adjustment
remarkably reduces the phase noise. The overall phasenoise appears unrelated to the optical pulse length. The
flash-lamp-pumped system does not necessarily have to
be noisier. Diode-pumped amplifiers present very minor
noise addition to the seed pulse. The gain-switched laser
is good for repetition rates over 100 MHz but needs
improvement to be used at sub-hundred MHz band.

High Power FEL
So far we have only talked about lasers with cavity
lengths of 1.5 m or shorter. We also studied the phasenoise properties of the high power JLab FEL, with output
power over 1kW (pulse-width about 200 fs andwavelength 1.6 um). The FEL laser cavity is composedof two mirrors separated by 32 m. The mirrors sit inside
vacuum chambers: the laser cavity length can be tuned
over 1 cm with resolution sub-micron but there is noactive cavity length control.
Phase noise measurements were made under different
FEL operating conditions. Results are presented in
Fig.10, together with the noise spectrum of the Antares
drive laser. The FEL timing jitter is on the same level asother lasers, even operating without cavity length

The Challenge of fs Pulses and Synchronisation

SUMMARYACKNOWLEDGMENT
The authors would like to thank M. Poelker for reviewing
and extensive editing. This work is supported by the
Office of Naval Research, the Joint Technology Office,
the Commonwealth of Virginia, the Air Force ResearchLaboratory, and by DOE Contract DE-AC05-84ER40150.

REFERENCES[1] D. von der Linde, Appl. Phys. B 39,201 (1986).
[2] S. V. Benson, M. Shinn, 16th IEEE Particle
Accelerator Conference (PAC 95) and International
Conference on High-energy Accelerators (IUPAP),
Dallas, Texas, May 1995. PAC, vol. 2(1052-1054).
[3] S. Zhang, S. Benson, et al., in Proceedings of the 27th
International FEL Conference, SLAC, CA, August,
2005, pp. 351-354.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

A MECHANICAL SHUTTER TO SELECT SINGLE BUNCH TRAINS AT
THE FLASH FACILITY AT DESY
Martin Bräuer, now at SIEMENS Medical Solutions, 91052 Erlangen, Germany
Ulrich Hahn, and Sven Toleikis, Deutsches Elektronen-Synchrotron DESY, 22603 Hamburg,
Germany.
Abstract
A fast mechanical shutter to select single photon bunchtrains of the free electron laser FLASH is described.
FLASH is installed at the Deutsches ElektronenSynchrotron DESY in Hamburg and is based onsuperconducting linear accelerator technology. The
accelerator provides bunch-trains with a repetition rate
between 5 and 10 Hz. This time interval of down to 100
ms makes it possible to use a mechanical shutter system
to select single bunch-trains for sample excitation.
A programmable logic controller (PLC) is used to steer
a servo system based on an electronically commutated(EC) low-voltage motor. To select a bunch-train, themotor is started at the time when one train passes thestation. During the following 100 ms, the cylinder isturned by 180°, leading to a movement of the shutter by
48 mm to the fully open position, thus allowing thepassage of the following bunch-train. During the next 100
ms the rotation is continued to the 360° position, thus
blocking the next bunch-train by pushing the shutter backto the fully closed position.

The fast shutter consists of a glassy carbon [2] shutter
blade with a thickness of 4 mm. The blade motion is
generated by a special linear drive developed for fast wire
scanners for FEL electron beam diagnostics [3, 4]. The
shutter covers the beam aperture of 20 mm.
In this paper, we report on the technical layout of thefast shutter, and first experimental results of a timeresolved damage and ablation measurement are presented.

TECHNICAL LAYOUT
Mechanical Set Up
Figure 2 shows the mechanical design of the fast
shutter. The central part is the glassy carbon blade
connected to the linear drive unit. Glassy carbon is chosenbecause of its low density of 1.6 g/cm3 combined withhigh mechanical stability, good reflectivity in the spectral

fast shutter

INTRODUCTION
Since 2005 the first FEL user facility for soft X-ray
coherent light experiments FLASH is in operation at
DESY [1]. The facility consists of a superconducting
accelerator in combination with a 30 m long undulator
producing highly intense (~GW) and extremely short(~10 fs) photon pulses. The superconducting linear
accelerator creates and accelerates bunch-trains with up to7200 bunches within 800 ȝs (at 10 Hz).
The experimental hall of the user facility is locatedapproximately 30 m behind the last dipole magnet which
separates the electron and the photon beam. The photon
beam transport system delivers the FEL radiation underultra high vacuum conditions to the five different end
stations, which can be used alternatively.
The photon pulses energies are generated with anaverage energy of 10 ȝJ. Solid state samples irradiated innormal incidence are easily destroyed when the photons
are focused to a spot size of ~20 ȝm. To study suchdamage processes it is important for FEL users to control
the irradiation process. The 5 to 10 Hz repetition rate of
the bunch trains allows the use of a mechanical shutter toselect single bunch trains for sample irradiation.
The fast mechanical shutter is installed in the sharedpart of the first three beamlines. Figure 1 shows the
shutter installed in the beamline system.

470

beam
ion pump
beamshutter
control cabinetwith PLC
Figure 1: The fast shutter installed in the FLASH beamline system.
range of the FEL and the thermal robustness of carbon.
The fast shutter has to be operated under ultra highvacuum conditions. As linear vacuum feed through awelded bellow is used. An incremental length gauge forposition detection is connected to the linear drive. The
essential features of the fast shutter are the stroke of 48
mm combined with a maximum shutter speed of 1 m/s inthe linear velocity range of 24 mm. The speed is needed
to shorten the opening and closing times into the ms
range. The movement of the shutter blade is based on aslot winding cylinder (see Fig. 2 + 3) transforming therotation of the servo motor into a linear motion [3, 4].

X-ray Optics and Detectors

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH064

speeds of the shaft of 450rpm and accelerations of
6750rpm/s are needed.

linear drive

stroke

Servo
motor

[mm]
velocity

slot winding
cylinderacceleration

shutterblade

strokeFigure 3: The transfer functions of the slot winding
cylinder (Bestehorn sinuide).

Electronic Set Up
beam

Figure 2: The mechanical layout of the fast shutter.
The cam of the slot winding cylinder uses the transfer
function of a Bestehorn-sinuide (see Fig. 3):

S

s 0 >Ȧ t  1 2 ʌ sin 2 ʌ Ȧ t @0 d Ȧt d 1

where S is the stroke of the run up and down phase, s0
the maximal stroke of 24 mm and Ȧt the normalized
transmission angle. The region Ȧt = 0 until Ȧt = 1/2
represents the run up phase while Ȧt = 1/2 until Ȧt = 1
describes the run down phase. The speed and acceleration
is given bySc

s 0 Ȧ > 1  cos 2 ʌ Ȧ t @Scc

s 0 Ȧ 2 2 ʌ sin 2 ʌ Ȧ t
0 d Ȧt d 1

At a stroke of 0mm the shutter is totally closed. The start
up range between 0 and 12 mm accelerates the shutter tothe opening speed of 0,36m/sec. Between 12 and 36 mm
the shutter blade releases the photon beam aperture of
20mm. In the range from 36 to 48 mm the shutter blade
changes the moving direction. When the blade transfers
this range the photon bunch train can pass the shutter.
Figure 3 shows the stroke, speed and acceleration of theblade during one turn, assuming that the shaft is rotatingwith constant speed.
The motor is connected to the slot-winding cylinder
with a gearing-ratio of 15:1. For 10Hz operation, rotation
X-ray Optics and Detectors

The electrical setup of the fast shutter is shown in Fig.
4. The central part is a PLC-controller with IO-Modules[5]. The controller acts on a servo system via a field-bus(CAN open [6]). The servo system consists of the servo
controller/amplifier, the motor and two integrated
feedback systems [7]. These components alone allow the

PLC

PC

IO modules

Profibus
masterencoder
readout
linearencoder

CANopenmaster- trigger in- temperature- lamps out- buttons in

servocontroller

motor

encoder
feedbackhall feedback
standalone system

Figure 4: Layout of the electronic set-up.
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Proceedings of FEL 2006, BESSY, Berlin, Germany

operation of the fast shutter. In addition a PC, housing a
Profibus-master card, was connected to the PLC. With the
PC the parameterization and programming can be
performed. Furthermore a Profibus-interface to read out
the linear gauge is connected to the Profibus line. The
linear gauge can only be accessed by the PC and be used
for an independent feedback of the shutter position for
diagnostics. All major components are described in thefollowing.
All electronics parts are standard components from thegeneral automation market. They are contained in astandard compartment, as shown in Fig. 1. Most space is
occupied by the power supplies and the terminals to routethe various electrical signals.
The PLC controller is programmed and parameterised
from an external PC, but operating in a standalone mode
afterwards. The cycle time for the SPS program waschosen to run at 3ms, which means that the whole
program is running within 3ms under any condition whilesampling inputs and setting outputs. The controller acts asa client on the Profibus and reactions to Profibus
commands can be programmed. This allows the control
from a master PLC in our case running on the PC. The
connection to the beamline interlock system can be routed
via this bus.
For the CANopen subsystem, the controller acts as amaster. The CANopen subsystem is running with thecycle time of the PLC, allowing a fast reaction on events.
Inputs and outputs are provided by appropriate IOmodules. Most important inputs are the user commands,
generated by output cards of the FLASH experimental
control system, by button states and the bunch signal.
The bunch signal, derived from the FLASH-timing,announces the arrival of a photon bunch. This signal isstretched to 10 ms to be detected by the PLC.
The servo system uses an electronic commutated motor.
While the controller/amplifier is connected to 48V DC,
the motor is provided with two sinusoidal voltages to its
static coils. The rotating permanent magnet follows thegenerated current. In contrast to a stepper-motor, the rotor
position is measured by hall-elements to determine theabsolute position of the magnet. To reach the ultimate
precision for the velocity and position-control loops, anadditional incremental encoder is attached to the motor
shaft.
The controller firmware enables the user to work withthe three nested servo-loops (current, velocity andposition) in an easy way. Parameters are determined by anautomatic tool and are stored together with further
application specific data on the internal flash memory.
Due to the CANopen standard, devices of various vendors
can be mixed and exchanged, securing investments overthe coming years.
In contrast to stepper-motors, the servo system can use
a much larger speed-torque parameter space due to theactive regulation.

472

Operational Principle
The shutter can be opened and closed by electricalsignals, i.e. generated by buttons. The user commands arerouted by the FLASH-control system via output-cards to
5V inputs of the PLC. Status information is transferredfrom the PLC via 5V terminals and input-cards to theuser.
The states of the shutter are: ‘open’, ‘close’, ‘single
shot’, ‘synchronized shot’ and ‘home’.
The home-mode is needed to orient the controller after
power up. The shutter is driven to the open position until
a precision switch mounted close to the open position istriggered.
All other movements are always executed
synchronously to the bunch-trains.
After an open or close signal, the next following bunchtrain-clock is waited for. When the PLC detects a risingedge on the bunch-signal, the motor is commanded toperform a 180ºrotation of the cylinder. This is thuschanging the state of the shutter from closed to open or
vice-versa.
After the detection of a single-shot signal, theprocedure is executed in the same way but initiating a
360º turn of the cylinder. The timing of the later
procedure is depicted in Fig. 5.

arriving bunches

time

open
close

Start

bunch
signal
PLC cycle

Figure 5: Timing scheme of the synchronous movements.
The synchronised move allows to trigger a single shoton an external 5V or TTL signal, generated by users
instrumentation.
Since the bunch-train-frequency of FLASH can be
adjusted by the operation-crew, a part of the PLCsoftware evaluates the frequency of detected bunch
signals and automatically adjusts the appropriate velocity
and acceleration values.

FIRST EXPERIMENTS
One of the first experiments that used the fastmechanical shutter at FLASH was a time-resolved
damage and ablation measurement [8]. The aim of thisexperiment was to study the interaction of ultra short FEL
pulses in the VUV wavelength range with solid state
surfaces at moderate irradiation intensities (I=1011-1014
X-ray Optics and Detectors

Proceedings of FEL 2006, BESSY, Berlin, Germany

W/cm²). The irradiation with ultra short VUV pulses
permits a high degree of electronic excitation but
essentially without any non-linearity. In addition, theincreased absorption depth for some materials helps tominimize the influence of transport effects, e.g., carrier
diffusion and heat conduction. Therefore, ultra short VUVpulses allow the preparation of rather well defined
excitation conditions in relatively large sample volumes
as compared to femto second optical pulses. To directly
study the dynamics of ultra fast VUV-induced phasetransitions and ablation, time-resolved measurements of
the optical reflectivity have been performed in a VUVpump - optical probe configuration. The VUV pulse(Ȝ=32 nm) is used for sample excitation and a delayed
visible probe pulse (Ȝ=532 nm) serves as illumination inan optical microscope. This allows to follow thereflectivity evolution of the VUV irradiated surfaces withboth temporal and spatial resolution.

TUPPH064

duration to about 10 ps, this transition is most likely ofelectronic nature and occurs on sub-ps time-scales.
Already after 10 ps the decrease of the reflectivity in thecentre of the spot, where the fluence is highest, marks theonset of ablation. However, even after 18 ns ablation has
not come to an end and the irradiated surface has notreached its final state.
The main goal of this measurement at FLASH was toestablish the experimental technique and to obtain a first
overview of the dynamics of the induced processes.
Further measurements with enhanced temporal (<100 fs)
and spatial resolution will follow which would provide amore detailed picture of these processes. Compared withfemto second optical excitation distinct differences in thematerial response have been observed that are attributed
to the larger absorption depths of the VUV radiation andthe absence of non-linearity.

CONCLUSIONS
On the basis of existing wire scanner technology a fast
shutter has been implemented in the FLASH beamline
system. This allows users to choose single bunch trains
with a repetition frequency of up to 10 Hz. First
experimental results show the benefit of the fast shutter.

REFERENCES[1] V. Ayvazyan, et al., “First operation of a FreeElectron Laser generating GW power radiation at 32
nm wavelength”, Eur. Phys. J. D 37, (2006), 297-303[2] Glassy carbon, SIGRADUR®, HTW Hochtemperatur
Werkstoffe GmbH, Germany

Figure 6: Surface of Si-wafer after irradiation with a <50
fs FLASH pulse (Ȝ=32 nm) with a fluence of 1 J/cm².
Frame size is 120 x 80 μm².
During the measurement FLASH was running in asingle bunch operating mode having only one bunch inthe bunch train. The mechanical shutter allowed theirradiation of the samples with exactly one ultra short
VUV pulse of known intensity which was measured witha gas monitor detector system [9]. After irradiation thesample is moved to a new non-irradiated position and thereflectivity of the optical pulse is then measured at adifferent time delay. Figure 6 shows a sequence of timeresolved snapshots obtained on a bulk silicon sample foran excitation fluence of ~ 1 J/cm².
At early time (10 ps) a pronounced increase of thereflectivity is observed which can be attributed to a solidliquid phase transition of the material. Although thetemporal resolution was limited by the probe pulse

X-ray Optics and Detectors[3] H. J. Grabosch, U. Hahn, M. Sachwitz, and H. Thom,„Wire Scanner System for Undulator Section of VUVFEL at DESY“, MEDSI-2004, Proceedings – 04 – 31
[4] P. Castro, U. Hahn, O. Hensler, S. Karstensen, M.
Sachwitz and H. Thom, “Wire scanner system for
FLASH at DESY”, to be published[5] BX3100 controller, Beckhoff Industrie Elektronik,
33415 Verl, Germany.
[6] CANopen, Controller Area Network, Can
Automation group, 91058 Erlangen, Germany.

in[7] Servo system with EPOS 70/10 controller/amplifier
and an EC-max 40 Motor with HEDL5540 Encoder
by Maxon Motor AG, CH-6072, Switzerland.
[8] K. Sokolowski-Tinten, et al., to be published[9] A.A. Sorokin, et. al., “Gas-Monitor Detector for
Intense and Pulsed VUV/EUV Free-Electron Laser
Radiation”, Proceedings SRI2003, San Francisco, AIP
Conf. Proc.705 (2004), 557-560

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COMMISSIONING OF A NEW EMITTANCE MEASUREMENT SYSTEMAT PITZ∗
L. Staykov† , J. Bähr, H.J. Grabosch, S. Khodyachykh, S. Korepanov, M. Krasilnikov,
A. Oppelt, B. Petrosyan, F. Stephan, DESY, 15738 Zeuthen, Germany
J. Rönsch, Hamburg University, 22761 Hamburg, Germany
G. Asova, I. Tsakov, INRNE-BAS, 1407 Sofia, Bulgaria.
The goal of the Photo Injector Test facility in Zeuthen(PITZ) is to test and optimize high brightness electron
sources suitable for FEL’s like FLASH and the European
XFEL. Such sources are characterized by very low emittance at high bunch charge. The new Emittance Measurement SYstem (EMSY) described in this paper uses YAG
and OTR screens to measure the transverse beam size andthin Tungsten slits to measure the divergence of the beam.
It has been optimized to measure emittance for a beam of
1 nC in the energy range 5 - 30 MeV. The new EMSY wasdeveloped in a cooperation between DESY Zeuthen andthe Institute for Nuclear Research and Nuclear Energy (INRNE) in Sofia. It was installed in the PITZ tunnel in the
beginning of June and commissioning and first measurements are ongoing.

XY RMS beam size and emittance

Abstract
3
2.5
2
1.5

EMSY3
EMSY1

1

EMSY2

0.5
0
0

2

4

6

8

10
Z, [m]

Figure 1: ASTRA simulation of the rms beam size inmm (blue) and normalized emittance in mm·mrad (red).
The charge is 1 nC; accelerating gradient at the gun is
60 MV/m, phase of maximum energy gain; the focusing
solenoid is at 385 A; the gradient of the booster cavity is
28.9 MV/m, phase of maximum energy gain.

INTRODUCTION
The Photo Injector Test Facility at DESY in Zeuthen(PITZ) was built to test and to optimize electron sources
which are capable for SASE FEL operation. The main
PITZ components are a photocathode laser, an L-band RF
gun and space charge compensating solenoids. A major
upgrade on the existing PITZ facility is ongoing since lastyear [1]. This upgrade includes the installation of an additional accelerating RF booster cavity and various diagnostics elements. The laser system was also upgraded in thelast year, by improving the transverse imaging to the photo
cathode (see [2]) and the overall stability. One of the goalsof the facility is to study and optimize the conditions for theconservation of emittance compensated electron beam withshort pulse length and low transverse emittance [3, 4]. Extended optimization of the photoinjector with ASTRA [5]showed that transverse emittance smaller than 1 mm.mrad
at 1 nC charge can be reached (fig. 1). The Emittance Measurement SYstem used at PITZ was upgraded for better
performance in the extended momentum range [6]. Threeof such devices were produced by the HITECH HEP Groupin INRNE Sofia and are already installed in the PITZ tunnel. In this paper details about the new EMSY as well as
first experience from the commissioning are given.
∗ This work has partly been supported by the European Community,
Contract Number RII3-CT-2004-506008, and by the ’Impuls- und Vernetzungsfonds’ of the Helmholtz Association, contract number VH-FZ-005.
† Presenting author, e-mail: lazaraza@ifh.de

474

PITZ SETUP
A detailed layout of the current PITZ setup is shown on
Fig. 2. The electrons are produced in the RF gun (on theright hand side) and transported through the low energy
diagnostic section, further acceleration up to the maximumof 30 MeV is given in the booster cavity after which thehigh energy diagnostic section is installed.
The low and high energy diagnostic sections consist ofdifferent view screens, BPM’s, charge measurement devices and longitudinal phase space diagnostics. The charge
per bunch can be monitored non-destructively at four positions along the beamline using Integrated Current Transformers (ICT’s). The beam momentum and momentum
spread are measured at two dispersive dipole arms, one in
the low energy section and one after the booster cavity. The
low energy dispersive dipole is also equipped with a streak
camera readout providing full knowledge about the longitudinal phase space distribution (see [7]). Three EMSY’s
are located after the booster cavity in positions 4.3, 6.6 and9.8 m from the cathode.
For the transverse phase space characterization we rely on
YAG and OTR screens and the so called slit scan technique[8]. For this technique the uncorrelated local divergence isestimated by cutting the electron beam into thin slices andmeasuring their size on a screen after a drift. The so called
sheared normalized RMS emittance is then calculated us-

X-ray Optics and Detectors

Proceedings of FEL 2006, BESSY, Berlin, Germany

12349

9041

DUMP

M8

M9

M13

M18
13326

HIGH2

EMSY

OY

EMSY

Wire
Scanner

OY



M2

M1
875

2084

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BOO
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3927

GUN

Low Energy Diagnostics Section

2084

527

0
Gun

Wire
Scanner

HIGH1.Scr4
Quads

OY

O

OY

HIGH2.Scr3

3927

High Energy Diagnostics Section 1

HIGH2.Scr1
Spectrometer

M3

M4
4387

HIGH1

High Energy Diagnostics Section 2

HIGH2.Scr2

M5
6101

7531

TUPPH067

EMSY

OY

HIGH1.Scr5

OY

 

  

HIGH1.Scr2

OY

HIGH1.Scr3





 

HIGH1.Scr1

LOW.Scr3

EMSY

OY

OY



LOW.Scr2

LOW.Scr1YOY

streakDISP2

streak





Y





streakDISP1
Version 3.7.06

Figure 2: Layout of PITZ.

ying the following definition (1) taken from [8]:pεn = βγ · hx2 i · hx02 i.
2

(1)

02

Here hx i and hx i are the second moments of the distribution ofpthe electrons in the so called trace phase space wherex0 = hp2x /p2z i represents the divergence of the beam. The
RMS beam size is measured on an OTR or YAG screen at
the position of the slits along the beam axis. The uncorrelated divergence is obtained by analyzing the profiles ofthe beamlets produced from the slits which drift some distance Ld downstream where the spatial distribution of thebeamlets corresponds to the local uncorrelated divergence,x0 can be derived from the size of the beamlet using theformula in Eq. 2.
phx2b i
0
x =
.
(2)
Ld
Here xb is the RMS size of the beamlet on the screen
after distance Ld . The βγ is measured using a dispersivearm after EMSY.

THE NEW EMITTANCE MEASUREMENTSYSTEMEMSY consists of two orthogonal actuators (Fig. 3)
which can be inserted separately to penetrate the beamin order to take images or to cut beamlets in the beamtransverse planes. The actuators are driven into the beamline with stepper motors and positioned with precisionbetter than 10 µm, their angular orientation with respect tothe electron beam can be adjusted during the measurement
again using stepper motors. Each actuator is equipped with
an YAG or OTRpscreen for measurement of the transverse
RMS beam size hx2 i and a single slit mask for estimationof the local divergence, multi slit masks are in production
and will be mounted on the actuators in the next shutdown
period. The design of the system enables us to measure
the beam transverse parameters expected in PITZ withuncertainty less than 10 % (see [6]).
During the design the following considerations weretaken into account:

X-ray Optics and Detectorsz
CCD cameraxrotation stage

goniometric cradle

Figure 3: Layout of EMSY.
• The slit opening must be small enough to produce
emittance and not space charge dominated beamlets,
but still large enough to provide good transmission.
• The contribution of the initial beamlet size to the measured one at the screen of observation must be as small
as possible.
• The distance betwen the slit mask and the screen must
be big enough to resolve small beam divergence. But
still short enough to prevent the space charge forces todegrade the beamlet and the overlapping of different
beamlets from the multi slit mask.
• The mask thickness must be large enough to scatterthe residual electrons from the beam in order to produce an uniform background for the beamlets measurements and still it must be thin enough provide sufficient acceptance angle.
The design of the slits was made using the above considerations, and GEANT4 [9] simulations for transport ofthe electrons through the masks and to assess the performance of the YAG screens to be used. Slits are made from1 mm thick Tungsten with 10 µm slit opening, the slits ofthe multi slit mask are separated with 0.3 mm. The screensare made from 0.3 silica waffers coated with YAG powder

475

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Proceedings of FEL 2006, BESSY, Berlin, Germany

70000

3.5

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10000

0.5

0

RMS size, [mm]Intensity, [a.u.]or with Al (for the OTR screens). The YAG screens areplaced at 90 degrees with respect to the electron beam andan Al coated silicon mirror is used to direct the light to the
CCD chip, the OTR screens are with 45 degrees orientation. Both the screens are observed with 8 bit CCD camera. It was found from the beam dynamics simulations, thatin some cases 8 bit camera cannot provide the desired sensitivity, therefore 12 bit cameras are ordered and are soon
to be installed. On fig. 4 a scan of the position of the slit
trough the beam is shown, a good signal from the camera
is obtained (blue line), with red the RMS beamlet size isplotted.

77

78

79

80

81

ACKNOWLEDGMENT
We would like to thank to Evstati Apostolov, Hristo
Yotov and Luchezar Yotov from INRNE for the precise
construction and Alexander Donat, Hartmut Lüdecke andJochen Bienge from DESY Zeuthen for their outstanding
support on the mounting and aligning the devices in the
PITZ tunnel.

REFERENCES[1] A. Oppelt, “Status of the PITZ facility upgrade”, LINAC
2006.
[2] J. B¨ahr et al., “Upgrades of the Laser Beam-line at PITZ”,
FEL’05.

[4] L. Serafini, J. Rosenzweig, “Envelope analisys of intense relativistic quasilaminar beams in rf photoinjectors: A theory ofemittance compensation”, Phys. Rev. E, Vol. 55, 1997.

Slit position, [mm]Figure 4: Scan with the 10 µm slit.

[5] K. Floetmann,ASTRA,http://www.desy.de/˜mpyflo

1400001.11200001

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[6] L. Staykov et al., “Design Optimization of an Emittance Measurement System at PITZ”, DIPAC’05.
[7] J. Rönsch et al., “Investigations of the Longitudinal Phase
Space at PITZ”, EPAC’06.
[8] V. Miltchev, “Investigations on the transverse phase space ata photo injector for minimized emittance”, PhD thesis.
[9] GEANT collaboration, CERN/LHCC 98-44, GEANT4: “AnObject Oriented Toolkit for Simulation in HEP”; see also
website: http//wwwinfo.cern.ch/asd/geant4/geant4.html

RMS size, [mm]Further optimization of the readout can be made by adjusting the angular orientation of the slit, as can be seen in
fig. 5. The slit at position 79 mm in fig. 4 was selected
for the angular optimization, improvement of the intensityof the signal from the camera is seen (blue dots) as well as
stable reading for the beamlet size (red line) in the angularrange -10 to +8 mrad, for larger angular deviations lower
signal transmission takes place as well as additional effects
such as scattering of the electrons from the inner surface ofthe slit, etc.

Intensity, [a.u.]

The 10 µm slits can provide sufficient signal for beamlet
measurements with proper angular orientation. The emittance measurement system in PITZ is installed and commissioned. All the component from the system are tested
and ready for use.

[3] M. Krasilnikov et al., “Recent developments at PITZ”,
PAC’05, May 2005, Tennesy USA.

076

CONCLUSIONS

0.4
-20

-10

0

10

20

Slit orientation, [mrad]

Figure 5: Scan of the angular orientation of 10 µm slit.

476

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Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH071

SIMULATION OF MIRROR DISTORTION IN FREE-ELECTRON LASEROSCILLATORS*
H.P. Freund#, Science Applications International Corp., McLean, VA 22102, U.S.A.
M. Shinn and S.V. Benson, Thomas Jefferson National Accelerator Facility, Newport News, VA
23606, U.S.A.
Abstract
Thermal distortions in high-average power FEL cavity
mirrors can alter mode quality and degrade performance.
We address these issues by developing simulation tools,
and then benchmarking the simulation against
observations on the 10 kW-Upgrade experiment at theThomas Jefferson National Accelerator Facility in
Newport News, VA. The modelling and simulation will
rely on the MEDUSA code, which is a three-dimensional
FEL simulation code that is capable of treating both
amplifiers and oscillators in both the steady-state andtime-dependent regimes. MEDUSA employs a Gaussian
modal expansion, and treats oscillators by decomposing
the modal representation at the exit of the wiggler into thevacuum Gaussian modes of the resonator and thenanalytically determining the propagation of these vacuum
resonator modes through the resonator back to theentrance of the wiggler in synchronism with the next
electron bunch. Knowledge of the power loading on the
mirrors allows us to model the mode distortions using
Zernike polynomials, and this technique will beincorporated into MEDUSA.

resonator back to the entrance of the wiggler insynchronism with the next electron bunch. Knowledge ofthe power loading on the mirrors allows us to model themode distortions using Zernike polynomials [4], and thistechnique will be incorporated into MEDUSA.
In this paper, we report on the progress to date in thisactivity. The first step is to compare MEDUSA
predictions with the observed performance of theexperiment at low duty factor where mirror distortions areunimportant. We then go on to determine the effects ofthe so-called first order properties, which include changes
in the Rayleigh range and shifts in the position of themode waist. Higher order distortions such as coma,
astigmatism, and spherical aberration, collectively known
as third-order aberrations, will be incorporated in the
future. The organization of the paper is as follows. In thesecond Section we discuss the formulation used in
MEDUSA. A description of the experiment is given in thethird Section, and of the numerical results in fourth
Section. A summary and discussion is given in the fifth
Section.

INTRODUCTION

THE NUMERICAL FORMULATION

Thermal distortions in cavity mirrors in high-average
power FELs can alter mode quality and negatively impact
performance; hence, it is important to predict thecharacter and magnitude of the distortions and to be able
to model their effect on FEL performance. To this end, we
address these key issues by developing modelling andsimulation tools that can accomplish these goals, and thenbenchmarking the simulation against observations on the
10 kW-upgrade experiment [1] at the Thomas Jefferson
national accelerator facility in Newport News, VA(henceforth referred to as Jefferson Laboratory). The
facility is undergoing continual upgrades; in particular, a
new permanent magnet wiggler has been installed thatwill be used in comparing the experimental andsimulation results (see Table 1). The modelling andsimulation will rely on the MEDUSA code [2,3], which isa three-dimensional FEL simulation code that is capableof treating both amplifiers and oscillators in both thesteady-state and time-dependent regimes. MEDUSA
employs a Gaussian modal expansion, and treats
oscillators by decomposing the modal representation at
the exit of the wiggler into the vacuum Gaussian modesof the resonator and then analytically determining the
propagation of these vacuum resonator modes through the

The MEDUSA code [2,3] employs a three-dimensional
formulation that includes the slippage of the radiation
relative to the electron beam. MEDUSA can model bothhelical and planar wiggler geometry and treats theelectromagnetic field as a superposition of either GaussHermite or Gauss-Laguerre modes in the slowly-varying
amplitude approximation, where___________________________________________*Work supported by the Joint Technology Office.
#henry.p.freund@saic.com

FEL Oscillators and Long Wavelength FELsδA x,t =e xΣ e l,n x,y δ A l,n1 cos ϕ x,t + δ A l,n2 sin ϕ x,t , (1)l,nwhere “l” and “n” are transverse mode numbers, “h” isthe harmonic number, el,n,h = exp(−r2/wh2)Hl(√2x/wh)
Hn(√2y/wh), Hl is the Hermite polynomial of order l, andwh is the spot size, ϕh = h(k0z – ω0t) + αhr2/wh2 (k0 = ω0/c).
1,2
We assume that δ A l,n,h, wh, and αh, vary slowly in z and t.
The dynamical equations are

d + wh'dz wh12
δa l,n,hδa l,n,hs1+ K l,n,h= l,n,h,221s l,n,h−δa l,n,hδa l,n,h(2)

1,2= eδ A l,n,h /m ec 2, d/dz = ∂/∂z + c−1∂/∂t, thewhere δa l,n,h“prime” superscript denotes the total z-derivative,
1,2

w ' α ' 1 + αh
K l,n,h = l + n + 1 α h wh − h −h2
hk 0wh2

2

,

(3)

477

Proceedings of FEL 2006, BESSY, Berlin, Germany

1
2ωb Fl,n
s l,n,h=2
s l,n,hhω0c wh22

cos ϕ hυxe l,n,h− sin ϕ h
υz

,

(4)

where ωb(z,t)2 = 4πe2nb(z,t)/me for a beam density nb, andFl,n = [2l + nl!n!]−1, and <(…)> describes an average overthe complete 6-D phase space. The spot size and radius ofcurvature for each harmonic component are given by
wh' =

α h'
2

2α h
− whYh ,hk 0wh1 + αh− X h + α hYh .
hk 0wh2

(5)

2

=

(6)

These equations constitute the source-dependent
expansion [5], which is a self-consistent adaptive
eigenmode representation that tracks the optical guidingof the mode based upon the interaction with the electron
beam. The field equations are integrated simultaneouslywith the complete three-dimensional Lorentz force
equations for an ensemble of electrons. No wiggleraverage orbit approximation is used so that the spatial
step size must be small enough to resolve the wiggler
motion.
Table 1: Nominal experimental parameters
ELECTRON BEAM
EnergyPeak Current
Normalized Emittance
Energy Spread
Bunch Length
Bunch Charge
Initial Beam Size
Twiss-α Parameter
WIGGLER
Amplitude
PeriodLengthOPTICAL MODE
Wavelength
Rayleigh Range
Mode Waist Position

115 MeV
310-370 A
9 mm-mrad/7 mm-mrad
0.35%
380-420 fsec
79 pC
257 microns/212 microns
1.25
3.746 kG
5.5 cm30 periods/1.65 m
1.57 microns
1.5 (±0.30) m
1.03 (±0.05) m

THE JEFFERSON LAB EXPERIMENTThe Jefferson Lab IR-Upgrade FEL operates an energy
recovery accelerator with a high power FEL wiggler andresonator. The electron beam consists of a core
distribution and a halo distribution. The charge,
emittance, and peak current are of that core beam. The
wiggler is very well characterized and is essentially ideal.
The optical resonator is nearly concentric, and consists ofa high reflector at the upstream end and a transmissive
element at the downstream end that out-couples
approximately 10% of the power. The Rayleigh range
can be varied in the experiment by changing the radius ofcurvature of the high reflector. However, the cavity is478slightly astigmatic and can lead to a difference between
the Rayleigh range in the two axes. The uncertainty in
the Rayleigh range is about 20%. The measured gain andefficiency are 70±5% and 1.6±0.1% respectively.
The nominal parameters for the experiment that areused in simulation are given in Table 1. Observe that thenormalized emittances and beam dimensions shown in thetable refer to the wiggle-plane and the plane transverse to
the wiggler-plane respectively. In addition, the Twiss-α
parameter shown corresponds to a beam that is focused toa waist near the center of the wiggler. The estimate of theRayleigh range and the location of the mode waist containsome uncertainty, and the values given are the best
estimate at the present time. In particular, we note that themode waist is located about 15 cm downstream from thewiggler center.
NUMERICAL RESULTS

As we mentioned previously, our first goal is todetermine whether MEDUSA is in substantial agreementwith the experiment when distortion is absent or minimal.
This is the case when the experiment operates at low
average powers (i.e., low duty factors), where a single
pass gain of the order of 65-75% is measured for a peakcurrent of 310 A and a bunch length of 380 fsec.
The parameters shown in Table 1 are the nominal
experimental parameters, and we note that the optical
waist is located about 15 cm downstream from thewiggler center. The experiment was optimized byfocusing the electron beam to a waist near the center ofthe wiggler, which provides an optimal match to theresonator mode. This was also found in simulation, and is
obtained for a Twiss-α parameter of 1.25 in simulation.
The single pass gain found using MEDUSA operating in
steady-state mode for these parameters is of the order of
400%. However, the slippage time through the wiggler
for this experiment is of the order of 160 fsec, which is a
substantial fraction of the bunch length. Hence, slippage
is important and can be expected to substantially reduce
the single pass gain with respect to steady-statepredictions.
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Figure 1: Plot of the power versus time through the pulse
at the wiggler entrance and exit.

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany
The slippage of the electromagnetic pulse through the
wiggler is illustrated in Fig. 1 where we plot the pulse
shapes at the entrance and exit from the wiggler. It isevident from the figure that while the pulse is assumed
symmetric at the entrance to the wiggler, it has slipped byat least half the total pulse length over the course of the
wiggler. Amplification of the peak power over the pulse
has shrunk from the value of 400% found in steady-state
simulation to just over 100% when slippage is included.
However, in the time-dependent simulation, gain must be
calculated based on the overall energy of the pulse, notthe peak power. To this end, we plot the amplification of
the total pulse energy through the wiggler in Fig. 2. The
incident energy is 2.53 nJ and the energy at the output is4.68 nJ yielding a single pass gain of about 84%. Given
the uncertainties in the measured parameters, thisrepresents reasonable agreement with the experiment. For
example, there is a 20% uncertainty in the measurementof the Rayleigh range that would result in a reduction of
the predicted gain to 73%.

TUPPH071

displacement in Fig. 4 to better illustrate the performancesensitivity to these parameters, and the actual variation
with Rayleigh range in the experiment is between these
two lines. It is clear from Fig. 4 that the single pass gain
would be larger if the Rayleigh range were smaller, andthe optimal Rayleigh range found in simulation varies
from about 0.5 m for a wiggler-centered resonator mode
to 0.6 m when the mode waist is located 30 cm
downstream from the wiggler center. The advantages that
accrue from using a short Rayleigh range resonator werefirst pointed out by W. Colson and his collaborators [6].
The results shown in Figs. 3 and 4 indicate that weremirror distortions to either decrease the Rayleigh range orshift the mode waist upstream, then the single pass gain
and FEL performance may actually be enhanced. Whether
such an effect can actually be allowed for in the design ofa high power FEL oscillator is currently underconsideration.

90

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80

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0.0

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En e r gy ( nJ )

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z (m)

The lowest order mirror distortions involve variations
in both the location of the optical waist and the Rayleighrange. In order to study the effects of these distortions, we(1) varied the position of the optical waist while holding
the Rayleigh range fixed at 1.5 m, and (2) varied theRayleigh range for an optical waist that is located at the
wiggler center optical and 30 cm downstream from thewiggler center. These results are shown in Figs. 3 and 4
respectively. Figure 3 indicates that, for these parameters,
the FEL gain is maximized when the optical waist is
located about 20 cm upstream from the wiggler center, incontrast to the actual location that is 15 cm downstream
from the wiggler center. Observe that we show the gain
variation with Rayleigh range in Fig. 4 for an optical
waist that is wiggler-centered and shifted downstream
from the wiggler center by 30 cm. However, the optical
waist is located 15 cm downstream from the wiggler
center, and the actual location was used in the simulations
shown in Figs. 1-3. We chose to use the larger

FEL Oscillators and Long Wavelength FELs

0.8

1.0

1.2

1.4

1.6

Figure 3: Variation of the single pass gain with theposition of the optical waist.

150
wiggler-centered

Gain (%)

Figure 2: Plot of the amplification of the total pulse
energy through the wiggler.

0.6

Waist Position (m)100
30 cm downstream
from wiggler center
50

0
0.0

0.5

1.0

1.5

2.0

Rayleigh Range (m)Figure 4: Variation of the single pass gain with theRayleigh range.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

SUMMARY AND DISCUSSION
In this paper we report on the initial work involved in astudy of the effect of mirror distortions on theperformance of a high power FEL oscillator using the
MEDUSA simulation code. To this end, we firstundertook to validate MEDUSA for low power (and duty
factor) operation where mirror distortion was small. In
this case MEDUSA predicted a single pass gain of 84%,
which is in reasonable agreement with the measured
range of 65-75% given the experimental uncertainties in
the Rayleigh range, location of the optical waist,
astigmatism in the resonator, and uncertainties related tothe electron beam distribution. Experimentally, one
derives the mode waist and position from the radii ofcurvatures (ROC) of the cavity mirrors. Repeatedmeasurements set this uncertainty at ±5 cm. In turn, thiscreates a 20% uncertainty in the value of the Rayleighrange, but a relatively small (±5 cm) change in the waist
position. There are also uncertainties associated with theelectron beam parameters, especially those associatedwith the longitudinal distribution. Simulations indicatethat the predicted gain is very sensitive to uncertainties ofthis magnitude. For example, a 20% uncertainty in theRayleigh range and a ±5 cm uncertainty in the optical
waist position can lead to a variation in the predicted gainof between 71% - 96%. As a consequence, the simulation
is in substantial agreement with the experiment. Given theagreement between the simulation and experiment, wethen undertook to investigate the variation in performance480

versus the Rayleigh range and the location of the optical
waist. We found that the small signal gain would besubstantially larger for much smaller Rayleigh ranges andfor an optical waist located upstream from the wiggler
center.
Future work will involve the inclusion of higher ordermirror perturbations mentioned earlier, as well as
validation of the harmonic generation predictions of
MEDUSA.

REFERENCES[1] G. Neil et al., Nucl. Instrum. Meth. A557 (2006) 9.
[2] H.P. Freund, S.G. Biedron, and S.V. Milton, IEEE J.
Quantum Electron. 36 (2000) 275.
[3] H.P. Freund, Phys. Rev. ST-AB 8 (2005) 110701.
[4] S.V. Benson et al., Nucl. Instrum. Meth. A407 (1998)
401.
[5] P.A. Sprangle, A. Ting, and C.M. Tang, Phys. Rev. A
36 (1987) 2773.
[6] D.W. Small, R.K. Wong, W.B. Colson, and R.L.
Armistead, Nucl. Instrum. Meth. A393, 262 (1997).

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUPPH072

GENERATION AND CHARACTERIZATION OF THE MICROBUNCHEDBEAMS IN THE RANGE FROM 0.3 TO 500 FEMTOSECONDS
V. E. Yakimenko, M. Babzien, K. P. Kusche, Brookhaven National Lab., Upton, NY 11973, U.S.A,
X. Ding, University of Southern California, CA 90089, U.S.A,
E. Kallos, P. Muggli UCLA, Los Angeles, CA 90095, U.S.A,
W. D. Kimura, STI Optronics, Inc., Bellevue, WA 98004, U.S.A,
F. Zhou, Stanford Linear Accelerator Center, Stanford, CA 94025, U.S.A.
Abstract
The recent results include formation and measurementof the micro bunch structures of the different time scales.
Double beam structure produced and characterized at 100
fs – 0.5 ps range using beam splitting during compression
in the magnetic chicane – “dog leg” arrangement.
Arbitrary number of 10-50 femtoseconds micro bunches
are sliced out of 5 ps long beam using wire mesh. CSRinterferometer is used for detailed characterization of thebeams in the two techniques above. 0.3 fs bunches areproduced by IFEL and characterized by spectral
measurements of the multiple harmonics. Presentation
covers experimental results at Brookhaven Accelerator
Test Facility.

INTRODUCTION
Three distinct experimental methods are discussed inthis paper in the following 3 chapters. The first one
discusses measurements of micro bunched beams
generated with CO2 laser in the IFEL wiggler.
Comparison of the coherent transition radiation CTR
power in multiple harmonic leads to much more precise
information about micro bunch length. The second part ofthe paper discuses generation of micro bunched beams
that are not seeded with laser. Wire mesh targets wereshaping the beam in the dispersive region and converting
correlation between energy and time into current time
modulation. Tunable spacing is the result of thistechnique. We used an interferometer to characterize thesebeams. The last chapter of this paper discusses
controllable beam break up into two beam structure. The
two beam formation happens during its compression in
the magnetic chicane – dog-leg combination. Effects ofthe space charge and CTR are very important and stabilize
the process contrarily to initial expectations. We usedinterferometer and plasma wakefield capillary tocharacterize two 100 fs bunches formed in this process.

CHARACTERIZATION OF SUBMICRONMICROBUNCHES PRODUCED BY IFELWITH CTR IN MULTIPLE HARMONICS
We collect the coherent transition radiation (CTR) emitted
when the microbunches traverse two 1μm thin titanium
metal foils in order to diagnose the quality of the
microbunching of the IFEL modulated electron beam.
CTR is emitted because the electric fields of the electrons

The Challenge of fs Pulses and Synchronisationin the beam displace violently the free electrons in themetal surfaces, which in turn radiate due to theacceleration they suffer.
The first metal foil is placed perpendicularly to thebeam direction of propagation and serves the purpose ofblocking the CO2 radiation previously used at the IFEL
interaction that could interfere with the CTR signal. The
second foil is placed at 45o with respect to the direction of
propagation and emits radiation out of the beamline. The
sum of the radiation emitted from both foils is collected.
The spectrum of the CTR radiation contains
information about the geometry of the electron beam. The
on axis spectrum is proportional to the amplitude squaredof the Fourier transform of the beam and shown on figure
1.

Figure 1. The spectrum of the CTR emitted when the
microbunched electron beam passes through a metal foil.
The geometry of the electron beam is uniquely mapped
into its CTR spectrum. The low frequency (longwavelength) radiation on the right corresponds to theenvelope of the beam. In other wavelengths the radiationin general adds out of phase except at the harmonics ofthe separation wavelength λ0=10.6μm between the
microbunches.
Finally and most importantly, the amplitudes of theseharmonics are modulated by the Fourier transform of eachmicrobunch. The existence of radiation at each harmonicis a strong indication for the periodicity of the microbunchtrain. Also, the energy radiated at each harmonic depends

481

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Proceedings of FEL 2006, BESSY, Berlin, Germanyon the shape of each microbunch, hence it provides a
direct way of estimating its width, which is assumed to be
Gaussian in this case.

dispersive region of the beam transport to generate
microbunches with the spacing that is determined by thetarget period. The idea is very simple: a beam is chirped
in the linac and therefore energy-time correlation is
introduced. The target is installed in the location where
dispersion is large while betatron size in the plane of thedispersion is smaller then target period. This effectively
creates time-current modulation. We use 125-500μm
diameter wire to make targets. Low emittance 50 MeV
beam is effectively scattered by this wire.
Thephotograph of the taget is shown on figure 3.

Figure 2. The ratios of the energies radiated at each of theharmonics as a function of microbunch width. The 3 data
sets agree at the region around σz=0.7μm .
In order to collect the CTR, a cold detector sensitive
between 3μm-20μm wavelengths is used. Furthermore,narrow Gaussian bandpass filters with roughly 5%
FWHM transmission bandwidth were used to isolate theradiation of the first, second and third harmonic, in
successive measurements. After recording about 100
events at a roughly constant IFEL laser pulse energy(within a factor of 2) at all three harmonics, we calculated
the three possible ratios of the harmonics signals. The
data range for each ratio is shown on the vertical axis on
figure 2.
Using prediction for small angles and after accounting
for the response of the detector and the filters calibrated
with the black body source, we calculated the expected
theoretical ratio between the energy radiated under eachof the harmonics as a function of the microbunches’
widths. These three predicted ratios also are plotted infigure 2. It shows that the measured rations indicate awidth of σz=0.7μm for each microbunch. Although themicrobunch width was inferred using CTR [1] and staged
laser accelerator [2] before, this is its first direct
measurement that also utilizes information from different
harmonics.
In order to confirm the 10.6μm separation between the
microbunches the IFEL laser was tuned at 10.2μm, whilestill using the same narrow 10.6μm filter to detect the
CTR. In that case the signal recorded was at least 100
times less than when the IFEL was driven at 10.6μm andvery close to the noise level of the detector, thus
confirming the periodicity of the bunching at the laser’s
wavelength only.

TUNABLE MICROBUNCH TRAIN
The microbunched beam described above offers stable,
well defined by spacing the laser. It is a disadvantage if
the laser in not easily available in the range that is needed.
We attempted to use a periodic wire mask installed at the482

Figure 3. Photograph of the wire target for adjustablemicrobunch beam generation.
One can clearly see modulation in of current vs energy
on the electron beam energy spectrometer. It is evenpossible to see unintentional defect of the target “double
wire” approximately in the middle of the beam.

ΔE/E~1%Figure 4. Image from the beam energy spectrometer. It
shows 15 microbunches stretched over ~1% energy chirp
induced on the beam.
The translation of the microbunch spacing from target
period naturally depends on the chirp and dispersion value
at the target location. We operated with a set ofparameters where it is adjustable 10: target with 250 μm
period will generate microbunches spaced by 25 μm. We
use a pair of installed before target sextupole magnets tolinearize or chirp the spacing between micro bunches.
High energy slit opening that controls energy spreadenvelope of the beam can be used to select arbitrary
number of microbunches. The demagnification can be

The Challenge of fs Pulses and Synchronisation

Proceedings of FEL 2006, BESSY, Berlin, Germany

subsequent RF acceleration section downstream of thechicane, which can be used to compensate for residualenergy chirp on the electron beam (e-beam) exiting thechicane. Not being able to use a downstream acceleration
section was one reason the double-bunch formation
process was possible.
Spectrometer Output (arb. units)adjusted by change of dispersion, beam chirp or target
rotation.
CTR interferometer [4] was used to measuremodulation in time. Our attempt to measure individual
microbunches with the period of ~25-30 μm did not
produce the expected result due to cutoff of the windowtransmission around 30 μm. The signal strength on thedetector increased considerably for the modulated beam.
The interference showed expected envelope of the beamInterference curve was triangular that translates to the“square’ beam envelope. (Tails of the beam were cat byhigh energy slip.)
We detected individual bunches with correct periodicity
after switching to the 1mm target and retuning transportline for 1:5 demagnification. Interferogram is shown on
figure 5.

TUPPH072

120
100
80
60
40
20
0
56

58

60

62

64

Electron Energy (MeV)

Figure 7. Energy spectrums of double-bunch e-beam.
Three spectrums taken many minutes apart demonstratingstability of the double-bunch formation process

Figure 5. Interferogram of the microbunched beam
generated with the periodic wire target.

SUBPICOSECOND DOUBLE ELECTRONBUNCH GENERATION

Figure 7 shows energy spectrums of the double-bunch
beam. It shows two bunches separated in energy by 1.8
MeV. It is an overlay of three shots taken many minutes
apart. The good reproducibility of the spectrums indicatesthe energy distribution and positions are very stable.
A coherent transition radiation (CTR) interferometer
was used to characterize the compressed e-beam. The
CTR emission is in the THz range. An autocorrelation of
the CTR signal is obtained by scanning the translation
mirror shown in Figure 8
Analysis of this autocorrelation signal yields
information about the e-beam bunch characteristics [4].

As part of these efforts towards improving beam forvarious experiments related to advanced accelerator
research, a chicane, designed and built by UCLA [1], wasinstalled on the linac downstream of the RF accelerating
structures.
The chicane was designed to provide
approximately 30 times compression of the incoming
electron bunch. Figure 6 is a diagram of the chicane.

Figure 6. Diagram of ATF chicane.
It was discovered that when compressing the electron
bunch from the linac that the beam breaks up into two
distinct bunches with subpicosecond compressed bunch
lengths. It does this in a consistent and reliable manner.
Unlike most of other facilities that are utilizing a chicane
for pulse compression, the ATF does not have a

The Challenge of fs Pulses and Synchronisation

Figure 8: Example of raw data from CTR interferometer(circles) and the curve fits to the data (solid line)
calculated from the autocorrelation integral [2]. “Bumps”
around +- 0.5 ps indicate double bunch spacing.
For a single bunch, the curve fit of the autocorrelation
integral with the data requires selecting values for thebunch length and the cut-off frequency of the detection

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Proceedings of FEL 2006, BESSY, Berlin, Germany

system, where we have assumed a Gaussian bunch shape.
In particular, the width of the central peak of the
autocorrelation signal is primarily affected by the bunch
length. The shape of the curve on either side of the peakis mostly affected by the cut-off frequency.
For a double e-beam bunch, there are five freeparameters in the autocorrelation integral. We were able tocharacterize each bunch individually using CTR and beam
charge monitor. Single bunch data was obtained by using
the high-energy slit located downstream of the chicane toblock one of the bunches (either the low-E or high-E
bunch). Individual bunch data for each bunch of the
double bunches permits reducing the number of freeparameters to one, i.e., the time delay between the twobunches. For the example shown in Figure 8, the singlebunch CTR data indicates the lengths of the two bunches
is 144 and 90 fs, the cut-off frequency is 1.7 THz, and thesecond bunch has 60% of the charge in the first bunch.
Hence, for the curve fit shown in Figure 8, we find thetime delay between the bunches is 500 fs.
Results of simulations with Elegant [5] confirmed ourhypothesis that double beam structure is cased by the
combination of nonlinear energy chirp and different signof compression in the chicane and dog leg. Self induced
beam wakes narrowed energy spread in the beam and let
to complete separation.

ACKNOWLEDGMENTS
The authors wish to thank Samer Banna and ATF staff
for contributions to the experiments. This work was
supported by the U.S. Department of Energy, Grant Nos.
DE-FG02-04ER41294, DE-AC02-98CH10886, DEFG03-92ER40695, and DE-FG02-92ER40745

REFERENCES[1] Liu, Y. et al., Phys. Rev. Lett. 80, 4418–4421 (1998).
[2] Kimura, W. D., et al., Phys. Rev. Lett. 92, 054801(2004).
[3] R. B. Agustsson, UCLA, M.S. thesis, 2004.
[4] A. Murokh, et al., Nucl. Inst. Meth. Phys. Res., A
410, 452 (1998).
[5] M. Borland, “User’s Manual for elegant,” available
on-line at http://www.aps.anl.gov/asd/oag/manuals/
elegantver14.1/elegant.html.

484

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Proceedings of FEL 2006, BESSY, Berlin, Germany

TUCAU01

DESIGN OF A LONG WAVELENGTH FEL FOR EXPERIMENTS UNDERHIGH MAGNETIC FIELDS
Wim J. van der Zande#, Th. Rasing, J.C. Maan, A.P.M. Kentgens and F.J.M. Harren,
Institute for Molecules and Materials, Radboud University Nijmegen, PO Box 9010, 6500 GL
Nijmegen, The Netherlands.
Abstract
At the University of Nijmegen, a novel collaboration
has been established that combines a number ofspectroscopic laboratories. These laboratories form acentre for advanced spectroscopy and constitute thespectroscopic department of the (Research) Institute for
Molecules and Materials combining physical andchemical techniques. As part of the spectroscopic centre,
a long-wavelength far-infrared free electron laser (FIRFEL) operating between 100 μm/3 THz and 1.5 mm/200
GHz will be designed and constucted in the coming years.
The FIR-light should facilitate new experiments in theexisting high field magnet laboratory (HFML), a large
European Rerearch Infrastructure and in the NMR
pavillion equipped with NMR instrumentation operating
up to 800 MHz, especially for dynamic nuclear
polarization technology.

THE NIJMEGEN CENTRE FOR
ADVANCED SPECTROSCOPY
The Insitute of Molecules and Materials at the
University of Nijmegen houses a number of spectroscopic
laboratories. Theselaboratories
combinelaser
spectroscopy in the European Trace Gas Facility [1],scanning probe technology, employing various forms ofscanning tunneling and atomic force microscopic
techniques [2], nucelar magnetic resonance (NMR)
laboratory [3] and the high field magnet laboratory(HFML) [4]. Existing collaborations between the various
laboratories have resulted in experimetns ranging from a1.277 GHz NMR spectrometer built in a 30 Tesla Bittter
magnet to NMR on a chip employing force microscopy todetect the radiofrequency absorption, and experiments
exploiting diamagnetism to neutralize gravity in nearzero-gravity experiments inside strong magnetic fields.
In respons to a call from the Netherlands Government
named the National Programme for Investments in Large
Scale Facilities [5], we have proposed to strengthen
existing facilities and to develop two novel instuments, a
45 Tesla Hybrid magnet and a Free Electron Laser
operating in the far infrared (FIR).
The frequency window between the microwave region
on the low photon-energy side and the infrared radiationon the high photon-energy side is called Far Infrared or
THz regime. This energy regime knows many
applications and radiation sources with different_________________#

w.vanderzande@science.ru.nl

FEL Oscillators and Long Wavelength FELs

characteristics are rapidly developed. We believe that atpresent the most powerful and versatile THz radiation
source is a free electron laser. We have proposed theconstruction of a THz-FEL optimized for the demands ofadvanced material research in combination with highmagnetic fields and for advanced studies of molecular andmacromolecular systems. The design aims at generating
light between 100 μm and 1.5 mm with a spectral
bandwidth of Δλ/λ<510-5 while maintaining intensities ofthe order of 100 Watt during pulses of minimum duration
10 μs and maintaining the possibility of pump-probe
experiments at a 10 to 30 picoseconds time resolution.
The science driver that resulted in the success of our
proposal has been the ambition to bring material researcha significant step forward by performing saturation
experiments and pulse-echo experiments in magnetic
fields above 30 Tesla. In these fields, the relatively highenergy excitations reduce the interference of thermal
effects while studying material properties. The total
proposal encompassing a 40-45 Tesla hybrid magnet, theFEL and received about 26 M€ (excluding building costs,
including some exploitation funds). As the FEL will be apart of an operational large scale facility, and as
experience in free electron lasers is still small in
Nijmegen, some design specifications will be madeconservatively.

SCIENCE DRIVERS AND
EXPERIMENTAL LIMITATIONS.
The science call carried the intention to fortify in the
Netherlands the number of large scale facilities. It was
realized that the Netherlands could not play a sufficiently
large role as host country for important international
facilities and international researchers. In many othercountries the relative number of facilities was found to besignificantly larger. In our proposal, we express theambition that the University of Nijmegen may host many
scientific guests using scanning probe techniques, thelaser laboratory, and the high field magnets (using theTHz radiation source), NMR or the FEL in its own rightas versatile spectroscopic light source. The specifications
defined above have been formed in collaboration with the
FOM Institute Rijnhuizen, which hosts FELIX (freeelectron laser for infrared experiments). The FELIX staff
will not only provide a lot of experience and advice but
also forms an example for the management of a highly
successful FEL facility. The spectral range chosen for the
proposed FIR-FEL complements that of FELIX485

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Proceedings of FEL 2006, BESSY, Berlin, Germany

purposefully to optimize the collaboration between thetwo facilities.
An ideal laser source is easily tuneable in the THz
regime, has a flexible pulse structure allowing pumpprobe experiments, as well as bandwidth limited in thecase of long macro-pulses, and is (quasi-) continuous withan average power of about 1 kWatt. Although the physics
does not pose fundamental restrictions, the relative
inefficiency of the FEL principle, without energy
recovery, and more importantly, technological limitationsin the creation of high intensity, relativistic electron
beams requires choices optimizing specific aspects.
.

Science Drivers
In the following three of the science drivers are
identified. An important group of experiments study thespectroscopy and dynamics in solid state materials byobserving pulse-echo’s following electron spin excitations
or cyclotron resonances in magnetic fields. Depending on
the effective mass of the electron, FIR-radiation near 1
THz is required in a magnetic field around 35 T.
Saturation of these transitions in the form of excitation by
a π/2 pulse within about 100 ns requires powers of about
100 Watt with a bandwidth of Δλ/λ≈2 10-5. Pulse-echo
experiments further require the possibility to shape pulses
and delay pulses. Atypical experiment requires three of
even more of these pulses within a few μs separated atarbitrary time delays ranging from tens of nanoseconds toone microsecond. Hence, we require laser pulses with
about 10 μs duration that can be transformed by fast
mirrors into the requested pulse train.
A second group of experiments is the use of FIR
radiation to saturate electron spin transitions within an
NMR instrument. By exploiting the coupling between theelectron spin with nearby nuclear spin, the saturation of
the electron spin population may be transferred to the
nuclear spin. This process is called dynamic nuclear
polarization (DNP). Although in principle DNP canenhance the sensitivity of NMR by a factor of more than104, technological and system specific hurdles areenormous for a realization with a wide scope of
applications. For DNP, the need for a high absolute duty
cycle for FIR radiation may establish the largest obstacle
for FEL technology to be optimally applicable.
In the first two examples, large magnetic fields play animportant role. A third science driver makes optimal useof the flexibility to change the wavelength of a FEL
continuously. A research program is anticipated onmolecular spectroscopy of bio-organic molecules,
biomemetics (analogues of bio molecules), and smart
organic molecules often inspired on biological systems.
Characterization of the THz response may not only
provide spectroscopic information on the structure ofthese molecules but also on slow intra- and intermolecularmotions related to their functionality.

486

Technological Choices.
The anticipated design for the FIR-FEL is based on
experiments performed with the FELIX instrument in The
Netherlands. FELIX is a short-pulse Free-Electron Laser
operating in the IR from 5 to 250 μm. The spectral widthof the output ranges from 0.5 to 7% depending on thefrequency. The overall duty cycle is small with arepetition rate up to 10 macro-pulses per second of a
maximum duration of 10 μs each. Each individual macropulse consists of up to a few thousand micro-pulses eachconsisting of tens of optical cycles, implying duration of afew picoseconds for each micro-pulse.
In terms of the macro-pulse structure, the duty cycle of
FELIX is about 5 10-5 with an average output power ofabout 1 Watt, implying an average power of 20 kWattduring the macro-pulse. The maximum power in thepicoseconds micro-pulses is another three orders higher.
From here, we will describe the design for the Nijmegen
FIR-FEL. The pulse structure will be similar to the one of
FELIX and has the form of a low repetition rate 10 – 15
μs macro pulse structure. The macro pulse will consist of
micro pulses with a fixed repetition rate in the range from
1 to 3 GHz. The special property that we aim for is that
all micropulses have a very well defined phase relation. It
is of interest to note that a narrow bandwidth using thismechanism has been one of the original design ambitionsof FELIX. Oepts and Colson [6] presented the initialideas of phase locking otherwise independent
micropulses. Also Madey and coworkers started aroundthis time [7,8]. Initial measurements at FELIX were
performed by Bakker, Oepts van der Meer and coworkers [9,10], followed by Weits, Oepts and coworkers[11,12]. This research resulted in an experimental scheme
to create a pulse train of phase locked light pulses. Theseauthors observed significant phase stability between the
micropulses and drew favourable conclusions regarding
the bandwidth that may be achieved using externalfiltering using interferometers.
It is required to have a large number of optical pulses
circulating simultaneously in the normally very large FEL
cavity (more than 40 pulses in a cavity with an effective
length of about 10 meter). As the optical pulses are
generated from electron pulses moving at nearly the speedof light, an extra (optical) system has to couple the opticalphases in this train of light pulses. An interferometer
inside the cavity ensures that photons from a single
electron bunch will affect the coherence of the light
generated from many electron bunches injected later. The
resulting pulse train of coherent and phase coupledmicropulses constitutes a frequency comb with narrow
FIR lines spaced with the repetition rate of the electron
pulses (by the 1 to 3 GHz rf frequency) . These narrowlines have a width that is determined by the quality of theinterferometer and by the magnitude of the interpulse
phase-coherence. Each line in the frequency comb further
consists of one or more longitudinal modes of the large
FEL laser cavity, separated by 0.001 cm-1 for a 10 m

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Proceedings of FEL 2006, BESSY, Berlin, Germany
cavity. To achieve really a single longitudinal frequency
output, filtering of one interferometer mode outside of thelaser cavity is required. This filtering reduces the average
power of the macro pulse by factor of at least 50
depending on the quality of the filtering process.
At FELIX experiments have been performed at a fixedwavelength near λ=69 μm, achieving a spectral resolutionof 2 10-5 using a Fox-Smith type interferometer. Other
groups have simulated and employed Michelson typeinterferometers in the FEL cavity for the same purpose.
[9,10] The above specifications have resulted in the
expectation that a dedicated design for a FIR-FEL could
provide near single mode lasing at the average power of
100 Watt during a macro pulse even when starting with ashort pulse FEL instrument. It is realized that it will
require a careful design to establish continuous tuning insuch a FEL as the timing structure of the RF electron
accelerator system and the RF frequency generates
strongly preferred absolute frequencies.

DISCUSSION
Many of the specifications related to the science drivers
discussed above suggest designing a quasi CW-FEL suchas the high quality UCSB FIR FEL operating at the
University of Santa Barbara. This long-wavelength outputof the FIR-FEL in Santa Barbara combines many of thecharacteristics required for the experiments planned athigh magnetic fields. In fact, the power output of a CW–
FEL can be of the order of 1 – 6 kWatt during the macro
pulse clearly exceeding the expectations of a pulsed
frequency comb FIR FEL as suggested above. The
ambition of the Israeli FEL project to improve on the
UCSB FEL design such that an average power of kWattmay become feasible implying a near CW operation withvery high duty cycle while maintaining a large
wavelength range seems to bring very difficult
experiments such as DNP in NMR experiments morefeasible.
At this moment, the extra possibilities to use a pulsed
FEL for strongly non-linear experiments employing thevery high micro pulse peak powers and to use the FEL fortime resolved experiments with 10- 30 picoseconds timeresolution has resulted in the decision to study the

FEL Oscillators and Long Wavelength FELs

TUCAU01

possibilities of a pulsed frequency comb type FIR-FEL.
The planning of the project involves in the upcoming 18
months design studies and detailed planning of theconstruction phase of the FEL. Lasing and the opening ofa user facility along the lines of the present very
successful FELIX facility are foreseen in about five and ahalf years from now.

ACKNOWLEDGMENTS.
WJvdZ wants to express his gratitude to Dick Oepts,
Lex van der Meer and the rest of the staff at the FOM
Institute for Plasma physics for the many discussions andsupport while preparing the proposal and in preparing thedesign phase of the proposed FEL.

REFERENCES[1] http://www.ru.nl/tracegasfacility/[2] http://www.ru.nl/nanolab/[3] http://www.ru.nl/physchem/solid_state_nmr/[4] http://www.hfml.kun.nl/[5] //nwo.nl/nwohome.nsf/pages/NWOP_6GFARR_Eng[6] D. Oepts and W.B. Colson, IEEE J. of Quantum
Electron., 26 (1990) 723[7] E.B. Szarmes, E.D. Madden, and J.M. Madey, J. Opt
Soc. Am. B, 13 (1996) 452[8] E.B. Szarmes and J.M. Madey, IEEE J. of Quantum
Electron., 29 (1993) 452[9] D. Oepts, A.F.G. van der Meer, R.J.Bakker, and P.W.
Amersfoort, Phys. Rev. Letters, 70 (1993) 3255
[10] D. Oepts, R.J.Bakker, D.A. Jaroszynski, A.F.G. vander Meer, and P.W. Amersfoort, Nucl. Instr. And
Meth., A331 (1993) 42[11] H.H. Weits, A.F.G. van der Meer, D. Oepts, andMeisong Ding, Nucl. Instr. And Meth., A393 (1997)
61[12] H.H. Weits, Thesis, Technical University Eindhoven,
1998

487

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THE ROSSENDORF IR-FEL ELBE
P. Michel, H. Buettig, F. Gabriel, M. Helm, U. Lehnert, Ch. Schneider, R. Schurig, W. Seidel,
D. Stehr, J. Teichert, S. Winnerl, R. Wuensch
Forschungszentrum Rossendorf, Germany.
Abstract
The radiation source ELBE is the central researchfacility in the Forschungszentrum Rossendorf. The
machine is based on a 40 MeV superconducting RF Linac
which can be operated up to 1 mA in cw mode. Aftercommissioning the Bremsstrahlung and the X-ray
facilities in 2002 and 2003, respectively, and the firstlasing of the mid-IR FEL (3-22 µm) in 2004 about 7000
hours user beamtime have been provided. At present a
second FEL for long IR waves (20-150 µm) using apartial waveguide is under commissioning. First lasing
was demonstrated on August 21-st, 2006. Besides inhouse users particularly the IR beam is available toexternal users in the FELBE (FEL@ELBE) program
which is a part of the EU funded integrated activity on
synchrotron and free electron laser science. In thiscontribution the fundamental features of the ELBE IR
FEL’s and the operational experiences which werecollected during two years of FEL user operation are
described. Future projects like the combination of the new
High Magnetic Field lab with the ELBE-IR beams will
open up unique experimental possibilities.

INTRODUCTION
In the Forschungszentrum Rossendorf in Dresden,
Germany, the superconducting electron accelerator ELBE
(Electron Linac with high Brilliance and low Emittance)
has come into user operation in 2002. ELBE accelerates
electrons to energies up to 40 MeV with an average beam
current of 1 mA in quasi continuous wave (cw) mode.
The electron linac [1] serves as a driver to generate
several kinds of secondary radiation and particle beams,
which are FEL-Infrared Radiation for a very large field of
applications reaching from semiconductor physics tobiology, MeV Bremsstrahlung for nuclear (astro) physics,
monochromatic hard-X-ray channelling radiation forradiobiological experiments, and in near future also
neutrons and positrons for studies in nuclear reactor
science and materials research. The kind andcharacteristics of the produced secondary beams at ELBE
are in accordance with the scientific profile and theexperimental requirements of the Forschungszentrum
Rossendorf. For a layout of the ELBE building see Fig. 1.

ELECTRON LINAC
A driver for these different kinds of secondary radiationmust be characterized by a high average beam current anda small transverse and longitudinal emittance. For thisreason only a superconducting high frequency accelerator

488

was taken into consideration. Low energy electron
bunches are produced in a grid-pulsed thermionic gun
operating at 250 keV DC voltage. It delivers pulses with abunch charge up to 77 pC at 13 MHz repetition rate andabout 450 ps length. The transverse emittance in this caseis about 10 mm mrad caused by the electric-field
deformation close to the grid [2]. To generate beams withsmaller emittance values the grid can be pulsed with 260
MHz at drastically reduced bunch charge. In combination
with phase space cutting using apertures, emittancevalues below 2 mm mrad can be achieved in this regime.
For reduced average power, macro bunching is possible
as well, yielding 100 µs or longer macro pulses at a < 25
Hz repetition rate. Pulse compression down to 10 ps
which is necessary for injection into the 1.3 GHz RF
accelerator is done by a two-stage RF bunch compressor
operating at 260 MHz and 1.3 GHz, respectively.
The two main accelerator stages are based on two 9-cell
RF cavities which were developed for the TESLA projectat DESY [3] and are kept at 2 K using superfluid helium
delivered by a commercial helium liquefier (Linde). The
cavities are individually driven by 10 kW CPI klystron
amplifiers. The RF couplers consist of a double-window
arrangement and a door-knob shaped adapter for RF
transmission from rectangular waveguides to co-axial
cavity coupler antenna. The vacuum windows arerectangular plastic windows at room-temperature level
and circular ceramic windows cooled by liquid nitrogen.
The maximum acceleration field gradients of the cavities
exceed 10 MV/m. In practice only 9-9.5 MV/m areaccomplished limited by cavity heat loading and fieldemission. Taking into account that the total accelerationenergy is reduced by nearly two MeV due to the captureof low-beta electrons in the first accelerator stage, themaximum total energy is about 36 MeV in practice. To
achieve higher acceleration field the RF can be pulsed up
to a duty cycle of 1:2. Maximum energy of about 50
MeV can be obtained at a duty cycle of 1:10. A magnetic
bunch compressor with adjustable R56 < 500 mm islocated between the acceleration modules and serves,
together with the RF phase of the accelerator cavities, tomodify the longitudinal phase space configuration. The
electron beam parameters at ELBE will be considerably
improved by replacing the thermionic DC gun by asuperconducting RF photo gun [4] which is planned for2007.

FREE ELECTRON LASERS
To cover the required wavelength range two FELs are
required. The calculated ranges for both FELs are shown

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUCAU02

Figure 1: Layout of the Radiation Source ELBE
in Fig. 2. The U27 FEL consists of two 34-pole sections
with individually adjustable gaps. The undulator period is27.3 mm and the magnet material is NdFeB (hybrid type).
The distance between the two sections is adjustable forphase matching. The gaps can be varied independently
from 13.8 mm to 21 mm corresponding to Krms= 0.7 to
0.3. To optimize the extraction ratio over the whole
wavelength range mirrors with different outcoupling holesizes (1.5, 2, 3, and 4 mm in diameter) are used. The
mirrors are made of gold coated copper.
The U100 FEL for the far infrared range is based on a
SmCo hybrid undulator which consists of 38 magnet
periods each 100 mm long. The Krms can be adjusted from

0.3 to 2.7 which corresponds to gaps of 85 to 24 mm. It isalso equipped with interchangeable outcoupling mirrors(hole diameter 2, 4.5 and 7 mm). To obtain high enoughmagnetic fields in the undulator the gap and consequently
the optical mode has to be sufficiently small. To fulfill
this requirement the U100 FEL is equipped with a partial
parallel-plate waveguide 10 mm wide. The horizontal size
is wide enough to allow free propagation. The waveguidespans from the undulator entrance to the downstream
mirror. In the remaining part of the optical cavity the
optical mode propagates freely. Mirrors are toroidal on
the free propagation side (6.33 m and 3.61 m curvature)and cylindrical (6.33 m curvature) on the waveguideside. They are also made of copper with gold coating.

OPTICAL USER LABS

Fig.2: Wavelength ranges of the U27 and the U100
FELs at ELBE as a function of the electron kinetic
energy calculated for the indicated values of theundulator parameter Krms.

FEL Oscillators and Long Wavelength FELs

Experiments are performed in the IR user labs, that are
shown in the upper left corner of the sketch of Fig. 1. A
lot of ancillary equipment is provided, most importantly anumber of table-top optical sources like femtosecond
Ti:sapphire lasers and a ps Nd:YAG laser which can besynchronized with the FEL to better than a picosecond.
The labs are specially equipped for imaging of thin films
on surfaces by polarization-modulation IR reflectionabsorption spectroscopy and time resolved femtosecond(pump-probe) experiments. Scattering scanning-near-field
optical microscopy (SNOM) has been performed as well,
There is one user lab with permission for handling ofradioactive substances which allows IR spectroscopy onradioactive samples.
The IR beams coming from U27 or U100 both enter acommon beam path at the diagnostic station shown in
Fig. 3. Most of its components are designed for remotely
controlled operation. A scraper mirror is used tooutcouple a certain fraction of the main beam for489

TUCAU02

Proceedings of FEL 2006, BESSY, Berlin, Germany

Fig 3. Layout of the diagnostic station for the IR beam.
diagnostic purposes. It can be directed either to an MCT
detector which is used to monitor the start up of the laser
and its temporal structure and which also acts as areference detector for experiments or to one out of two
power meters. Several MCT detectors are available withpreamplifier bandwidth ranging up to 20 MHz enabling
us to detect individual micro pulses. For very longwavelengths or measurements with extremely highsensitivity a Ge-Ga detector can be set up. Via a beam
splitter part of the diagnostic beam can be sent through awide-range spectrometer. To cope with CW operation of
the FEL a chopper is included in the diagnostic beam path
which is synchronized to the macro pulse in pulsed-mode
operation. The main beam path to the user laboratories
first contains a remotely controlled attenuator. A noncollinear background-free autocorrelator can be used tocharacterize the optical pulse duration. For experiments
requiring lower repetition rates than the 13 MHz roundtrip time of the optical resonators a semiconductor plasma
switch driven by a Nd:YAG laser amplifier at 1 kHz rate
can be used as pulse picker. The optical beamline to theFig 4. Transient transmission change measured with thepump-probe technique in accelerator macro pulsed mode
(left) and in cw mode (right). Both pulses (15.8 µm) are
generated by the FEL.

490

user laboratories is designed for less that 15%transmission loss between 3 and 150 µm wavelength. The
typical horizontal polarization is conserved but can beswitched if necessary.
Proposals for FEL experiments are evaluated and selected
in a peer-review system. Under the name FELBE thefacility is a member of the EC funded “Integrating
Activity on Synchrotron and Free Electron Laser Science(IA-SFS)” which comprises most synchrotron and FEL
facilities in Europe and provides financial support to users
from the EC and associated states. Up to now 12
experiments have been running at the ELBE FEL facility.

OPERATIONAL EXPERIENCES
First lasing of the U27 FEL was achieved in May 2004[5]. Immediately after commissioning routine user
operation was started. Up to now more than 1300 hours
for user FEL experiments were delivered. The availabilityof the machine in 2006 has been higher than 90 %. The
following parameters are achieved in practice: Laser
radiation from 3.4 to 22 µm was generated. The
outcoupled beam power depends strongly on the
wavelength range. Low average power (<5 W) was
observed in the ranges shorter than 5 and longer than 13µm. In the range in between up to 25 W power could be
extracted. In the region above 20 µm the outcoupledpower is smaller than 1 W and finding stable conditions
for lasing is difficult due to the high diffraction andaperture losses in the undulator vacuum chamber. The IR
pulse duration can be varied by detuning the opticalcavity. At 11 µm, which was an often required
wavelength for user experiments, it could be adjusted
from 0.9 to 3.4 ps. It could be shown by comparing
autocorrelation traces with optical spectra that the pulses
are bandwidth limited. By many of the FEL users highaverage power implying cw operation is required. ApartFEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany
from the higher measuring rate and the associated better
signal to noise ratio a clearly higher stability of the laser
at cw operation was observed.
Reasons for thisobservation are the continuous loading of thesuperconducting RF cavities and the continuous laser
operation. Fluctuations due to build up of the laser into
saturation can be avoided. Fig. 3 demonstrates the
improved quality of the experimental data in cw mode. Itshows a typical time resolved transmission traces
measured by the pump-probe-technique in macro pulse
mode (left) and cw mode (right). The measurements weredone in the framework of an experiment to study electron
dynamics in superlattices [6].

TUCAU02

autocorrelation trace within 25 ms [8]. In general, no
synchronization of the FEL with magnetic field pulses isneeded, since the FEL runs continuously at 13 MHz in cw
mode which means that about 105 FEL pulses overlap
with one 10 ms-magnetic field pulse. This should provide
excellent measurement conditions.

ACKNOWLEDGEMENT
The authors thank Todd Smith from HEPL Stanford
University and A.F.G. van der Meer from FELIX
Nieuwegein for her useful help and advice. Furthermore
we thank the engineering stuff of the Forschungszentrum
Rossendorf for the successful cooperation.

OUTLOOKFirst lasing of the U100 FEL was demonstrated on
August, 21-st, a few days before the FEL2006 conference.
Now the actually available wavelength range and theparameters of the IR beam have to be determined. Thenthe extended wavelength range will immediately be madeavailable to the user experiments.
In the near future the beams of the two FELs will bedelivered into the new High Magnetic Field Lab Dresden(HLD) [7] which was built recently in immediate vicinity
to the ELBE building. The HLD will provide magneticfield pulses in the 60-100 Tesla range with 1000-10 ms
pulse duration, thus opening the way for many new
spectroscopic investigations, in particular in solid stateand semiconductor physics. For these investigations also
time resolved experiments are envisaged. The challenge
here is to obtain a complete time-delay scan during thetime of one magnetic field pulse. Recently we havedemonstrated the measurement of an FEL interferometric

FEL Oscillators and Long Wavelength FELs

REFERENCES[1] F.Gabriel et al., NIM B 161-163 (2000), 1143-1147.
[2] J. Teichert et al., Proceedings of the 6th International
Computational Accelerator Physics Conference,Darmstadt, Germany, 2000.
[3] TESLA Test Facility Linac – Design Report (Ed.
D.A. Edwards), DESY print TESLA 95-01.
[4] J.Teichert et al., Proceedings of the 2005 FEL
Conference, p. 534-537, Stanford, USA.
[5] P.Michel et al., Proceedings of the 2004 FEL
Conference, p. 8-18, Trieste, Italy.
[6] D. Stehr et al., Appl. Phys. Lett. 88 151108 (2006)[7] http://www.fz-rossendorf.de/HLD[8] H. Schneider et al., Appl. Phys. Lett. 89 (2006), in
print.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

STATUS OF THE NOVOSIBIRSK HIGH POWER TERAHERTZ FEL*
N.A. Vinokurov#, N.G. Gavrilov B.A. Knyazev, E.I. Kolobanov, V.V. Kotenkov, V.V. Kubarev,
G.N. Kulipanov, A.N. Matveenko, L.E. Medvedev, S.V. Miginsky, L.A. Mironenko, A.D.
Oreshkov, V.K. Ovchar, V.M. Popik, T.V. Salikova, M.A. Scheglov, S.S. Serednyakov, O.A.
Shevchenko, A.N. Skrinsky, V.G. Tcheskidov, Budker INP, Novosibirsk, Russia.
Abstract
The first stage of Novosibirsk high power free electron
laser (FEL) was commissioned in 2003. It is based on thenormal conducting CW energy recovery linac (ERL).
Now the FEL provides electromagnetic radiation in the
wavelength range 120 - 230 micron. The maximum
average power is 400 W. The minimum measured
linewidth is 0.3%, which is close to the Fourier-transform
limit. Four user stations are in operation now.
Manufacturing of the second stage of the FEL (based on
the four-turn ERL) is in progress.

INTRODUCTION
A new source of terahertz radiation was commissioned
recently in Novosibirsk. [1]. It is CW FEL based on an
accelerator–recuperator, or an energy recovery linac(ERL). It differs from other ERL-based FELs [2, 3] in the
low frequency non-superconducting RF cavities andlongerwavelength operation range.
Full-scale
Novosibirsk free electron laser is to be based on the fourorbit 40 MeV electron accelerator-recuperator (see Fig.
1). It is to generate radiation in the range from 5
micrometer to 0.24 mm [4, 5].

3

3

6

2
1

5

Figure 1: Scheme of the accelerator-recuperator based
FEL. 1 - injector, 2 - accelerating RF structure, 3 - 180degree bends, 4 – undulator, 5 – beam dump, 6 – mirrorsof the optical resonator.

ACCELERATOR-RECUPERATOR
The first stage of the machine contains a full-scale RFsystem, but has only one orbit. Layout of the accelerator–
recuperator is shown in Fig. 2. The 2 MeV electron beamfrom an injector passes through the accelerating structure,acquiring the 12 MeV energy, and comes to the FEL,
installed in the straight section. After interaction withradiation in the FEL the beam passes once more through___________________________________________*

The work was partially supported by SB RAS grant N174/06 andby grant 2.1.1.3846 of Russian Ministry of Science and Education.
#
vinokurov@inp.nsk.su

492

Table 1: Accelerator parameters (first stage)
RF frequency, MHz
180
Number of RF cavities
16
Amplitude of accelerating voltage at one 0.7
cavity, MV
Injection energy, MeV
2Final electron energy, MeV
12
Maximum bunch repetition rate, MHz
22.5
Maximum average current, mA
20
Beam emitance, mm·mrad
2
Final electron energy spread, FWHM, % 0.2
Final electron bunch length, ns
0.1
Final peak electron current, A
10
The electron source is the 300 keV DC gun with gridded
cathode. Maximum charge per bunch is 1.7 nC.

FEL

4
6

the accelerating structure, returning the power, and comesto the beam dump at the injection energy. Mainparameters of the accelerator are listed in Table 1.

The FEL is installed in a long straight section of asingle-orbit accelerator-recuperator. It consists of two
undulators, a magnetic buncher, and optical resonator.
Both electromagnetic planar undulators are identical. The
length of an undulator is 4 m, period is 120 mm, the gap
is 80 mm, and deflection parameter K is up to 1.2. The
buncher is simply a three-pole electromagnetic wiggler. It
is necessary to optimize the relative phasing of undulatorsand is used now at low longitudinal dispersion Nd < 1.
Both laser resonator mirrors are spherical, 15 m curvatureradius, made of the gold-plated copper, and water-cooled[6]. In the center of each mirror there is a hole. It serves
for mirror alignment (using the He-Ne laser beam) andoutput of small amount of radiation. The distance
between mirrors is 26.6 m. The forward mirror has thehole with the diameter 3.5 mm, and the rear one - with thediameter 8 mm (See Fig.3). The calculated transparencyof the mirror with the 8-mm hole, at the wavelength 150
micron, is 1.5%. At this wavelength the measured roundtrip loss are near 7%. The output radiation passes throughtwo windows, which separated the FEL and accelerator
vacuum from the atmosphere. After the forward mirror
the additional iris and the normal-incidence quartz
window are installed. After the rear one there is adiamond window, tilted at the Brewster angle.

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany

TUCAU03 

Figure 2: Scheme of the first stage of the Novosibirsk terahertz FEL. The loop lies in the vertical.

8.6 m
76 mm
R 15 m
8 mm

R 15 m

3.5 mm
26.6 mFigure 3: Scheme of the optical resonator.

RADIATION STUDY
The first measurements of radiation parameters werereported before [1].
Instead of the fine tuning of the optical resonator length
we tuned the RF frequency. The tuning curve is shown in
Fig. 4. The preliminary simulation results [7]demonstrated a reasonable agreement with measured data.
The experimental curve is wider, which may be explainedby the shortening of the optical resonator due to mirror
heating.
The average radiation power, passed through the hole atthe rear mirror, was about 400 W. Taking into account the
7% loss, one get approximately 2 kW of power, extracted
from the electron beam. The electron beam power was

FEL Oscillators and Long Wavelength FELs

200 kW. Therefore an electron efficiency is about 1%.
The radiation parameters are listed in Table 2.

Table 2: The radiation parameters
Wavelength, mm
Minimum relative linewidth, FWHM
Pulse length, FWHM, ns
Peak power, MW
Repetition rate, MHz
Maximum average power, kW

0.12...0.23
0.003
0.05
1
11.2
0.4

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Proceedings of FEL 2006, BESSY, Berlin, Germany

1,0

Average power, a.u.

0,8

100

Simulations
Experiment
50

0,6

0,4
0

0,2

0

5

10

15

20

25

Figure 5: Calculated size of equivalent Gaussian beam(mm) vs. distance along the beamline (m).

0,0
-5
-5
-5
-5
-6,0x10 -4,5x10 -3,0x10 -1,5x10

Detuning δf/f

0,00

Figure 4: Dependence of the average power on the RF
frequency detuning.

BEAMLINE AND USER STATIONS
To transmit the radiation from the rear mirror hole touser stations, the beamline from the accelerator hall to theuser hall was built. As the diffractional angulardivergence 1.22·/D = 0.03 (for 200 micron) is high, thespherical mirror is used to transform the radiation beam toalmost parallel one. The incidence angle is only 7
degrees, therefore astigmatism is negligible (see Fig. 5).

Other 5 mirrors are flat. The beamline is filled by dry
nitrogen. It is separated from the accelerator vacuum by
the diamond window, and from the air by thepolyethylene window. After installation of nitrogen dryer
we obtained almost complete transparency of thebeamline.
Now radiation may be delivered to 5 stations. Two ofthem are used for measurement of radiation spectrum, andother three – for users. In particular, the terahertz ablationof DNA and other biologically relevant molecules was
performed [8]. It was shown, that transfer from surface
occurred without molecular destruction.

FURTHER DEVELOPMENTS
We plan to increase further the output power. The
electron gun upgrade for the increase of the average

Figure 6: Scheme of the second stage of the Novosibirsk terahertz FEL. The terahertz FEL orbit lies in the verticalplain. Other four orbits lie in the horizontal one.

494

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Proceedings of FEL 2006, BESSY, Berlin, Germany
current up to 0.1 A is in progress.
The design and manufacturing of the full-scale fourturn ERL is underway. An artistic view of the machine isshown in Fig. 6. The existing orbit with the terahertz FEL
lies in the vertical plane. The new four turns are in thehorizontal one. One FEL is installed at the fourth orbit(40 MeV energy), and the second one at the bypass of thesecond orbit (20 MeV energy).

FEL Oscillators and Long Wavelength FELs

TUCAU03

REFERENCES[1] E. A. Antokhin et al. NIM A528 (2004) p.15-18.
[2] G.R. Neil et al. Phys. Rev. Lett. 84 (2000), p. 662.
[3] E.J. Minehara. NIM A483, p. 8, 2002.
[4] N.G. Gavrilov et al. IEEE J. Quantum Electron., QE27, p. 2626, 1991.
[5] V.P.Bolotin et al. Proc. of FEL-2000, Durham, USA,
p. II-37 (2000).
[6] Kubarev V.V., Persov B.Z., Vinokurov N.A., Davidov
A.V. NIM A528 (2004), No. ½, p. 199-202.
[7] O.A. Shevchenko, A.V. Kuzmin, N.A. Vinokurov.
NIM A543 (2005), No. 1, p. 114-117.
[8] A. K. Petrov et al., Russian Dokl. Acad. Nauk, v. 404(2005), No. 5, p. 1 – 3.

495

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Proceedings of FEL 2006, BESSY, Berlin, Germany

FEL ACTIVITIES IN INDIA
S. Krishnagopal*, B. Biswas, S. Chouksey, S. K. Gupta, U. Kale, A. Kumar, V. Kumar, S. Lal, P.
Mehta, P. Nerpagar, K. K. Pant, RRCAT, Indore, India.
Abstract
We are building a Compact Ultrafast TErahertz FreeElectron Laser (CUTE-FEL), designed to lase from 50 –100 µm. The FEL will be driven by a 10-15 MeV electron
beam from a Plane-Wave Transformer (PWT) linac. The
undulator is a 5 cm period, 2.5 m long PPM planar
undulator. We present details of the FEL design and thepresent status of activities. We also present very
preliminary plans for a short-wavelength SASE FEL in
India.

INTRODUCTION
FEL activity in India is presently restricted to the Raja
Ramanna Centre for Advanced Technology, Indore, wherea terahertz FEL is under construction. Earlier, however,there was some activity at Pune University, where a 26mm period, 39 cm long pure permanent magnet undulator
was built and characterized [1]. At the Institute for Plasma
Research, Ahmedabad, there was interest in FELs forplasma heating and diagnostics. A 50 period

observed [2].
In this paper we focus on ongoing activities at RRCAT,and present briefly our plans for the future.

THE CUTE-FEL PROJECT
The terahertz is a relatively unexplored part of theelectromagnetic spectrum, and there is presently
substantial interest in terahertz sources. For an FEL theterahertz is attractive because the long wavelength allows
for higher gain, and reduces the requirements on the beam
current and quality. A THz FEL is therefore a good greenfield FEL project.
The Compact Ultrafast TErahertz FEL (CUTE-FEL)
project aims to lase between 50-100 µm. The layout of thebeamline is shown in Figure 1. The main parameters of
the FEL are given in Table 1.
The electron source is a thermionic electron gun, thatwill provide 90 kV, 1 nC, 1 ns (FWHM) electron pulses at
36.62 MHz. The design normalized rms beam emittanceis 5π mm-mrad, and the rms energy spread will be better

Figure 1: Beam-transport line for the CUTE-FEL.
electromagnet undulator was developed, a 300 keV sheet than 1%. This gun is under procurement. In the meantime
electron beam from a Tesla transformer was transmitted we continue experiments with a 40 kV, 2 µs, triode gun
through this undulator, and spontaneous emission was that was built by another group in RRCAT [3].
___________________________________________*skrishna@cat.ernet.in

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Parameter

Value

Unit

Energy10-15

MeV

Peak current

20

A

Micro-pulse

20 @ 36.62

ps @ MHz

Macro-pulse

8 @ 10µs @ Hz

Und. period

5cm

Und. length

2.5

mUnd. param.

0.8

Wavelength50-100coupled power of around 0.5 MW. The small-signal gain
is 88%, while the round-trip loss is 15%.
Figure 3 shows the variation of the FEL beam size
down the undulator. At the entrance and exit of theundulator the maximum 1/e beam radius is around 5 mm.
Note that the matched rms vertical beam size of theelectron beam within the undulator is 0.8 mm.
5.5

Radiation beam 1/e radius (mm)The electrons from the gun will be bunched in a 476
MHz pre-buncher, which has been designed by us and ispresently being fabricated. The design is a standard reentrant pillbox cavity, and will compress the beam by afactor of around 18.
The buncher at 2856 MHz will be a 4-cell Plane Wave
Transformer (PWT) structure, and the linac itself willcomprise up to two 8-cell structures to go to a maximum
energy of 15 MeV. More details on the PWT structure,
which we have developed ourselves, are given in a later
section.
Table 1: Main parameters of the CUTE-FELTUCAU04

5.0
4.5
4.0
3.5
3.0
2.5
2.0
0.0

0.5

1.0

1.5

2.0

2.5

Distance down the undulator (m)Figure 3: Size of the radiation beam as a function of
distance down the undulator.

UNDULATORµm

The undulator is a standard Halbach configuration,
planar PPM undulator, using NdFeB magnets. It has aperiod of 5 cm and a total length of 2.5 m. We have
performed detailed design simulations using the code
TDAOSC [4] AND GENESIS 1.3 [5]. In order to make the FEL
compact, we have tried to keep the optical cavity as short
as possible – it is only 4.1 m long. The resonator is nearconcentric, to provide good mode stability.

The 5 cm period, 2.5 m long PPM undulator has been
constructed [6] in two equal segments of 25 periods each(Fig. 4). The undulator gap can be varied from 20-100
mm. The magnets are made of NdFeB, each 12.5 x 12.5 x
50 mm3 in size. Individual magnets were characterized,
and their arrangement in the undulator determined using a
global optimisation (simulated annealing) algorithm.
Field measurement of the assembled undulator segments
was done using a three-axis Hall probe (Senis GmbH),
with a spatial resolution of 0.1 mm.

800

Out-coupled power (kW)

700
600
500
400
300
200
100
0
0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Out-coupling hole radius (mm)Figure 2: Optimisation curve for the size of the outcoupling hole.

Figure 4: A view of the two undulator segments, eachof length 1.25 m.

Radiation is out-coupled through a hole at the centre of
one of the gold-plated copper mirrors. The optimal holeradius, to maximize the out-coupled power while
maintaining a good mode profile, was determined to be 2
mm (see Fig. 2). For our design we get a peak out-

A summary of the measurements is given in Table 2. It
can be seen that almost all the parameters are within thedesign specification. Our initial measurements showedthat the beam trajectory through U25.2 had a degree ofdrift. To correct this we built a corrector coil that gives a

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Proceedings of FEL 2006, BESSY, Berlin, Germany

small, 0.77 G, vertical field. With this correction the
trajectory straightens out to within acceptable limits (Fig.
5). Further improvements can be done by shimming themagnets.
Table 2: Design and measured parameters of the two
undulator segments
Parameter

Designvalue

U25.1
measuredU25.2
measuredError inpeak field

< 1%

0.9%

0.7%

Error inperiod< 100 µm

82 µm

85 µm

rms phaseshake

< 5°

2°

2°

Beam
wander

<1

1.14

0.33

Figure 6: Components of the 4-cell PWT linac
structure.
We have injected beam from a 40 kV thermionicelectron gun into this structure, and have accelerated it toan energy of 3.5 MeV, corresponding to an accelerating
gradient of around 25 MV/m. We also have ready asecond 4-cell structure, PWT4, and are presently in the
midst of fabricating an 8-cell PWT structure.

Horz. beam position (mm)1.5

Without corrector coil field
1

0.5

With -0.77 G (86.5 G-cm)
corrector coil field

0

S-BAND PHOTOINJECTOR

-0.5
-1

-1.5
0

500

1000

1500

Axial distance (mm)Figure 5: Electron beam trajectory through theundulator, with and without the corrector coil.

Independent of the CUTE-FEL project, we have also
been developing an S-band photoinjector, keeping in
mind the requirements of short-wavelength FELs [8]. Our
gun is based on the standard BNL/SLAC/UCLA Gun 4
design. We have performed extensive electromagnetic
and beam dynamics design simulations using SUPERFISH,
GDFIDL and PARMELA. We have also studied the injectionof beam from the gun into a PWT linac structure.

PWT LINAC
A major challenge has been the indigenousdevelopment of the linear accelerator technology. We alsochose to build a rather unconventional structure – theplane wave transformer (PWT) linac [6]. This is a much
more open structure, with strong coupling between thecells – and consequently with reduced fabrication
tolerances. The only PWT linac working in the world is at
UCLA [7], where it is routinely used, mainly for FEL
applications.
After building a number of prototypes and ascending asteep learning curve, we now have a four-cell, 21 cm long
structure, PWT3 (Fig. 6) that has been fabricated to therequired tolerances (30 µm) and surface finish (0.2 µm
CLA), which can hold UHV (1x10–8 torr), resonates at thedesired frequency of 2856 MHz, and has a loaded Q of
8,000.

498

Figure 7: Components of the ETP Cu prototypes of thephotocathode RF gun.
We have built a number of prototypes, of ETP and OFE
copper, to qualify machining and brazing issues (Fig. 7).
We have also built a number of aluminium prototypes forcold tests and for tuning the gun. We have developed atwo-step tuning procedure to get the desired gun
parameters – resonant frequency of the π-mode at 2856

FEL Oscillators and Long Wavelength FELs

Proceedings of FEL 2006, BESSY, Berlin, Germany
MHz, β = 1 and field balance of unity, directly, without
empirical tuning of the gun during cold-tests (Fig. 8). We
have now given an order to an Indian vendor for
fabricating four photocathode guns.

FB=1.

TUCAU04

three-stage roadmap has been proposed, summarized inTable 3.
There is already substantial interest amongst the user
community in the country, particularly in materials
science, for an IR-FEL facility (Stage I of the proposed
roadmap). Another user workshop is planned to be held
later this year.

CONCLUSIONS
A terahertz FEL, the CUTE-FEL, is in an advanced
stage of construction at RRCAT. We have developed a
PWT linac injector for the FEL, and have accelerated
beam to 3.5 MeV in a 4-cell structure. We have built a 5
cm period, 2.5 m long PPM undulator. We are also in the
final stages of development of an S-band photoinjector.
Based on this foundation, and on interest shown by theuser community, we expect a rapid expansion in the FEL
activities in India in the coming years, starting with an IRFEL facility, and perhaps continuing towards an XFEL in
the future.
Figure 8: Bead-pull of a tuned Al prototype
photocathode gun.

FUTURE PLANS
While we are presently focused on getting the CUTEFEL lasing, some thought is also being given to future
FEL activities in the country.
Table 3: Preliminary proposal of a 3-stage roadmap for
the FEL programme in India
Stage
I

Stage
II

Stage
III

Wavelength (nm)

1,000

10

0.1

Energy (GeV)

0.1

1

10

Norm. emitt. (mm-mrad)

5

3

1

Undulator period (mm)

50

30

30

Undulator length (m)

5

30

100

Undulator param. ‘K’

1

1.5

3

Peak current (A)

0.1

2

4

Pulse structure(fs @ Hz)

1,500
@ 50

150 @
50

75 @
??

Accel. Tech.

Norm.
cond.

Norm.
cond.

???

ACKNOWLEDGEMENTS
We thank Dr. R. V. Nandedkar and Dr. V. C. Sahni for
their constant support and encouragement. We also thanka large number of colleagues, too numerous to be listed,
for their support and contribution to the CUTE-FEL
project.

REFERENCES[1] V. B. Asgekar et al., Jap J Appl Phys, 37, 3563,(1998).
[2] A. V. Ravi Kumar at al., IEEE Trans. Plasma Sci. 26,
556 (1998).
[3] S. Mahadevan et al., Nucl. Instr. And Method A, 496,
26 (2003).
[4] S. Krishnagopal et al., Nucl. Instr. And Meth. A 318,
661 (1992).
[5] http://pbpl.physics.ucla.edu/~reiche/index.html[6] B. Biswas et al., InPAC’05, Kolkata, March 2005, p.
89.
[7] A. Kumar, K. K. Pant, S. Krishnagopal, Phys. Rev.
ST Accel. Beams, 5, 00033501 (2002).
[8] R. Zhang, Ph. D. Dissertation, UCLA, 1997.
[9] A. Kumar, K. K. Pant, S. Krishnagopal, Phys. Rev.
ST Accel. Beams, 5, 103501 (2002).

A joint Indo-French Workshop on FELs, was held in
Goa, India, in March 2006. The consensus that emerged
from this Workshop, especially from the Indian users who
participated, was that a phased approach towards shortwavelength FELs, perhaps ultimately culminating in an
XFEL, was highly desirable. To this end a preliminary

FEL Oscillators and Long Wavelength FELs

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Proceedings of FEL 2006, BESSY, Berlin, Germany

OUTPUT BANDWIDTH EFFECTS IN SEEDED, HARMONIC CASCADE
FELS
W.M. Fawley, G. Penn, A. Zholents, LBNL, Berkeley, California

Abstract
A number of laboratories are studying and/or proposing seeded
Harmonic Cascade (HC) FELs as a means both to reach soft
x-ray output wavelengths and to provide a degree of longitudinal coherence much greater than that normally possible
with SASE devices. While theoretically the output bandwidth of a HC FEL can approach the transform limit given ahigh quality input seed of reasonable power, there appear to
be a number of practical considerations that in many cases
can increase the output bandwidth many-fold. In particular, designs that employ dispersive sections following modulator sections in order to increase the amount of coherent
harmonic microbunching, can be very sensitive to temporalvariations in the electron beam energy, resulting in an output wavelength chirp. Unwanted microbunching inducedby the combination of longitudinal space charge instability
growth in the linac and CSR in compression sections also
can lead to variations in the output radiation phase and amplitude, thus increasing the bandwidth. We give some semianalytical results for the predicted bandwidth increase for
HC configurations and also some detailed numerical simulation results.1

PAPER NOTAVAILABLE

1 Work supported in part by the US DOE under Contract no. DE-AC02-

05CH11231.

500

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THAAU02

FOURIER OPTICS TREATMENT OF CLASSICAL RELATIVISTIC
ELECTRODYNAMICS
G. Geloni∗ , E. Saldin, E. Schneidmiller and M. Yurkov,
Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany.
Abstract
We coupled Synchrotron Radiation (SR) theory withlaser beam optics. In the space-frequency domain SR
beams are described by solutions of the paraxial wave
equation. They appear as laser beams with transverse size
much larger than the wavelength. In practical situations(e.g. undulators, bends), SR beams exhibit a virtual source,
similar to the waist of a laser-beam, strictly related with
the inverse Fourier transform of the far-field distribution.
The Fresnel formula can be used to propagate the field distribution from the waist to anywhere in space. The general theory of SR in the near-zone developed in this paper
is illustrated for the special cases of undulator radiation,edge radiation and transition undulator radiation (TUR). By
solving the inverse problem for the electric field we find analytical expressions for near-field distributions in terms of
far-field data. A more detailed explanation of this subject
is provided in [1].

INTRODUCTION
In previous works we developed a formalism ideallysuited for analysis of SR problems, where we took advantage of Fourier Optics ideas [1]. Fourier Optics provides an extremely successful approach which revolutionized the treatment of wave optics problems and, in particular, laser beam optics problems. The use of Fourier Optics
led us to establish basic foundations for the treatment of
SR fields in terms of laser beam optics. Radiation froman ultra-relativistic electron can be interpreted as radiationfrom a virtual source producing a laser-like beam. The virtual source is regarded as the analogous of the waist for alaser beam, and often exhibits a plane wavefront. In thiscase it is specified, for any given polarization component,
by a real-valued amplitude distribution of field. The laserlike representation of SR is intimately connected with theultra-relativistic nature of the electron beam. In particular,
paraxial approximation always applies. Then, free spacebasically acts as a spatial Fourier transformation, and thefar-zone field is, aside for a phase factor, the Fourier transform of the field at any position z down the beamline. It isalso, aside for a phase factor, the Fourier transform of thevirtual source. Once the field at the virtual source is known,
the field at other longitudinal positions, both in the far andin the near zone up to distances to the sources comparable with the radiation wavelength, can be obtained with thehelp of the Fresnel propagation formula. This means thatthe near-zone field can be calculated from the knowledge∗ gianluca.aldo.geloni@desy.de

FEL Theoryof the far-zone field, that is possible because the paraxial approximation applies. The knowledge of the far-zone
field completely specifies, through the Fresnel integral, thenear-zone field as well. In the case when the electron generating the field is not ultra-relativistic, though, the paraxial approximation cannot be applied. Typically, the wavelength is comparable with the radiation formation length,
and it is impossible to reconstruct the near-field distribution from the knowledge of the far-field pattern [2]. An
arbitrary SR source is equivalent to several virtual sources
inserted between the edges of each magnetic device. This
provides conceptual insight of SR sources and should facilitate their design and analysis. In fact, since the analysis of SR sources can be reduced to that of laser-likesources, it follows that any result, method of analysis ordesign and any algorithm specifically developed for laser
beam optics (e.g. the code ZEMAX, see [1]) is also applicable to SR sources. We first apply our method to undulator radiation around resonance. We find the field distribution of the virtual source with the help of the far-zone
field distribution and we propagate to any distance of interest. Similarly, we treat edge radiation [1], studying theemission from a setup composed by a straight section andtwo (upstream and downstream) bends. We derive an expression for the field from a straight section that is valid
at arbitrary observation position. Due to the superposition
principle, this expression can be used as building block formore complicated setups. We use this idea to analyze a
TUR setup consisting of an undulator preceded and followed by straight sections and bends (upstream and downstream). The first study on TUR constituted a theoreticalbasis for many other studies [1], dealing both with theoretical and experimental issues. More recently, TUR has
been given consideration in the framework of large XFEL
projects. A method was also proposed [1] to obtain intense
infrared/visible light pulses naturally synchronized to x-ray
pulses from the LCLS XFEL by means of Coherent TUR.
In view of these applications, there is a need to extend theknowledge of TUR to the near zone. We address it here.

FAR-FIELD DATA INVERSE PROBLEM
 r , t) as
We represent the electric field in time domain E(a time-dependent function of an observation point located r , t)at position r = r⊥ + zz . In free-space, the field E(satisfies the source-free wave equation. For monochromatic waves of angular frequency ω the wave amplitude
 (z, r ) exp[−iωt]+C.C., ⊥ (z, r⊥ , t) = Ē
has the form E⊥⊥
where the frequency ω is related to the wavelength λ by

501

THAAU02

Proceedings of FEL 2006, BESSY, Berlin, Germany

 describes the variation of the wave
ω/c = 2π/λ, and Ē⊥ actually repamplitude in the transverse direction. Ē⊥resents the amplitude of the electric field in the spacefrequency domain. We assume that the ultra-relativistic
approximation is satisfied, that is always the case for
SR setups. In this case the paraxial approximation applies [1]. This implies a slowly varying envelope of the
field with respect to the wavelength. We therefore in
troduce E⊥ = Ē ⊥ exp [−iωz/c]. In paraxial approxi
mation and in free space, E⊥ obeys the paraxial wave
equation along any fixed polarization component, that is⊥ = 0, where derivatives in the Lapla[∇⊥ 2 +(2iω/c)∂z ]Ecian operator ∇ ⊥ 2 are taken with respect to the transverse
coordinates. Solving this equation with given initial conditions at z gives
⎡ 
2 ⎤





iω

r
−
r
 ⎥
iω
⎢  o⊥dr E⊥ (z, r ) exp ⎣E⊥ =⎦2πc(zo − z)2c(zo − z)(1)where the integral is performed over the transverse
plane.
A propagation equation for F(z, u) =⊥ (z, r ⊥ ) exp [ir ⊥ · u], that is the spatial Fourierdr ⊥ E
transform of the field, reads instead:ic|u|2 (z − zs ),F (z, u) = F (zs , u) exp −2ω

(2)where zs is identified with the position of a virtual source.
Identification of the position z s = 0 with a virtual source
position is always possible, but not always convenient (although often it is). From Eq. (1) and Eq. (2) a relation
follows between the far-zone field distribution, dependent and the field distribution at theon the observation angle θ,
virtual source position z s :⊥ (zs , r⊥ ) =Eiω|θ|2dθ exp −(zo + zs )2c⊥ (θ) exp iω r⊥ · θ .
(3)
×E
c
iωzo
2πc



Finally, the transverse components of the envelope of the
far field can be written as [1]:iωe ∞ vx (z  )

E
=
−
dz
exp
[iΦ
]
⊥
T
2
c
o −∞
 c z
xovy (z  ) yo
−
x +
y ,
−
zo
c
zo
(4)
where the total phase Φ T iss(z  ) z −+ωΦT = ω
v
c

502



z
1
+ 2
zo
zo



[xo − x (z  )] + [yo − y  (z  )]
2c
2

×

2

(5)

and the charge of the electron is (−e). Eq. (4) can beobtained starting directly with Maxwell’s equations in thespace-frequency domain. Here v x (z  ) and vy (z  ) are thehorizontal and the vertical components of the transverse
velocity of the electron, while x  (z  ) and y  (z  ) specify thetransverse position of the electron as a function of the longitudinal position. Finally, we defined the curvilinear abscissa s(z  ) = vt (z  ), v being the modulus of the velocityof the electron. Eq. (4) can be used to characterize the far
field from an electron moving on any trajectory as long as
the ultra-relativistic approximation is satisfied. Then, once
the far field is known, Eq. (3) can be used to calculate
the field distribution at the virtual source. Finally, Eq. (1)solves the propagation problem at any observation position
zo . Note that part of the phase in Eq. (5) compensates withthe phase in |θ|2 in Eq. (3) at z s = 0. If Eq. (4) describes
a field with a spherical wavefront with center at z = 0,such compensation is complete. The centrum of the spherical wavefront is a privileged point, and the plane at z = 0
exhibits a plane wavefront. This explains why the choicezs = 0 is often privileged with respect to others.

DISCUSSION
It makes sense to ask what is the range of observation
positions where our algorithm applies, and what is the accuracy of our result in this range. We show that the paraxial
approximation holds with good accuracy up to observation
positions such that its distance d from the electromagnetic
sources in the space-frequency domain, when d  λ. To
do so, we compare results from the paraxial treatment withresults without the help of the paraxial approximation. The
paraxial equation must then be replaced with Helmholtz
 + ω 2 Ē
 = 4πc2 ∇ρ̄ − 4πiωj̄ , ρ̄(r, ω)equation c2 ∇2 Ēand j̄ (r, ω) being the Fourier transform of the charge density ρ(r, t) = −eδ(r − r (t)) and of the current densityj(r, t) = −ev(t)δ(r − r (t)). Application of the proper
Green’s function yields:1β − ndz vz (z  ) |ro − r (z  )|
−∞ 

 
ic
n
s(z ) z −
exp iω
−ω |ro − r (z  )|2
v
c


|ro − r (z  )| zo − z 
−
.
(6)
+
c
c

iωe

E(
ro , ω) = −c ∞Eq. (6) is an exact solution of Maxwell’s equations withboundary conditions at infinity. The exactness of Eq. (6)allows us to control the accuracy of the paraxial approximation. A conservative estimate shows that when d  L f
this accuracy is of order c/(ωL f ), but quickly decreases
as Lf  d  c/ω remaining, at least, of order of c/(ωd).

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany
The integrand term scaling as 1/R 2 (with R = |ro −r (z  )|)can be dropped in Eq. (6) whenever d  λ. This is always the case in paraxial approximation. Note that the inverse field problem cannot be solved without applicationof the paraxial approximation. In this case we should solve
the homogeneous Helmholtz equation with boundary conditions constituted by the knowledge of the field on a open
surface (for example, a transverse plane) and additionally,
Rayleigh-Sommerfeld radiation condition at infinity (separately for all polarization components). This is not enoughto reconstruct the field at any position in space. However,if the paraxial approximation is applicable, the inverse fieldproblem has a unique and stable solution. We recognize a
few observation zones of interest. Far zone. d is suchthat n = const. Formation zone. Defined by d  L f .
Radiation zone. The field can be interpreted as radiation.
1/R−zone . The term in 1/R 2 can be neglected in Eq.
(6). Reconstruction zone. The inverse problem based on
far-field data can be solved.
In all generality, from Eq. (6) follows that the 1/R−zone
always coincide with the reconstruction zone. Any system
of interest is characterized by a size a, a formation length
Lf and the radiation wavelength λ. In the case of ultrarelativistic systems a  Lf  λ. Then, the near zone isdefined by d  a, the formation zone by d  L f , the radiation zone, the reconstruction zone and the 1/R−zone byd  (c/ω). Ultra-relativistic cases present an increased
level of complexity with respect to others. This complexity
is at the origin of several misconceptions. Usually textbooks do not follow a direct derivation of Eq. (6). They
start with the solution of Maxwell’s equation in the spacetime domain, the Lienard-Wiechert fields, and they apply a
Fourier transformation:


 ∞


n − β 2 R(t )2γ 2 (1 − n · β)−∞
 × β]˙
n × [(n − β)R(t )
exp iω t ++ 2 R(t )cc(1 − n · β) r , ω) = −e
Ē(
o

dt



(7)


where β̇ = v̇/c. Inspecting Eq. (7) it looks paradoxical thatthe near field, including velocity and acceleration terms,
can be characterized starting from the far zone, including
acceleration term only. However, the magnitude of terms
in 1/R2 and 1/R in Eq. (7) does not depend on λ, whilethat of terms in 1/R and 1/R 2 in Eq. (6) does. Eq. (6) andEq. (7) are equivalent, as can be shown by addition of thefull derivative dΦ(t  )/dt of a properly chosen Φ(t  ) function to the integrand of Eq. (7) (and using t  = z  /vz (z  )).
Addition of different full derivatives yields an infinite number of equivalent representations for the field, and physicalsense can be ascribed to the integral only. The terms in
1/R and in 1/R 2 in Eq. (6) appear as a combination of theterms in 1/R (acceleration term) and 1/R 2 (velocity term)in Eq. (7). They differ from each other. As a result, there
are contributions to the radiation from the velocity part in

FEL Theory

THAAU02

Eq. (7). The presentation in Eq. (6) is most interesting
because the magnitude of the 1/R 2 -term in Eq. (6) can bedirectly compared with the magnitude of the 1/R-term inside the sign of integral, that is related to the 1/R-zone andto the reconstruction zone. If one forgets about this fact
one would incorrectly conclude that far-field data cannot
be used to reconstruct the field in the near-zone.

UNDULATOR LASER-LIKE SOURCE
Let us apply our algorithm in the case of undulator
radiation at resonance, i.e. ω/(2γ 2 c)(1 + K 2 /2) =2π/λw . Here λw is the undulator period, and K =λw eHw /(2πme c2 ), me being the electron mass and H w
being the maximum of the magnetic field produced by the
undulator on the z axis. Position z = 0 is in the undulator center. A well-known, axis-symmetric expression for⊥ (zo , θ) from athe distribution of the first harmonic field E
planar undulator in the far-zone as a function of the observation angle θ is2⊥ = − KωeLw AJJ exp i ωzo θ2 sinc ωLw θ , (8)E
c2 z o γ2c4cwhere the field is polarized in the horizontal direction,
Lw = λw Nw is the undulator length, N w the numberof undulator periods and A JJ = Jo [K 2 /(4 + 2K 2 )] −J1 [K 2 /(4 + 2K 2 )], Jn being the n-th order Bessel function of the first kind. Eq. (8) describes a field with spherical wavefront centered at z = 0. Eq. (3) yields the field
distribution at the virtual source (also axis-symmetric) [1]:⊥ (0, r⊥ ) =EKωei 2 AJJ π − 2Si
c γ



2
ωr⊥
Lw c


, (9)

Si(·) being the sin integral function and r ⊥ the distancefrom the z axis on the virtual-source plane. In laser physics,
the waist is in the center of the optical cavity and theRayleigh length is related to the resonator geometrical factor. Our virtual source is in the center of the undulator andthe Rayleigh length is related to L w . In both cases we havea plane phase front, and the transverse dimension of thewaist is much larger than λ. Also, the phase of the wavefront in Eq. (9) is shifted of −π/2 with respect to the wavefront in the far zone in analogy with the Guoy phase shift.
Eq. (1) gives the field at arbitrary observation position z o :⊥ = KωeAJJ
E
2



 c γ 2
2
iωr⊥
iωr⊥
− Ei
× Ei
2zo c − Lw c
2zo c + Lw c

(10)Ei(·) being the exponential integral function. The field singularity at zo = Lw /2 and r⊥ = 0 is related with the use of
the resonant approximation. Introducing normalized unitsr̂ = ω/(Lw c)r⊥ , θ̂ = ωLw /cθ and ẑ = z/Lw weobtain the intensity profile at the virtual source

503

THAAU02

Proceedings of FEL 2006, BESSY, Berlin, Germanyx^I

Screen
zo

1
0.8

A

O

z

B

0.6
0.4
0.2

-2

^I

-1

1

2

1
0.75
0.5
0.25
0
-2
2

Figure 3: Edge radiation geometry.

^r

where θ̂ = r̂⊥ /ẑo . Iˆ at the virtual source is plotted in Fig.
1. The evolution of the intensity profile for different z o ,Eq. (12), is given in fig. 2. A virtual source can be used
as an input for wavefront propagation codes (as ZEMAX ,PHASE, SRW [1]), allowing for the presence of complicate
optics, likewise it has been used as an input to Eq. (1) forfree-space propagation. Spontaneous SR from an electron
beam can be treated as an incoherent collection of laser-likebeams with different offsets and deflections (summing up
the intensities), while if the electron beam is distributed coherently, radiation can be described as a coherent collectionof laser-like beams.

2
1
0

^y

-1
-1

0

^x

1
2

-2

Figure 1: Intensity pattern Iˆ at the virtual source.

2

1.5

1.5

1

1

0.5

-6

-4

0.5

-2

2

4

6

-6

-4

θ^

^
z = 0.6

-2

2

-4

2

2

1.5

1

1

0.5

0.5

2

^
z=1

6

θ^

^
I

1.5

-2

4

^
z = 0.75^
I-6

EDGE RADIATION

^
I

^
I
2

4

6

θ^

-6

-4

-2

2

^
z=4

4

6

θ^

Figure 2: Evolution of the intensity profile as in Eq. (12)(solid lines) compared with far field asymptotic (dashedlines).

 2 2ˆ r̂⊥ ) = 1 π − 2Si r̂⊥
,
I(0,
2
π

(11)

and at any distance ẑ o , both in the near and in the far zone:
 


2


2 2
2 2
iẑ
θ̂
θ̂
iẑ


o
o
− Ei
Iˆ ẑo , θ̂ = ẑo2 Ei
 , (12)
2ẑo − 12ẑo + 1 


504



We consider the system depicted in Fig. 3. An electron enters the setup via a bending magnet, passes througha straight section (segment AB) and exits the setup via another bend. Edge radiation (see references in [1]) is collected at a distance zo from the center of the straight section. The trajectory and, therefore, the space integrationin Eq. (4) consists of the two bends b 1 and b2 , and of thestraight section AB. Let L be the length of AB. Points A
and B are thus located at z A = −L/2 and zB = L/2. In
general, one should sum the contribution due to the straightsection to that from the bends. In some cases the presence of the bending magnets can be ignored as if they had
zero length, and what may be called ”zero-length switchers
approximation” applies. Magnets act like switchers: thefirst magnet switches the radiation harmonic on, the second switches it off. Switchers may have different physicalrealizations, depending on the setup. There is no limitation to the length of the switcher. The only common feature between different switchers is that the switching process depends exponentially on the distance from the beginning of the process. Since electrodynamics is a linear theory, when the straight-section contribution cannot be considered a good approximation to the total field, it can still
be considered as a fundamental building block for a more
complicated setup. This justify our choice to deal with thestraight-section contribution to the field only. It is interesting to discuss when the field due to switchers is negligible in our study-case. For L  γ 2 (c/ω), the formation
length for the straight section is γ 2 (c/ω), while the formation length for the bend is ((c/ω)ρ 2 )1/3 , ρ being the radius

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

THAAU02

There are two asymptotic cases for the problem parameter φ̂: φ̂  1 and φ̂  1. The behavior of the far-fieldemission is well-known in literature [1]. We take this as thestarting point for investigations based on Fourier Optics.

Method of virtual sources
Edge radiation as a field from a single virtual source.

Eq. (3) and Eq. (13) yield the virtual source E(0,r⊥ ):
2 

eLω

E
=−
2πc3

 iω θ · r  Lω 1 ⊥
θ2 + 2expdθθsinc
4c
γ
c
(14)

Figure 4: Directivity diagram (solid lines) of the radiationfrom the setup in Fig. 3 and envelope of the directivity
diagram (dotted lines).

of the bend. Let the ratio between the latter and the former
be 2 = (λc /λ)2/3  1, where λc = 4πρ/(3γ 3 ) is the critical wavelength for SR and λ  λ c , as we are interested
in edge radiation. The distance d c = γ 2 (ω/c) turns out
to constitute an extra characteristic-length for our system.
When d  dc , the straight section contribution dominates
the bending magnet one for r ⊥ > γ(ω/c), while for othervalues of r⊥ the two contributions are comparable. Whend ∼ dc the zero-length switcher approximation cannot be
used. When d  dc we the straight section contribution
dominates for 0 < r⊥  ((ω/c)2 ρ)1/3 , the characteristic
size of the radiation being ((ω/c) 2 ρ)1/3 . Finally, whend  γ 2 (ω/c), the straight section contribution dominates
for 0 < θ  ((ω/c)/ρ)1/3 , the characteristic angle of theradiation being ((ω/c)/ρ) 1/3 .

Far field pattern of edge radiation
Field contribution calculated along the straight section. Accounting for the geometry in Fig. 3 we haves(z  ) = z  for zA < z  < zB . Use of Eq. (4) yields
the field contribution from the straight section AB:iωeLωLiωθ2 zo θ sincexp
E
AB = 2
c zo
2c
4c



1
2
θ + 2
.
γ
(13)

Eq. (13) is describes a spherical wave and explicitly depends on L. The formation length L fs for the straight section AB can be written as L fs ∼ min[γ 2 (c/ω), L]. The
far-zone asymptotic is independent of such value and always valid at observation positions z o  L.
Energy spectrum of radiation. With the help of normalized quantities θ̂ = ωL/cθ and φ̂ = ωL/(γ 2 c) we
may write the directivity diagram Iˆ of the radiation asIˆ ∼ θ̂2 sinc2 [(θ̂2 + φ̂)/4]. This is plotted in Fig. 4 forseveral values of φ̂ as a function of the normalized angle θ̂.
The natural angular unit is evidently (2πL/λ) −1/2 .

FEL Theory

The Fourier transform in Eq. (14) is difficult to calculate
analytically in full generality. An analytic expression for
the field amplitude at the virtual source for φ̂  1 reads:

ω
4ωe

2
E(0,
r⊥ ) = 2 r⊥ sinc|r⊥ | .
c L
Lc

(15)

For any value of φ̂, Eq. (15) explicitly depends
on L, as
the far-field emission does. Using r̂ = ω/(Lc)r⊥ theˆ ∼ r̂2 sinc2 (r̂2 )intensity pattern of the virtual source is I(r̂)
and is plotted in Fig. 5. The Fresnel formula yields the fieldin the near and the far zone for φ̂  1

2
2
ωr⊥
2e r⊥
−iωr⊥

exp
exp
i
E
=−
2
c r⊥
2czo
2czo (1 + 2zo /L)
2
iωr⊥
,
(16)
− exp
2czo (−1 + 2zo /L)
where the singular behavior at r ⊥ = 0 and zo −→ L/2
cannot be resolved within the paraxial approximation. The
intensity profile associated with Eq. (16) is




2


2
2
−i
θ̂
ẑ
ẑ
i
θ̂
1


o
o
− exp
Iˆ =
 exp
 ,
2(1 + 2ẑo )2(−1 + 2ẑo ) 
θ̂2 
(17)
where θ̂ = r̂o /ẑo and ẑo = zo /L. A comparison between
intensity profiles at different observation points ẑ o is plotted in Fig. 6. When condition φ̂  1, studied until now, is
not satisfied, the integral in Eq. (14) can be calculated numerically. The intensity distribution for the virtual sourceat φ̂ = 0.1, φ̂ = 1, φ̂ = 10 and φ̂ = 50 are plotted in Fig.
7. An enlarged plot of the case φ̂ = 50 is given in Fig.
8. Fine structures are now evident, consistently with Fig.
4 for the far zone. Once the field at the virtual source is
specified for any value of φ̂, Fourier Optics can be used topropagate it. However, we prefer to use an alternative way
to solve the field propagation problem for any value of φ̂,capable of giving a better physical insight at φ̂  1.
Edge radiation as a superposition of the field fromtwo virtual sources. The far field in Eq. (13) can be writ




ten as E(zo , θ) = E 1 (zo , θ) + E 2 (zo , θ̂), where

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THAAU02

Proceedings of FEL 2006, BESSY, Berlin, Germany

1,0

0,8

0,6

0,4

0,2

0,0
-5

-4

-3

-2

-1

0

1

2

3

4

5

^r

s

Figure 7: Intensity profiles of the virtual source for different values of φ̂ (solid lines) compared with the case φ̂  1(dotted lines).
4

^I

2

-4

0
-2

^y

-2

0

^x

2
4

-4

ˆ
Figure 5: Intensity distribution of the virtual source, I.

^
I

^
I

-10

3

3

2.5

2.5

2

2

1.5

1.5

1

1

0.5

0.5

-5

5

10 -10-5θ^^z = 0.6

5

^
I

3

3

2.5

2.5

2

2

1.5

1.5

1

1

0.5

0.5

-5

5

^
z=2

10

θ^

^
z=1

^
I

-10

Figure 8: Intensity pattern at the virtual source for φ̂ = 50.

10 -10

θ^

-5

5

^
z=5

10

θ^

Figure 6: Evolution of the intensity profile for edge radiation for φ̂  1 at different observation distances (solidlines) compared to the far-zone intensity (dashed lines).

506

Figure 9: Edge radiation intensity profile at φ̂ = 50 fordifferent observation distances.

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany





E
1,2 ẑo , θ̂ = ±

x

2eθ
2
2
czo (θ + 1/γ
 )

2
1
iωL
zo
iωLθ
±
. (18)exp
× exp ±
4cγ 2
2c
L
2


The two terms E
1 and E 2 represent two spherical waves
centered at zs1 = L/2 and zs2 = −L/2, corresponding to
two virtual sources. Their field distribution is given by




L
iωL r⊥
2ieω
ωr⊥

E
± , r⊥ = ∓ 2 exp ±
,
K
1
2
c γ
4cγ 2 r⊥cγ
(19)where K1 (·) is the modified Bessel function of the firstorder. It should be noted that Eq. (19) is identical to
the well-known frequency-domain expression for the transverse component of the field from an ultra-relativistic electron moving in uniform motion. Both far zone field and thefield at the virtual sources exhibit dependence on L throughphase factors only. Application of the Fresnel formula allows to calculate the field at any distance z o in frees space.
Using the definition θ̂ = r̂o /ẑo we obtain Iˆ ∼ |A1 + A2 |2 ,
where
!




 2i φ̂ exp ±iφ̂/4θ̂iθ̂2 ẑo2
exp
A1,2 = ∓ẑo ∓ 122 ẑo ∓ 12
θ̂




 ∞
!
θ̂ξ ẑo
iξ 2


exp
dξξK1 ( φ̂ξ)J1×ẑo ∓ 122 ẑo ∓ 12
0
(20)
In Fig. 9 we plotted results for the field propagation for thecase φ̂ = 50. Radiation profiles are shown as a function ofθ̂ at ẑo = 0.52, ẑo = 0.6, ẑo = 1.5 and ẑo = 100.0. Let
us discuss the two limiting cases for φ̂  1 and for φ̂  1.
Consider first φ̂  1. The field at any observation distanceis given by Eq. (16). There are only two observation zones
of interest. Far zone, in the limit for ẑ o  1 and Nearzone, when ẑo  1. From Eq. (16), the total field resultsfrom the interference of the two virtual sources. The transverse size of these sources is γ(c/ω), independently of L.
In the centerof the setup instead, the virtual source has adimension (c/ω)L (see Eq. (16)). The source in the center of the setup is much smaller than those at the edge, as
the two sources at the edges interfere in the center of the
setup. Consider now the case φ̂  1. Let d1,2 = zo ∓ L/2
be the distances of the observer from the edges. One canrecognize four regions of interest, that are more naturally
discussed in the two-source picture. Two-edge radiation.
Far zone. When d1,2  L we are summing far field contributions from the two edge sources, see Fig. 9 for ẑ o = 100.
Two-edge radiation. Near zone. When d 1,2 ∼ L bothcontributions from the sources are important, but d 1 and d2
become sensibly different, see Fig. 9 for ẑ o = 1.5. Singleedge radiation. Far zone. When γ 2 (c/ω)  d1  L the

FEL Theory

THAAU02

Screen
zo
A

B

C

z

D

Figure 10: TUR geometry.
contribution due to the near edge is dominant, see Fig. 9
for ẑo = 0.6. Single-edge radiation. Near zone. When0  d1  γ 2 (c/ω) we have the near-field contribution
from a single edge, and the intensity distribution tends toreproduce the behavior of the square modulus of Eq. (19).
See Fig. 9 for ẑ o = 0.52.

TRANSITION UNDULATOR RADIATION
Consider the system in Fig. 10. An electron enters the
setup via a bending magnet, passes through a straight section AB, an undulator BC, and another straight section
CD. Finally, it exits the setup via another bend. TUR (seereferences in [1]) is collected at a distance z o from the origin of the reference system, located in the middle of theundulator. As before we ignore the presence of the bending
magnets having already discussed the applicability of the”zero-length switcher approximation”.

Far field pattern calculations
Field contribution from the undulator. We first consider the contribution E
u from the undulator. We assume aplanar undulator
and we introduce the longitudinal Lorentz
factor γz = γ/( 1 + K 2 /2). Frequencies of interest areω  2γz2 ckw (with kw = 2π/λw ). As a result one obtains
iωe

E
u = 2
c zo

 zC

dz  exp [iΦBC ] (θx x + θy y)

(21)

zB

with


θx2 + θy2zzo +Φu = ω
2c2c



1+ θx2 + θy2
γz2


.

(22)

Field contribution from the straight sections. The
field contribution from a straight section has been dealt
with in the previous Section. Accounting for the properphase shift, one obtains the contributions E
1 from AB and
E 2 from CD:iωeE(1,2) = 2c zo

 z(B,D)dz  exp iΦ(1,2) (θx x + θy y )z(A,C)(23)

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THAAU02

Proceedings of FEL 2006, BESSY, Berlin, Germany

where Φ(1,2) in Eq. (23) is given by
Lw
Lw
z
θ2
zo −
+
+
Φ(1,2) = ω
2c
4cγz2
4cγ 2
2c



1
+ θ2
γ2

^
I (a.u.)^I (a.u.)


.
(24)

2

Total field and energy spectrum of radiation. The
contributions from the segments AB, BC and CD are:
iωeL(1,2) ωL(1,2) 1
2
E (1,2) =+θθsincc2 z o4cγ2 iωLw 1iωθ2 zo
exp −
+ θ2
× exp
2
2c
4c
γ
z


iωL(1,2) 1
2
,
(25)
+
θ
× exp ∓
4cγ2
iωeLw iωθ2 zo
ωLw 1

2
exp
Eu = 2
+
θ
θsinc
c zo
4c
γz2
2c
(26)
The total field produced by the setup is obtained by summing up these contributions. The resulting energy densityof radiation is known in literature [1].

Virtual source specification. Field propagation.
Eq. (25) and Eq. (26) can be interpreted as far fieldradiation from separate virtual sources with plane wavefronts, located at z s1 = −Lw /2 − L1 /2, zsu = 0 and
zs2 = Lw /2 + L2 /2 and characterized byω 2 eL(1,2)
L(1,2)
iω Lw

E
=
−
exp
∓
+
s(1,2)
2πc3
4c γz2γ2ωL(1,2) 2
1iω θ + 2 exp
θ · r⊥ ,
× d
θ
θsinc
4c
γ
c
(27)
2

ω eLw

E
su = −
2πc3



1
iω 
ωLw
θ2 + 2
θ · r⊥ .
exp
× d
θ
θ sinc4cγzc(28)
L1 , L2 and Lw can assume different values. γ and γ z
are also different. We prescribe the same normalization φ̂ = ωLtot /(γ 2 c)
ωLtot /cθ,for all quantities: θ̂ =and r̂⊥ = ω/(Ltot c)r⊥ . Then, we introduce parameters L̂1 = L1 /Ltot , L̂2 = L2 /Ltot , L̂w = Lw /Ltot andφ̂w = (γ 2 /γz2 )φ̂. Finally, we define ẑ s = zs /Ltot . One
may check that, in the limit for φ̂  1 and φ̂w  1 one
obtains the same results as for edge radiation from a single
straight section. A second region of interest in the parameter space that can be dealt with analytically is for φ̂  1
and φ̂w  1. In this limit, the contribution from the undulator can be neglected, because the sinc(·) is strongly= (ωe/c2 )Ê.
suppressed. Then, Ê(ẑsu , r̂ s )  0, where E
The surviving virtual sources are:

508

4

6

8

10

12

14

2

6

8

10

12

14

θ^

^
z=1
^
I (a.u.)^I (a.u.)

2

4

θ^

^
z = 0.6

4

6

8

10

12

14

2

4

6

θ^

^
z=2

8

10

^
z = 101214

θ^φw = 12 π^

Figure 11: Evolution of the intensity profile for TUR forφ̂w = 12π (solid lines) and comparison with far-zone intensity (dashed lines).



 

4r̂⊥
iL̂w φ̂w 2Ê s(1,2) =sinc r̂⊥  /L̂1 . (29)exp −4L̂(1,2)
Eq. (29) describes virtual sources characterized by plane
wavefronts. Use of the Fresnel propagation formula, Eq.
(1) allows reconstruction of the field in the near and in the
far zone. The two surviving contributions to the field are:


2
ir̂⊥
4r̂⊥
iL̂w φ̂w
Ê (1,2) = − 2 exp ∓+r̂⊥
42(ẑo − ẑs(1,2) )2iL̂1 r̂⊥× exp −2(ẑo − ẑs(1,2) )(L̂(1,2) + 2ẑo − 2ẑs(1,2) )2iL̂(1,2) r̂⊥− exp
2(ẑo − ẑs(1,2) )(−L̂(1,2) + 2ẑo − 2ẑs(1,2) )(30)
Eq. (30) solves the propagation problem for the near andthe far field when φ̂  1 and φ̂w  1. The intensity pattern is obtained by summing up contributions in Eq. (30)and taking square modulus of the sum. To give an example
we study the case L1 = L2 = Lw = Ltot /3. The intensity
pattern periodically depends on φ̂w  1 with a period 12π.
For illustration, in Fig. 11 we plot the intensity profile forφ̂w = 12π at different distances ẑ o and we compare these
profiles with the far field asymptote.

REFERENCES[1] References and a more detailed description of this subject
are included in: G. Geloni, E. Saldin, E. Schneidmiller
and M. Yurkov, DESY 06-127 (2006), downloadable at
http://arxiv.org/abs/physics/0608145.
[2] It is not so if near and formation zone do not coincide.

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

THAAU03

A SCALLOPED ELECTRON BEAM FREE-ELECTRON LASER *D.C. Nguyen#, Los Alamos National Laboratory, Los Alamos, NM 87545, U.S.A.
H.P. Freund, Science Applications International Corp., McLean, VA 22102, U.S.A.
W.B. Colson, Naval Postgraduate School, Monterey, CA 93943, U.S.A.
Abstract
Typical high-gain FEL amplifiers employ an electron
beam that is “matched” to the wiggler so that theenvelope remains constant throughout the wiggler. This
paper describes a novel approach in which the electronenvelope undergoes scalloping motion along the wiggler
because the beams are deliberately mismatched at the
wiggler entrance. We present an analysis of the electron
scalloping motion and the FEL interaction with ascalloped electron beam. Using MEDUSA simulations,
we show the advantages of the scalloped-beam FEL andthe properties of the radiation beam it produces.

INTRODUCTION
In high-gain FEL amplifiers, the electron beam radius
plays a crucial role in determining the FEL interaction
strength. Most FEL amplifiers use a tightly focusedelectron beam to enhance the FEL interaction, i.e. both
the FEL gain and saturated power increase with smaller
electron beam radius. A typical FEL employs electron
beams that are “matched” to the wiggler so that theenvelope remains constant throughout the wiggler. Since
the matched beam radius is proportional to √εn, a small
beam radius requires a small normalized rms emittance.
The use of external magnets to focus the electron beam
to a radius smaller than allowed by the normalized rms
emittance in order to pinch the optical beam was firstsuggested by Sprangle et al. [1]. In this paper, we suggest
the use of natural betatron motion in a weak focusing
wiggler, to refocus the electron beam periodically in the
wiggler, resulting in pinching near the wiggler exit (Fig.
1). It is possible to select a combination of input laser
power and wiggler length such that the FEL saturates near
the second waist. Optical guiding causes the radiation
beam to follow the electron beam’s motion, resulting inpinching of the radiation beam near the exit [2].
RadiusWiggler

Electron beamz
Wiggler
Exit

Figure 1: Illustration of a scalloped electron beam FEL
with a uniform wiggler.

___________________________________________*Work supported by the Office of Naval Research and the High-Energy
Laser Joint Technology Office. Author email: dcnguyen@lanl.gov

FEL Theory

The evolution of the rms radius σ of a relativistic,axi-symmetric beam with equal transverse emittance andequal two-plane focusing can be written as follow
ε
d 2σ
2I
= − k β2 σ + 3+ 2n 3 ,2dz
γ I Aσ γ σ2(1)where kβ is the betatron wavenumber, I the peak current,
IA the Alfven current, γ the relativistic factor, and εn thenormalized rms emittance. Under steady-state condition,
the emittance-dominated rms matched beam radius is
B

B

B

σ0 =

2ε n .
k waw

B

(2)

Using a first order perturbation analysis of Eq. (1) we canshow thatσ = σ 0 − δ 0 sin(kΣ z )(3)

where δ0 = (σ0− σmin) is the initial deviation from thematched radius, and kΣ , the scalloping wavenumber, as
given byBk. Σ = 2k β 1 −B

1II A γ 2kβ ε n(4)The power gain length in a high-gain FEL amplifier
scales with the electron beam radius as follow [3]
13

γ ⎛

⎞
IA
⎜
⎟ σ 2 3 (1 + Λ 3 D )LG =⎜ a2 f 2k I ⎟3⎝ w B w ⎠(5)where fB is the difference in Bessel functions, and Λ3D isthe three-dimensional effect. Since the electron beam
radius varies slowly with distance, the FEL power gain
length also varies along the wiggler. The saturated power
scales inversely with electron beam radius.
Ps =FEL beam

Wiggler
Entrance

THEORY1 ⎛ aw f B ⎞⎟⎜γ ⎜⎝ 2 2kwσ ⎟⎠

2/3

1/ 3

⎛ I ⎞
⎜
⎟
⎜I ⎟
⎝ A⎠

Pbeam

(1 + Λ3 D )2(6)

where Pbeam is the electron beam power. The scalloped
beam FEL performance depends on how the electron
beam is focused in the wiggler and the scalloping period.
We look at two cases: 1) the electron beam waist is
focused near the entrance, and 2) the waist is the centre of
the wiggler. In the first case, the electron comes to second
waist near the wiggler exit and the FEL output power,
which scales inversely with radius, is at a maximum. In
the second case, the beam radius is largest near the
wiggler exit and the output power is at a minimum [4].

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THAAU03

Proceedings of FEL 2006, BESSY, Berlin, Germany

10

9

0.1

10

8

0.08

10

7

0.06

10

6

0.04

10

5

0.02

w(cm)

Power(W)

SIMULATION
Table I summarizes the FEL and beam parameters usedin the MEDUSA simulations. These parameters arechosen for a 1.06-micron wavelength where high-power
seed lasers exist. The wiggler is a conventional
permanent-magnet design with parabolic pole faces toprovideequal
two-plane,
sextupole
focusing.
Alternatively, the magnets can be notched to approximate
sextupole focusing [5]. We chose an input power of 106
W (1 μJ pulse energy and 1 ps FWHM, for instance) toachieve saturation in about 2 m of wiggler length with amatched electron beam. For the scalloped beam FEL, thesaturation length is 2.6 m. The scalloping period is about
2 m so the second waist of the electron beam envelope isnear the exit of the wiggler in both cases. The effects ofusing matched- and scalloped-beams in the two-stage
wiggler are illustrated in Figs. 2 and 3. The power reaches
a maximum of 0.84 GW in the matched case, and 1.03
GW in the scalloped case. The extraction efficiency
increases correspondingly from the usual 1% to 1.27%.
The only drawback is a 30% increase in the wiggler
length required to reach saturation.

0
0

0.5

1

1.5

2

2.5

3

z(m)

Figure 2: FEL power (red), optical beam radius (blue),and electron beam radius (green) for the matched case.

ValuesBeam Energy

80.8 MeV

Peak Current

1000 A

Emittance

10 mm-mrad

Energy Spread

0.25%

Wiggler Period

2.18 cm

Wiggler Peak Magnetic Field

8.247 kG

rms Wiggler Parameter

1.187

Wiggler Length

2.6 m

Matched Beam Radius

0.27 mm

Scalloped Beam Minimum Radius

0.16 mm

Scalloping Period

2.05 mWavelength

1.058 μPeak Injected Power

1 MW

Injected Radiation Waist

0.305 mmMatched Beam Peak Power0.84 GW

Matched Beam Efficiency

1.0%

Matched Beam Saturation Length

1.96 mScalloped Beam Peak Power1.03 GW

Scalloped Beam Efficiency

1.27%

Scalloped Beam Saturation Length

2.6 m

10

9

0.1

10

8

0.08

10

7

0.06

10

6

0.04

10

5

0.02

w(cm)

Parameters

Power(W)

Table 1: MEDUSA simulation parameters and results.

0

510

0

0.5

1

1.5

2

2.5

3

z(m)

Figure 3: FEL power (red), optical beam radius (blue),and electron beam radius (green) for the scalloped case.
It is noteworthy that the lethargy region is reduced in
the scalloped beam FEL as a result of high gain (shortgain length) at the wiggler entrance. In the middle of the
wiggler, exponential gain is reduced and the reduction in
optical guiding causes the radiation beam to expand
rapidly. At saturation, the scalloped beam optical waist islarger than the matched beam case. Thus, scalloping theelectron beam in a uniform wiggler does not pinch theoptical beam to a smaller radius. To significantly pinch
the optical beam, we need additional optical guiding, forinstance with the addition of a step-taper wiggler.

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

E =80.8 MeV a =1.187 Detuning Curve
k

w

10

0.2

10

9

0.15

10

8

0.1

10

7

0.05

10

6

Power (W)

10

0
0

1.2

Radius (cm)For seeded FEL amplifiers, it is advantageous to tune
the input wavelength while keeping the electron beamenergy constant in order to find where the power ismaximized. In the matched beam case, the FEL output
power increases toward larger detuning, namely longer
wavelength at a fixed electron beam energy (or higher
electron beam energy at a fixed wavelength) and thendrops sharply. In the scalloped beam case, the FEL output
power decreases rapidly on both side and the detuning
bandwidth is narrower. This is a result of lower FEL gain
due to the scalloped electron beam, but the FEL saturated
power is higher than the matched beam case.

THAAU03

0.5

1

1.5

2

2.5

3

z (m)
Matched
Scalloped

0.8

Figure 6: FEL power (red), optical beam radius (blue),and electron beam radius (green) for scalloped beam FEL
with a step-tapered wiggler.

0.6

SUMMARY AND DISCUSSION

Power (GW)

1

0.4

0.2

0
1.035

1.04

1.045

1.05

1.055

1.06

1.065

1.07

Wavelength (microns)

Figure 4: Detuning curves for the matched (red) andscalloped (blue) electron beam FEL.
We also study scalloped beam FEL with a step-taper
wiggler to increase the extraction efficiency (Fig. 5). The
step-taper starts at z = 1.92 m and the magnetic field is
reduced to 8.032 kG while the period remains the same.
The FEL peak power grows to 1.45 GW, corresponding to
1.8% efficiency (Fig. 6). The optical beam is pinched to a
0.3 mm radius in the second wiggler segment, compared
to a 0.6 mm radius of the uniform wiggler. The optical
divergence angle is increased from 0.8 to 1.6 mrad.

We have studied a new kind of FEL interaction inwhich the electron beam’s envelope undergoes scalloping
motion and the exponential gain varies along the wiggler
length. For maximum power, the optimum approach is tofocus the electron beam near the wiggler entrance andchose a wiggler length that is slightly longer than thescalloping period so that the second waist occurs nearsaturation. The smaller electron beam radius at saturation
increases the saturated power of a uniform wiggler. The
scalloped beam FEL detuning spectrum is narrower thanthe matched beam case. This is indicative of a lower net
gain for the scalloped beam FEL.
As a result of this study, we conclude that the use of ascalloped-beam is advantageous even at the expense of alonger wiggler length to reach saturation. In addition, thecombination of scalloped electron beams and a steptapered wiggler can double the output power, and thus the
FEL efficiency. The radiation beam is also pinched near
the exit and expands rapidly afterward, thereby reducing
the risk of damaging optics intercepting the FEL beam.

REFERENCES
RadiusStair-step Taper Wiggler
FEL[1] P. Sprangle, B. Hafizi, and J.R. Penano, IEEE J.
Quantum Electron. 40 (2004) 1739.
[2] D.C. Nguyen, H.P. Freund, and W. Colson, Phys.
Rev. ST-AB 9 (2006) 050703.

ElectronbeamzWiggler
Entrance

Wiggler
Exit

Figure 5: Illustration of a scalloped beam FEL with a
step-tapered wiggler.

FEL Theory[3] M. Xie, Proceedings of the IEEE Particle Accelerator
Conference, 1995, V.1, 183-185.
[4] P.P. Crooker et al., these Proceedings, paper
MOPPH075.
[5] C. Fortgang, Nucl. Instrum. Meth. A393 (1997) 385.

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THAAU04

Proceedings of FEL 2006, BESSY, Berlin, Germany

INFLUENCE OF OPTICAL FEEDBACK ON THE COHERENCE
PROPERTIES OF FEL OSCILLATORS
S. Bielawski, PhLAM/CERCLA, Villeneuve d’Ascq Cedex;
M.-E. Couprie, CEA, Gif-sur-Yvette;
M. Hosaka, M. Katoh, A. Mochihashi, UVSOR, Okazaki;
C. Szwaj, PhLAM/CERCLA, Villeneuve d’Ascq Cedex

Abstract
When detuned, the output of a FEL oscillator is dominatedby a transient amplification of the spontaneous emission
noise (SE). Here, we show that FEL oscillators in this situation appear to display a strong sensitivity to optical feedback. From a Dattoli-Elleaume type modeling, we showthat a very small amount of reinjected power (typically 
1 · 10−8 in the case of the UVSOR SR-FEL) modifies dramatically the FEL operation. In particular, we demonstrateexperimentally and numerically a strong spectral narrowing, correlated with a disappearance of the laser pulse microstructures. This is also accompanied by a suppression of
SR-FEL instabilities for a wide range of parameters (half ofthe detuning curve). These topics (strong amplification of
SE noise, and control using tiny reinjection), are of course
more general. We propose a theoretical approach of thesequestions, using in particular the concept of convective instabilities.

PAPER NOTAVAILABLE

5512

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

THAAU05

SPACE-FREQUENCY MODEL OF ULTRA WIDE-BAND INTERACTIONSIN FREE-ELECTRON LASERS
Y. Pinhasi , Yu. Lurie, and A. Yahalom
The College of Judea and Samaria, Ariel, Israel.

Abstract

THE MODELThe principle of operation of intense radiation devices
such as microwave tubes, free-electron lasers (FELs) andmasers, is based on a distributed interaction between an
electron beam and radiation. We developed a threedimensional, space-frequency theory for the analysis andsimulation of radiation excitation and propagation in electron devices and free-electron lasers operating in an ultra
wide range of frequencies. The total electromagnetic field
is presented in the frequency domain as an expansion interms of cavity eigen-modes. The mutual interaction between the electron beam and the field is fully described bycoupled equations, expressing the evolution of mode amplitudes and electron beam dynamics. The approach is applied in a numerical particle code WB3D, simulating wideband interactions in free-electron lasers operating in the linear and non-linear regimes. The code is used to study thestatistical and spectral characteristics of multimode radiation generation in a free-electron laser, operating in various
operational parameters. The theory is demonstrated also inthe case of ”grazing”, resulting in a wide-band interaction
between the electron beam and the radiation.

In the frequency domain the total electromagnetic field
can be expanded in terms of transverse eigenmodes of themedium in which it is excited and propagates (see [1, 2]
for the details). The perpendicular component of the electric and magnetic fields are given in any cross-section as alinear superposition of a complete set of transverse electricfiled   and magnetic field    eigenmodes:

INTRODUCTION

Spectral energy distribution of the electromagnetic field
is defined in the model as a sum of energy spectrum of theexcited modes:

In this paper we continue development of the previously
stated space-frequency, 3D model, which describes broadband phenomena occurring in electron devices, masers andFELs [1, 2, 3, 4]. In the model, the total electromagnetic
field is presented in the frequency domain in terms of transverse eigen-modes of the cavity, in which the field is excited and propagates. A set of coupled excitation equations,describing the evolution of each transverse mode, is solved
self-consistently with beam dynamics equations.
This coupled-mode model is employed in a threedimensional numerical simulation code WB3D (see [1, 2]
for the details). In the present work, the code is used
to study the statistical and spectral characteristics of multimode radiation generation in a free-electron laser, operating in various operational parameters. The theory isdemonstrated also in the case of “grazing”, when the groupvelocity of the radiation mode is equal to the axial velocityof the electrons, resulting in a wide-band interaction between the electron beam and the generated radiation.
 -mail: yosip@eng.tau.ac.il

FEL Theory                          (2)(1)

here     is amplitude of the mode  , that may befound from the excitation equations:    

 
  










         
 
(3)

 








      

(4)

MULTIMODE SUPER-RADIANT
EMISSION
To demonstrate the utilization of the model, we present
a study of super-radiant emission in a waveguide-based,
pulsed beam free-electron maser (FEM), with operationalparameters are given in Table 1. Such FEM is expected
to operate at millimeter and sub-millimeter (THz) wavelengths. When a FEL utilizes a waveguide, the axial
wavenumber of transverse mode  follows the dispersion
relation:



 







 

(5)

where    is the cut-off frequency of the mode.
In synchronism with that mode, the dispersion relation for

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THAAU05

Proceedings of FEL 2006, BESSY, Berlin, Germany

Table 1: Operational parameters of millimeter and submillimeter wave free-electron maser.

1000

Accelerator
Electron beam energy:
Electron beam current:Electron beam pulse duration:

Frequency [GHz]  =1 6 MeV
  =1 A =0.1 pSec

WigglerMagnetic induction:
Period:Number of periods:

 =2000 G
 =5 cm
 =20
15 7.5 mm
Cut-off frequency
20.0 GHz
28.3 GHz
44.7 GHz
60.0 GHz









 






514


   
¼



½¾

  is the slippage time. The cor-

½¾

3

4

5

6

responding temporal wave-packet (shown in Fig. 3b) consist of two “slow” and “fast” pulses with durations equal
to the slippage times modulating carriers at their respective synchronism frequencies. Lowering the beam energy
to   MeV, results in grazing between the -beamand the waveguide dispersion curves at a single synchronism frequency 69.6 GHz. The spectrum in the case ofgrazing, as well as the corresponding temporal wavepacket
are shown in Fig. 4.
As the acceleration energy is increased, transverse
modes of higher orders are being excited simultaneously(in addition to the mode TE  ) extending the radiation
spectrum over a wide rage of frequencies from few tensof GHz to more then THz. Fig. 5 shows the energy spectral densities of the excited waveguide modes as the beamenergy is increased.

8

Ek=2.00 MeV(7)

is the group velocity of the excited mode  .
The effect of super-radiance emerges when the durationof the electron beam pulse is much less then the period of
the electromagnetic waves expected to be excited at synchronism frequencies according to Table 2. The waveguide and -beam dispersion curves when the accelerationenergy is    MeV are shown in Fig. 2. In this case asingle waveguide mode TE  is excited at two separated
synchronism frequencies (“slow” and “fast”) 46.1 GHz
and 149.5 GHz, respectively. The spectral density of energy flux calculated with the code WB3D is shown in Fig.
3a. The spectrum peaks at the two synchronism frequen , where
cies with main lobe bandwidth of  ½¾

TE21 ,TM 21

TE01

Figure 1: Energy dependence of the dispersion solutions.

(6)



TE41 ,TM 41

Beam Energy [MeV]

where  is the average velocity of the accelerated elec ( is the wiggler’s period). The cortrons and
responding curves of synchronism frequency vs. beam energy for the FEM are shown in Fig. 1. Only waveguidemodes which have in their field profile components that interacts efficiently with the wiggling electrons are shown.
Table 2 summarizes several examined cases resulted from
Eq. (6) in the multi-transverse mode operational regime.
For each transverse mode  , the acceleration energy  
can be set to excite two frequencies corresponding to the“slow” (    ) and “fast” (    ) synchronism frequencies or to the special case of “grazing”, where    and a single synchronism frequency is obtained.
Here
 

400

2

f1=46.1 GHz
f2=149.5 GHz

6f / f co





TE03

600

0

the electron beam is given by

 

800

200

Waveguide
Rectangular waveguide:
mode
TE
TE , TM
TE , TM
TE



1200

4

waveguide

grazing2

Ek=1.62 MeV
f0= 69.6 GHz

beam
0
-5

0

5

10

15

20

25

kz / k w

Figure 2: Dispersion solutions for TE  transverse modefor    MeV.

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

THAAU05

Table 2: Synchronism frequencies for several beam energies.
Beam Energy
[MeV]
1.62
2.00
2.44
3.00
4.09
5.00
5.60

Synchronism frequencies [GHz]TE ,TM
TE ,TM
————
136.2 (grazing)—
88.9 , 299.3—
78.1 , 592.9
336.1 (grazing)
75.0 , 890.3
217.5 , 747.8
73.9 , 1114.5
203.6 , 984.8

TE
69.6 (grazing)
46.1 , 149.5
42.0 , 230.5
39.8 , 348.4
38.2 , 632.9
37.5 , 927.8
37.3 , 1151.0

TE
—
—
—
—
—
—
602.6 (grazing)

(a)

(a)
0.4

d W / d f [pJ/GHz]d W / d f [pJ/GHz]

0.3

0.2

0.1

0.0

0.3

0.2

0.1

0.0
0

25

50

75

100

125

150

175

200

0

25

50

f [GHz]
(b)

75

100

125

150

175

200

f [GHz](b)

149.5 GHz

1.0

2

46.1 GHz1[kV/m][kV/m]

0.5

0

Ex

Ex

0.0

-1

-0.5

-2

-1.0

3.3

3.4

3.5

3.6

3.7

3.8

t [ns]

Figure 3: Super-radiant emission from an ultra short bunchwhen the beam energy is   =2 MeV and a single TE 
mode is excited: (a) Energy spectrum, and (b) temporal
wavepacket.

FEL Theory

3.3

3.4

3.5

3.6

3.7

t [ns]

Figure 4: That of Fig. 3, but at grazing condition for mode
TE (the beam energy is    MeV).

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THAAU05

Proceedings of FEL 2006, BESSY, Berlin, Germany
(a)

(b)

TE 21

TM 21

d W / d f [pJ/GHz]d W / d f [pJ/GHz]

TE 21

1.2

TM 21

1.5

1.0

0.5

TE 01

TE 21
TM 21

0.8

0.4

TE 01

TE 01

TE 01

0.0

0.0
0

50

100

150

200

250

300

0

100

200

f [GHz]300

400

f [GHz]
(c)

TE 41

TE 41

1.2

TM 41

1.0

TE 21

TE 21

TM 21

TM 21

0.5

TE 01

d W / d f [pJ/GHz]

1.5

d W / d f [pJ/GHz]

(d)

TM 41
TE 41
TM 41

0.8

TE 21
TM 21

TE 21

0.4

TM 21

TE 01

TE 01

0.0

0.0
0

175

350

525

700

f [GHz]

0

200

400

600

800

1000

f [GHz]Figure 5: Energy spectra for different acceleration energies: (a)     MeV (grazing in the TE  ,TM modes); (b)   MeV; (c)    MeV (grazing in the TE  ,TM modes); (d)    MeV.

CONCLUSIONSThe presented coupled-mode theory, formulated in
the frequency domain, enables development of a threedimensional model, which can accurately describe wideband interactions between radiation and electron beam inelectron devices and free-electron lasers. Space-frequency
solution of the electromagnetic equations considers dispersive effects arising from the resonator and gain medium.
Such effects play a role also in the special case of grazing,
and can not be accurately treated in approximated spacetime approaches. We also note that our space-frequency
model described here, also facilitates the considerationof statistical features of the electron beam and the excited radiation, enabling simulation of the interaction ofa free-electron laser operating in the linear and non-linear
regimes.

516

REFERENCES[1] Y. Pinhasi, Yu. Lurie and A. Yahalom, Nucl. Instr. and Meth.
in Phys. Res. A, 475, 147 (2001).
[2] Y. Pinhasi, Yu. Lurie, A. Yahalom, and A. Abramovich,
Nucl. Instr. Meth. Phys. Res. A, 483, 510 (2002).
[3] Y. Pinhasi, Yu. Lurie, A. Yahalom, Phys. Rev. E 71, 036503(2005).
[4] Y. Pinhasi and Yu. Lurie, Phys. Rev. E 65, 026501 (2002).

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

THAAU06

PARAMETRIC OPTIMIZATION OF A X-RAY FEL BASED ON A
THOMSON SOURCE*
L. Serafini, A. R. Rossi, V. Petrillo, C. Maroli, A. Bacci, INFN-Milano, Milano, Italy
M. Ferrario, INFN-LNF, Frascati, Italy.
Abstract
We present a study based on a parametric optimizationof a Thomson Source operated in FEL mode. This deals
with the proposed scheme to use a high intensity laser
pulse colliding with a high brightness electron beam of
low to medium energy (around 10 MeV). Electrons
undulating in the incoming laser field may emit radiation
in a FEL coherent mode as far as some conditions are
satisfied. A set of simple analytical formulas taking into
account 3D effects is derived, in order to express these
conditions in terms of three free parameters, namely the
wavelength of the colliding laser pulse, the amplitude of
the ripples in the time profile of the laser field, and thepeak current carried by the electron beam. A few
examples of possible operating points are compared withresults of 3D numerical simulations, showing the FEL
coherent emission of X-rays in the 0.1 to 5 nm range withtens of MeV high brightness electron beams colliding
with high intensity ps-long laser beams carrying pulse
energies of about 10 J.

flux of real photons (to be compared with virtual photons
for the case of a magnetostatic undulator), the resonancerelationship for a Thomson source is at all similar to the
FEL resonance apart for a factor 4 in the denominator.

λR =λ(1+ a02 + γ 2ϑ 2 )4γ 2

where λ is the wavelength of the colliding laser pulse,γ the kinetic energy of the electron beam (expressed interms of its dimensionless relativistic factor), λR the

wavelength of the forward emitted radiation (within asmall angle ϑ around the electron beam propagationaxis) and a0 is the laser parameter (dimensionlessamplitude of the vector potential associated to the laser
field), given by

a0 = 8.5 ⋅10−6

INTRODUCTION
It has been recognized by several authors in the past
[1,5] that the interaction between a high brightness
electron beam and a counterpropagating - head-on
colliding - high intensity laser pulse could lead tocoherent emission of radiation, in the direction of theelectron beam motion, according to a FEL-likemechanism driven by a collective instability that induces
exponential growth of the radiation intensity. This
coherent part of the emitted radiation overlaps with the
spontaneous incoherent radiation generated by theThomson back-scattering effect. Only recently, however,detailed 3D simulations[6] able to model the FEL
collective instability showed the potential existence of
this effect under particular conditions of electron beamemittance and current as well as laser field amplitude in
the focal region, where the interaction between the two
beams occurs. In this paper we derive a set of practicalanalytical formulas describing the existence of operating
conditions in the dynamical range of the system where 3D
effects can be mitigated so to allow the onset of the FEL
instability, hence the generation of coherent radiation in a
SASE-FEL emission mode.
Generally speaking, the situation is at all similar to aconventional SASE-FEL based on a magnetostatic
undulator through which the electron beam propagates:
the magnetostatic field of the undulator is replaced by thee.m. field of the incoming laser pulse, which causes theelectrons to wiggle while they propagate through thepulse. Since the laser field is a classical description of a

FEL Theory

(1)

λ P

(2)

R0

where R0 is the laser focal spot size and P the peak
power in the laser pulse (in TW).
The interaction between the electron beam and the laser
pulse is assumed to take place in a drift space where no
external forces (focusing or deflecting) act on the two
beams, which are tightly focused by their individual final
focus lens systems, taking them down to micron-size
focal spots. Under the assumption that the laser pulse hasa uniform transverse intensity profile of hard edge radius
R0 in the focus position, we can neglect ponderomotivetransverse effects on the electron trajectories[7].
τ

2σ 0

2R0

β0
Z0

Figure 1: Electron orbits in the focal region (intersecting
thin solid lines). Electron beam envelope (bold solidlines) and laser beam envelope (dashed lines) are also
shown. Electrons are moving to the right, laser pulse(duration τ ) is moving to the left.

517

THAAU06

Proceedings of FEL 2006, BESSY, Berlin, Germany

As depicted in Fig.1, electrons cross the focus area
traveling on rectilinear orbits: when they traverse the laser
field their secular trajectories remain rectilinear, with asuperimposed slightly wiggling motion.

PARAMETER DEFINITIONS
We break-up the set of parameters describing the wholesystem into three groups, one for each of the threeinteracting beams: the electron beam, the colliding laser
beam and the emitted FEL radiation beam, respectivley.
The system is described by 11 main free parameters: 4
parameters for the electron beam, summarized in Table 1,
5 parameters for the laser beam, summarized in Table 2,
and 2 parameters for the FEL radiation beam, summarizedin Table 3. Note that units indicated in the tables are justthe ones used for simplicity in the final set of formulas:
all intermediate calculations are performed in standard
MKS units.

γ

Current
I [A]

Focal spot

Emittance

µm]
σ0 [µ

µm]
εn [µ

There are some other additional parameters which
represents ancillary quantities useful for handling thesystem of conditions relating the 11 main free parameters.
These are: the electron beam beta-function in the focus,
β 0 , which is defined by the usual relationσ0 =εn β 0γ(3)the electron bunch rms length, σ z , and the electron
beam rms relative energy spread∆γγ. These last two

quantities do not enter in the derivation of the final set of
formulas: they are only used for an afterward check on
additional ancillary conditions.
Table 2: Laser parameters
Wavelength

Power

Pulse
lengthFocal
spot

Intensity
ripplesµm]
λ [µP [TW]

τ [ps]]

R0 [µ
µm]

∆ [%]

Additional parameters for the laser beam are theRayleigh range Z 0 , given by

Z0 =

4 πR0

λ

∆≡

2

(4)

∆a0
a0

(5)

which represents the fluctuations of laser field
amplitude along the pulse, which is assumed to have (at∆ = 0 ) an ideal flat-top time profile.
Table 3: FEL radiation parameters
Wavelength λR [Å]FEL parameter ρAdditional parameters for the FEL radiation beam are
the gain length, Lg =ρ=ρTable 1: Electron Beam parameters
Energyand the laser pulse energy, defined by U = Pτ . Notethat the definition of the laser ripple parameter ∆ is

γλR
λC

(with

λ
, and the quantum parameter,
4 πρ

λC = 0.024 Å).

Asdiscussed

elsewhere[8], as far as ρ ≥ 0.5 quantum effects are
negligible ant the system can be described by means ofclassical FEL-like equations[6].

CONDITIONS FOR FEL EMISSION
Let us now analyze what are the conditions to besatisfied by the 11 main parameters ( γ , I , σ0 , εn , λ ,P , τ , R0 , ∆ , λR , ρ ) in order to operate theThomson source as a Free Electron Laser.
The FEL resonance conditionλR =λ1+ a02 )
2 (
4γ

(C.1)

The definition of the FEL parameterρ=

10−2 3γ

Iλ4 P σ 04

(C.2)

Two conditions for optimal geometrical beam overlapof the envelopes of the two colliding beams: the first one
is to ensure that the electrons will observe transversally
constant undulator fieldR0 ≥ 2σ 0(C.3)

and the second one is to minimize the hour-glass effectin the collision of the two beamscτ ≤ 2 Z 0(C.4)

Note that we will further check that the condition

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THAAU06

β 0 ≥ Z 0 is satisfied (assuring that the electron beamenvelope is contained within the laser beam envelope).
However, this condition is not explicitely used in order tosimplify the following derivation.
We want of course that the interaction between the two
beams, i.e. the equivalent undulator length, be longer thanthe FEL saturation length, which is typically set at 10times the gain length. Hencecτ ≥ 10Lg(C.5)

Now we must take into account how 3D effects andnon-uniformities in the laser filed (which is our undulator
field) may affect the FEL instability, avoiding
inhomogeneous broadening effects of the gain bandwidththat may damp the onset of the FEL exponential
instability. We know that the gain bandwidth of a SASE
FEL is set by ∆λR λR = 2 ρ . This implies that 3D and
non-uniformity effects must produce bandwidth
broadening smaller than 2ρ .
For a Fourier trasnform limited laser pulse the spectrum
line width is

∆λ

=

λ

λ
∆λR ∆λ λ, therefore
=
= ,
λR
λ cτ
cτ

hence the condition

cτ ≥

λ
2ρ

(C.6)

The FEL frequency broadening due to fluctuations in
the undulator field amplitude, in our case represented by∆ , is given by

∆λR

λR

2a02
=
∆ , which in turns implies
1+ a02

1+ a02
∆≤ρ 2
a0

(C.7)

The transverse motion of the electrons in the focal
region, which is mainly determined by the electron beamemittance, produces a random distribution of the angle ϑin the resonance relationship reported in eq.1, which inturns induces a broadening of the FEL bandwidth. As
extensively discussed elsewhere[6,9], the limitation on
this random angle can be casted in terms of an upper limiton the emittance. This criterion is generally known as
Kim-Pellegrini criterion: it has been generalized in ref.6
to the expression

Z R λR γ
LG 2π

εn ≤

(C.8)

FINAL SET OF FORMULAS
In order to simplify the derivation of a solution for thesystem of equations (C.1-C.8) we assume equalities for
all the conditions instead of inequalities: this will allow toderive the minimum condition that 8 parameters have tofulfill, expressed as functions of three free parameters. We
choose as free parameters the laser wavelength λ , theelectron beam current I and the laser ripple parameter ∆ .
The electron beam parameters must obey:

εn = 0.18 λ (F.1);

γ = 0.05 3

FEL Theory

4 πR0

λR

2

.

(F.2)

σ 0 = 0.21λ / ∆ (F.3) ; β 0 = 0.009 λ 3
the ancillary condition
2

I
(F.4)
∆5

β 0 ≥ Z 0 , as anticipated, isrespected if I > 576 ∆ , which is easily satisfied, since∆ assumes values definitely lower than 0.1, while thebeam curent I has expected values in excess of several
hundreds Amps. Note that the additional condition∆γ γ ≤ ρ has to be satisfied, though it was not
explicitely considered in the derivation.
The laser parameters must obey:

P = 0.0018 ∆ (F.5) ; U = 18.6 λ ∆2 (F.6) ;a0 = 1. (F.7) ; τ = 1.1⋅10−8 λ ∆ (F.8) ;Z 0 = 1.6λ ∆ (F.9)
The FEL radiation is characterized by:

λR = 200 λ 3∆4I2(F.10) ; ρ = 0.25∆ (F.11) ;LG = 0.32λ /∆ (F.12) ; ρ = 1012 λ 3∆5(F.13)I

EXAMPLES
A relevant example is for the case of a CPA Ti:Sa laser
system, which is nowadays capable of delivering fs to pslong pulses carrying energies in excess of a J, focuseddown to micron-size spots. In this case, setting
λ = 0.8 µm , the formula set (F.1-F.13) reduces to thefollowing (expressing ∆ in units of %):whewre Z R is the Rayleigh range of the emitted FEL
radiation, Z R =I∆2εn = 0.14 µm ; γ = 1.08 3

I
1.4; σ0 =
µm
2
∆
∆

519

THAAU06

Proceedings of FEL 2006, BESSY, Berlin, Germany

0.015 3 I
0.18[mm] ; P =[TW] ;
2
∆
∆
∆
0.15
0.85
0.13
U = 2 [J] ; τ =[ps] ; Z 0 =[mm] ;∆∆∆∆
λR = 3436∆ 3 2 [Å] ; ρ = 2.5 ⋅10−3 ∆ ;I∆226[µm] ; ρ = 386∆ 3
.
LG =
∆
I

is plotted as a function of ω fluct ω L ( ω L ≡ 2πc λ ) for

β0 =different values of the laser ripple parameter ∆ .

We take into account now two specific examples, one
in the classical SASE-FEL regime, the other in thequantum regime: all parameters now depend only on the
beam current and the laser ripple parameter.

Figure 2: Saturation intensity in presence of laser ripples.

1) we set ∆ = 0.15 % ; I = 1500

A : we findεn = 0.14 µm ; γ = 44 ; σ 0 = 3.7 µm ;β 0 = 4.1 mm ; P = 1.2 TW ; U = 6.6 J ;τ = 5.6 ps ; Z 0 = 0.85 mm ; λR = 2.1 Å ;ρ = 4.⋅10−4 ; LG = 159 µm ; ρ = 1.4 .
2) we set ∆ = 0.05 % ; I = 2500

A : we findεn = 0.14 µm ; γ = 108 ; σ 0 = 6.4 µm ;β 0 = 30 mm ; P = 3.5 TW ; U = 60 J ;τ = 17 ps ; Z 0 = 2.5 mm ; λR = 0.35 Å ;ρ = 1.2 ⋅10−4 ; LG = 531 µm ; ρ = 0.2 .
The paremeter values predicted for case 1), which is in
the calssical regime, are in agreement with the results of
3D simulations reported in ref.6,9, where a 15 MeV
electron beam carrying 1.5 kA of current, focused down
to 10 µm rms focal spot size, was considered colliding
with a Ti:Sa pulse with a0 = 0.8 , and a 20 µm spot size,
which corresponds to a power of 5.5 TW. The saturationof the FEL instability is reached, for an emittance of 0.44µm, at 4 ps of laser pulse length, implying the need of 22
J of laser pulse energy and an effective gain length ofabout 120 µm. The radiation wavelength was 3.64 Å.
Since these simulations were performed before deriving
the set of formulas reported in this paper, the agreement isonly on a general frame. More detailed comparisons
between this set of formulas, that are meant to drive theinitial choice of parameters for the simulations, and thesimulation results, will be the subject of a future work.
As a last remark we report here the results of 1D
simulations (performed with a code described
elsewhere[10]) evaluating the effects of laser ripples on
the growth of the FEL instability, taking same laser andelectron beam parameters as for the previously mentioned
3D simulations. The laser amplitude modulation was(

It is clearly visible in Fig.2 how the FEL instability isdamped, i.e. the exponential growth is no longer attained,
when ∆ assumes values greater than a few percent, foralmost any value of the modulation scale length k fluct .
Also, the system seems to tolerate laser amplitude
modulations occurring on a scale much shorter than thegain length, as indicated by the fact that the saturation
intensity goes to zero for any value of ∆ when the scaleof the laser modulation gets close to gain length, i.e. whenLG/λ = ωfluct/ ωL=1/4πρ = 0.0055 .

REFERENCES[1] J. Gea-Banacloche, G.T. Moore, R.R. Schlicher,
M.O. Scully, and H. Walther, IEEE Journ. of Quantum
Electron., QE-23, 1558 (1987).
[2] B.G. Danly, G. Bekefi, R.C. Davidson, R.J.
Temkin, T.M. Tran, and J.S. Wurtele, IEEE Journ. of
Quantum Electron., QE-23, 103(1987).
[3] J.C. Gallardo, R.C. Fernow, R. Palmer, and C.
Pellegrini, IEEE Journ. of Quantum Electron. QE-24,
1557 (1988).
[4] C.B. Schroeder, C. Pellegrini, and P. Chen,
Phys. Rev. E 64, 056502 (2001).
[5] R. Bonifacio et al., FEL-2005 Proceedings,
SLAC-R-791, JACoW / eConf C0508213, 71 (2005).
[6] A. Bacci, M.Ferrario, C. Maroli, V. Petrillo, L.
Serafini, PRST-AB 9 (2006) 060704.
[7] L. Serafini, AIP CP 335, 666 (1995).
[8] R. Bonifacio et al., Nucl. Instr. and Methods, A
543, 645 (2005).
[9] A. Bacci et al., X-Ray Generation with a FEL
based on an Optical Wiggler, this conference.
[10] A.Bacci et al., ”Collective effects in theThomson back-scattering between a laser pulse and a
relativistic electron beam” EPJAP (in print).

)

taken as ∆ sin k fluct z + ct . The FEL saturation intensity

520

FEL Theory

Proceedings of FEL 2006, BESSY, Berlin, Germany

THBAU01

APPLE UNDULATORS FOR HGHG-FELS
J. Bahrdt, BESSY, Berlin, Germany.

INTRODUCTION
FEL facilities are powerful sources for ultra shortpulses and longitudinally and transversely coherent
radiation in the soft X-ray and X-ray regime. Three Xray FELs based on the SASE principle are currently
under construction [1-3].
In the soft X-ray regime various seeding schemes havebeen proposed and realized which improve the spectral
characteristics and the time structure. A cascaded HGHG
FEL [4,5] starts with the coherent radiation of a highpower Ti:Sapphire laser which interacts with the electron
beam in a modulator. In a dispersive section the energy
modulation is converted to a spatial modulation. The
following radiator takes advantage of the higher ordersof the electron beam bunching producing a seed for the
next stage. Several stages can be cascaded achieving
frequencies down to 1nm.
The number of stages can be reduced if the seedwavelength of the first stage is already in the few 10s nm
regime which can be accomplished using the HHG
process [6].
Only the light of the last radiator will be delivered tothe experiment. All other undulator modules serve toprovide a sufficient bunching of the electron beam in thelast stage. For simplification all these modules can berealized as planar devices though they might be slightly
longer than helical devices. The last radiator has toprovide the full flexibility concerning the polarization
control. APPLE type structures are suitable for thispurpose. In this paper we concentrate on the design of
APPLE undulators to be used as final radiators. We
discuss the technical challenges and their solutions. For

FEL Technology

MAGNETIC STRUCTURE
APPLE undulators provide the highest fields among
all variably polarizing insertion devices. A single pass
FEL permits the installation of a circular beam pipe
without performance loss. In this geometry additional
magnetic material can be arranged at the side of thevacuum chamber. Additionally, the angle ofmagnetization can be rotated by 45° (APPLE III [7]).
The demagnetizing fields are slightly higher for an
APPLE III than for an APPLE II (figure 1). The
magnetic stability can be recovered with another magnet
grade and the field gain is still about a factor of 1.4 ascompared to an APPLE II [7].

H / kA/m

Cascaded HGHG-FEL facilities have been proposed byseveral groups. In these machines the beamcharacteristics of the initial seeding laser like coherence,
short time structure and small bandwidth aretransformed to shorter wavelengths where seeding lasers
are not available. The first stages are equipped withplanar devices. For full polarization control the last
amplifier and the final radiator can be realized as
APPLE devices. The specific demands on the polarizing
devices as compared to planar hybrid devices are
discussed for the example of the proposed BESSY HEFEL to be operated at 1nm. The field optimization
procedure requires specific strategies. An improvementof the magnetic material is helpful in this context. The
small good field region implies tight geometricaltolerances. Gap and phase dependent focussing effects
have to be compensated. Other important issues are thecomplexity of the control system and the radiation
protection system.

illustration we will apply the parameters of the proposed
BESSY Soft X-Ray FEL.
The tolerances for HGHG and SASE FEL undulators
are similar for comparable photon energies. The
complexity of a HGHG undulator system is, however,higher. A 200m SASE undulator consists of 40 identical
5m modules whereas a cascaded FEL can be composedof 18 modules with 9 different lengths and 5 different
period lengths (BESSY HE-FEL). This affects theconcept of series production and modularity, the control
system and the operation.
In contrast to an X-ray FEL undulator system theundulator focussing is an important issue for soft X-ray
systems (in particular for polarizing devices) because theelectron energies are generally lower.

H / kA/m

Abstract

300
200
100
0
-100
-200
-300
-400
-35
-30
x / -25-20
mm-15
-10
-5 0
0

-10

-30
-20 / mm

z

300
200
100
0
-100
-200
-300
-400
-500
-35
-30
-25
x / -20-15-10
mm
-5 0
0

-30
-20
-10

z/

mm

Figure 1: Difference of reverse fields between APPLE
III and APPLE II design for the example of the planned
BESSY UE50 (LE- and ME-FEL). Left: A-magnet(long. magnetized), right: B-magnet (vert. magnetized).
Today APPLE undulators can be built with the same
field quality as planar devices using specific sorting andshimming techniques. At BESSY the magnets of the
APPLE undulators are characterized individually withrespect to the dipole moment (automated Helmholtzcoil) and the inhomogeneities (stretched wire system).
The data are used in a simulated annealing code which

521

THBAU01

Proceedings of FEL 2006, BESSY, Berlin, Germany

field integral / T mm

minimizes the phase errors and reduces the multipoles
by a factor of 5-10 as compared to an unsorted structure[8]. The field quality of devices consisting of 1000
magnets can be predicted with an accuracy of about 1.5
Gm (figure 2).
1

UE49

z = -20mm

0.8
0.6

z = -10mm

0.4
0.2

z = 0mm0-0.2

z = 10mm

-0.4
-0.6

z = 20mm

3,0

1000

1500

2000

2500

3000

3500

x / mmFigure 2: Prediction from single block characterization(red) and Hall probe measurements (black) of the
BESSY UE49 field integrals at five transverse positions.
The field properties are optimized with various
techniques:- trajectories: block movements- shift dependent terms: Fe-shims- shift independent terms: permanent magnet arrays
at both ends of the devices.
- dynamic multipoles: Fe-shims
Details can be found in [8,9,10]. The required magnet
quality of FEL undulators can be achieved with state of
the art techniques which can, however, be rather time
consuming and are not suitable for a series production.

MAGNET MATERIAL
The new FEL facilities will consist of many undulator
segments with totally 10.000s of individual magnets.
Today, permanent magnets have typical remanence andangle errors in the order of 1-2% and 1-2°, respectively,
where the distributions within one batch can besignificantly narrower. The inhomogeneities areimportant as well and determine the field quality at small
gaps. In principle, the required magnet field performancecan be achieved with a detailed characterization of themagnets, sorting and shimming. The production process
can, however, significantly be simplified if the magnet
quality can be improved.
Triggered by the need for high quality magnets for theEuropean X-Ray FEL at DESY and the BESSY Soft XRay FEL a BMBF funded joint collaboration between
DESY, BESSY and Vacuumschmelze has started. The
collaboration has the goal to reduce remanence andangle errors by a factor of 5-10 and to improve the block
homogeneity. At a certain level the quality is determinedby the geometrical tolerances of the blocks and hence,these tolerances have to be reduced to a level of 10μm.
Magnet measurement equipment built at BESSY andDESY has been shipped to the magnet manufacturer

522

angle of magnetization [degree]

-0.8
-1

who will use the machines to optimize the production
process. BESSY provides a stretched wire system for thecharacterization of block inhomogeneities whereas
DESY has built an automated Helmholtz coil system.
The north south effect (field difference between two
opposite sides of a block) is not a useful quantity inparticular for APPLE devices where the electron beam islocated close to a magnet corner. Block inhomgeneities
can be determined by cutting the magnet into slices andmeasuring the slices in a Helmholtz coil. Results areshown in figure 3 where a systematic variation of themagnetization angle over the position inside the magnet
is plotted. The systematic trend can be minimized withanappropriate
settingoftheproduction
parameters.
2,5
2,0
1,5
1,0
0,5
0,0
-0,5
-1,0
-1,5
-2,0
-2,5
-3,0
-40

0

40

position inside magnet block [ mm ]Figure 3: Variation of the magnetization angle inside
four individual magnet blocks. The blocks have been
produced with different production parameters (bycourtesy of Vacuumschmelze, Hanau).
The magnet cutting and the characterization of theslices is time consuming. Similar information can begathered with the new stretched wire setup in a much
shorter time from the complete magnet. The magnet is
moved with respect to a single wire in a distance of 510mm and induced voltages are measured (figure 4).
Measurements from different sides give the informationon the magnetization distribution inside the magnet.
Since the measurements are done in a strong field
gradient a good positioning accuracy is essential.
Temperature stabilized linear motors with absolute
encoders and air bearings allow for fast and precise
movements. Fe shieldings around the motors reduce theelectrical noise.

Figure 4: Stretched wire system for the measurementof magnet block inhomogeneities.

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

x 100

A-magnet
-50

0

50

8
6
4
2
0
-2
-4
-6
-8

x 10

0.8

dB/B0

dB/B0

-3

HE-FEL

0.6

parallel

0.4

0.8
HE-FEL

0.6

anti parallel

0.4

0.2

0.2

planar

0

0

-0.2

-0.2

-0.4

-3

0

5

-0.4

10

0

5

10

phase / mm

B-magnet-50

0phase / mmFigure 6: Relative field variation 0.1mm horizontal(red) and vertical (blue) off axis for APPLE III (solid)and APPLE II (dashed) undulator operating in theparallel (left) and antiparallel (right) mode.

x 1000z / mm50z / mmFigure 5: Reproducibilities of the stretched wire
system. One hundred blocks of both types have beenmeasured (black) and sigma values (red) have been
determined. The distance to the single wire is 10mm and3
the block dimensions are 40x40x28mm .

TOLERANCES
The tolerances for HGHG and SASE FELs aredifferent from those of storage ring IDs. A good overlap
between the photon and electron beam (x  0.1 x(eelctron, photon)) defines the maximum trajectory walk
off. For a Pierce parameter of 0.001 (BESSY HE-FEL) a
maximum variation in the K-parameter of ±5 x 10-4 canbe tolerated (E < 0.16 x bandwidth). This defines thefollowing tolerances: The temperature dependence of themagnet remanence of 0.0011 / °C requires a temperaturestability T  ±0.1°C. The gap positioning accuracy
must be gap  ±1μm and the transverse alignment
tolerance has to be x  ±40μm. The largest
contribution to K / K is attributed to the transversealignment error (see below). The phase error due toenergy spread dominates the total phase error if
 1
 rms   3Assuming an energy spread of 2 x 10-4 the tolerance
for the phase error of the magnetic field is rms < 6.6°
for the BESSY HE-FEL. Apart from quadrupole terms(see later in this paper) static or dynamic multipoles areless important for single pass devices.
The trajectory errors can be measured and minimized
with state of the art measurement and shimming
techniques. Phase errors below 5° can be achieved evenfor the complicated APPLE II design without explicit
phase shimming as demonstrated for the six BESSY
APPLE II devices. A gap positioning accuracy of±1.5μm has already been achieved [7] (see also next
chapter). In the following, we will concentrate on thechallenging transverse alignment tolerances.

FEL Technology

x 10

The good field region of an APPLE device issignificantly reduced as compared to a planar device(figure 6) though it is larger for the APPLE III design ascompared to the APPLE II.
In figure 7 the transverse charge distribution of the
BESSY FEL electron beam is compared to the field
variations in various operation modes. For a maximum
transverse displacement of 40μm more than 2 of theelectron beam are within K / K < 5 x 10-4.
x 10

dB/B0

0.06
0.04
0.02
0
-0.02
-0.04
-0.06

∫ By dx / Tmm∫ By dx / Tmm

Figure 5 shows a reproducibility of 3.0e-4 Tmm formagnets with the magnetization vector parallel to thewire (A-magnets) and 1.5e-3Tmm for magnets with anorientation perpendicular to the wire (B-magnets). In
case of the B-magnets the measurement noise isdominated by a contribution which is proportional to themain signal. A positioning accuracy <4.0μm and atemperature stability of <0.2° is needed to bring theelectrical noise to this level.

THBAU01-3

0.6
vertical direction
antiparallel

0.5

vertical direction
max phase

0.4
0.3
0.2

horizontal direction
max phasevertical direction
planar undulator

0.1
0

0

0.02 0.04 0.06 0.08

0.1

0.12 0.14 0.16 0.18

0.2

z / mmFigure 7: Averaged transverse size of the BESSY FELelectron beam compared to the field roll off for various
operation modes.
Figure 8 shows all possible girder misalignments.
They are classified as follows:
1. No circle: this movement is uncritical.
2. Black circle: the motion can be minimized witha stiff support structure. The motion is not
driven by any force.
3. Blue circle: the movements are well controlledwith a closed loop servo system.
4. Red dotted circle: The movement shifts thefield amplitude and the center of the good fieldregion. It shows up for antiparallel motion
where longitudinal and transverse forces
between the upper and lower magnet girders arepresent.
5. Red circle: The movement enhances K / K. It
shows up for antiparallel motion.

523

Proceedings of FEL 2006, BESSY, Berlin, Germany

displacement of individual girder relative to the nominal position

Gap change

_x1

_y1

_z1

displacement of girder pair relative to the nominal position
_z 2
_y2

_x 2
angle error of individual girder relative to the nominal position

_1

_1

_1

angle error of girder pair relative to the nominal position

_2

_2

_2

In principle an APPLE II type final amplifier of a
HGHG cascade can be realized as a fixed gap device.
The energy and polarization tuning can be performed bymagnet row movements [11]. The BESSY final
amplifiers will be of the APPLE III type. In this case thegap drive is necessary to install and remove the modules
from the beam pipe without breaking the vacuum.
The magnets are assembled onto Aluminum girders
with a length of up to 4m. They are gimbal-mounted topermit a tapering and to cope with the different thermal
expansion coefficient of the Fe-support structure. The
straightness of the assembling surfaces of such girders
can be within ±8μm resulting in a gap variation of only
±15μm (figure 10). This remaining gap variation can be
reduced to ±6μm using appropriate mechanical shims
under the magnet holders.
The bending of the magnet girder can be minimized
by choosing appropriate locations for the support. The
bending can be further reduced by more than one orderof magnitude with four supports instead of two using
two crossbars inside the magnet girders. This has been
demostrated for the BESSY undulators UE46, UE49 andUE112.
height / μm

THBAU01

Figure 8: Classification of geometrical tolerances.

50
40
upper girder

30
20

SUPPORT AND DRIVE SYSTEM

10
0

The tolerances discussed in the previous section
define the mechanical design of the support and drive
system.

lower girder

-10
-20
-30

Gap Accuracy
The gap setting has to be done with a closed loop servo
system which uses a direct gap reading. The encoders
have to be located in a vertical line with the electron
beam to avoid Abbe’s comparator error [7] (figure 9).
Differential thermal expansion coefficients of the
support structure (Fe) and the magnet girders and themeasurement system (Al) result in a temperaturedependent gap error of only 1.1μm/°C for the systemdescribed in [7] and can be ignored if compared to thethermal variation of the magnet material remanence.

Figure 9: Approaching the third harmonic of the
BESSY UE49 from two different directions results in avery small energy shift which corresponds to a gap errorof only ±1μm. The device employs the newmeasurement system described in [7].

524

-40
-50

gap variation

0

0.5

1

1.5

2

2.5

3

3.5

4

distance / m

Figure 10: Straightness of upper and lower UE112
magnet girder and corresponding gap variations.

Bearings
In antiparallel mode strong longitudinal and transverse
forces between the upper and lower magnet girder show
up. The transverse forces can be supported withtransverse flexible joints connecting the girders to the
support structure. These joints have to permit alongitudinal motion (thermal expansion) and an
intentional longitudinal taper of the girders.
The longitudinal forces produce a torque around thevertical axis and around the horizontal (transverse) axis
where the strength depends on the location of the joints
that keep the girders longitudinally in place. As a result
the girders rotate and K / K on axis is enhanced. The
transverse motion can be kept within the acceptable
limits with stiff joints between the girders and the
support structure. The vertical parallel inclination of thegirders can principally be compensated using four
motors for the gap drive. Such a drive system can also
compensate for the residual transverse girder crossing
via a deliberate inclination of the girders. This concept
implicates however a complication of the control system

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany
and the gap measurement arrangement. Another solution
is the positioning of the longitudinal fixed bearing
vertically at the height of the magnets and longitudinallyclose to the drive system for the row phase. This
arrangement eliminates any torque around the transverse
axis (figure 11) and hence, any girder inclination or
girder bending.

THBAU01

All BESSY undulators are based on cast ironstructures. The last APPLE device (UE112) has a single
piece support structure (figure 13) which significantly
simplifies the assembling procedure.

Figure 13: The support structure of the 4m long
UE112 is made from a single piece of cast Fe.
Figure 11: The vertical location of the longitudinalbearing (red arrow) is chosen such that there is no torquearound the transverse axis.

Support Structure
The support structure of an APPLE undulator
operating in the antiparallel mode has to cope with thestrong longitudinal and transverse forces which areabsent in a planar or elliptical device.
The support structure can be either a welded structure
or a cast structure. The latter one has several advantages:- The structure can be made extremely stiff
without additional effort because literally any
shape can be realized.
- A bionic optimization can be applied wherematerial is added at locations with large
stress and removed at locations of low stress(figure 12).
- The complete support structure can be castand milled as a single piece.
- The procedure is suitable for series
production since wooden forms can be used
for many casts. Modular forms can beadapted to different undulator lengths.

Figure 12: Bionic optimization of the support structureof the BESSY UE112 undulator (by courtesy of
Heidenreich und Harbeck AG).

FEL Technology

Alignment
The magnet centers of all final amplifier modules haveto be aligned with an accuracy of ±40µm with respect toeach other (assuming APPLE type devices). This can not
be accomplished with standard alignment tools. Beambased alignment techniques have to be applied instead.
For this purpose the modules have to be assembled onto
moveable supports with an accuracy of 10µm.

UNDULATOR FOCUSSING
An undulator is a series of alternating dipole magnets
which shows an edge focusing. Planar devices focus in
the vertical direction. This second order effect can not be
described with normal 2-dimensional multipoles.
Polarizing devices show also a horizontal defocusing
under certain operating conditions which results in an
additional focusing in the vertical plane. For Halbach
fields the focusing strength in the horizontal plane isgiven by:Kx ="2 $ e22
2
2
k x#eff $ k 2 $ !n=1 ( Bxn+ B yn)(%mc) 22

2"

k x#eff = !n=1

2

2

2

2

2

Bxn $ k xxn / n!+ Byn $ k xyn / n!
Bxn / n!+ B yn / n!

and similar for the vertical plane (summation over the
Fourier components n). The focusing strength in the
antiparallel mode can not be described in this compact
form since the fields are not of the Halbach type.
These effects influence the beam size and it has to beconsidered whether the transverse overlap between theelectron beam and the photon beam is still maintained.
Figure 14 shows the variation of the horizontal andvertical beam size for the BESSY HE-FEL. The values
change by more than a factor of two which is not
acceptable. For the BESSY ME- and the LE- FEL theeffects are larger by factors of 9 and 45, respectively,

525

THBAU01

Proceedings of FEL 2006, BESSY, Berlin, Germany

beam size / mmdue to the larger period length and larger field (ME- andLE-FEL) and the lower beam energy (LE-FEL).
Obviously, additional quadrupoles are essential to keep
the beam size within acceptable limits and they have tobe adapted during gap drive and row phasing.

many research laboratories. Many drivers have been
written. Useful tools are available such as an archiver forthe process variables or a network protocol for the
distribution of the process variables. GUIs can be easily
built with a “point and click” tool.

0.25
Master-IOC

planar device

0.225
0.2

APPLE, phase = 0

0.175

APPLE, phase = π

ethernet
Slave-IOC

Slave-IOC

Slave-IOCother undulator modules

0.15
0.125

horizontal planeother undulator modules
ethernet

CAN bus0.1

trigger line

0.075

axis
controller

0.05

vertical plane

axis
controller

axis
controller

PLC

limit switch
tilt sensor
air pressure

CTNet bus

0.025
0CTSync bus

0

2

4

6

8

10

12

14

16

18

20

emergency stop, actually point-to-point connections to PLC

distance / m

Figure 14: Horizontal (solid) and vertical (dotted)
beamsize within the final amplifier of the BESSY HEFEL at smallest gap without additional quadrupoles. The
data are given for different operation modes of an
APPLE III device and for a planar device.

CAN buscorrection
coil

correction
coil

correction
coil

CAN bus

MOTION CONTROLA cascaded HGHG FEL requires a sophisticatedmotion control system. Each HGHG stage consists of amodulator and a radiator (maybe several submodules),steerer to compensate residual dipole errors, quadrupoles
for tune compensation and phase adapting units between
the modules. Between two stages fresh bunch dispersive
sections are installed. All components have to be driven
in synchronism. Reproducibility is essential and can berealized with closed loop servo systems for motion
control, permanent magnet phase adapting units andquadrupoles and air coils to avoid hysteresis effects.
In the following we describe the BESSY system as
one possible solution. Other hardware and softwareconcepts are also possible.
Figure 15 shows the control system of a single
undulator, the BESSY UE112, which can be adapted to
the FEL requirements. The undulator control programruns on a VME-bus based computer called IOC. It is areliable system and many interface cards are available on
the market. The user interface does not run on the IOC
but on an independent workstation, which communicateswith the IOC via ethernet. In principle, one IOC cancontrol all modules (modulator, radiator, etc.) of one
HGHG stage. Four of these systems are required for the
BESSY four stages HE-FEL. A fifth IOC operates as amaster to synchronize the individual IOCs.
A PLC is useful for a low level safety control of thesystem checking parameters like air pressure (needed forthe brakes), inclination of magnet girders, hard andsoftware limit switches etc.
EPICS is used as a robust and reliable software
framework for the undulator control software. All
sources are available and it is actively developed in

526

quadrupole

phase
shiftertemperature
moduletemperature
moduleFigure 15: Control system of the BESSY UE112.
Each motor has its own detached motor controller
which is connected to the IOC via CAN bus. Absolute
linear encoders simplify reference procedures. Modern
motor controllers as used for the UE112 can operate
several tasks with different priorities. User definedparameters can be stored permanently in the controller
and can even be modified during motor movement. The
motor controllers can communicate among each otherand with the IOC via CTNet (ruggedized version of
ARCNet) and a synchronization between the modules
can be realized via CTSynch.

BEAM PROTECTION SYSTEM
The electron beam can cause a demagnetization of theundulator magnets if it propagates severely off axis [1214]. The electrons produce a shower of secondary
electrons and photons in the vacuum chamber which
may deposit energy into the magnets. Detailed
experiments have been done to study the influence ofvarious parameters on the process like the geometry,material, working point of the magnets, temperature etc.
[15]. A reduced dose (electron energy > 20MeV) of 70
kGy produces already a remanence loss of 1% in a
typical magnet material with a coercivity of 1800 kA/m
[16].
For the layout of a beam protection system the
maximum beam charge which may be dumped into thevacuum chamber without loss of performance has to be

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Proceedings of FEL 2006, BESSY, Berlin, Germany

0.25
0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
-1000

phase error / degree

In the 0.1mrad case the region of interaction is spreadout over more periods and the local degradation is much
lower. Since the magnet degradation extends over
several periods the trajectory errors are negligible evenfor the 1mrad case (figure 18). The averaged phase error
introduced in this case is 7° (figure 18) which results in ashift of the first harmonic and a splitting of the fifth
harmonic (figure 19).
traj. diff. / Tmm**2

determined. In the following we discuss theconsequences on the spontaneous radiation spectrum.
Simulations for the impact on the stimulated radiation
will be done in the future using GENESIS. Two
scenarios have been studied where the electron beam hits
the vacuum chamber under grazing angles of 1mrad and
0.1mrad, respectively. Due to the small vacuum
apertures larger angles are unlikely. Monte Carlosimulations with GEANT [17] have been done for bothcases. The deposited charge was 300.000 nC. The
magnets have been subdivided into 5x5 (1mrad case)and 7x7 (0.1mrad case) segments (figure 16). Doses
have been evaluated for each of the segments.

THBAU01

1.0 mrad0.1 mrad1.0 mrad0.1 mrad

15
10
5
0
-5
-10

-500

0

500

1000

-1000

0

1000

z / mmz / mmFigure 18: Trajectory errors for angles of incidence of
0.1mrad and 1mrad (left) and phase errors for bothcases.
3500
3000

x 10 12brightness

brightness

x 10 12

1st harmonic

2500
2000

field reduction / %local demagnet. / %

10
8
6
4
2
0

-1000

0

1000

z / mm

0
-0.2
-0.4
-0.6
-0.8
-1
-1.2
-1.4
-1.6
-2

-1

0

1

2

z / mmFigure 17: Maximum demagnetization of magnet
segments (left) for 1mrad and 0.1mrad angle ofincidence and field variation (right) for 1mrad.

FEL Technology

5th harmonic

2500
2000
1500

1000

1000

0
620

In the 1mrad case a maximum reduced dose of
700kGy has been detected close to the vacuum pipe.
This corresponds to a maximum demagnetization of
10%. Based on the doses in each magnet segment thecorresponding remanences have been evaluated. Then,the undulator on axis field has been derived from thecontributions of all segments (totally about 70.000
segments). The field reduction close to the point ofinteraction is 1.6% (figure 17).

3000

1500
500

Figure 16: Monte Carlo simulations with GEANT.
The geometry for the BESSY HE-FEL with APPLE III
magnets (red) and a circular vacuum pipe (blue) has
been used. Secondary electrons (red) and photons (blue)
are plotted as well.

3500

500
640

660

680

energy / eV

0
3220

3240

3260

3280

energy / eV

Figure 19: Spectra of the first (left) and fifth (right)
harmonic for the unperturbed case (black) and thedegraded magnets (red).
Even if the undulator is used only at the first harmonic
the spectral shift has to be avoided. The simulations
show that a deposited charge of 30.000nC (1mrad) shifts-4
the first harmonic by only E/E=2x10 which isacceptable.
The simulations show that a collimating system for theoff axis particles as well as for the off energy particles isessential for a safe operation. The dog-leg collimator forthe planned BESSY Soft X-Ray FEL collimates thebeam transversally to ±30 and energetically to 5%.
Fibre monitors are needed for several purposes: i) A
fast interlock system which can switch off the gun laser
has to be triggered, ii) information on the total depositeddose is required to estimate the lifetime of the magnets,iii) information on the longitudinal distribution of thedeposited radiation helps to detect the hot spots. Twotypes of fast monitors have been tested at FLASH: i)
Cerenkov monitors [18] and ii) fibres for optical time
domain reflectometry used in power-meter mode [19].
The latter ones can be used also for spatially resolved
measurements. Fibre Bragg gratings can be used as highdose radiation sensors on the scale of many kGy [20].

527THBAU01

Proceedings of FEL 2006, BESSY, Berlin, Germany

They provide also information on the spatial distributionof the dose.

CONCLUSION
Various technological aspects for using APPLE
undulators in HGHG FELs have been discussed.
Experiences gained with APPLE undulators at 3rd
generation light sources have been extrapolated andstrategies to meet the tight tolerances of HGHG FEL
insertion devices have been proposed.
New concepts for the magnet field optimization, forthe motion control, for a new support structure and forradiation dose monitoring have already been tested andwill be further improved at a 3rd generation facility.

[7]

[8]
[9]

[10]

ACKNOWLEDGEMENT
The author thanks M. Scheer for doing the GEANT
simulations and H.-J. Bäcker, W. Frentrup, A. Gaupp, S.
Gottschlich, G. Pfeiffer, B. Schulz for many fruitful
discussions.

[11]

[12]

REFERENCES
[1]
[2]
[3]
[4]
[5]

[6]

528

TESLA-Technical Design Report, TESLA XFEL, Technical Design Report, 2002-9, 2002.
Linac Coherent Light Source (LCLS),
Conceptual Design Report, SLAC-R-593, 2002.
T. Shintake, Nucl. Instr. and Meth. in Phys.
Res. A, 507 (2003) pp 382-397.
L. H. Yu, Nucl. Instr. and Meth. in Phys. Res.
A, 483 (2002) pp 493-498.
X. J. Wang et al., Proceedings of the 26th
International FEL Conference, Trieste, Italy,
2004, pp 209-211.
C. Bochetta et al., Proceedings of the 27th
International FEL Conference, Stanford, CA,
2005, pp 632-685.
The BESSY Soft X-ray Free Electron Laser,
Technical Design Report March 2004, eds.: D.
Krämer,E.
Jaeschke,W.
Eberhardt,
ISBN 3-9809534-08, BESSY, Berlin (2004).
J. Bahrdt et al., Proceedings of the EPAC
2006, Edinburgh, Scotland, pp 59-61.
M.-E. Cuprie et al., Proceedings of the 27th
International FEL Conference, Stanford, CA,
2005, pp 55-58.
A. Andersson et al., Proceedings of the 26th
International FEL Conference, Trieste, Italy,
2004, pp 190-192.
D. Wang et al., Proceedings of 2005 PAC,
Knoxville, Tennessee, pp 1961-1963.
J. Wu, Z. Huang, Proceedings of the 27th
International FEL Conference, Stanford, CA,
2005, ppxx.
J. Qi-ka et al., Proceedings of the 26th
International FEL Conference, Trieste, Italy,
2004, pp 494-497.
O. Tscherbakoff et al., Proceedings of the
EPAC 2006, Edinburgh, Scotland, pp 47-49.

[13]
[14]

[15]

[16]

[17]

[18]
[19]

[20]

G. Lambert et al., Proceedings of the EPAC
2006, Edinburgh, Scotland, pp 44-46.
J. A. Clarke, Proceedings of the EPAC 2006,
Edinburgh, Scotland, pp 181-183.
Gullens et al., Proceedings of the EPAC 2006,
Edinburgh, Scotland, pp 142-144.
J. Bahrdt et al., Proceedings of the 26th
International FEL Conference, Trieste, Italy,
2004, pp 610-613.
J. Bahrdt et al., Nucl. Instr. and Meth. in Phys.
Res. A, 516 (2004) pp 575-585.
J. Bahrdt et al., Proceedings of the International
Conferenceon
Synchrotron
Radiation
Instrumentation, Daegu, Korea, 2006.
J. Bahrdt, G. Wüstefeld, Proceedings of the
EPAC 2006, Edinburgh, Scotland, pp 35623564.
T. Schmidt et al., Proceedings of theInternational Conference on Synchrotron
Radiation Instrumentation, Daegu, Korea, 2006.
P. Colomp, T. Oddolaye, P. Elleaume, “Partial
Demagnetization
of
ID6
and
Dose
Measurements on Certain Ids”, MachineTechnical Note 1-1996/ID, 1996.
M. Petra et al., Nucl. Instr. and Meth. in Phys.
Res. A, 507 (2003) pp 422-425.
P. Colomp, T. Oddolaye, P. Elleaume,“Demagnetization of Permanent Magnets to
180 MeV Electron Beam”, Technical Report
ESRF/MARCH-ID/93-09,
EuropeanSynchrotron Radiation Facility, ESRF March
1993.
T. Bizen, T. Tanaka, Y. Asano, D.E. Kim, J.S.
Bak, H.S. Lee, H. Kitamaru, Nucl. Instr. andMeth. in Phys. Res. A 467-468 (2001) pp185189.
M. Marechal, T. Shintake, SRI2003,
Conference Proceedings, AIP 705, (2004) pp
282-285.
H. Schlarb, “Collimation System for the VUVFree-Electron-Laser at the TESLA Test
Facility”, Thesis Work, Universität Hamburg,
DESY-THESIS-2001-055, Nov. 2001.
GEANT, Detector Description and Simulation
Tool, Computing and Networks Division,
CERN Geneva Switzerland.
E. Janata, M. Körfer, H. Schlarb, Nucl. Instr.
and Meth. in Phys. Res. A 253 (2004) 256-261.
H. Henschel, J. Kuhnhenn, M. Körfer, F. Wulf ,Nucl. Instr. and Meth. in Phys. Res. A, 507(2003) pp 422-425.
K. Krebber, H. Henschel, U. Weinhand, „Fibre
Bragg Gratings as high dose radiation sensors”,
Meas. Sci. Technol. 17 (2006) pp 1-8.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THBAU02

ELECTRON BEAM ALIGNMENT STRATEGY IN THE LCLSUNDULATORS*
H.-D. Nuhn#, P.J. Emma, G.L. Gassner, C.M. LeCocq, F. Peters, R.E. Ruland, Stanford Linear
Accelerator Center, 2575 Sand Hill Road, Menlo Park, CA 94025, U.S.A.

Abstract
The x-ray FEL process puts very tight tolerances on thestraightness of the electron beam trajectory (2 µm rms)
through the LCLS undulator system. Tight but lessstringent tolerances of 80 µm rms vertical and 140 µm
rms horizontally are to be met for the placement of theindividual undulator segments with respect to the beamaxis. The tolerances for electron beam straightness canonly be met through beam-based alignment (BBA) basedon electron energy variations. Conventional alignment
will set the start conditions for BBA.
Precisionfiducialization of components mounted on remotely
adjustable girders and the use of beam-finder wires(BFW) will satisfy placement tolerances.
Girdermovement due to ground motion and temperature changes
will be monitored continuously by an alignment
monitoring system (ADS) and remotely corrected. Thisstabilization of components as well as the monitoring andcorrection of the electron beam trajectory based on BPMs
and correctors will increase the time between BBA
applications. Undulator segments will be periodicallyremoved from the undulator Hall and measured tomonitor radiation damage and other effects that might
degrade undulator tuning.

symbol

λr
λu
K
Bpk
Ls
Ns
Ls
g
Ll
Ls
NQ
NBPM

value

unit

1.5
Å
3.0
cm
3.
1.25
T
3.4 5 m
33
132
m
6.8
mm
0.898
m
0.470
m
33
33+3

INTRODUCTION
The undulator system for the Linac Coherent Light
Source (LCLS), under construction at the Stanford Linear
Accelerator Center (SLAC), is comprised of 33 identical
3.4-m-long undulator segments, separated from each otherby short and long breaks. Every third break is long. The*#

Work by U.S. Department of Energy contract DE-AC02-76SF00515
nuhn@slac.stanford.edu

FEL Technology

COMPONENT DESCRIPTION
The components relevant to the SASE (self-amplified
spontaneous emission) lasing process in the LCLS
undulator system include• Undulator Segments• Segment Slide Supports• Quadrupoles• Beam Position Monitor (BPM) System• Girder Motion Supports• Beam Finder Wire (BFW) Devices• Fixed Girder Supports• Vacuum chamber• Alignment Diagnostic System (ADS) Sensors• Temperature Sensors• Air Temperature Stabilization
A brief description for each of these components isprovided in this section

Undulator Segments

Table 1: LCLS undulator parameters
Parametermin. fundamental wavelength
undulator period lengthnom. undulator parameterpeak field
undulator segment length
number of segments
full undulator lengthnom. undulator full pole gap
long break length
short break length
number of quadrupoles
number of BPMs

space provided by these breaks is used to place devices
for controlling and monitoring the electron beam. A
parameter summary is given in Table 1.

The undulator segments [1] are fixed-gap permanent
magnet planar undulators with a period length of 3 cm
and a nominal K value of about 3.5, and are mounted
inside a 3.4-m-long Ti strongback of circular crosssection. The undulator gap is arranged such that theelectron wiggle motion is in the horizontal plane. The
upper and lower pole face planes are canted with respect
to each other by an angle of 4.5-mrad, which makes the Kvalue dependent on the electron beam’s horizontal
position in addition to its dependence on the vertical
position for the regular planar undulator. Each undulator
will be operated at a different effective K value tocompensate for energy losses during the radiation process
and to optimize the SASE process. The magnetic axis,
i.e., the ideal average beam trajectory, through theundulator segment will be determined during the tuning of
the device and fiducialized to tooling balls on the device
body. Undulator magnet tuning will be done in the
Magnet Measurement Facility (MMF), which has been
specially built for this purpose.

Segment Slide Supports
Each undulator segment is mounted on two parallel
horizontal slides that allow remotely controlled
repositioning of the segment relative to the electron beam
and a full translation to a ‘removed’ position at 8 cm.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Quadrupoles
The quadruple magnets in the LCLS undulator system
are arranged in a FODO lattice. They are designed tooperate with an integrated quadrupole field gradient of
3 T over the entire LCLS operational energy range
between 4.3 GeV to 13.6 GeV. Each quadrupole magnet
has dipole correction coils integrated into its design toprovide independently controllable horizontal and vertical
dipole fields superimposed on the quadrupole fields.
The quadrupole magnets are based on electromagnetic
technology, each with its own power supply, and theirintegrated gradient can be changed in the range between
0 T and 4 T. By varying the gradient, the quadrupoles canbe used to measure the transverse distance of the electron
beam trajectory from the magnetic center of thequadrupoles, which is fiducialized to the magnetic centerof the upstream undulator segment. This enables controlof the alignment of the electron beam to the magnetic axisof the undulator segment at its down stream end, where
the quadrupole magnet is located. The electromagnetic
technology also provides the options of modifying the
focusing optics.

Beam Position Monitor (BPM) System
The electron beam position monitor system uses RF
cavity BPMs. It has been demonstrated that this type of
BPM can provide relative beam position information at
better than 1 µm resolution in the 0.2-1 nC charge range,
at which the LCLS electron bunches will be operated.
Their circular cavity body, machined to have a welldefined mechanical center, will be used in the alignmentof this component. One BPM is located just downstreamof each quadrupole magnet. An additional 3 BPMs of thesame type are mounted upstream of the first segment tomonitor the horizontal and vertical launch position andangle of the electron beam.

Girder Motion Supports
Each undulator segment and its beamline components
are mounted on a remotely moveable support structure,
called a girder [2]. The remote motion is controlled
through cam shafts [3] and allows changing the horizontal
and vertical position as well as yaw, pitch, and roll of thegirders. The components mounted on each of the 33
identical girders include an upstream Beam Finder Wire
(BFW) device, two horizontal slides supporting one
undulator segment, a downstream quadrupole magnet, an
RF cavity BPM, and a Cerenkov radiation detector, as
well as the supports for the vacuum chamber throughout
the girder, and the mounting plates for the Alignment
Diagnostic System (ADS) sensors. The BFW device, theundulator segment, and the quadrupole are fiducialized in
the MMF. The complete girder assembly will initially bealigned on the Coordinate Measurement Machine (CMM),
which has been specially designed for that purpose. The
undulator segment is mountable on and removable fromthe girder with the vacuum chamber in place and withoutcompromising the alignment of the vacuum chamber.
Segments will be swapped on the girder for magnetic

530

measurements and will be interchangeable without theneed for renewed CMM alignment.

Beam Finder Wire (BFW) Devices
The BFW device is a special wire scanner [4], with
only two positions for the horizontal and vertical wire
pair: the wires will be either in a well reproducible “in”position, in which they can be brought in collision withthe electron beam, or they will be in a “park”-position,
where they won’t affect the electron beam. The locationsof the wires in the “in” position will be fiducialized totooling balls mounted on the device body.
Each BFW device enables control of the alignment of
the electron beam at its up-stream end. After all
quadrupoles are aligned using BBA (see below), thegirder can then be moved to bring the wires of the BFW
device into collision with the beam, which will complete
the alignment of the undulator segments relative to thebeam axis. The BFW device will provide a means toaccomplish a beam-based undulator segment alignment
from the control room without the need for tunnel access.
The BFW device is only needed for occasionalverifications. The alignment can be achieved at eventighter tolerance levels using portable Hydrostatic
Leveling System (portable HLS) and portable Wire
Position Monitor (portable WPM) devices without theneed for the electron beam to be present [5]. The use of
these devices requires, however, extended tunnel accessand will be used prior to the beam–based commissioning
process. It is expected that the ADS (see below) will be
used to monitor the girder positions from then on.
Although not their primary purpose, the BFW wires
will also provide transverse beam profile and rms size
information. This functionality will be preserved as longas the wire diameter is not larger than about twice the rms
beam width. With an rms beam width of 36 µm, a
maximum wire diameter of 40 µm is a reasonable upper
limit and the choice of a Carbon wire will adequately
limit beam loss on the downstream undulators [6]. The
transverse position of the wires will be monitored with thecam mover readback system and also, at sub-micron
resolution but at a slower rate, with the ADS. Local
BPMs can also be used to measure and compensate forany shot-by-shot trajectory jitter during the scan.

Fixed Girder Supports
Each girder is supported by two thermally isolated,sand-filled pillars, with manual adjustments at the top(Figure 4), which allow pre-alignment of the cam movers.

Vacuum chamber
The vacuum chamber of the LCLS undulator system
has a 5 mm×12.5 mm rectangular inner cross section
through the undulator segments and circular (both 8 mm
and 10 mm diameter) cross sections in the breaks. Theinteraction of the electron beam with the vacuum chamber
generates longitudinal and transverse wakefields. The
amplitude of the latter is limited by keeping the beam at
the center of the chamber with a ±200 µm tolerance. The

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Proceedings of FEL 2006, BESSY, Berlin, Germany
vacuum chamber will not be moved when the undulator
segment is horizontally repositioned on the slides.

Alignment Diagnostic System (ADS) Sensors
The alignment of the girders will be continuously
monitored by the ADS, which is a combination of a Wire
Position Monitor (WPM) system and a Hydrostatic
Leveling System (HLS), both permanently installed.
There are four sensors for each of the two subsystems
mounted on each girder, two each close to either end of
the undulator segment. The sensors are supported by amounting plate. The HLS is most sensitive to vertical
positioning, while the WPM is best for horizontal
positioning.

Temperature Sensors
The temperature will be monitored at several control
points on girder components, at girder supports, and at themounting plates of the ADS sensors.

Air Temperature Stabilization
The temperature of the LCLS undulator tunnel iscontrolled by a constantly flowing, thermally regulated,
air stream [7]. The air enters upstream of the first girder
and is blown through the 170-m-long tunnel indownstream direction. Temperature monitoring is done at
the entrance point. As the air travels through the tunnel itis expected to pickup heat from the tunnel equipment at a
rate of less than 50 W/m. The system is designed suchthat the air temperature will stay in the range of 19.5º C20.5º C at all times along the entire undulator system.
The undulator K value has been measured to change by
0.015% over a temperature range of 0.28º C.

TOLERANCES AND ALIGNMENTSTRATEGY OVERVIEW
The purpose of the undulator system is to enable the
SASE process, which is based on the interaction between
an electron bunch and its spontaneous undulator radiation.
For obtaining and maintaining high gain in the SASE
process, it is important that the electron bunch is in goodoverlap with the radiation field and that the individual
electrons maintain a well defined phase relationship withthat field. The radiation field is initially produced in thefirst undulator segment and will proceed in a straight line,
while the electron beam trajectory will deviate from astraight line in the presence of magnetic and electricfields. The ideal undulator magnetic field will generatetiny periodic deviations from the straight line, which arenecessary for the SASE process; the first and second field
integrals over each undulator segment are ideally zero.
Problems arise from off-axis fields of misaligned
quadrupoles and undulator segments, the earth’s magnetic
field [8], other environmental fields, as well as fromerrors in the undulator fields that create finite field
integrals or increase the electrons’ path lengths throughthe undulator. The primary mitigation tool includes
tuning [9], (for undulator field errors and earth’s magnetic

FEL Technology

THBAU02

field), and shielding, (for environmental fields as well as
earth’s magnetic field).
The remaining error-fields (off-axis fields inquadrupoles and undulator segments, remnants ofundulator field errors, the earth’s magnetic field, and theenvironmental field) will be corrected through beam
based alignment, which compensates the net effect ofthese fields by adjusting the transverse positions of thequadrupoles, through girder motion and by adding small
dipole correction fields through trim coil adjustments.
This process will automatically take the largest error fieldsource, (e.g., misaligned quadrupoles), out of the system
by moving the centers of the quadrupole magnets to agoal position, close to a common straight line. The goal
position will be slightly away from that line, just enoughto compensate for other remaining error sources. Thus,
the goal position of each quadrupole will be precisely
defined through the BBA process, and will be deviatingfrom the electron beam trajectory (beam axis, defined by
BBA) by about 20 µm (rms), a calculated number basedon error amplitude estimates.
Table 2: Alignment tolerances for component alignment
on girders for the LCLS undulator system
Horizontal Alignment of Quadrupoleand BPM to Segment (rms)
Vertical Alignment of Quadrupoleand BPM to Segment (rms)Horizontal Alignmentof BFW to Segment (rms)
Vertical Alignment of BFW to
Segment (rms)

Value
125

Unit
µm

60

µm

100

µm

55

µm

For best FEL performance, the effective magnetic
centers of all quadrupoles need to be within ±2 µm oftheir goal position in both the horizontal and verticaldirections. Additionally, the magnetic axes of theundulator segments need to be aligned to the beam axis toan accuracy of 140 µm (rms) horizontally and 80 µm(rms) vertically.
Table 3: Alignment tolerances for girder alignment in the
LCLS Undulator Hall
Initial rms uncorrelated x/yquadrupole alignment tolerance wrt
straight line
Longitudinal Girder alignment
tolerance
Undulator Segment yaw tolerance(rms)
Undulator Segment pitch tolerance(rms)
Undulator Segment roll tolerance
(rms)

Value
125

Unit
µm

±1

mm

240

µrad

80

µrad

1000

µrad

The precise alignment of the quadrupoles can only beachieved using a beam based alignment method (energyscan) while the relative alignment (see Table 2) of the531

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Proceedings of FEL 2006, BESSY, Berlin, Germany

undulator segments to the quadrupoles and the BFW
devices is aided by mounting the components oncommon, remotely movable girders (see above). The
tolerances for the conventional alignment of the girders in
the tunnel are reasonably achievable (see Table 3).

ALIGNMENT DIAGNOSTIC SYSTEM
The ADS continuously tracks changes in the transverse
position, tilt, yaw, and roll of all girders to better than
1 µm [10]. This position information together withtemperature measurements on the girders will be used to
calculate the motion of the geometric centers for BPMs
and quadrupoles to better than 2 µm (rms) with respect to
the ADS sensors.
The information will be used between BBA
applications to correct for girder/quadrupole positionchanges due to ground motion and temperaturefluctuations and to correct the offset used in evaluating
the BPM readings.

Wire Position Monitor (WPM) System
The WPM system is based on two 140-m-long stretchedwires, running parallel to the beam line axis on one sideof the Undulator as illustrated in Figure 1.
The wire position monitors are mounted to the girders
kinematically, as shown in Figure 1. The vertical positionof monitors has to be adjustable at different girders
according to the wire sag of about 15 cm. Each girder
will be equipped with four wire position monitors, two on
each end. With this geometry, positions of each girder
can be measured in horizontal and vertical direction withrespect to both stretched wires. Pitch, roll and jaw of thegirders will be calculated.
Transverse position ofquadrupoles can be determined within 0.5 µm (rms) bymeasurements of support temperatures within ±0.1 K.
As extensive test measurements have shown [11], thereadout resolution of the WPM system is much better than
100 nm and instrument drifts are lower than 100 nm perday.
Undulator

Quadrupole

Wire Position Monitor

objective for the quadrupoles. Therefore, the vertical
position of both wires will be correlated to the horizontal
plain defined by the Hydrostatic Leveling System.

Hydrostatic Leveling System (HLS)The HLS system is based on a system of water pipes
also covering the entire 140-m-long undulator system.
Four sensors are mounted to the sides of each girder.
The sensors are located at the same position as the WPM
system sensors on each side of the girder.

Figure 2: Functional cross section diagram of an HLS
capacitive sensor
The system consists of two types of HLS sensors,which complement each other. One sensor type is basedon capacitive measurements, which has the advantage ofbeing widely used and having a lower purchase cost, see
Figure 2. The repeatability of the sensor is 1 μm with anaccuracy of 5 μm over the 5 mm measurement range. A
disadvantage of this sensor type is that capacitive sensors
drift by about 1 – 2 μm per month due to aging ofelectronic components. Ideally, the determination of theabsolute distance between the sensing electrode and thewater surface would require knowing the exact dielectric
constants involved and the exact distance between thesensing electrode and the other electrode (vesselgeometry). However, it is not possible to determine thesevalues with sufficient accuracy to derive height readings
directly from the capacitances of the sensors. Therefore, acalibration is performed by measuring the capacitance at
different water levels and referring them to actual heightreadings.

Wire 1
Beam
Wire 2Girder

GirderCross section
Front view
Figure 1: Functional cross section diagram of wire
arrangements for the WPM system

Due to the unavoidable large sag of long wires, theuncertainty of the wires in vertical direction will be higher
than one micrometer, which is the required design

532

Figure 3: Functional cross section diagram of an HLS
ultrasound sensor.
The second type of sensor is based on ultrasonicruntime measurements, see Figure 3. The measurements

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Proceedings of FEL 2006, BESSY, Berlin, Germany
are self calibrating and therefore no drifts are expected.
The repeatability of the sensor is 1 μm with an accuracyof 5 μm over the 5 mm measurement range. The
ultrasound sensors measure the runtime to the two
reference surfaces of the probe and to the water surface.
This provides information about the water level withrespect to the external fiducial of the probe. The
ultrasound sensors, once mounted to the girder, aremeasured with the CMM. They are used to set the heightof the girder in the tunnel during the conventionalalignment step. Since the ultrasound sensors provide
actual height differences to the water surface they can beused to calibrate the capacitive sensors.

THBAU02

pedestals (see Figure 4). Relative alignment of girdercomponents to the magnetic axes of the undulator
segments (on the CMM) is done by using the manualadjustable supports of the quadrupole, BPM and BFWcomponents, which provide a range of ±2 mm in thehorizontal and vertical directions with a resolution of
2 µm. The height of the magnetic axes of the undulator
segments above the segment supports is controlled bypermanent shims created specially for the undulator after
the tuning process and permanently bolted to its bottom.
This makes all undulator segments interchangeable witheach other.

Remote Controls
MONITORING ELEMENTS SUMMARY
Monitoring elements are used to detect girder position
as well as electron beam position. The following list
provides a summary:• Hydrostatic Leveling System (HLS)o monitors y, pitch, and roll
• Wire Position Monitoring System (WPM) [11]o monitors x, (y), (pitch), yaw, and roll
• Temperature Sensors
o in support of HLS/WPM readout corrections,
undulator K corrections, and component motion
interpretation• Beam Position Monitors*o monitors x and y positions of the electron beam
• Quadrupoles*
o can be used to measure x and y offsets of theelectron beam with respect to the quadrupole
center

ALIGNMENT CONTROLS
A number of manual (local) and remote adjustments areavailable for the alignment of the beamline components of
the LCLS undulator system.

The transverse positions of the girders are (remotely)
controlled based on cam mover technology• during initial conventional alignment (see above)• for quadrupole position control, i.e., beam steering
during BBA.
• for BFW scans• for compensation of ground motion effects etc.
The motion range is such that each quadrupole magnet
can be moved ±0.7 mm in any transverse direction fromits neutral position. The motion control allows moving asingle quadrupole independently in the horizontal andvertical direction without affecting the adjacentquadrupoles and without introducing roll to the girder
assembly. All girder components will be moved together
when a quadrupole is repositioned so that the BFW
device, the undulator segment, the quadrupole, the BPM
and the vacuum chamber will stay aligned relative to eachother. The horizontal position of the undulator segment isremotely controlled for• field strength adjustment (change of K)• reductionofradiation
exposureduringcommissioning (full roll-out position),• measurement of FEL gain as function of z (fullroll-out position),• measurement of K using spontaneous radiationfrom only two adjacent, interfering undulators [12].

CONVENTIONAL ALIGNMENT

Figure 4: Undulator segment supports

Local Controls
Alignment of the cam supports is done using themanual adjustment controls on top of the support*

Transverse Locations Tracked by HLS and WPM

FEL Technology

The conventional alignment of the undulator system
focuses on bringing the quadrupole magnets into astraight line at tolerances specified in Table 3.
To achieve this goal, the first step is to establish amonument network inside the undulator hall. This set ofcoordinates assigned to the network points serves as therepresentation of the coordinate system and is the basis
for all component set-ups. In practice, the points are nests
compatible with 1.5" spherical tooling. They can beequipped
with
SMRs(Spherically
MountedRetroreflectors) for laser tracker observations, or solid
sphere based rods for leveling observations. Simulations
have been made with a regular pattern of both floor andwall targets. Figure 5, below, represents the middle
section of the undulator hall with the red rectangles
representing quadrupoles. A floor point is installed in the533

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Proceedings of FEL 2006, BESSY, Berlin, Germany

middle of the tunnel at every other quadrupole location.
The laser tracker positions are placed in front of the otherquadrupoles with a staggered offset from the beamline.
The tracker observations (purple lines) have a-priori
standard deviations based on recent experiences andstandard observation practices: 30 µm for the distances
and an inverse function of the distance for the two angles(30 µm and 50 µm at one meter for the horizontal and thevertical, respectively).
The weight of the levelingobservations (green lines) is based on 50 µm as a-priori
standard deviations.

Figure 5: The undulator hall network, used in Simulation,is shown relative to quadrupole locations. Floor and wallmonuments as well as tracker positions are shown. The
largest semi-major axis of the error ellipses is below
50 µm.
Figure 5 shows the resulting error ellipse at 1 sigma fora free-net approach. All semi-major axes are below
50 µm. This free-net approach assumes that the locationand orientation of the LCLS undulator coordinate system[13] has been established through the inclusion of anumber of points known in the SLAC linac system.
Once the network is established, the points can be used
for the markings on the floor, the alignment of the fixedsupport pillars and finally the pre-alignment of thegirders. For all these tasks, total station set-ups are
performed. A solid resection of the instrument, based on
at least two floor monuments and three wall monuments,
can guarantee the necessary requirement for point
determination.
Depending on the duration of theinstallation and the characteristics of the floor curing, anadditional survey of the monument network will beobserved to control and update the coordinates.
After the undulator segments are installed, a final
mapping of all monuments and all fiducials is performed.
The scenario for the laser tracker position andmethodology is identical to the one used to derive themonument network.
The fiducials of the girders,undulator segments, quadrupoles, BFW devices and HLS
ultrasound sensors are observed from multiple laser
tracker stations.
Leveling observations between
monuments and selected fiducials are added. The
adjustment of all observations is again performed with afree-net approach. Finally the measurements with thelaser tracker and the digital level are combined with theportable HLS and WPM observations. If moves are534

required, they can be checked by the ADS readings anddo not require a full remapping of the undulator hall.

BEAM-BASED ALIGNMENTThe electron beam trajectory through the FEL undulator
must be straight to a level of about 2 µm over one FEL
gain length (~5 m). This level is difficult to achieve using
standard component survey methods, and therefore
requires a special electron Beam-Based-Alignment (BBA)
algorithm [5] which samples undulator BPM readings at
three different beam energies (13.6, 6.5, and 4.3 GeV).
Changing the linac energy will require a change in manymagnetic components upstream of the first undulator tokeep the beam matched to the undulator optics, and tokeep the horizontal and vertical position and angle of the
trajectory at the entrance to the undulator independent ofenergy. The latter will be monitored by a set of three RF
cavity BPMs located between the last quadrupole of thelinac-to-undulator beam transport line and the first
undulator segment. Detailed simulations have been made,which indicate that adequate beam-based alignment canbe achieved if undulator quality and beam stability arewithin the tight tolerance specifications described here.
BBA will use quad motion and dipole trims for beamcorrections. The BBA algorithm uses the off-axis field in
the quadrupoles for trajectory correction. Changes areapplied through cam-based girder motion, which willautomatically align the quadrupoles in the process. Thus,
the main source of the original trajectory errors, i.e.,quadrupole misalignment, will be taken out by BBA.
Secondary sources, such as undulator field errors, theearth’s magnetic fields, and other environmental fields are
expected to be small and will require slight off-center
positioning of the quadrupoles to generate the required
correction field on beam axis. The largest of these
corrections can then be partially taken over by dipole trim
correctors, which are integrated in the quadrupole design.
Their range is equivalent to ±100 µm of quadrupole
motion. The BPMs must have a relative position
measurement resolution of <2 µm rms in order to achieve
trajectory straightness adequate to support 1.5-Å FEL
operations. This resolution definition implies that the
BPM readback offsets (electrical or mechanical) must be
stable to <2 µm over the one hour required to accumulate
the BBA data.

TOLERANCE ZONES
A systematic plan for trajectory correction during
operation has been developed based on tolerance zones
and different levels of correction. This plan integrates theresults of global tolerance studies, which predict anamount of FEL power loss as a function of the size of theerrors, with a sequence of correction operations withincreasing disruption to the FEL beam. Starting at thecompletion of a full BBA session, there will be
continuous trajectory feedback systems running at
120 Hz, based on LTU (Linac-To-Undulator transportline) BPMs, and at 0.1 Hz, based on undulator BPMs,

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Proceedings of FEL 2006, BESSY, Berlin, Germany

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Figure 6: Alignment Function Diagram.
which are tracked by the ADS (Zone 1). Every few hours(Zone 2) small girder position corrections, based on ADS
measurements, will keep the quadrupoles at their goal
positions to restore most, but not all, of the beam power
which is expected to sag by up to 10%. This can be done
without disruption of the FEL beam. Once a day (Zone3), re-adjustment of the FEL beam pointing direction may
be done. Once a week or less (Zone 4), a full BBA
session will be used to get back to the original tolerancezone, which will interrupt FEL beam delivery for lessthan an hour. Before the BBA is applied, the FEL power
level is expected to drop by no more than 25%. Full BBA
should fully restore the FEL power to the original level.
At an interval of roughly once every six months (Zone 5),a cam mover may range-limit and a planned access will
be used to reset cam blocks as necessary.

ALIGNMENT FUNCTION DIAGRAM
The main function block of the undulator alignment
system is given in Figure 6. Alignment functions are
performed in the Magnet Measurement Facility (MMF)
and in the Undulator Hall (UH). Alignment tasks
performed in the MMF include the tuning andfiducialization of the undulator segments as well as thefiducialization of the quadrupoles and the BFW devices.
The components are then mounted on the girder andaligned. The alignment is checked on the CMM, which isalso located in the MMF. The undulator segments are
stored separately from the girders until they are installedin the UH. In preparation for the girder installation, fixedsupport pillars are installed in the UH and aligned. The
girders are then installed and pre-aligned on the fixedsupport pillars after the environmental magnetic field has
been measured and recorded along the entire undulatorline. After installation of the ADS system, the continuous

FEL Technology

measurement and recording of the girder positions will
start. The undulator segments are then mounted onto thehorizontal slides on top of the girders, and thequadrupoles are aligned onto a straight line withconventional alignment. Then, portable WPM and HLS
systems [14] will be used for a precise alignment of theundulator segments between neighboring quadrupole
magnets.
Every few hours small girder position corrections basedon ADS measurements will keep the quadrupoles at theirgoal position (which will be reset after BBA) to better
than ±2 µm over a 1-hour period and to better than ±5 µm
over a 24-hour period, in order to support BBA. The nextalignment steps involve the electron beam. BBA basedon BPMs and quadrupoles under observation of the ADS
will be used to straighten the electron beam trajectory to
the level required to achieve FEL gain. At this point,
continuous position corrections based on BPM readings
will start. The BPM readings will be corrected for any
device motion, as reported by the ADS.
The BFW devices can now be used to check thealignment of the upstream end (‘loose end’) of theundulator segments.
Every 2-4 weeks, the procedure loops back to BBA(one iteration, rather than the initial three, may besufficient), which requires interrupting beam delivery.
Once per month, three undulator segments will beswapped out of the tunnel and brought back to the MMF
to be checked for detuning effects, such as radiation
damage. At the same time, three of the six replacement
undulator segments, which will have been prepared aheadof time, will be installed in the empty slots. As mentioned
above, the undulator magnets are mechanically shimmed
that the magnetic axis will come to lie in the same x, y
location when placed onto a given girder. Every six
months, when cam movers might have run out of range535

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Proceedings of FEL 2006, BESSY, Berlin, Germany

due to the expected continuous ground motion, there will
be a maintenance shutdown for re-baselining, i. e.,realignment of the cam movers using the manualadjustments on top of the support pillars.

SUMMARY
The X-ray FEL demands very tight tolerances onmagnetic field quality, electron beam straightness, andundulator segment alignment. These tolerances can beachieved through BBA procedures based on BPMs andquadrupoles (with energy scan) as well as BFW devices.
Relative component alignment to the required
tolerances will be achieved through common girder
mounting. Main tasks of the conventional alignment andmotion systems are:• Component fiducialization and alignment on girder• Conventional alignment of girders in Undulator
Hall as prerequisite for BBA.
The ADS measures and enables the correction of girder
movement due to ground motion, temperature changes,
and cam mover changes. A strategy is in place for using
the monitor systems and the controls in order to establish
and maintain a straight FEL trajectory.

[6] J. Welch, "Estimate of Undulator Magnet Damage
Due to Beam Finder Wire Measurements." LCLSTN-06-6, 2006.
[7] J. Welch, "Air Temperature in the Undulator Hall."
LCLS-TN-06-2, 2006.
[8] K. Hacker, Z. Wolf, "Earth's Magnetic Field
Measurements for the LCLS Undulators." LCLS-TN05-4 , 2005.
[9] Z. Wolf, "Introduction to LCLS Undulator Tuning."
SLAC-TN-05-043, 2004.
[10] J. Welch, "Ground Motion Expectations for the
LCLS Undulator Hall." SLAC-TN-05-013, LCLSTN-04-14, 2004.
[11] F. Peters, G. Gassner, and R. Ruland, "First
Measurements and Results With a Stretched Wire
Test Setup." LCLS-TN-05-7, 2005.
[12] J. Welch, et al., these FEL’06 proceedings.
[13] E. Bong, P. Emma, C. LeCocq, T. Montagne, and
J. Welch, "LCLS Undulator Coordinate System."
SLAC-TN-05-021, LCLS TN-03-8, 2004.
[14] G. Gassner, "Proposal for the Alignment of the‘Loose End’." LCLS-TN-06-11, 2006.

ACKNOWLEDGEMENTS
It is a pleasure to acknowledge contributions by
Argonne National Laboratory’s LCLS team.

REFERENCES[1] I. Vasserman, R. Dejus, P. Den Hartog, E. Moog, S.
Sasaki, E. Trakhtenberg, and M. White, "LCLS
Undulator
DesignDevelopment."
FEL2004
Proceeding, 2004.
[2] E. Trakhtenberg, J. Collins, P. Den Hartog, and M.
White, "Design of a Prototype Precision Positioning
System for the Undulators of the Linac Coherent
Light Source." PAC2005 Proceedings, 2005.
[3] G. Bowden, P. Holik, S.R. Wagner, G. Heimlinger,
and R. Settles, "Precision Magnet Movers for the
Final Focus Test Beam." SLAC-PUB-95-6132, 1995.
[4] J. Wu, P. Emma and R.C. Field, "Preliminary Studyon Electron Signal Detection for the Beam Finder
Wire of the LCLS Undulator." LCLS-TN-06-7,
2006.
[5] P. Emma, H.-D. Nuhn, and R. Carr, "Beam Based
Alignment for the LCLS FEL Undulator." Nucl.
Instrum. Meth. A429:407-413, 1999.

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HOW TO OBTAIN HIGH QUALITY ELECTRON BUNCHES IN PRESENCEOF NORMAL CONDUCTING LINAC WAKEFIELDS
S. Di Mitri*, ELETTRA, Trieste, Italy

Abstract
The dynamics of electron beams involved in Free
Electron Lasers (FELs) projects is an interplay between
sources of 6-dimensional emittance dilution andmethods of emittance preservation. Relatively longbunches are required for harmonic cascade seeded
FELs in order to accommodate the timing jitter and theseed provided by the bunch itself at each stage of thecascade. A high quality is required from such electron
beams (small transverse emittance and energy spread)
together with a uniform distribution in time along theusable part of the bunch; non-linearity in thelongitudinal phase space and in the transverse planes
are also issues. A complex longitudinal phase space
dynamics characterizes the study often in presence ofby the Coherent Synchrotron Radiation (CSR)
generated in magnetic compressors. This paper reviews
specific problems related to the electron beam
dynamics dominated by bunches of kA peak current
and varying length (0.1 to 2 ps) in the presence of
normal conducting linac wakefields. Methods
implemented to minimize the 6-dimensonal phasespace degradation are discussed. Results of high beam
quality performance are illustrated with particles
tracking codes.

INTRODUCTION
This paper describes the degrading effects on theelectron beam performance of wake fields present innormal conducting linacs for single pass FELs; inparticular: (i) geometrical wake fields in accelerating
structures [1–4]; (ii) Coherent Synchrotron Radiation(CSR) [5–8]; (iii) Longitudinal Space Charge (LSC)[9–12]. Their impact on the electron beam quality is
discussed in terms of the properties relevant for
Spontaneous Emission Self Amplified (SASE) [13–15]
and seeded [16–19] FELs.
All the mentioned wake fields couple the 6dimensional particle dynamics by putting someconflicting constraints on the design of the beam
delivery system dedicated to the formation of electron
bunches. This paper reviews some strategies for themachine design to compensate the emittances growthand improve the beam quality. The conclusions
demonstrate the validity of manipulation techniques tocontrol the electrons 6-dimensional phase space tounprecedented levels.
___________________________________________*simone.dimitri@elettra.trieste.it

FEL Technology

WAKE FIELDS AFFECTING THE
ELECTRON BEAM QUALITY
In order to make the FEL process more efficient andthe undulators chain reasonably short, the electron
beam quality has to be characterised by high peakcurrent, small transverse emittance, small energy
spread. Due to the cooperative FEL process, priority isgiven to the slice beam quality.

Longitudinal phase space
Short range longitudinal wake fields generated byrelatively short bunches with σz<<a, being σz thebunch length and a the beam pipe radius, travelling
into periodical structures induce a maximum FWHM
relative energy loss [20]:

Δγ

γ

=

eW0QL
Ef

(1)

which is valid in the approximation (σz /s0)1/2 <<1 withs0 the characteristic parameter of the structure.
Assuming a linear energy gain in the linac, (1) showsthat the impact of very long accelerators can becomparable to that of smaller machines. For example,
the energy loss in the LCLS Linac 3 relative to thefinal average energy is about 0.5% [21], while that in
the FERMI Linac 4 is 1.4% [22]. Off-crest accelerationis then needed to reduce the induced energy chirp
below the FEL threshold and to re-establish thelinearity in the longitudinal phase space.
With an appropriate positioning of the magnetic
chicanes, longitudinal wake fields acting in the last partof the linac work for free to cancel the linear energy
chirp required by the compression. In this way thechicane momentum compaction can be relaxed, thus
reducing the influence of CSR, while using larger
energy chirps.
Even after cancellation of the linear contribution,
residual higher order energy chirps affect the final
beam quality. A quadratic chirp D(2) = d 2 E d 2 z
increases the correlated energy spread, thus reducing
the SASE FEL gain. It also enlarges the bandwidth of aHigh Gain Harmonic Generation (HGHG) FEL to
unwanted levels, corrupting the goal of producing a
Fourier transform limited signal with narrow
bandwidth of the order of few meV [23–25]. Figures
1–4 illustrate this topic comparing two cases withdifferent values of the quadratic energy chirp.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Phase spaces and bandwidths were produced
respectively by mean of Elegant [26] and Genesis [27].
The use of sextupoles [28] and of a high harmonic
cavity [29–31] (also called “linearizer”) to compensate
the quadratic chirp is well-established. Nevertheless, it
was also shown that a residual cubic chirp in thecompression process can have a large impact on the
final current profile [32].

Current profile
Figure 1. Longitudinal phase space affected by 0.9
MeV/ps2 quadratic energy chirp.

Figure 2. Spectral bandwidth of 40 meV FWHM
generated by the electron bunch in Figure 1 through
FERMI HGHG with fresh bunch technique at 10 nm.

SASE FELs generally require a high peak current(kAs) in the bunch core, while HGHG FELs desire a
uniform current distribution along the whole bunch,especially if based on fresh bunch injection technique.
Even if with different purposes, both the first and thelatter need a control of the final current distribution. A
proper manipulation of the cubic energy chirp
D (3) = d 3 E d 3 z is useful to maximize the current
along the bunch and to avoid current spikes at thebunch edges. In fact, they are related to several
dangerous effects: (i) introduce nonlinearity in thephase space (i.e., bifurcations); (ii) attract particles
reducing the current in the bunch core; (iii) induce
CSR instability at shorter wavelength than the bunch
length; (iv) wake field excited by a leading edge spike
may cause additional energy spread in the undulator
vacuum chamber.

Transverse emittance

Figure 3. Longitudinal phase space affected by areduced 0.5 MeV/ps2 quadratic energy chirp.

Figure 4. Spectral bandwidth of 10 meV FWHM
generated by the electron bunch in Figure 3 through
FERMI HGHG with fresh bunch technique at 10 nm.

538

Apart from SC forces at low energy, slice emittanceis directly affected by transverse CSR forces [6,33,34].
A coherent behaviour of the emitted radiation has been
also observed at wavelength smaller than the bunch
length [12,35]; due to the interplay of LSC and CSR on
wavelengths which are a fraction of the bunch length,
microbunching instability (μBI) [36–40] leads to phasespace fragmentation and to slice emittance growth.
The projected emittance of high charge, shortbunches is indirectly affected by CSR emitted on thescale of the bunch length [41–43]. Due to the absenceof stochastic processes, the slices lateral offset can becancelled through a –I transport matrix between two
identical dispersive regions [44].
The transverse wake field contributes to theprojected emittance growth by mean of the induced
beam break up (BBU) instability [45,46]. The coupling
between the electron bunch and the wake field at agiven energy can be estimated by mean of thefollowing dimensionless parameter [47]:4πε 0W0 lb L2 I pk
(2)
εr =
γ iIA
It multiplies the resonant term acting on the transverse
motion of the slices centroid, thus it should be made as
small as possible.

CUBIC ENERGY CHIRPThe sign of the cubic energy chirp in the photoinjector (PI) is mainly determined by the SC force and,FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

according to the present simulations, it is always
negative for a flat-top charge distribution (bunch headon the left side of phase space) [48]. After theinteraction with longitudinal wake fields, this sign isreversed at the entrance of the second compressor,
enhancing the energy-position correlation of the bunchedges w.r.t the core. The edges are there overcompressed producing current spikes. On the contrary,a negative cubic chirp at the chicane provides undercompression of the edges. This mechanism is
illustrated in Figure 5, where the longitudinal phasespace and the corresponding current profile generated
by LiTrack [49] are shown.

Figure 5. Longitudinal phase space (left) and current
profile (right) at the end of the FERMI Linac. Cubic
chirp at the PI is –3.9x10-4 mm-3 at top and 8.1x10-4
mm-3 at bottom.

THBAU03longitudinal phase space and current profile. In
addition, it was demonstrated [50] that the linearizer
can be used to relax until an order of magnitude thesensitivities of the final beam properties to the linac
phase and voltage. Unfortunately, this techniqueassumes a negligible effect of the cubic chirp on thelongitudinal beam dynamics and considers it a freeparameter.
The reverse tracking [32] suggests how to improve
the global quality of the longitudinal phase space for agiven configuration of the wake potential, eventuallyleaving the linearizer free to be moved for jitter
purposes. It applies to ultra-relativistic particles and isbased on the assumptions of no stochastic processes inthe beam transport and of negligible energy loss from
CSR. CSR with wavelength in the range of the bunch
length can be neglected in presence of an appropriate
shielding [32,51,52] of the vacuum chamber.
Moreover, the induced energy loss is relatively small
for long bunches.
Within these approximations, the equations of
motion can be reversed and a unique solution exists.
The density distribution obtained at the beginning of
the linac will automatically compensate all the effects
perturbing the beam dynamics in the forward tracking,like RF curvature, wake fields and higher order optics.
It is clear this method calls the beam shaping at thephoto-cathode to be a fundamental contribution to thefinal beam quality. For the FERMI specific case [32], afinal beam with a flat current profile and a linear phasespace corresponds to an initial beam with a ramped
current profile (see, Figure 6).

Voltage and phase of the high harmonic cavity allow
to control the cubic chirp in the following transport linethat is the final current profile. For a 1-stagecompression the following parameters are defined:
k=2π/λrf is the RF wave number and λrf is the RF
wavelength; U0 is the voltage amplitude of a first linac
accelerating on-crest; U1 is the amplitude of a second
linac with off-crest acceleration at phase φ1 (referred tothe crest of the RF wave); U4 and φ4 are the amplitude
and phase of the 4-th harmonic cavity. Thus, the third
derivative of the energy gain is:15
U (′′s′=0 ) = −k 2U (′s =0) + + k 3 (U 0 + U1 cos(φ1 )) tan(φ4 ) (3)4The quadratic chirp is cancelled if:

U 0 + U 1 cos(φ1 )(4)16 cos(φ4 )(3) and (4) define the space where parameters of theharmonic cavity can be moved in order to linearize thelongitudinal phase space up to the 3rd order.
U4 = −

REVERSE TRACKING
Due to the complexity of the interplay of SC,
longitudinal wake fields and higher order energy
chirps, it is not obvious to control simultaneously
FEL Technology

Figure 6. Top, electron beam desired at the undulators’
entrance. Bottom, electron beam required at the PI end.
LiTrack [49] output.
The approximate prediction of the reverse tracking
was confirmed by the forward tracking, obtaining thephase space in Figure 3. In addition, it was proved thatthe convolution of the longitudinal wake function with539

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Proceedings of FEL 2006, BESSY, Berlin, Germany

a ramped particle distribution results in a mostly linear
wake potential (see, Figure 7), while an initialparabolic current profile brings nonlinear contributions
to the phase space.

Since each longitudinal slice of the beam contains a
differing amount of charge, each one evolves in adifferent way from the other. Thus, the so-called
Ferrario’s working point [57] can be only
approximately adopted for the emittance compensation.
Figure 9 shows the resulting slice emittance and theslice energy spread for the bunch in Figure 8 at the
injector exit; results were produced through the GPTcode [58].

BBU SUPPRESSION
Figure 7. Longitudinal wake field generated in the
FERMI Linac 4 resulting from the convolution of thewake function with a particles distribution
characterized by a ramped current profile (left) and aparabolic one (right).

BEAM SHAPING AT THE PHOTOINJECTOR
As discussed before, in presence of wake fields theinitial electron density distribution plays an importantrole in formation of the electron bunches at the end of
the accelerator [53–55]. As for the FERMI case, theLSC field at the cathode was investigated [56], since it
is mainly responsible for blowing out the particles.
Figure 8 shows the desired current profile at thecathode and the evolved charge distribution at the
injector exit (at 100 MeV) for a 0.8 nC bunch.

BBU instability induces a lateral deviation of thebunch tail w.r.t. the head axis. The persistence of such
oscillations tend to transform the temporal coordinate
into the transversal one, thus inducing projected
emittance dilution. A “banana” shape in the (t, x) and(t, y) plane is assumed by the electron bunch [59]; itmakes a large part of the bunch travelling with a
trajectory offset in the undulator. This fact reflects into
an optical mismatch in the undulators and can also
induce an effective K-value for the tailing particles
different from the nominal one. The impact of alaunching error of the bunch in an undulator for SASE
FEL was studied and experimentally observed [60].
The off-axis motion in the device leads to power
reduction and bandwidth enlargement because of theprocesses addressed above.
As for seeded FELs, if the bunch tail deviation is
sufficiently larger than the beam size, it causes a
missed overlap between the seeding laser and thebunch in the undulator, thus reducing the emitted
photon pulse length and the peak power [61]. Figure 10
illustrates the horizontal banana shape exiting from the
FERMI Linac (Elegant simulation) and a schematic of
the seeding laser overlapping the beam.

Figure 8. Ramped current distribution just after thecathode (left) and at the injector exit (right) for a 0.8
nC bunch.

Figure 9. Slice emittance and slice energy spread along
the bunch at the exit of the injector. εxn,80% = 1.2 mm
mrad. Inside plot: longitudinal phase space including
longitudinal wake fields. Head is on the left.
540

Figure 10. Horizontal banana shapes induced in the
FERMI Linac. Bunch head is on the left. The solid
curve shows a tail deviation 8 times larger than the 80
μm rms beam size. The dashed one corresponds to adifferent trajectory in the Linac for which the taildeviation is within the rms beam size. The superimposed rectangle sketches the seeding laser and points
out its overlap with the bunch in the two cases.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 11 represents the dependence of peak power
and phase shift for the FERMI FEL-1 scheme at 40 nm
on the off-axis displacement error of the electron bunchat the undulator entrance [61].

THBAU03

parameter of interest for the FEL. Dots represent a 0.6
nC charged beam which is compressed twice (dotsmove from right to left) by a total factor of 15;
triangles show the same dynamics for a 0.3 nC charged
beam.
Due to the monotonic behaviour of the wake
functions in the range of bunch length considered, abunch with lower charge always suffers from a minor
energy loss w.r.t. the higher charge option (look at theheight of the yellow and orange bars). Obviously, for a
fixed peak current a shorter bunch is required from the
PI and will be provided at the end of the accelerator.

Figure 11. Effect of an off-axis displacement error of
the electron bunch at the undulator entrance on peak
power (decreasing with offset) and phase shift(increasing with offset) for FERMI FEL-1 HGHG
scheme tuned at 40 nm. Seeding laser spot size is here
assumed to be 210 μm.
In single pass FELs the BBU instability can besuppressed through trajectory bumps [59,62]. This
technique looks for a “golden trajectory” for which all
the kicks generated by the transverse wake fieldcompensate each other and the banana shape is finallycancelled. Dashed curve in Figure 10 shows acompensated banana shape which maximizes theoverlap with the seeding laser; the solid curve is thebanana shape obtained in absence of bumps.
Since the bump is a local method of correction, it
depends on the particular condition of operation at its
location. For this reason, the sensitivity of the bump to
the trajectory jitters has to be checked and madesufficiently small [59].
Reducing the average β-function along the linac isalso useful since its square is proportional to the
induced relative emittance growth [63]. On the other
hand, in a FODO lattice the quadrupole strength k ~1/β and the trajectory affected by errors uerr ~ k√β.
Thus, lowering the β-function increases the sensitivity
to the elements misalignment.

LOW CHARGE OPTION
The previous paragraphs describe techniques ofelectron beam manipulation in order to compensate thewake fields effects. Now a more general prescription of
low charge beam production is exposed to minimize
the wake fields once the compression factor, the final
peak current and the final average energy are fixed.
The curves in Figure 12 represent the loss factor of a
Gaussian charge distribution travelling in one
accelerating structure of the FERMI Linac 4 vs. therms bunch length; each curve is drawn for a given peakcurrent (upper curve is at higher current), which is the

FEL Technology

Figure 12. Loss factor in the FERMI Linac 4
accelerating structure vs. rms bunch length (a Gaussian
charge distribution is assumed). Dots refer to the 0.6
nC electron bunch in a 2-stage linear compression(from right to left, the peak current increases as thebunch length decreases). Triangles refer to the 0.3 nC
case.
Limitations to the shorter bunch length achievableare: (i) CSR instability; in the steady state
approximation the induced rms energy spread σδ,CSR ~I/σz1/3 [5]. This has an impact in terms of both energy
modulation and brightness degradation [56]; (ii) timing
jitter, especially for HGHG FELs with fresh bunch
injection technique; the final bunch has to be
sufficiently long in order to accommodate the timing
jitter of the electron bunch w.r.t. the seeding laser.
A 0.2 nC low charge solution has been recently
adopted by LCLS [64] instead of the 1.0 nC initiallychosen; their dynamics is compared in Figure 13; there
the low charge bunch shows an improvement in thelongitudinal phase space linearity, a reduction of thecurrent spikes at the bunch edges and a suppression of
the BBU instability up to 10% of emittance growth.
Reduction of the emittance from 1.2 to 0.85 mm mrad
allows to obtain the same saturation length of the 1.0
nC case with a lower peak current (2.1 kA instead of
3.4 kA).
In some cases, a low charge option can also
minimize the impact of CSR and SC forces on the541Proceedings of FEL 2006, BESSY, Berlin, Germany

transverse emittance. For the TESLA-XFEL, a low
charge working point [65] of 0.25 nC was found with agood compromise between the slice emittance growth,
due to stronger CSR transverse forces at shorter bunch
length, and the preservation of the projected emittance,
which is no longer affected by the optical mismatch
generated by SC forces at low energies.

applying the reverse tracking to the single compression
scheme [67].

ENERGY MODUL. [keV]

THBAU03a)

40

LANDAU DAMPING
In the last 10 years microbunching instability (μBI)
has been extensively studied and recently observed inexperiments. The gain of the instability was calculated
analytically in the 2-dimensional approximation[37,38]. Numerical solution was obtained including
Landau damping from the beam finite emittance [39].
According to the linear theory, the longitudinal
Landau damping can be made more effective by
increasing the relative energy spread and thecompression factor, like in a 1-stage compression. In
fact, when adopting a 2-stage compression, analyticalestimations confirmed by simulations demonstrate thefundamental role of the second compressor in thedevelopment of the μBI: it transforms all the LSC
induced energy modulation accumulated in the
upstream linac into density modulation; this effectsums to the enhancement of the density modulation
already developed by the first compressor.
Figure 14 compares the spectral gain function of the
2-stage and of the 1-stage compression in the FERMI
Linac [66]. The maximum of the instability gain is
reduced by a factor 100 in the latter case.
The 1-stage compression is a pretty attractive
solution but forces a very short bunch to travel along alarge part of the linac; as a consequence, linearity of
the longitudinal phase space is strongly affected bywake fields. This problem could be overcome by
542

ENERGY MODUL. [keV]

Figure 13. Longitudinal phase space (left plots) andtransverse normalised projected emittance (right plots)in LCLS for the 1.0 nC charged bunch at top and forthe 0.2 nC charged bunch at bottom.

b)

80

Figure 14. Spectral gain function of the microbunching
instability in the FERMI Linac in case of double (a)and single (b) compression. Calculation is based on the
2-dimensional model for CSR and LSC in the linear
approximation. μBI starts from realistic shot noise.
A 2-stage magnetic compression is generally
associated with a laser heater at low energy for thereasons addressed above. This tool was proposed [9] tosuppress the instability by increasing the relative
energy spread just before the compression; on the other
hand, its final value has to be still maintained below
the FEL threshold. This is not obviously reached in low
and medium energy machines and becomes more
stringent for multi-stage harmonic cascade FELs.
Figure 15 shows the final slice energy spread asfunction of the energy spread induced by the laser
heater in FERMI. μBI is supposed to start from shotnoise in the initial density distribution. Figure 15
allows a comparison between the 2-dimensional
analytical solution and the simulation of a Vlasov
solver [68]. A Vlasov solver (see also [69]) avoids the
problem of numerical noise in the simulation andautomatically includes a nonlinear evolution of theinstability which manifests itself in a folded phasespace. This is not considered in the linear theory.
Figure 15 shows a discrepancy in the results obtainedwith the two methods. Such studies, of general interest,
are still in progress; the preliminary results indicate

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THBAU03dimensional full s2e simulations is still work inprogress. Nevertheless, recent results demonstrate theimportance of shot noise as adriving term.

REFERENCES

Figure 15. Rms slice energy spread in the final bunch
for FERMI vs. the rms energy spread added by thelaser heater at 100 MeV. Dots are the analyticalprediction; squares are the results of the Vlasov solver.
The solid line shows the expected energy spread in
absence of any collective effect assuming acompression factor of 10 in linear approximation.
that the final prediction can often depend on details of
the calculation.

CONCLUSIONS
The main effects on the electron beam quality byaccelerating structures wake fields, CSR and LSC werereviewed in terms of the most relevant beam
parameters for single pass FELs. This analysis points
out the correlations between the 3 degrees of freedomof the electron dynamics in the accelerator generated
by the wake fields.
A double magnetic compression results to be asuitable compromise to minimize instabilities induced
by SC, longitudinal and transverse wake fields; at thesame time, longitudinal wake field in the linac
structures can be used to reduce the CSR effect in thesecond chicane.
Simultaneous control of the linearity in thelongitudinal phase space and of the current profile canbe achieved, under some approximations, by following
the predictions of the reverse tracking. This techniqueforces the electron density distribution at the injector tocover an important role in formation of the electron
bunches at the end of the accelerator. PI laser can beused to provide such suitable distribution for given
wake potential; at the same time, special care has to betaken as for the emittance compensation scheme forunusual charge distributions exiting the photo-cathode.
A general prescription of low charge beam
generation was investigated. Simulations demonstrate
thatit brings several advantages in achieving a highbeam quality; essentially, it reduces the effects of theaccelerating structures wake fields, allows acompromise between slice and projected emittance
growth, maximizes the current along the bunch.
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[7] E. Saldin, E. Schneidmiller, M. Yurkov, “On thecoherent radiation of an electron bunch moving in anarc of a circle”, NIM A, 398, 373 (1997).
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[11] K. Tian et al., “Experimental observation of
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[27] http://corona.physics.ucla.edu/~reiche/[28] R. England et al., PRST-AB, 8, 012801 (2005).
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Sweden.
[37] E. Saldin, E. Schneidmiller, M. Yurkov, “Klystroninstability of a relativistic electron beam in a bunch
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synchrotron radiation microbunching in a bunch
compressor chicane”, PRST-AB, 5, 074401 (2002).
[39] S. Heifets, S. Krinsky, G. Stupakov, “Coeherent
synchrotron radiation instability in a bunch
compressor”, PRST-AB, 5, 064401 (2002).
[40] Z. Huang et al., “Suppression of microbunching
instability in the linac coherent light source”, PRSTAB, 7, 074401 (2004).
[41] M. Dohlus, T. Limberg, “Emittance growth due towake fields on curved bunch trajectories”, NIM A,
393, 494 (1997).
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through coherent energy spread generation in bending
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[44] D. Douglas, “Suppression and enhancement of
CSR-driven emittance degradation in the IR-FEL
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to short-range transverse wakefields in the FERMI
linac”, Proc. FEL 2005, SLAC, California, USA.
[48] G. Penco, private communications.
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Tennessee, (2005).
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radiation by electrons in a synchrotron”, PR, 96, 1(1954).
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[54] C. Limborg-Deprey, Proc. of FEL 2005.
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[56] S. Lidia, G. Penco, M. Trovo’, “Optimization
studies of the FERMI@Elettra photoinjetor”, Proc. of
EPAC 2006, Edinburgh, Scotland.
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instability in the FERMI@Elettra linac”, Proc. of
EPAC 2006, Edinburgh, Scotland, UK.
[60] G. Andonian et al., “Observation of anomalously
large spectral bandwidth ina high-gain self-amplified
spontaneous emission free-electron laser”, PRL, 95,054801 (2005).
[61] G. De Ninno, W. Fawley, G. Penn, “Effect of OffAxis Displacement Errors on FEL-1”, ST/F-TN-06/01(2006).
[62] P. Tenenbaum, SLAC-TN-04-038 (2004).
[63] K. Bane, Proc. of EPAC 2004, Lucerne,
Switzerland.
[64] P. Emma et al., “An optimized low-charge
configuration of the linac coherent light source”, Proc.
of PAC 2005, Knoxville, Tennessee.
[65] T. Limberg et al., “Optimized bunch compression
system for the European xfel”, proc. Of PAC 2005,
Knoxville, Tennessee, USA.
[66] A. Zholents, ST/F-TN-05/15[67] A. Zholents, private communications[68] M. Venturini, R. Warnock, and A. Zholents,“Development of a 2D Vlasov Solver for Longitudinal
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FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THBAU04

STAIR-STEP TAPERED WIGGLER FOR HIGH-EFFICIENCY FEL *D.C. Nguyen#, Los Alamos National Laboratory, Los Alamos, NM 87545, U.S.A.
H.P. Freund, Science Applications International Corp., McLean, VA 22102, U.S.A.
Abstract
A concept of a high-efficiency wiggler called thestair-step tapered wiggler is presented. The stair-steptapered wiggler consists of several uniform wiggler
segments with decreasing wiggler periods (or decreasingaw). The relatively large bucket in each wiggler segment
enables a substantial fraction of the electrons to be
captured, resulting in high extraction efficiencies. The
stair-step tapered wiggler provides other advantages, suchas ease of fabrication and flexibility in the taper rate.
Numerical simulations using MEDUSA will be presented
to show the high-efficiency performance of arepresentative FEL with a stair-step tapered wiggler.

electrons as they execute synchrotron oscillations inside
the ponderomotive potentials.
λw

zFigure 1: Plot of wiggler period versus z in a stair-steptapered wiggler with taper in wiggler period.
g

INTRODUCTIONz

The FEL is known for its wavelength tunability andscalability to high power. However, the extraction
efficiency, defined as the FEL power divided by theelectron beam power, can be low, with typical values
around 1%. The low extraction efficiency increases therequirements for the electron beam’s average power andputs stringent demands on the high-power RF systems
driving the accelerators. One way to increase theextraction efficiency is through the use of tapered
wigglers. Most tapered wigglers are continuous, i.e. theperiods (λw) or dimensionless field (aw) decreases
continuously to maintain the resonance condition,

γR =

λw
(1 + aw2 ) ,2λ(1)

where γR is the resonance Lorentz factor; and λ is the
wavelength.
Continuously tapered wigglers are only optimized for anarrow range of input radiation intensities andwavelengths. For an oscillator FEL, extraction
efficiencies as high as 4.6% inside the resonator havebeen achieved but the efficiency outside the optical cavity
is not significantly higher than that of a uniform wiggler[1].
In this paper, we discuss a different concept of tapering
to achieve high extraction efficiency using a series of
uniform wigglers. Our approach is an extension of thecompound wiggler [2], also known as the step-tapered
wiggler [3]. In our approach, a long uniform wiggler isused to bunch the electrons longitudinally and a numberof short uniform segments with decreasing the wiggler
periods (Fig. 1) or increasing the gaps between themagnets (Fig. 2) are used to extract the energy from the___________________________________________*Work supported by the Office of Naval Research and the High-Energy
Laser Joint Technology Office. Author email: dcnguyen@lanl.gov

FEL Technology

Figure 2: Plot of gaps between magnets versus z in astair-step tapered wiggler with taper in magnetic field.

THEORYIn a uniform wiggler, the FEL extraction efficiency is
the product of the capture efficiency (ηc) and the height ofthe bucket, as given by [4]η = 2ηCaw as
1 + aw2,(2)

where the term in the radical denotes the half-height ofthe bucket, and as the dimensionless optical field, is
proportional to the square root of the optical intensity, Is

as =eλ 2 Z 0 I s
2πmc 2(3)where e is electronic charge, Z0 impedance of free space,m electron mass, and c speed of light.
As the electrons interact with the high optical intensity,
they undergo synchrotron motion in the first uniform
wiggler and, after becoming trapped, rotate to the bottomof the bucket. With a judicious combination of λw and aw(see Eq. 1), the resonance energy of the next uniform
wiggler segment can be lowered such that the electrons
are at the top of the bucket of the new wiggler segment(Fig. 3). The electrons that are trapped in the bucket of the
new segment now undergo synchrotron motion in thisbucket to an even lower energy. The step-tapered wiggler
efficiency is the sum of the first and second segments’efficiencies.
η = 2η C1

a w1 a s1
a w2 a s 2+ 2η C 2
1 + a w21
1 + a w2 2

(4)

545

THBAU04

Proceedings of FEL 2006, BESSY, Berlin, Germany
scalloped beam could be used to enhance the FEL
interaction and/or to pinch the optical beam [5].

180

Table 1: MEDUSA simulation parameters and results.
170

150

140

130

120
0

1

2

3

4

5

6

P haseFigure 3: Longitudinal phase space of electrons at thetransition between the first and second wiggler segment.
The red line denotes the separatrix of the second wiggler.
The indices 1 and 2 in Eq. 4 correspond to the first two
wigglers, respectively. The typical efficiency for a twosegment step tapered wiggler is twice that of a uniform
wiggler, i.e. 2%. If there are n segments, then theefficiency can be increased n-fold. The limit in how far
we can taper the wiggler is due to a steady reduction in
the capture efficiency in each subsequent bucket, and in
the induced energy spread. This is due to the nonadiabatic transitions from one segment to the next.
However, since the bucket heights are large, it is possible
to maintain high capture efficiency, and thus highextraction efficiency.

SIMULATION
We use the three-dimensional code MEDUSA [6,7] tomodel a seeded FEL amplifier with a stair-step tapered
wiggler and a comparable linearly tapered wiggler. Table
I summarizes the FEL and beam parameters used in the
MEDUSA simulations. These parameters are chosen for a
1.05-micron wavelength where high-power seed lasers
exist. Both wigglers are of a conventional permanentmagnet design with parabolic pole faces to provide equal
two-plane, sextupole focusing. The first wiggler segment
is the same for both linear and stair-step tapered wigglers.
With an input power of 106 W (1 µJ pulse energy and 1 ps
FWHM, for instance) the first wiggler saturates in 1.83 m.
The subsequent wiggler segments are different for the twocases. For the linear taper, it has one 2.44-m longcontinuously tapered segment with a field taper rate of
0.48 kG per meter of wiggler length. For the stair-steptaper, there are four short uniform wiggler segments, eachwith a smaller aw. These wiggler segments can be shortbecause the electrons are already bunched at the entranceof these segments. The pre-bunched electrons radiate
power immediately and the electrons execute thesynchrotron motion to the bottom of the bucket in each
wiggler segment. For these simulations, the electron beam
is matched in the wiggler. It is conceivable that a

546

Parameters
Beam energy

Values80.8 MeV

Peak current

1000 A

Emittance

10 mm-mrad

Energy spread

0.25%

Wiggler period

2.18 cm

Wavelength1.052 µFirst wiggler segment aw

1.187

First wiggler segment length

1.831 mSecond wiggler segment aw

1.159

Second wiggler segment length

0.698 mThird wiggler segment aw

1.116

Third wiggler segment length

0.567 mFourth wiggler segment aw

1.058

Fourth wiggler segment length

0.523 mFifth wiggler segment aw

1.007

Fifth wiggler segment length

0.654 mLinear taper segment length

2.44 mLinear taper rate

0.48 kG/m

Input power (peak)

1 MW

Stair-step taper output power (peak)

3.6 GW

Stair-step taper efficiency

4.5%

Linear taper output power (peak)

3.5 GW

Linear taper efficiency

4.4%

8.4

8.2

8

7.8

Bpeak (kG)

Gamma

160

7.6

7.4
B stairstep
7.2
B linear
7

6.8
0

1

2

3

4

5

z (m)

Figure 4: Plots of magnetic field versus distance along the
wiggler for the linear (red) and stair-step (blue) tapered
wigglers.

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany
0.04
Linear P(E)
Stairstep P(E)

0.035

0.03

Fraction of electrons

The MEDUSA simulation results are shown in Fig. 5.
The stair-step and linear tapered wigglers achieve peak
powers of 3.6 and 3.5 GW, respectively, corresponding to
extraction efficiencies of 4.5% and 4.4%. While the FEL
power grows continuously for the linear taper wiggler, theFEL power growth curve in the stair-step taper wiggler
exhibit plateau regions in between segments. This is notdue to a lack of wiggler magnets in the transition regions(there are no gaps in the stair-step wiggler). Rather, theseplateaus are needed to rotate the electrons in the bucket sothat they enter the next bucket in the correct phase of thesynchrotron oscillation period. It is worth noting that the
FEL peak power increase is approximately 0.7 GW per
wiggler segment, and the extraction efficiency of the
five-segment stair-step tapered wiggler is about 5 times
that of the uniform wiggler.

THBAU04

0.025

0.02

0.015

0.01

0.005

0
70

72

74

76

78

80

82

84

Power (W)

Energy (MeV)
4 10

9

3.5 1093 10

92.5 1092 10

91.5 10

9

1 10

9

5 10

8

Figure 6: Energy distribution of electrons exiting thestair-step tapered wiggler.

SUMMARY

Stair-step
Linear

0
0

0.5

1

1.5

2

2.5

3

3.5

4

z (m)

We have studied a different approach to high-efficiency
wiggler called the stair-step tapered wiggler. The
stair-step wiggler consists of uniform wigglers withdecreasing magnetic fields (or wiggler periods) to extract
power from a decelerated electron beam. MEDUSA
simulations show the performance of the stair-steptapered wiggler is the same as that of a comparable linear
tapered wiggler. For a representative example of an
infrared FEL, the peak power (and extraction efficiency)that can achieved with a five-segment stair-step tapered
wiggler is five times that of a uniform wiggler. The fullenergy spread of the electron beam exiting the stair-step
wiggler is three times the extraction efficiency.

ACKNOWLEDGMENT

Figure 5: Plots of power versus distance for the linear(red) and stair-step (blue) tapered wigglers.

We thank Luca Giannessi for valuable assistance inprogramming a one-dimensional FEL code.

An important consideration in designing any highefficiency wiggler is the energy spread in the electron
beam exiting the wiggler. For energy recovery linac, it isnecessary to minimize the energy spread of the spentelectron beam so that one can transport the electron beamback through the linac for energy recovery. To this end,
we plot the energy distributions of the electrons exiting
the linear taper (red) and stair-step taper (blue) wigglers
in Fig. 6. While the linear taper has a double-humped
distribution with most electrons localized near the
injected energy and maximum decelerated energy, thestair-step taper has electrons distributed in multiple peaks
within the same energy bandwidth. The full energy spreadfor both tapered wigglers is 13%, three times theextraction efficiency of 4.5%. This energy spread ispresently outside the 8% energy acceptance of the energy
recovery linac [8]. However, we expect a reduction inelectron energy spreads will be realized with further
optimization of the stair-step tapered wiggler.

REFERENCESFEL Technology[1] D. Feldman et al., Nucl. Instrum. Meth. A285 (1989)
11-16.
[2] R.W. Warren and D. Piovella, Nucl. Instrum. Meth.
A304 (1991) 696.
[3] J. Blau et al., Nucl. Instrum. Meth. A483 (2002) 148.
[4] C.A. Brau, Free Electron Lasers, Academic Press,
Oxford (1990).
[5] D.C. Nguyen, H.P. Freund, and W. Colson, Phys.
Rev. ST-AB 9 (2006) 050703.
[6] H.P. Freund, S.G. Biedron, and S.V. Milton, IEEE J.
Quantum Electron. 36 (2000) 275.
[7] H.P. Freund, Phys. Rev. ST-AB 8 (2005) 110701.
[8] L. Merminga, D.R. Douglas and G.A. Krafft, Annu.
Rev. Nucl. Part. Sci., 53 (2003) 387-429.

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PRECISION MEASUREMENT OF THE UNDULATOR K PARAMETERUSING SPONTANEOUS RADIATION ∗J. Welch† , J. Arthur, P. Emma, J. Hastings, Z. Huang, H.-D. Nuhn, P. Stefan,
SLAC, Stanford, CA 94309, USA
R. Dejus, B. Yang, ANL, Argonne, IL 60439, USA
R. Bionta, LLNL, Livermore, CA 94550, USA.
Abstract

Several methods have been proposed to measure in situ
undulator K differences by alternately comparing spontaneous radiation spectra from two undulator segments [2].
We are looking into the possibilities of using the combined
radiation spectrum produced by two nearby segments.
The ﬁrst harmonic peak of the on-axis spontaneous radiation energy spectrum from a single undulator has a bandwidth equal to the inverse of the number of periods. The
combined radiation from two such undulators has a bandwidth that is narrower by a factor of two. Compared witha single undulator, combined undulators produce twice thenumber of photons in half the bandwidth, so the spectrum
has four times the peak height and therefore eight times
steeper slopes. Integrating the spectrum over angles about
the beam axis produces a complication, since the off-axis
undulator spectral peak shifts to lower energy. Such integration causes the low-energy edge to extend lower by anamount depending on the integration angle, but the highenergy edge will remain stationary, though the slope becomes somewhat less steep. Based on a far-ﬁeld undulator
radiation formula, angle-integrated spectra are calculated∗ This work is supported by the U.S. Department of Energy, contract
DE-AC02-76SF00515, and was performed under the auspices of the U.S.
Department of Energy, by University of California, Lawrence Livermore
National Laboratory under Contract W-7405-Eng-48, in support of the
LCLS project at SLAC.
† Welch@SLAC.Stanford.edu

548

1.5
1
0.5
0
1

0.5

0
/ (%)

0.5

1

Figure 1: Angle-integrated spectra of a single undulator(solid-red) and two identical undulators (dashed-blue).

2
Number of photons (arb.)

INTRODUCTION

Number of photons (arb.)

2

Obtaining precise values of the undulator parameter,K, is critical for producing high-gain FEL radiation.
At the LCLS [1], where the FEL wavelength reaches
down to 1.5 Å, the relative precision of K must satisfy(ΔK/K)rms  0.015% over the full length of the undulator. Transverse misalignments, construction errors, radiation damage, and temperature variations all contribute toerrors in the mean K values among the undulator segments.
It is therefore important to develop some means to measure relative K values, after installation and alignment. We
propose a method using the angle-integrated spontaneousradiation spectrum of two nearby undulator segments, andthe natural shot-to-shot energy jitter of the electron beam.
Simulation of this scheme is presented using both ideal andmeasured undulator ﬁelds. By ‘leap-frogging’ to different pairs of segments with extended separations we hope
to conﬁrm or correct the values of K, including proper tapering, over the entire 130-m long LCLS undulator.

1.5
1
0.5
0
0.4

0.2

0
/ (%)

0.2

0.4

Figure 2: High-energy edge of spectrum for two cases:
identical K (dashed-blue), and ΔK/K = +0.2% (solidgreen) .

for one, and two identical undulators without any phase error between them, and shown in Figure 1.
If the two undulators have different mean values of K,
the slope of the high-energy spectrum edge will be reduced,
depending on the relative difference, ΔK/K. Figure 2
shows the high-energy edge of the angle-integrated spectrum of two undulators for two cases: identical K, andΔK/K = +0.2%. As clearly shown, the slope of the highenergy edge of the spectrum is sensitive to the relative K
differences of two adjacent undulators (phase errors will
be addressed below). In this ﬁgure the left-right spectrum
K2
shift, − 1+K
2 /2 (ΔK/K), has been subtracted off to allow

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Proceedings of FEL 2006, BESSY, Berlin, Germany
more convenient comparison of the slopes at Δω/ω = 0.
The LCLS undulator consists of 33 almost identical segments, each 3.4 m long. Each segment is provided with“roll-away” capability; and can be independently displaced
up to 8 cm horizontally, effectively turning it ‘off’. The
segments are also constructed with a 4.5 mrad cant angleof the poles, which allows K-value adjustment by small
horizontal displacements (about 1.5 mm per 0.1%), using the same “roll-away” mechanism. If the slope of thehigh-energy edge of the spectrum is measured with sufﬁcient precision as a function of the horizontal displacement,(equivalent to scanning ΔK/K), two undulator K values
can be set equal within the required precision (0.015%),
and this relative correction might be applied repetitively
over the full 130-m undulator to adjacent, or nearly adjacent, segment pairs.

METHODThe method proposed here requires retracting all but two
adjacent, or nearly adjacent, undulator segments from thebeamline so that all x-rays detected come only from thesegments under test. The electron trajectory must thenbe brought to essentially beam-based alignment quality, sothat the kinks in the trajectory between segments are lessthan 1μrad. Beam-based alignment is done by mechanically moving the quadrupoles to obtain a dispersion-freetrajectory. The quadrupoles are mechanically tied to theundulator segments and both move together, so this step
also insures that the undulator segments are brought vertically to within about 100 μm of the ideal position before
starting.
On each machine pulse, a small portion of the x-ray
spectrum is sampled in the region of the high-energy edgeof the ﬁrst harmonic, using a silicon crystal spectrometer, set for diffraction at a ﬁxed Bragg angle from the(111) crystal planes. (The LCLS electron beam-angle jittershould be < 1μrad, which is small compared to the Darwin
width of the crystal reﬂection.) As a result of the naturalelectron energy jitter (∼ 0.1% rms), the photon spectrum israndomly sampled. The electron energy jitter is measured
on each pulse (see below) and the inferred photon energy
shift is then associated with the detector data; the underlying spectrum is then reconstructed by plotting the detector
data against the inferred photon spectrum shift.1
About 100 pulses will be needed to reconstruct a spectrum. After a spectrum is collected in this manner for agiven arrangement of two adjacent undulator segments, theK value of the second undulator is changed by 0.05% bytranslating it Δx = 0.75 mm, and then a new spectrum isobtained. This process is repeated for 9 separate K values,
ranging over about ±0.2%.
The electron energy jitter is precisely measured by two
1 Electron energy loss from radiation is ≤ 0.005% per segment andwill be taken into account in setting the appropriate K values. Wakeﬁeld
losses are expected to be even less. Both types of energy losses are ignoredin the following discussion.

FEL Technology

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beam position monitors (BPMs) located upstream of theundulator, at points of high horizontal momentum dispersion. The BPMs are separated in betatron phase advanceby 2π and have opposite sign dispersion, such that the difference in their position readback values is proportional to
the relative electron energy variation and completely insensitive to incoming betatron oscillations. With dispersion of±125 mm at each BPM, and a 5-μm rms single-pulse position resolution, the√relative electron energy resolution is(5 μm)/(125 mm)/ 2 ≈ 3 × 10−5 , and the corresponding
photon energy resolution is twice this, or 6 × 10−5 .
Since the spectrum shifts towards Δω/ω > 0 for
ΔK/K < 0 (see Fig. 3), the data tends to be poorly
centered on the spectrum edge for ΔK/K = 0. To improve resolution, we adjust the mean electron energy byK2− 1+K
2 /2 (ΔK/K) for each new setting so that the energy
always varies around the center of the edge. These small
adjustments are possible using the BPM-based feedback
loop, which maintains the desired average electron energy,
but cannot remove the random pulse-to-pulse jitter.
The slope of each high-energy spectrum edge is foundby ﬁtting the data for each K value. The Δx at which
the slope is steepest corresponds to equal K values in thetwo segments. At a 10 Hz machine rate, this process will
require 90 seconds, plus the time required to translate theundulators nine times, for a total of about 4 minutes per undulator pair. A description of a simulation of this process,including realistic errors, follows.

SIMULATION
A simulation is performed using a computer-generated,
two-undulator, spectrum integrated over all angles, atnine values of ΔK/K: (−0.2% to +0.2% in steps of
0.05%). To simulate measured data, the perfect, computergenerated spectrum is sampled at random values of twice
the electron energy error (Δω/ω = 2ΔE/E). The electron energy varies randomly in a Gaussian distribution with
0.1% rms. In practice, either the average electron beam energy or the Bragg angle can be adjusted to best center thedata on the high-energy edge of the spectrum.
A cubic spline is used to interpolate the computergenerated spectrum for each randomly selected energy. An
error of 6 × 10−5 rms is added to the photon energy to account for the BPM-based electron energy measurement resolution. An error is also added to the number of photons detected at that energy, assuming the bunch charge randomly
varies from pulse to pulse, but a toroid charge monitor, capable of resolving the relative charge variation to within
0.5% rms, is used to normalize the data. In addition, thebeam angle is assumed to vary by 0.5μrad rms (one-halfthe nominal rms beam divergence), adding another sourceof undetermined energy error based on small variations of
the Bragg angle. Detector noise is also added assuming anoise level of 100 photons with respect to the the peak signal of 105 photons. And ﬁnally, a photon statistics error is
included, which is proportional to the inverse square-root

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Proceedings of FEL 2006, BESSY, Berlin, Germany
380

Parametere− energy
bunch charge
undulator parameterfund. wavelength
Bragg spacing (111)
Bragg angle (111)rel. e− energy jittere− energy meas. res.
bunch charge jittercharge meas. res.
e− angle jitter
detector noise levelpeak signal

symbol
E0
q
K0
λr
d
θ
(ΔE/E)rms(ΔE/E)res(Δq/q)rms(Δq/q)resθrms
Nγnoise
Nγpk

value
13.6
1.0
3.50
1.5
3.14
13.8
0.1
0.003
2
0.5
0.5
100
105

unit
GeV
nC
Å
Å
deg
%
%
%
%
μrad
photons
photons

Number of photons (arb.)

2
1.5
K/K = 0

K/K = +0.2%

0.5
0
1

0.5

0
/ (%)

0.5

1

Figure 3: High-energy spectrum edge for each of nine values of ΔK/K: (−0.2% to +0.2%). Solid curves are perfect spectra and plot points are simulated noisy data.

of the number of photons detected in each pulse. Table 1
lists the simulation parameters.
Figure 3 shows the perfect, computer-generated spectrum for each of nine values of ΔK/K as solid curves,and the simulated, imperfect data as points randomly sampled on the frequency axis due to electron energy jitter.
The scatter of the data points with respect to the curves
is due to the various sources of error, such as BPM resolution, charge measurement resolution, unmeasured beam
angle jitter, detector noise levels, and photon statistics, as
described above.
The data shown in Fig. 3 must now be used to determine
the slope of the high-energy spectrum edge for each valueof ΔK/K. The method used here is to ﬁt the core of thedata, which is between 15-20% below the signal peak and
15-20% above the signal minimum (see horizontal cut lines
in Fig. 3), with a 3rd-order polynomial and solve for the
steepest slope. The ﬁtted polynomial form is
N = N0 + a(Δω/ω) + b(Δω/ω)2 + c(Δω/ω)3 .

550

K/K = 0.003±0.004%
400
420
440
460
0.2

0.1

0
K/K (%)

0.1

0.2

Figure 4: Maximum negative slope vs. ΔK/K. Any
ΔK/K error is resolved to within ±0.004%. The goal of|ΔK/K| < 0.015% is shown as vert. green lines.

This steepest slope (inﬂection point) on the cubic-ﬁtted
curve is then


b2
dN
(2)
=a− .
Δω/ω max
3c

K/K = 0.2%

1

maximum slope (arb.)

Table 1: Simulation parameters.

(1)

The nine determined steepest slopes of Eq. (2) are thenplotted versus ΔK/K, which is taken from the deliberate
undulator displacements, Δx, and the known pole cant angle. The data is ﬁtted to a simple parabolic curve in order
to ﬁnd the minimum. Figure 4 shows this plot where thesteepest slope is found at ΔK/K = −0.003%, with a statistical error of ±0.004%, well within the goal of 0.015%.
The error bars are the propagated statistical errors, from the
cubic ﬁt, through each evaluation of Eq. (2).
Similar estimations are repeated for simulated radiation
spectra using magnetic measurements from the real, imperfect prototype undulator. A systematic ΔK/K error of up
to 0.008% is seen in this case, which is not fully understood, but is still within the required acceptance. It should
be noted that the prototype is of lower magnetic quality
than the ﬁrst few production undulators.
In addition to statistical errors and imperfect undulators,
the possibility also exists for a relative phase error between
the two interfering undulators. Simulations were run forphase errors of 20 and 70 degrees. For reference, the maximum allowable net error within LCLS undulator speciﬁcations is 20 degrees. The 20 degree error has no signiﬁcant
impact on the result. The 70 degree error shown in Fig. 5,clearly affects the data, but the effect can be excluded fromthe ﬁt if the lower data cut level is set no lower than 20%

DISCUSSION
Beam Angle and Alignment Systematics
There are two kinds of alignment errors that, when combined, can in principle lead to signiﬁcant error in the measured ΔK/K. One is a change in the electron beam angle

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THBAU05

Number of photons (arb.)

~741
647

515

2

8 μradDetector

Undulator Vacuum Chamber, +/- 2.5 mm

1.5+ / - 6.7 μrad FWHM 'Core'1

Beam Path
SEG 1

SEG 33Adjustable
slits

0.5
0
1

0.5

0
/ (%)

0.5

1

Figure 5: High-energy, two-undulator spectrum edge for 9
values of ΔK/K with a 70-degree relative phase error.

between segments (non-straightness). The other is a misalignment, with respect to the central ray of the beam, ofthe effective aperture (usually the vacuum chamber) which
deﬁnes the angular distribution of photons detected.
Synchrotron radiation produced by undulator segments
has a strong angle/energy correlation, whereby the spectrum is shifted to lower energy for ﬁnite angles between thecentral ray and the observation point. Theoretically, in themethod presented above, the spectrum is integrated over
all angles, so the measured spectrum should not change
if there are alignment errors — all photons are collected.
However, in practice the range of angular integration islimited by the vacuum chamber aperture, especially forthe ﬁrst segments, where there is only ±20(32) μrad vertical(horizontal) acceptance, assuming a perfect chamber
and a perfectly aligned beam.2 The angle-energy correlation implies that, in part, the alignment of the aperture withrespect to the central ray determines the spectrum of photons that pass through.
The FWHM angular spread for the resonant photon energy is ±6.7μrad. It is representative of the core angularsize over which photons contribute to the high-energy edgeof the spectrum. Figure 6 shows that beam angles of morethan about ±8 μrad will result in scraping ofthe core x-raysby the vacuum chamber. However, this situation will resultin an error in the ΔK/K measurement only if there is alsoa change in beam angles between the segments being measured, because otherwise the effect would be the same forboth segments.
We plan to avoid this error by using beam-based alignment, which will reduce the residual segment-to-segment
angles to order 1μrad or less. In addition, we plan to check
where the central ray is by scanning a 1 mm2 ‘pinhole’aperture and ﬁnding the position that maximizes the average photon energy. If necessary, the beam orbit can be
adjusted so that the central ray passes comfortably throughthe aperture so that no scraping of the core will occur.
2 The angular acceptance of the detector, when properly aligned, is assumed to be larger than the angular acceptance of the vacuum chamber.

FEL Technology

Figure 6: The ‘core’ synchtrotron radiation will start toscrape off on the vacuum chamber if the central angle isgreater than 8 μrad.

Leap Frogging and Near Field Effects
The proposed method gives a measurement of the relative difference in K values between two nearby undulator
segments. The complete undulator is composed of 33 segments and is 130 m long, with the last segment about 100 mfrom the detector. Simple pairwise measurement of adjacent segments builds up the expected√ error between the ﬁrst
and last segment by a factor of 33. By ‘leap frogging’over two segments, only 11 measurements are needed toconnect the ﬁrst and last√ segments so the relative error between them would be 11 times more than the individual
measurement error. If two segments are skipped, the phasedifference that results from the missing segments can be adjusted using a closed orbit bump. Skipping more segments
would tend to further reduce the error build-up. However,as the distance between the segments being measured increases, the possibility of signiﬁcant electron trajectory angle errors increases as well. Also near-ﬁeld effects can start
to appear. The optimum strategy will become apparent during measurement.
In the theoretical model of the undulator segments, it
is implicitly assumed that the observation angle from thebeam to the detector is the same for the two segments, i.e.,the detector is in the far-ﬁeld of the spontaneous radiation.
If the distance between segments is comparable with the
distance to the detector, then the observation angles will besigniﬁcantly different and the detector will see a red-shifted
spectrum from the nearer segment. For the LCLS, segmentspacing 10 m or less (roughly consistent with skipping overtwo segments) can be considered to be the far-ﬁeld case.3

REFERENCES[1] LCLS Conceptual Design Report, SLAC-R-593 (2002),
http://www-ssrl.slac.stanford.edu/lcls/cdr/.
[2] www-ssrl.slac.stanford.edu/lcls/undulator/meetings/200511-14 bbkm workshop/ The web page contains several
relatively recent talks on the topic of in situ K measurement.
3 Differences in angle of less than 1μrad have negligible effect on thethe measured spectrum. If the integration of radiation from one segment
is over ±15 μrad then a difference in the integration angle of 1μrad forthe other segment corresponds to a segment spacing on the order of 10 m
or three segments.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

TEMPORAL ANALYSIS AND SHAPE CONTROL OF UV HIGH ENERGYLASER PULSES FOR PHOTOINJECTORS∗
D. Garzella† , O. Gobert, Ph. Hollander, F. Lepetit, M. Perdrix
Commissariat à l´Energie Atomique (CEA-France)
T. Oksenhendler
FASTLITE, Ecole Polytechnique, Palaiseau (France).
Abstract
This work shows a survey of the studies conceived for
obtaining Ultraviolet, high energy laser pulses, totally controlled and characterized in shape, on the kHz, Chirped
Pulse Amplification (CPA)-based Ti:Sa laser system PLFAat CEA-Saclay. The pulse shaping deals with the amplitude and phase control of the stretched laser pulses issued
from an amplifier before entering the compressor and thetripling unit. The work presents the theoretical backgroundand the proposed experimental setup, before showing thepreliminary promising results.

INTRODUCTION
In order to generate high power, subpicosecond XUVradiation by following the classical Self Amplified Spontaneous Emission (SASE) scheme [1, 2] and/or seeded
FELs [3, 4, 5, 6, 7], tight specifications on the electron
bunch are required, noteworthy in terms of highly reduced emittance, both for achieving very short wavelengthor high average power, thus high duty cycle continuous
electron beams (repetition rates ≥ 1 kHz). Even thoughemittance compensation schemes [8] are used, or ”RFfocusing” ones [9] for superconducting RF photo-injectors,
for obtaining high brightness electron bunches, the laser
pulses impinging onto the photocathode must meet special
requirements not only in terms of wavelength and delivered
energy per pulse. High repetition rate systems like the one
retained for photo-injector operation at Arc-en-Ciel [10]will have to fulfil the following requirements:• Up to 50 μJ pulse energy in the UV (following thecathode material work function, between 240 and 300nm), for a 1 nC electron bunch production on a photocathode with ρ ≈ 0.1 − 1% quantum efficiency(QE) (as in the case of the most commonly used semiconductor Cs 2 T e). This calls, before a very highly
efficient third harmonic generation, for laser amplifiers delivering at least 1 mJ in the IR (800 nm), and,for high repetition rates, on Chirped Pulse Amplified(CPA), Ti:Sa based systems.
• A final duration in the UV, before the cathode, between 5 and 20 ps [10].
∗ This work has been supported by the EU Commission in the Sixth
Framework Program, Contract No. 011935 - EUROFEL.
† david.garzella@cea.fr

552• A precise measurement and control of longitudinal
and transverse features (dimensions and shape) in order to prevent non-linear contribution to the emittanceincrease.
Indeed, it has been shown [11, 12] that in order to minimize the bunch emittance at the issue of the electron gun,temporally and spatially shaped UV pulses are needed toprevent non linear space charge forces and then minimize
the electron emittance. Shaping techniques for ultrashortlaser pulses (in the sub-ps range) are well known. In transverse space an homogeneous energy distribution with a circular symmetry is needed. This can be obtained by use ofmask filters or deformable mirrors and lenses. In longitudinal space, shaping techniques are mostly based on theutilisation of spatial masks, in some cases by using programmable liquid crystals structures at the fourier planeof a 4f zero-dispersion line [13], or by using an AcoustoOptic Programmable Dispersive Filter (AOPDF), or DAZZLER [14]. Both techniques have been already used in
the framework of accelerator and FEL studies [15, 16]. In
the EUROFEL program framework, our goal is to obtain a
few picosecond, 100 μJ laser pulses in the UV (266 nm)with a totally controlled and characterized longitudinal andtransversal shape. This work presents the experimental
setup and the main diagnostics designed to obtain every desired pulse shape from the ”beer can” profile (corresponding to a cylindrical bunch in the 3D-space) to a parabolicone (”waterbag” bunch distribution) starting from the IR
ultrashort pulse issued by the kHz, Chirped Pulse Amplification (CPA)-based Ti:Sa laser system PLFA (Frenchacronym for Tunable Laser Femtosecond Platform) [17] at
CEA-Saclay. The pulse manipulation is based on the amplitude and phase control of the stretched laser pulses issued from the amplifier, which is performed by the DAZZLER before entering the compressor and the tripling unit.

FEMTOSECOND LASER PULSES
Direct temporal manipulation of an ultrashort laser pulse
is rather complicated. Thanks to Fourier Analysis, every
temporal feature of a laser pulse has its corresponding one
in the frequency domain. Thus, an ultrashort pulse in time
space exhibits a very broadband spectrum (several tens of
nm). The electric field E(ω,φ) can be described in termsof the spectral components of amplitude E 0 (ω) and phaseφ(ω):

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

1. The user builds the target amplitude and phase terms.

E(ω,φ) = E0 (ω) · ei(ω0 t+φ(ω))

φ(ω) = φ0 + (ω − ω0 ) ·THPPH001

(1)



δφ 
(ω − ω0 )2 δ 2 φ ·+δω ω02
δω 2 ω0(ω − ω0 )n δ n φ 
· n
...+
(2)
n!
δω
ω0

In the polynomial approximation of the phase term (eq.
2), the constant and the first order term coefficient, called
respectively the ”absolute” phase and the group delay, arenot crucial for the propagation of the pulse, as they account respectively for the position of the peak amplitudeof the field in the phase and the delay undertaken by thecentral frequency component E 0 (ω0 ) propagating between
two reference planes [18]. The second-order term coefficient becomes extremely interesting for pulse manipulation
as it accounts, for example, for the different response of thefrequency components to the propagation of the pulse in a”dispersive” medium. Thus, an original transform-limited
δ2 φ 
laser pulse will be stretched by a factor ∝ δω2  . Higher

2. Amplitude loop:• Initial filter amplitude.
• spectrum measurement.
• Modification of the filter by dividing the ”target”
amplitude by the measured amplitude.
• spectrum measurement ... loop until the measurement fits the ”target”.
3. Phase Loop: Analog process is made on the ”target”
phase.
4. Experimental amplitude and phase are acquired andan initial check in the time domain is made by IFT
on the experimental data, thus retrieving the temporal
duration and shape (fig. 2).

ω0order terms account for symetric and antisymetric distortion terms of the pulse shape.

EXPERIMENT
Pulse Shaping Technique
The principle of the AOPDF [14] is based on the coupling between the laser pulse and an acoustic wave in abirefringent crystal. For IR laser pulses, around 800 nm,
a T eO2 crystal is cut in such a way that the acoustic wave
energy and the optical waves energy travel along the same
axis. The incident optical pulse polarized on the ordinary
axis is diffracted by the Bragg grating made by the acoustic wave onto the extraordinary axis. Shaping the pulse isequivalent to programmming the associated suite of acoustic grating, so that the spectral amplitude and phase of thelaser pulse is directly linked to the acoustic wave ones.

Target, Filter and Correction Loop
Defining a ”target” pulse here means defining ”target”
spectral amplitude and phase. As the DAZZLER is a linear
filter, the output optical pulse is the product of the input
pulse by the filter response in the spectral domain:in (ω, φ) · S(ω, φ)out (ω, φ) = E
E(3)where S(ω, φ) is the filter response.
Therefore, knowing the input pulse, the target pulse is directly obtained by fitting the filter response (see fig. 1). The
spectral amplitude and phase shapings can be separated asthey are independently measured and controlled.
In practice, amplitude loop preceeds phase loop becauseof bandwidth limitation. The complete procedure can be
described as the following steps:

FEL Technology

Figure 1: Blue curve : computed target spectral intensity;
Red curve: experimental spectral intensity; Green curve:
target spectral phase.

Spectral Interferometry
The crucial point in the laser pulse analysis is the retrieval of the spectral phase. Indeed, the spectrum intensity acquisition is not enough to characterise a non Fourierlimited pulse (i.e when its phase is not flat over all the
spectral range). In our experiment, we want to measure
the spectral phase on a single shot, simple, sensitive andextendable to UV range measurement. Spectral interferometry [21] between a reference pulse and the unknown
pulse gives directly, through Fourier transform, access tothe phase difference between these two pulses (cf. fig. 3).
In our case, the reference pulse is the input pulse and themeasurement confirms only the phase shaping. For complete phase shaping, the phase of the reference pulse isneeded. As the reference pulse is close to Fourier transform
pulse, any self-referenced measurement (SPIDER [19],553THPPH001

Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 2: Blue curve : Fourier Limited laser pulse taking
into account only the target spectral amplitude; Red curve:
target temporal shape taking into account the target spectralphase.

First studies are being performed on the laser facility
LUCA (Tunable Ultra Short Laser) which delivers 50 f s
long, 800 nm laser pulses, with an energy of up to 100 mJ,
at a 20 Hz repetition rate. The pulse is split into the twoarms of the interferometer (cf. fig. 4). On the first arm thelaser passes through the acousto-optical device, thus undergoing a phase and/or amplitude manipulation. The second
one travels through a delay line and it is then superposedon the first one. The two recombined beams enter the spectrometer where they interfere on the sensor. Single-shot
interferograms are then collected on a personal computer.
This latter also handles the transfer of the target or reference amplitude and phase files, as well as the associatedreconstruction process. In practice the difficulty is to isolate the secondary lobe without information losses when
the contrast is not very high. Also, to correctly recover the
spectrum, a great care should be taken with the spectrometer calibration, and the signal processing to convert fromthe wavelength to the frequency space.

FROG [20]...) is able to measure the residual phase of thispulse. This phase is then added to the measured one byspectral interferometry.

Figure 3: Layout of the Interferogram retrieving protocol.

Experimental Setup

Figure 4: Experimental set-up for spectral interferometry.
The red line shows the path for the two arms of the interferometer.

554

Figure 5: Typical interferogram acquired on the spectrometer.

Figure 6: Retrieved Spectral Amplitude (blue curve) andPhase (red curve).

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH001

to achieving the next-generation X-ray light source”, Nucl.
Inst. Meth., A475, (2001) 401-406.
[3] F. Ciocci et al., ”Design considerations on a high-power VUVFEL” IEEE Jour. Quant. Elec.,Vol. 31, No.7, July 1995, pp.
275-281.
[4] R. Bonifacio et al., ”Generation of XUV light by resonant
frequency tripling in a two-wiggler FEL amplifier”Nucl. Inst.
Meth., A293, (1990) pp.627-629.
[5] L. H. Yu et al., ”High-Gain Harmonic-Generation FreeElectron Laser”,Science, Vol. 289, 11 August 2000, pp.932934.

Figure 7: Temporal shape computed with IFT of the experimental data. Blue curve : Fourier Limited laser pulse
taking into account only the target spectral amplitude; Red
curve: with the target spectral phase.

PRELIMINARY RESULTS[6] D. Garzella et al., ”Using VUV high-order harmonics generated in gas as a seed for single pass FEL” Nucl. Inst. Meth.
A528, August 2004, pp. 502-505.
[7] G. Lambert et al., ”Seeding the FEL of the SCSS Phase 1
facility with the 13th laser harmonic of a Ti:Sa laser producedin Xe gas”, Proceedings FEL 2004,Trieste, Italy, 29 August-3
September 2004, pp.155-158.
[8] L. Serafini and J.B. Rosenzweig, ”Envelope analysis of intense relativistic quasilaminar beams in rf photoinjectors: A
theory of emittance compensation”, Phys. Rev. E 55 (1997)
pp.7565-7590.

The experiment has been implemented on the LUCA
laser facility. Very low energy IR pulses (≈ 10 μJ) havebeen processed up to now. The few obtained preliminary
results are very encouraging. A first example for a rectangular laser shape has been performed. Fig. 6 shows the retrieved amplitude and spectral phase behaviours, this latterwithout the constant and first order terms, whereas in fig. 7
the computed temporal shape, obtained with only one iteration, highlights the difference between the gaussian shapepulse which is obtained when only the spectral amplitudeis taken into account, and the rectangular shape, when the
spectral phase is inserted. The obtained pulse has a duration of 1.3 ps F W HM , with leading and trailing edges
lasting around 170 f s. In order to get rid of the observed
modulation on the top of the pulse, a higher signal-to-noise
ratio should be achieved, always in a single shot configuration.

[14] F. Verluise et al., ” Arbitrary Dispersion Control of ultrashort optical pulses with acoustic waves ” Jour. Opt. Soc. Am.
B, n 17 (2000), pp. 138-145.

CONCLUSIONS[15] S. Cialdi and A. Boscolo,”A shaper for providing long laser
target waveforms”, Nucl. Inst. Meth., A538, (2005) pp.1-7.

The spectral interferometry setup has been implemented
on LUCA. Future steps will deal with the improvement of
the laser beam spatial profile, the completion of the corrective loop for several different longitudinal shapes, a big
increase of the pulse energy injected in the Dazzler, up to 1
mJ before compression. Afterwards the grating compressor will be installed on the beamline, together with a third
harmonic generation stage and a further prisms stretcher, inorder to obtain shaped pulse in the UV at 266 nm, with anenergy of several tens of μJ.

REFERENCES[1] C. Pellegrini, ”Design considerations for a SASE X-ray
FEL”, Nucl. Inst. Meth., A475, (2001) 1-12.
[2] S. G. Biedron, S.V. Milton, H.P. Freund, ”Modular approach

FEL Technology[9] M. Ferrario et al., An Ultra-High Brightness, High Duty
Factor, Superconducting RF Photoinjector”, Proceedings of
EPAC 2004, Lucerne, June 2004, pp. 402-404.
[10] M. E. Couprie et al., ”The ARC-EN-CIEL FEL proposal”,
these Proceedings.
[11] M. Ferrario et al., ”Frontiers of RF Photoinjector”, Proceedings of PAC 2005, Knoxville, USA, May 2005.
[12] C. Limborg-Deprey and P. R. Bolton, “Optimum electron
distribution for space charge dominated beams in photoinjectors”, Nucl. Inst. Meth. A557 (2006), p. 106-116.
[13] A. M. Weiner, ”Femtosecond pulse shaping using spatial
light modulators”, Rev.Scient. Inst. Vol 71, No. 5, MAY 2000,
pp. 1929-1960.

[16] C. Vicario et al.,”Preliminary results using an acousticooptic dispersive filter for laser pulse shaping”, SPARC Internal Note, SPARC-LS-04/001, 15 January 2004.
[17] http://www-femtodrecam.cea.fr/[18] I.A. Walmsley et al. ”The role of dispersion in Ultrafast optics”, Rev.Scient. Inst. Vol 72, No. 1, January 2001, pp. 1-29.
[19] C. Iaconis and I. A. Walmsley, Spectral phase Interferometry for direct electric-field reconstruction of ultrashort opticalpulses, Optics Letters 23, pp. 792794 (1998).
[20] D.J. Kane and R. Trebino, ”Characterization of arbitrary
femtosecond pulses using frequency-resolved optical gating”
IEEE Jour. Quant. Elec. 29 (2), February 1993 pp. 571-579.
[21] L. Lepetit et al., ”Linear techniques of phase measurementby femtosecond spectral interferometry for applications inspectroscopy” Opt. Lett., Vol. 12, No. 12, December 1995,
pp. 2467-2474 and references therein.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

CHARACTERISATION OF MICROPHONICS IN HOBICAT ∗Oliver Kugeler, Wolfgang Anders, Jens Knobloch, Axel Neumann, Bessy GmbH, Berlin, Germany.
Abstract

Input coupler
Pin diodepiezo

Klystron

pickup antenna
Circulator

Masteroscillator
Frequency modulation

The HoBiCaT test-facility at BESSY, which is designed
for cryogenic testing of superconducting TESLA units has
been equipped with a 9-cell TESLA-type cavity. Mechanical vibrations in the cryostat result in microphonic detuning of the cavity resonance. These microphonics have beencharacterized, and their sources analyzed, including the impact of operating conditions such as LHe pressure, cavity
field and heater power. Furthermore, the mechanical transfer functions needed for the eventual compensation of the
microphonics have been recorded.

1.3 GHz

CavityPower meter
Mixer?
Phase shifterPre-amplifier

Leveled amp

DAQ / PC

Figure 1:
Phase-lock-loop used for cavity RFmeasurements.

INTRODUCTION
For CW operation of a superconducting, TESLA-type
cavity microphonics represent the largest disturbance ofthe resonant frequency. In particular at a small bandwidthΔf = ω/QL, according to the equation
P∝1+(δf )2(Δf )2(1)

the microphonics δf lead to a significant increase of thegenerator power P, which is required to maintain a constant cavity field. Therefore it is highly desirable to minimize the microphonics. Measurements characterizing the
microphonics and their impact on the cavity operation arepresented below. The perspectives on possible countermeasures are described elsewhere [1].

MICROPHONICS MEASUREMENTS
Microphonics have been recorded in two different ways.
In a first method, the RF-feedback signal, see Figure 1,
is recorded over time. This is preferably done in open
loop configuration, because obtaining a calibration factor
is more straightforward here, than in closed loop configuration. A second method utilizes the sensor-actuator designof the piezo tuner to record the induced piezoelectric voltage over time. In this design, two high-voltage piezos areattached to the tuner, thus piezoelectric forces can be exercised on the cavity and measured simultaneously. The
latter is only an indirect method, as the mechanical influence from cavity and tank on the frequency response does
not necessarily lead to a linear relationship between cavityand piezo position. The results presented here were solely
obtained from the RF-feedback signal.
∗ Work funded by the European Commission in the Sixth Framework
Program, contract No. 011935 EUROFEL.

556

Calibration of RF-feedback signal
In order to interpret the voltage value from the RFfeedback in terms of a detuning frequency, a calibration
factor has been determined. This was done by mechanically detuning the cavity with the piezo stack, which exhibited a detuning behavior of Δf/ΔV = 1.131 Hz/V. By
varying the piezo voltage the cavity resonance was scanned
open loop at a fixed master oscillator frequency over several bandwidths. The RF-feedback value varied by 0.84 V.
Hence, all voltages could be easily interpreted as frequencies. This procedure is only possible because a leveled amplification is applied to the cavity pickup-signal. This ensures that the mixer output signal is solely dependent on
the phase difference between master oscillator and cavity.
Note that the frequency stability of the Rohde & Schwartz
master oscillator at 1.3 GHz is better than 0.1 Hz.

Measurements at cryogenic temperatures
Microphonics have been measured at cryogenic temperatures. In Figure 2 the Fourier transform of a 30 second
long measurement of the RF-feedback signal sampled at 5
kHz is depicted. An immediately identifiable feature is theconstant signal of a turbo vacuum pump (18000 rpm) at 300
Hz. Furthermore, prominent features occur at 41 Hz, 90
Hz, and 170 Hz and are resonances of the cavity-tank-tuner
system. The feature at 30 Hz is a so far unidentified source
not related to any of the mechanical cavity resonances. It
was further investigated whether the measured microphonics would change with the quality factor, or the bandwidth,
respectively. For that purpose, the quality factor was varied
over a wide range (a) by changing the coupler position and(b) by using a three stub tuner.
In Figure 3 the integrated microphonics frequency spectra taken at different values of Q L are plotted. It can beseen that in general the RMS value of the microphonics in-

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH002

Microphonics and pressure variation

unidentified

8

0.03

6

Resonances

Detuning (Hz)Pressure (mbar)

0.02

4
0.01

Detuning / Hz

2

Power spectrum (Hz )

f

0.5

0.04
Equilibrium pressure = 16 mbar

σ =2.4 Hz

He pressure variation / mbar

0.6

0.4
0.3

2

0

0

-0.01
-0.02

-2

0.2

-0.03

Turbo pump

-4

0.1

-0.04

-6

-0.05
0

5

10

15

20

25

30

Time / sec

50

100

150
200
Frequency (Hz)

250

300

Figure 4: Microphonics and He-pressure difference.
Figure 2: Microphonics in cavity measured open loop at
1.8 K.
1.4

Bandwidth
RMS nicrophonics contribution

1.2

16.25 Hz1

14.77Hz

0.8
0.6

7.56 Hz

0.4

4.06 Hz
0.2
0
-2
10

1.55 Hz
-1

10

0

10

1

10
Frequency [Hz]

2

10

3

10

4

10

Figure 3: Integrated microphonics frequency spectra at different cavity bandwidths. The main contributions to theoverall RMS value of the microphonics come from low microphonics frequencies (< 1 Hz). Microphonics increase
with higher cavity bandwiths.
creases with the bandwidth, or in other words the cavity becomes less susceptible towards microphonics with increasing QL . It can also be seen that the largest contributions to
the RMS-microphonics are at low frequencies.

Influence of cryogenics on the microphonics
The heavy machinery in our cryogenic system consistsof a Sogevac SV200 Leybold pump and two pairs of Leybold SV1200 and RA7001 SO pumps. They operate at
24 Hz, 11.66 Hz, and 50 Hz, respectively. Note that thesemechanical vibrations can not be found in the microphonics spectra which was also confirmed by slightly varying
the pumping frequencies. This observation suggests thatthe decoupling of the pumps from the HoBiCaT facility is
sufficient.
The main contribution to the microphonics was found to be

FEL Technology

Figure 5: Pearson correlation between Helium bath pressure and microphonic detuning The 0.4 seconds offset isdue to the preset sampling time of the pressure sensor. The
occurrence of side maxima suggests, that there is some periodicity within the microphonics.

from within the cooling medium itself. A change in Heliumpressure (measured with a Rosemount sensor) was measured to lead to a detuning of the resonant frequency of 55
Hz/mbar. Figure 4 shows the microphonics recorded over a
period of 30 seconds in correlation with the He-bath pressure. In Figure 5 the Pearson correlation between the two
signals is plotted. The maximum correlation occurs at anoffset of 400 ms, which is due to the sampling time of thepressure sensor. This observation suggests, that a significant portion of the microphonics can be compensated witha feed forward system, provided fast and accurate pressure
sensors are used. The microphonics created by the Helium heater, which is part of the cryogenic system and supports the Joule-Thomsen expansion of the cooling medium,
were also investigated. In Figure 6 microphonics have beenrecorded as a direct fft from the RF feedback signal at different values of the heater power. It can be seen that different heater powers create significantly different microphonics spectra, suggesting that the heater itself is a source of
microphonics.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

0,007

90
30 Watt
40 Watt
50 Watt
60 Watt
80 Watt

0,006

80

kLF = 1.4206 Hz/(MV/m)²

70
60

(Hz)

0,004
0,003

cav

Amplitude (a.u.)

0,005

Δf

0,002

50
40
30

0,001

20

0
0

50

100

150

200

250

300

350

Frequency (Hz)100Figure 6: Influence of the heater power on the microphonics spectra

0

10

20

30
40
E ² (MV/m)²

50

60

70

acc

Normalized number of events

Figure 8: Lorentz Force Detuning vs. field gradientFigure 7: Long-time microphonics measurement.

Figure 9: Transfer function of the cavity-tank-tuner system
recorded over a frequency range of 0-400 Hz.

Long-time measurements of microphonics

Transfer function

As the RF-system has to be laid out to deal with the maximum possible microphonics detuning, several long-time
microphonics measurements have been performed. Fromthese measurements the probability for a certain detuning
within a given time period could be determined. The measurement presented in Figure 7 is a histogram of measured
detuning values. It was taken over 1000 seconds and gives
a maximum detuning frequency of 26.8 Hz and a rms detuning of 4.4 Hz. A 24 hours+ measurement is planned, but
has so far been postponed due to long time stability issuesof the klystron.

The reaction of the cavity resonance frequency on microphonic vibrations is determined by the mechanical eigenmodes of the tank-tuner-cavity system. Such Q-modes aremeasured via the transfer function. Here, the piezos areused to create sinusoidal vibration at distinct frequencies
over a certain frequency range. The RF-feedback signal isrecorded over time, yielding amplitude and phase information of the mechanical response, see Figure 9. Such modes
arouse from transverse and longitudinal vibrations with respect to the cavity axis. Note, that only longitudinal symmetric stretch modes can be excited with the present piezo
setup and thus only such modes can eventually be compensated. Numerical simulations by Luong et al. [3] suggestthat these modes make up for the largest contribution to thedetuning of the cavity.

Lorentz force detuning
The static response of our setup to Lorentz force detuning has also been measured. We have obtained a value of
kLF = 1.42 Hz/(MV/m)2 , see Figure 8, which is within
the range of values of 1–2 Hz/(MV/m) 2 gained at DESY
[2].

558

Influence of passive cavity stabilizers
Titanium fixtures that can be attached between thecavity’s stiffening rings and the helium tank have beendeveloped by FZ Rossendorf and manufactured at AC-

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH002

thumper response without fixtures

1.2

thumper response with fixtures installed

Amplitude, KeBe (a.u.)

1
0.8
0.6
0.4
0.2
0
0

50

100

150

200

250

300

thumper frequency (Hz)Figure 10: Integrated frequency response signal of cavity
mounted in a He-tank (a) with and (b) without fixtures attached.
CEL. While they were originally intended for earthquakeprotection, we have investigated to what extent they candampen mechanical vibrations or shift resonances towards
higher frequencies, and thus reduce the impact of microphonics. Room-temperature measurements were done at
ACCEL with such a cavity. For the experiment, an acoustic thumper, operating between 30 Hz and 300 Hz, was attached to one end of the cavity (perpendicular to the cavityaxis). The response was measured with KeBe inductive velocity meters attached at different positions of the tank. It
was found that the fixtures contributed only marginally toa decrease of the microphonics response signal. As can beseen from Figure 10 the response function with and without
fixtures is practically identical. The only significant deviation occurs at 80 Hz, but no significant microphonics were
measured in HoBiCaT at this frequency.

OUTLOOK
The next step after characterization of microphonics is
to take countermeasures to compensate them. Such a compensation does not have to be complete as even small improvements lower the required RF-power significantly. The
correlation between He-pressure and low frequency microphonics suggests, that a feed-forward algorithm might befeasible. Such work is underway and will be presented
soon. Also we are investigating adaptive feed forward compensation of higher frequency microphonics.

REFERENCES[1] A. Neumann, et al., “Characterization of a Piezo-based Microphonics Compensation System at HoBiCaT”, EPAC’06,
Edinburgh.
[2] H. Gassot, “Mechanical Stability Of The RF Superconducting Cavities”, Proceedings of EPAC 2002, Paris, 2002.
[3] M. Luong, et al., “Analysis of microphonic disturbancesand simulation for feedback compensation”, Proceedings of
EPAC’06, Edinburgh.

FEL Technology

559

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Proceedings of FEL 2006, BESSY, Berlin, Germany

A HIGH AVERAGE POWER RF PHOTOINJECTOR GUN CAVITYDEVELOPED FOR THE BESSY SOFT X-RAY FEL*
F. Marhauser#, M. Dirsat, A. Meseck, D. Richter, V. Dürr, E. Weihreter,
BESSY, 12489 Berlin, Germany
G. Asova, J. Bähr, H.J. Grabosch, S. Khodyachykh, S. Korepanov, M. Krasilnikov, A. Oppelt,
B. Petrosyan, L. Staykov, F. Stephan, F. Tonisch, DESY, 15738 Zeuthen, Germany
O. Kalekin, Humboldt University, 12489 Berlin, Germany
J. Roensch, University of Hamburg, 22761 Hamburg, Germany.
Abstract
Based on the 1.3 GHz normal conducting RF photogun
installed at the Free Electron Laser in Hamburg (FLASH)
a new RF gun prototype with an optimized cooling layout
has been developed at BESSY with the objective tooperate in the 100 kW average power regime. This would
significantly enhance the capability of present L-Bandguns towards operation at higher accelerating fields
or/and duty factors. High power RF-conditioning at the
Photo Injector Test Facility at DESY in Zeuthen (PITZ)
has recently been performed achieving 47 kW average
power and an electric peak field of 53 MV/m inmaximum respectively, so far only limited by power
constraints of the RF-system. In this paper the RFconditioning results and relevant simulation results are
discussed. Tracking studies for the photoinjector
including two linac modules and a subharmonic cavity
section are presented.

INTRODUCTION
RF photoinjectors bear the potential to generate
electron pulses of extraordinary high peak brightness
suitable for future FELs and linear colliders. For the
proposed BESSY Soft X-Ray FEL (“BESSY FEL”) [1]with its superconducting CW driver linac asuperconducting RF (SRF) gun would be the ideal
electron source to deliver most flexible pulse patternconsidering the manifold demands of experimental users.
Superconducting guns are therefore a very active researcharea. For example, FZR, DESY, MBI and BESSY arecollaborating to commission an SRF 1.3 GHz 3½-cell
photoinjector gun cavity at FZR in 2007. Initially, thisgun will accelerate 1 nC, but schemes have been
identified and investigated that are capable of achieving
slice emittances in the order of 1.5 π mm mrad at 2.5 nC
bunch charge [2].
At present, though, normal conducting (NC) photoguns
are more established and will therefore be used tocommission the BESSY FEL. Still, a very high rep rate____________________________________________* This work has partly been supported by the European Community,
contract numbers RII3-CT-2004-506008 (IA-SFS) and 011935(EUROFEL) and by the “Impuls- und Venetzungsfonds” of theHelmholtz Association, contract number VH-FZ-005#
corresponding author: marhauser@bessy.de

560(1 kHz) is planned to approach CW operation. Later thisNC gun can be replaced by an SRF gun. In particularmuch progress has been made by the PITZ collaboration
which has developed a series of 1.3 GHz NC guns (1 ½
cells) characterized at the PITZ facility [3]. So far aminimum projected emittance of 1.6 π mm mrad
(geometrical average of horizontal and vertical emittance)
for a bunch charge of 1 nC could be demonstrated [4].
This system has also been operational at FLASH.
Improvements at PITZ are expected by further optimizing
the transverse and temporal profile of the photocathodelaser, increasing the electric field at the photocathode to
Ec = 60 MV/m and by utilizing a booster cavity, whereby
the emittance conversation principle will be studied [5].
Beam operation hitherto was performed typically with
Ec = 40-45 MV/m and a duty factor of 0.9 % (10 Hz RF
pulse repetition rate) corresponding to an average powerin the range of 30 kW. The European XFEL [6] and the
proposed BESSY FEL however require even higher
values to be achieved as listed in Table 1.
Table 1: Target parameters of NC RF guns as proposed
for the European XFEL and the BESSY FEL at
commissioning phase
Parameter

European
XFEL

Frequency / GHz
1.3
Number of cells (copper)
1½
Bunch charge / nC
1
Single bunch rep. rate / MHz5
RF pulse rep. rate / Hz
10
Peak field / (MV/m)
60~6.5
Peak power* / MW
650 (max.)
Beam pulse length** / μs
Duty factor / %~0.67
Average power / kW
~44
Beam parameters at undulator
Trans. norm. slice emittance /1.4
π mm mrad
Max. beam energy / GeV
20
*

BESSY
FEL
2.5
1/3
1000
40
~3
6
~2.5
~75
1.5
2.3

depending on Q0 (~23000), ** excluding RF rise/fall time (~20 μs)

Gun cavity thermal drifts as a source of severe phaseand amplitude jitters may then become more apparent.
Despite the progress of RF field stability control [7], one
challenging task remains the mitigation of these drifts.
Thus elaborate cooling concepts for the gun have to be

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany
considered. With respect to this issue a high average
power 1 ½-cell RF gun cavity with an optimized coolinglayout has been developed at BESSY (“BESSY Gun”) as
described below. A prototype of the cavity has been
produced and thermal tests without photoemitted
electrons were performed at PITZ. This gun also served
as the basis for new beam dynamics simulations.

BESSY NC RF GUN CAVITY
A picture of the BESSY Gun and its outer water
connections is shown in Fig. 1 (left), whereas the CAD
model (right) reveals the inner cooling circuits. To
provide sufficient water to the cavity a total number of 43
water inlets and outlets have been implemented with eachwater circuit separately addressable. Thus a sufficiently
high water volume flow can be delivered to the cavity
body and the water temperature rise within each meander
can be kept rather low. Still emphasis has been placed ona simple conceptual design using drilled water holes ofsame dimensions throughout except in the iris aperture.
Further details on the technical layout and cooling scheme
can be found in [8].

THPPH003

The cooling scheme was optimized with the help of
thermal simulations using the FEA Code ANSYS [10].
Hence the BESSY Gun exhibits moderate temperatures(< 100°C) at an average power of Pave = 75 kW, i.e. thenominal operation power for the BESSY FEL. As
illustrated in Fig. 2 this has been achieved for areasonable water inlet temperature of Tin = 42°C. Circularnotches at each endplate (‘tuning rings’) have been
implemented to ease a possible tuning effort. The reduced
cooling efficiency at the tuning rings is taken into accountfor this prototype yielding the maximum local
temperatures. Mechanical stresses however are not an
issue [10].
As a feature the BESSY Gun was equipped with asmall pickup port (Ø = 8mm) in the full cell
implementing an antenna, loosely coupled to produce
only a negligible field distortion. The antenna amplitude
and phase information is beneficial for RF field stability
control, critical for the overall jitter stability of theelectron beam. Else - as practised at FLASH - the cavity
field has to be artificially determined from the forward
and reflected power signals of a directional waveguide
coupler [7].

RF CONDITIONING
The first pulsed high power RF-conditioning tests of
the BESSY Gun have been completed in May 2006 in theframe of the PITZ-collaboration. The conditioning test
stand at PITZ is shown in Fig. 3. A 10 MW multi-beam
klystron (MBK) was used to feed in the RF power to thegun via a standard DESY axially symmetric coupler. Dueto the limited power capability of state-of-the-art RF
vacuum windows the MBK output power is distributed
into two separate WR650 waveguide arms. A T-combinerwith two RF windows was flanged to the input coupler to
add both RF-waves.

Figure 1: The copper 1 ½-cell BESSY Gun (photo left)
with the outer water connections and the corresponding
CAD model (right) revealing the inner water circuits.

Figure 3: BESSY Gun on the conditioning test stand at
PITZ. For conditioning no solenoids were installed.

Figure 2: Temperature distribution in the BESSY Gun
calculated at Pave = 75 kW with Tin = 42°C for a quarter
symmetric ANSYS model.

FEL Technology

After only 90 hours conditioning time -with a cavity
vacuum interlock threshold of 10-7 mbar- a peak power ofattRF = 100 μs
wasreachedPpeak = 2.9 MW(Pave = 2.9 kW) corresponding to a peak field of
Ec = 40 MV/m as required for the BESSY FEL. It should

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Proceedings of FEL 2006, BESSY, Berlin, Germany

be noted, that prior to the installation at PITZ the integrityof the gun was checked at BESSY operating several days
in CW mode at 10 kW, which might have been beneficial
to achieve this rather rapid progress. Since the repetition
rate of the low level RF-system at PITZ is limited tofrep = 10 Hz, the average power could only be increasedby operating with both the peak power and the pulse
length far beyond the desired BESSY FEL specifications(see Table 1). This “thermal” conditioning was time
consuming, particularly because of sparking in the
waveguide arms of the klystron at peak power levels
above 3 MW. Despite the constraints of the RF-system,
conditioning could be carried out successfully to a
maximum operable peak power of Ppeak = 5 MW withtRF = 540 μs corresponding to an electric field of
Ec = 53 MV/m. The maximum average power ofPave = 47 kW was reached at the maximum pulse length oftRF = 1 ms with Ppeak = 4.7 MW (Ec = 51 MV/m). Higher
power levels and longer pulse lengths could not bereached because of operational limitations of the RFsystem. However up to 47 kW average power no thermalor technical limitations attributable to the gun wereencountered. The main RF-conditioning results are listed
in Table 2.
Table 2: BESSY Gun RF-conditioning results at PITZ
Parameter
Pave
Ppeak
Ec
tRF
frep
d.f.
*

Achieved at limitof RF system
47
4.7*
51*
1000
10
1

Desired

Unit

75
3
40
25
1000
2.5

kW
MW
MV/m
μs
Hz
%

Fig. 4 (top) depicts a screen shot of the measured gun
cavity temperatures using external PT100 sensors at
distinctive locations (green dots). Here the temperaturesare shown when operating at a thermal load ofPave = 40 kW with an inlet water temperature of
Tin = 27°C. At the bottom corresponding numericalresults using ANSYS are plotted in good agreement withthe monitored data. This is also true for the hot spots
located at the tuning rings. At the antenna port nosignificant heat enhancement has been produced. The
antenna port has been omitted in the calculation due tomesh size constraints.
To further check the reliability of numerical data, thefrequency shift Δf caused by thermal deformation of the
gun cavity has been measured at a constant inlet watertemperature of 27°C when increasing the average power.
Hereby the resonance was kept adjusting the master
oscillator frequency to gain a reflected power below 1%.
To evaluate Δf the resonance frequency at room
temperature is taken as reference. In Fig. 5 the measured
data are plotted as compared with numerical results. The
latter have been computed by transferring the thermallydeformed cavity profile given by ANSYS to Superfish[11]. This method has been extensively described in [12].
A linear drift in the order of Δf ~ -10 kHz/kW over theobserved power regime at Tin = 27°C was obtained,
consistent with the simulations.

max. Ppeak = 5 MW corresponding to Ec = 53 MV/m at tRF = 540 μs

Figure 5: Thermal frequency drift in dependence on the
average power as measured (red dots, frep = 10 Hz,
tRF = 1 ms) and calculated (blue line) both at Tin = 27°C.

BEAM DYNAMICS

Figure 4: Measured (top) and simulated (bottom) gun
temperatures when operating at Pave = 40 kW and
Tin = 27°C (Ppeak = 4 MW, frep = 10 Hz, tRF = 1 ms).

562

Former beam dynamical studies using the accelerating
field of the BESSY Gun as an input revealed that thephotoinjector is able to deliver the required transverse
slice emittances [10]. Further studies employing a
multiparameter optimization with ASTRA [13] have been
performed, the results being depicted in Figs. 6 and 7.
Here 100000 macro particles have been tracked throughthe first two cryogenic linac modules comprising eightstandard 1.3 GHz 9-cell TESLA-cavities. An intermediate
section with quadrupoles as well as eight 9-cell 3.9 GHz
cavities (under investigation at FERMILAB [14]) have

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany
been implemented to linearize the longitudinal phasespace serving the needs of the subsequent first bunch
compressor. A thermal energy of 0.55 eV for electrons
emitted from a Cs2Te photocathode illuminated by a UV
laser (262 nm) has been taken into account. For the laser a
temporal profile of 38 ps (flat top) with 4 ps rise/fall timeand a spot size of 3.3 mm have been chosen. Furthermore
a peak field of Ec = 40 MV/m has been presumed, which
already has been exceeded by the BESSY Gun during thehigh power tests. As mentioned above this value howeveris rather constrained by thermal considerations.

THPPH003

The rms bunch length is 3.5 mm and a projectedlongitudinal rms emittance of 65 π keV mm has beenobtained due to phase space linearization with thesubharmonic cavity section (Fig. 7).

CONCLUSION
A high average power RF gun prototype developed at
BESSY has been high power conditioned at the Photo
Injector Test Facility at DESY in Zeuthen. The gun wastested up to an average power of 47 kW so far only
limited by the maximum operable power of the RFsystem. Similarly, the maximum electric field achieved at
the cathode was 53 MV/m so far. All observations atpresent indicate that the gun is thermally stable at thedesired power level of 75 kW or beyond. This isconfirmed by corresponding thermal calculations.
Operation of this prototype with photoemitted beams was
not planned. However, new numerical tracking studies
demonstrate that the gun is capable of producing the beam
quality required for the BESSY FEL.

REFERENCES

Figure 6: Evolution of the normalized transverse rms
emittance εn (100% and 95% core emittance) and beam
size σx,y for a bunch charge of 2.5 nC up to the exit of
the 2nd linac module.
For a bunch charge of 2.5 nC the normalized projectedtransverse emittance “frozen” at the exit of the second
linac module (Ekin = 223 MeV) is 1.8 π mm mrad(1.2 π mm mrad for the 95% core emittance). At thispoint the slice emittance averaged over the whole bunch
amounts to 1.5 π mm mrad fulfilling the design goal of
the BESSY FEL.

Figure 7: Evolution of the longitudinal rms emittance εz
and average beam energy Ekin for a bunch charge of
2.5 nC up to the exit of the 2nd linac module.

FEL Technology[1] D. Krämer et al. (editors), “The BESSY Soft X-Ray Free
Electron Laser”, Technical Design Report, ISBN 39809534-0-8, BESSY, Berlin, 2004.
[2] D. Janssen at. al., “Progress of the Rossendorf SRF Gun
Project”, Proc. of the 2006 Europ. Acc. Conf., Edinburgh,
Scotland, 2469.
[3] A. Oppelt et. al., “Tuning, Conditioning, and Dark Current
Measurements of a New Gun Cavity at PITZ”, theseproceedings.
[4] F. Stephan, “Status and Perspectives of Photo Injector
Developments for High Brightness Beams”, Conf. on the
Physics and Applications of High Brightness Beams, Erice,
Italy, 2005.
[5] A. Oppelt et. al.,”Status of the PITZ Facility Upgrade”,
Proc. of the 2006 Lin. Acc. Conf., Knoxville, USA.
[6] M. Altarelli et al. (editors.), “The European X-Ray Free
Electron Laser”, Technical Design Report, ISBN 3935702-17-5, DESY, Hamburg, July 2006.
[7] E. Vogel at. al.,” FPGA Based RF Field Control at the
Photo Cathode RF Gun of the DESY Vacuum Ultraviolet
Free Electron Laser”, Proc. of the 2006 Europ. Acc. Conf.,
Edinburgh, Scotland, 1456.
[8] F. Marhauser, “High Power Tests of a High Duty Cycle,
High Repetition Rate RF Photoinjector Gun for the BESSY
FEL”, Proc. of the 2006 Europ. Acc. Conf., Edinburgh,
Scotland, 68.
[9] www.ansys.com.
[10] F. Marhauser, “Photoinjector Studies for the BESSY SoftX-Ray FEL”, Proc. of the 2004 Europ. Acc. Conf.,
Lucerne, Switzerland, 315.
[11] K. Halbach, R.F. Holsinger, Poisson Superfish, Particle
Accelerators 7 (1976), page 213, distributed by the Los
Alamos Accelerator Code Group (LAACG).
[12] F. Marhauser, “Finite Element Analyses for Photoinjector
Gun Cavities”, DESY Hamburg, January 2006, TESLAFEL-Report 2006-02.
[13] K. Flöttmann, http://www.desy.de/~mpyflo/.
[14] N. Solyak et. al, „The Progress in Developing Superconducting Third Harmonic Cavities”, Proc. of the 2006
Europ. Acc. Conf., Edinburgh, Scotland, 804.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

PHOTOCATHODE LASER FOR THE SUPERCONDUCTING
PHOTO INJECTOR AT THE FORSCHUNGSZENTRUM ROSSENDORF
Ingo Will#, Guido Klemz, Max-Born-Institute Berlin, Germany
Friedrich Staufenbiel, Jochen Teichert, Forschungszentrum Rossendorf, Germany.
Abstract
We report on the design of the photocathode laser for a
superconducting RF gun, which is presently underdevelopment at the Forschungszentrum (FZ) Rossendorf.
This laser is foreseen to drive the RF gun in CW modewith up to 1 nC bunch charge. It generates pulses of
12...14 ps duration with 500 kHz repetition rate and0.8 μJ pulse energy at 263 nm wavelength. This should
provide sufficient pulse energy for generation of buncheswith 1 nC charge using caesium telluride photocathodes.
Due to two active modelockers in the laser oscillator, thelatter operates in tight synchronism to the RF master
oscillator of the linac.
The laser consists of a short-pulse oscillator, a pulse
picking Pockels cell, a regenerative amplifier and awavelength conversion unit. The latter converts theinfrared laser radiation to the ultra-violet (UV). This unit
turns out to be a particularly critical element of such aphotocathode laser driving a RF gun in CW mode.

signal, while the second one is an electro-optical phasemodulator for 1300 MHz. A detailed description how to
operate several modelockers in a single cavity can befound in [2] and the references therein.

INTRODUCTION
Photo injectors within RF guns are important for FELs,
since they provide an efficient means for generating highdensity electron bunches with low emittance. Most of theexisting photo injectors are operated in pulsed or in burst
mode.
At the FZ Rossendorf a superconducting RF gun isbeing developed [1], which needs an appropriate laser for
illumination of the caesium telluride photocathode. Thislaser should deliver pulses of 500 kHz repetition rate at awavelength within the range of 260 to 270 nm. The
desired bunch charge of 1 nC demands a UV pulse energy
in the order of 0.5 to 1 μJ. The present paper describes a
first setup for a suitable laser system.

LAYOUT OF THE LASER
Fig. 1 shows the general scheme of the laser system,
which consists of the following main building blocks:• the laser oscillator,• a pulse picker,• a regenerative amplifier,• a wavelength conversion stage.
The laser oscillator generates the initial picosecond
seed pulses. Its Nd:YLF laser rod is pumped by two fibercoupled laser diodes of 805 nm wavelength. Modelocking
for generation of short picosecond pulses is accomplishedby two active modelockers. One of them is a standard
acousto-optic modelocker driven with a 27.08 MHz RF#

will@mbi-berlin.de564

Figure 1: Optical scheme of the present photocathodelaser.

The oscillator generates a CW pulse train of 54.16 MHz
repetition rate and provides a single-pulse energy of
0.05 μJ. Since the signals for the active modelockers arederived from the electronic RF master oscillator of thegun, the laser pulses are synchronized with an accuracy of
about 1 ps.
A subsequent electro-optic pulse selector reduces thehigh repetition rate of the pulses from the oscillator to thedesired value of 500 kHz. This pulse train is further
amplified by a regenerative amplifier (regen). The regenis based on a folded resonator with 25 ns round-trip time.

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany
In addition to the diode-pumped Nd:YLF laser rod, it
contains two BBO Pockels cells. The first one switches
the laser pulse from the oscillator into the cavity of theregen. Subsequently, this pulse performs 14 round trips in
the resonator and is thereby amplified to an energy of
8.5 μJ.

THE WAVELENGTH CONVERTER
After switching the amplified pulses out of theresonator with the second Pockels cell, they are directed
towards the wavelength conversion stage. This stage
contains two consecutive nonlinear frequency doubling
crystals that convert the infrared laser pulses of 1053 nm
wavelength to the ultra-violet (263 nm wavelength).
The general scheme of this conversion unit is similar tothe one used in the photocathode lasers of FLASH and
PITZ. At first, a 12 mm long LBO crystal converts thepulses to green light. A further 8 mm long BBO crystal
generates from this the UV output pulses
It turns out that both, the energy of the generated UV
pulses as well as the profile of the UV beam depend in ahighly sensitive way on the size of the beam waist in the
BBO crystal. Tab. 1 as well as Fig. 1 show the results ofappropriate measurements done for four different
diameters of the beam in this crystal. Although thehighest output energy of 0.83 μJ is achieved for thestrongest focusing down to a diameter of 260 μm, thisleads to a non-circular beam profile.
On the other hand, the most homogeneous output beamthat largely maintains the original circular cross section is

THPPH006

obtained when the beam diameter in the BBO crystal islarger. The optimum in this respect amounts to 703 μm.
Unfortunately, this is accompanied by a drop of the laser
intensity in that crystals by a factor of two, and only asmaller portion of the green light is converted to the UV.
Since the conversion process is now operated far fromsaturation, the energy stability becomes much worse andwe typically obtain a pulse energy between 2 and 4 μJ.
Table 1: Dependence of the resulting UV pulse energy
on the focussing condition at the BBO crystal
Diameter of the beam
waist [μm] in the BBO
crystal
260
352
527
703

Measured output energy[μJ] of the UV pulses
0.83
0.71
0.49
0.45

Although the average power of the CW laser incomparison to the pulsed lasers at FLASH and SHARP(table 2) is significantly larger, its peak power is at least
one order of magnitude less. This is reflected by themeasured peak intensity in the UV. So, the abovemeasurements show, that the present design of the
wavelength converter cannot be used together with thephotocathode laser for a CW gun without substantial
modification.

Week focussing into BBO:
– Low UV yield+ Nice, circular UV beam

Strong focussing into BBO crystal:+ Highest UV yield– Non-circular UV beam
beam Ø = 260 μm
LBO

beam Ø = 703 μm

BBO

LBO

BBO

e n e rg y o f th e UV pu lse s[ μ J]
1,0
0,8
0,6
0,4
0,2
0,0
1

2

3

4

Figure 2: Intensity profile of the UV output at four different sizes of the focussed beam diameter in the BBO crystal(from left to right: 260, 352, 527 and 703 μm).

FEL Technology

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Proceedings of FEL 2006, BESSY, Berlin, Germany

In order to still reach a reasonable conversion efficiency,
the laser radiation must be stronger focused into theconversion crystals. This, in turn leads to a significant
perturbation of the beam profile due to the limited
acceptance angle as well as due to the walk-off between
green and UV light in the BBO crystal.

[2] I. Will, G. Koss, I. Templin, The upgradedphotocathode laser of the TESLA Test Facility,
Nuclear Instruments and Methods in Physics research
A 541 (2005), pp. 467-477.

Table 2: Comparison of the pulse parameters of thephotocathode lasers at FLASH/PITZ and at the FZ
Rossendorf
ELBE
ELBE
FLASH,(f = 0.5(f = 13
PITZ
MHz)
MHz)
pulses per s

0.008·106

0.5·106

13·106

pulse energy
(UV)

20 μJ

1 μJ

0.08 μJ

pulse duration

20 ps

20 ps

4 ps

average UV
power

0.16 W

0.5 W

1W

peak intensity
(UV)

1

0.05

0.02

CONCLUSION AND OUTLOOKFrom the above described measurements follows, thatthe photocathode lasers for RF guns in CW mode should
be set up for the shortest pulse duration possible. This
would yield better conversion efficiency to the UV at thesame laser pulse energy. Since even sub-picosecond
lasers with an average power larger than 10 W exist, thelower limit for the pulse duration is determined by spacecharge effects in the RF gun. Too short pulses however,will lead to an increased longitudinal emittance of theelectron beam.
Further work is mainly required to develop an
improved wavelength conversion unit to end up withreasonable conversion efficiency and simultaneously anearly circular profile of the UV laser beam. A possible
solution that is presently investigated at the MBI might bebased on cylindrical lenses for focusing the beamdifferently in horizontal and vertical direction.
Compensation of the walk-off between fundamental andharmonic wave that occurs in the crystals is anotheroption.

ACKNOWLEDGEMENT
This work was supported by the German Ministry for
Edjucation and Science, contract no. 05 ES4BM1/1 and
05ES4 BR1/8.

REFERENCES[1] http://www.fz-rossendorf.de/pls/rois/Cms?pNid=604

566

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THPPH007

1ST RF-MEASUREMENTS @ 3.5-CELL SRF-PHOTO-GUN CAVITY IN
ROSSENDORF
A. Arnold#, H. Buettig, D. Jannsen, U. Lehnert, P. Michel, K. Moeller, P. Murcek, Ch. Schneider,
R. Schurig, F. Staufenbiel, J. Teichert, R. Xiang, FZR, Dresden, Germany
A. Matheisen, B. v. d. Horst, DESY, Germany
J. Stephan, IKS, Dresden, Germany
W.-D. Lehmann, IfE, Dresden, Germany
T. Kamps, D. Lipka, F. Marhauser, BESSY, Berlin, Germany
V. Volkov, BINP, Novosibirsk, Russia
Abstract
At the Forschungszentrum Rossendorf the development
and the setup of the 2nd superconducting radio frequency
photo electron injector (SRF-Photo-Gun) is nearlycompleted. In this report we present the results of thecavity treatment. The warm tuning was carried out
considering pre-stressing and the tuning range of both
tuners (half cell and full cells). The optimal antenna
length of the main coupler and both fundamental pickups
were determined by practical external Q studies.
Furthermore the characteristic tuning curves of the choke
filter and both HOM filters were simulated, measured andtuned at the pi-mode frequency. The preparation (etching
and rinsing) and the vertical cold test were done at DESY.

INTRODUCTION
For future FEL light sources and high energy linear
accelerators a high current electron gun with highbrilliance is absolutely essential. Thus, an innovative
superconducting RF photo injector (SRF gun) is underdevelopment at the Forschungszentrum Rossendorf(ELBE), which is a collaboration of BESSY, DESY, MBI
and FZR and supported by the European Community.
Table 1: rf cavity parameters calculated with MWS©
normalized to 50MV/m peak axis field
stored energy U
32.5 J
quality factor Q0
1x1010dissipated power Pc
25.8 Wgeometry factor G
241.9 Ω
acceleration voltage Vacc
9.4 MV
acceleration gradient Eacc
18.8 MV/m
2
1.72x1012 Ω
shunt impedance R = V / 2 Pa

Ra/Q0
Epeak/Eacc
Bpeak/Eacc

accc

166.6 Ω
2.66
6.1 mT/(MV/m)

This gun allows continuous wave operation at anenergy of 9.4 MeV and an average current of 1 mA. It cangenerate short pulses and high-brightness electron beams,
as known from the conventional photo-injectors.
Moreover, the use of the superconducting cavity allows

cw-mode operation and thus high average currents. Table
1 shows some simulated rf cavity parameters.
The current progress of this project is presented in [1].
This paper deals with the treatment of the cavity itself,
one of the main parts of the SRF-Gun. Fig. 1 shows aschematic of its design which is described more in detailin [2].

Fig. 1: cross section of the cavity design.

CAVITY WARM TUNING
In order to get the right field distribution and theaccurate frequency at operation inside the cryostat, one
has to consider different tuning parameters.
Table 2: evaluation of the estimated frequency @ 300K
operating frequency @ 2K
cool down shrinking (measured @ ELBE)
50μm BCP @ DESY (simulated)pre-stressing half cell (measured)pre-stressing three TESLA cells (measured)required frequency @ 300K

1300.0 MHz- 1.97 MHz+ 0.55 MHz+ 0.10 MHz+ 0.22 MHz
1298.9 MHz

The correct frequency at room temperature mainly
depends on cool down shrinking, additional chemicaltreatment and pre-stressing of both cavity tuners. Thesetuners permit an axial deformation of ±400μm and±500μm for the half cell and the three TESLA cells,
respectively. The induced frequency shifts have beentaken into account. Thus, the estimated tuning frequency
follows from Table 2.
Table 3: field detuning caused by pre-stressing half cell
Gun Cell TESLA1 TESLA2 End Cell
detuning
-7.3%
-1.8%
+1.4%
+3.1%
axis field________________#a.arnold@fz-rossendorf.de

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Proceedings of FEL 2006, BESSY, Berlin, Germany

A non-negligible detuning of the π-mode field, as
shown in Table 3, is caused by pre-stressing of the halfcell. This measurement has to be considered inversely by
pre-tuning to obtain the right field profile in the cryostat.

room temperature. As shown in equation 2 one has tomeasure incident and reflected power at the input port, thetransmitted power at the main coupler as well as theunloaded quality factor of the cavity.
Qext =

Q0

β ext

with

βext =Pt
Pi − Pr − Pt

(2)

The results presented in Fig. 3, point to the best
coupling at a distance of 46.4 mm from axis. An
additional calculation, using the results of MWS©simulations with different boundary conditions as shownin [4], gives a similar performance.

TUNING HOM-COUPLER

Fig. 2: measured vs. simulated π-mode field profiles
before and after tuning.
Based on these target values, the tuning process was
realized as presented in [3]. It succeeded in the measured
field profile shown in Fig. 2 and met the calculated
requirements.

EXT. Q STUDY MAIN-COUPLER
In order to maximize the rf power transfer fromklystron to the electron beam, it is absolutely necessary tomatch the coupling. The applied Rossendorf main coupler
is not adjustable, thus the antenna is optimized for
maximum beam power with an external quality factor of:
Qext =

Q0= 2.7i107
1 + Pbeam PC(1)

We use the welded DESY TTF II HOM-couplers. Dueto the asymmetric design caused by the cathode and its
cooling support, both couplers are welded to the coupler
section at the end of the beam tube. To estimate theprecision achieved by trap circuit tuning, we measured theexternal quality factor at the π-mode frequency versus
tuning displacement and frequency shift. To preventcrosstalk it is necessary to place the input antenna probe
at the opposite side of the HOM couplers. The result ispresented in Fig. 4. It is obviously hard to get a better
external quality factor than Qext=1011. In that case lessthan 10% of the dissipated power is transmitted out ofeach HOM-coupler.
-0,09

-0,06

displacement from optimum in mm
-0,03
0,00
0,03
0,06

0,09

0,12

reachable tuning precision

1E12

1E11

pullingpushing

Qext
1E10

MWS simulation
measurement
10

8

1E9

+

Qext

-20
10

7

optimal distanceto axis = 46.4 mm

-15

-10

-5
0
5
10
frequency shift in MHz

15

20

25

Fig. 4: external quality factor vs. detuning from best πmode suppression.
10

6

TUNING CHOKEFILTER
30

35

40

45

50

55

distance antenna tip to axis of rotation in mm

Fig. 3: external quality factor vs. antenna length.
The determination of the suitable distance between
antenna tip and axis of rotation is done by an additional
probe antenna added at the opposite side of the cavity at

568

The choke filter is situated next to the first gun cell anddescribed more in detail in [5]. It prevents the leakage ofRF power through the coaxial line out of the cavity whichis caused by the cathode and its coupling to the gun cell.
The filter is designed as a coaxial trap filter. Its band passfrequency will be adjusted during the assembling of thecryostat. To estimate the transmitted power, we measured

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

the external quality factor versus detuning of the choke
cavity by crushing and stretching. For this purpose anantenna probe with the same diameter as the original
cathode was used. Thus the power behind the choke filter
depending on the dissipated power through the walls canbe measured (Fig. 5).

RS =

G
Q0

THPPH007

G = 241.9Ω

with
Δ

1 −
RS = AS iω 2 i e k T + Rres
T
i

für

(3)

T < TC / 2(4)

Based on the BCS-theory the surface resistance canalso be calculated analytically. Fitting the measured data
points by using eq. 4 leads to the following material
parameters:
AS = 2.42i10−15

Ωi° K
Hz 2

;

Δ = 1.53meV ;Rres = 3.43nΩ

T in K4,5

4,0

RS in nΩ

5,0

3,5

3,0

2,5

2,0

1,5

1,0
1E11

Q0 vs. Temp.
surface resistance RS=G/Q0
exponential fit based on BCS

Fig. 5: assembly to measure π-mode suppression.

1E10

u100

As a result one gets a tuning curve shown in Fig. 6.
Because of mechanical tolerances during the assemblingof the cryostat, it is hard to improve the accuracy better
than ±100 microns. Within this range, the external quality
factor is better than Qext=1012 and the transmitted power
behind the choke is less than 1% of the dissipated power.
An additional MWS simulation yielded comparable
results.
displacement from optimum in mm ∗
-1,0
1E14

-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

reachable tuning precision

Q0
1E9
10

Rres
1E8
2

3

4

5

6

7

8

TC/T

Fig. 7: surface resistance and unloaded quality factor
versus temperature.

Qext
1E13

In view of the measured, unloaded high quality factor
Q0(@1.8K)=3x1010 and the calculated low residual
resistance of Rres=3.4nΩ the preparation of the cavity
proceeded well.

stretchingcrushing

0,5

starting x-ray
Q0

0,4

1E11

peak axis-field

first Q-switch
0,3

1E10

-10

-8

-6

-4

-2

0

2

4

6

8

X-ray in mGy/min

1E12

10

frequency shift from optimum in MHz

second Q-switch

Fig. 6: external quality factor vs. choke filter detuning
measured by frequency shift and deformation.

1ST VERTICAL COLD TEST
Following the tuning procedures the cavity was
prepared at DESY Hamburg by buffered chemical
polishing (40μm BCP) and high pressure rinsing (HPR).
Afterwards the cavity was tested in a vertical cold test, as
described in [6]. During the cool down from 4.4K to 1.6K
the unloaded quality factor was measured at low rf power(Fig. 7). The illustrated surface resistance follows fromeq. 3 and the numerical calculated geometry factor G.

FEL Technology

0,2

0,1

limited by FE
and quench
1E9

0,0
0,0

10,0M

20,0M

30,0M

40,0M

50,0M

Epeak in V/mFig. 8: Q0 vs. peak axis field Epeak @1.8K.
Another matter of substantial interest is the Q vs. E
chart. The corresponding measurement also takes place at
DESY. In order to get comparable values, Q0 is plottedversus peak axis field in the TESLA cells (design value

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Epeak=50MV/m). Furthermore the radiation caused byfield emitters is included into the same chart. As shown in
Fig. 8 field emission started early and the quality factor
decreases. Further increasing of rf power results in strong
field emission and two Q-switches, which are probably
caused by thermal breakdown at activated field emitters.
After the second Q-switch the field was limited by
quench. Especially the behaviour the Q-switches are most
likely due to defects in the bulk niobium or to surface
pollution. This might be induced by the hardly cleanablechoke filter. Because of the narrow cathode feed throughbetween choke filter and gun cell, direct cleaning of thefilter cell wasn’t feasible. Furthermore contaminatedwater runs out of it into the cavity which leads into
polluted surface.

CONCLUSION
So far all measurements and tuning procedures yield
acceptable results. In the next steps an improved HPR and
BCP treatment will be established to achieve the designed
peak field. Nevertheless the reached field of
Epeak=39MV/m and the high quality factor of Q0=1.5x1010
demonstrates first of all the proper design of the gun
cavity.

570

ACKNOWLEDGEMENT
This work is supported by the European Commission
within the framework of the CARE project, EU contract
number RII3-CT-2003-506395.

REFERENCES[1] D. Janssen , et al., “progress of the Rossendorf SRF
Gun project”, proc. of EPAC 2006, Edinburgh, UK.
[2] J. Teichert, et al., “a superconducting photo-injector
with a 3.5-cell cavity for the ELBE linac”, proc. of
EPAC 2004, Lucerne, Switzerland.
[3] A. Arnold, et al., “field profile measurements of the
3½ cell SRF Gun”, proc. SRF Workshop, Ithaca,
USA, 2005.
[4] P. Balleyguier: “External Q studies for APTT SCCavity Couplers”, CEA/DPTA, Bruyères-le-Châtel,France.
[5] P. v. Stein, internal report, FZR-227, Forschungszentrum Rossendorf, 1998.
[6] Jens Knobloch: Basic Concepts of Measurements
Made on Superconducting RF Cavities, Laboratoryof Nuclear Studies, Cornell University, August 1991.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH008

HIGH PEAK CURRENT DESIGN OF A SUPERCONDUCTING CAVITY
FOR A SRF PHOTOINJECTOR
D. Janssen, FZ-Rossendorf, Dresden, Germany, F. Marhauser, BESSY, Berlin, Germany
V. Volkov, BINP, Novosibirsk, Russia.
Abstract
A 1.5-cell cavity for a superconducting RF gun has
been designed and a magnetic RF mode for emittancecompensation is applied. For a peak current of 125A atransverse emittance of 1.8 mm mrad has been obtained.

INTRODUCTION
In collaboration between BESSY, DESY, FZR, MBI
and BINP a 3½-cell superconducting RF electron gun is
under development. The status of the project and theprogress obtained is reported on this conference. The
motivation for the design of a new gun cavity is the
proposed FEL project at BESSY. This FEL requires abunch charge of 2.5 nC with transverse slice emittances
around 1.5 π mm mrad. In the following we will discuss
the design of a 1½-cell cavity with a frequency of 520
MHz for the accelerating mode (TM mode) and1560 MHz for the magnetic mode (TE mode). The designof a 1½ cell superconducting cavity with a frequency of
1.3 GHz has been also reported in [5].

DESIGN CONSIDERATION USING THE
PILLBOX MODEL
In order to find some general rules for the cavity
design, we will discuss a simple pillbox model, where thefrequencies and RF fields are known analytically.

Figures of merit
In order to avoid a quench of the cavity, the maximum
magnetic field on the cavity surface should be clear below
180 mT. Otherwise an optimal beam dynamics needs
large electric and magnetic fields on the cavity axis. So
the expressions

F nTmMl =

F0TM
ml [

Ez

(r = 0)Bz(r = 0), F 0TmEl =m ax
B s nm l
B s 0mma lx

m ax
nm l

MV / m
]
mT

l=0
l=1

m ax
0ml

m=1

m=2

m=3

0.587
0.351

0.587
0.502

0.587
0.543

are essential parameters for the quality of the cavity. For apillbox with length L and radius R one obtains:
Table 1: Figures of merit of the TM mode for R = L
From the first table follows, that at the surface limit of
180 mT the pillbox has an accelerating field of
105 MV/m! Therefore our cavity design should be as
close as possible to the pillbox geometry. The main

FEL Technology

difference between a pillbox and a realistic cavity cell isthe beam tube. In order to minimize the influence of thebeam tube on the RF field of the cavity cell, the ratio of
the cell to the tube radius should be large. The lower limitof the beam tube radius is fixed by wake field effects ofthe bunch charge. Therefore the cell radius should be aslarge as possible. This radius is inversely proportional tothe cell frequency, so we fix the frequency of the TM
mode to 520 MHz, which is the TESLA frequency
divided by 2.5.
Table 2: Figures of merit of the TE mode for
R/L ≥ J1

π l / ( J 0 ( qm ) qm ) , J1 ( qm ) = 0

F0TE
ml

m=1

max

m=2

m=3

l=1
2.48
3.33
4.00
The second table shows that the axial magnetic field isenhanced when increasing the radial node number for agiven surface field. Therefore a high frequency TE mode
should be preferred.

Third order effects
The power expansion of radial RF field components
with respect to the radius r starts with a linear term and isfollowed by third order terms. These third order terms
produce an increase of the transverse beam emittance. In
the pillbox cavity for the TM modes with l = 0 the thirdorder terms are zero. For the magnetic TE modes the ratioof the third order term divided by the first order term isgiven by

( B z ''' +ω 2

2
B z ')⎛ q⎞c2(1)= ⎜ m ⎟Bz '⎝ R ⎠Therefore the nonlinear effects increase quadratic withincreasing node number m of the TE mode and decreasing
radius R of the cavity cell. From this point of view thegun should work at the lowest TE mode frequency.

Comparison of the TE mode with a static
magnetic field
Neglecting terms in r2 in the equation of motion for anelectron in the RF field of the TE mode the following
equations are obtained:2eB z, r '' = − e B z 2 r(2)ϕ' = −2mγ
4γ 2These are the same equations as in the static magnetic
field. Assuming β ≈ 1 we can replace the time571

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Proceedings of FEL 2006, BESSY, Berlin, Germany

dependence in the RF field by z/c and calculate the focal
distance of the corresponding magnetic lenses.
∞
z
1
e2
=
Bz 2 dz , Bz = b( z ) sin(ω + ϕ0 )2 2 2 ∫
c
f 4m c γ −∞(3)

In this case the focal distance is a function of the phase
ϕ0 of the TE mode. For the case of a pillbox cavity weobtain:co s(α π + 2ϕ 0 ) ⎞
1
e2
L 2⎛π
=
B 0 ⎜ + sin (α π )
⎟
2 2
2 2
f
4m c β γ π
4α (α 2 − 1) ⎠
⎝ 4

α =

⎛ qm L ⎞⎜⎟⎝ π R ⎠

2

+1

(4)

For α = 2,3, … the focal distance is independent of φo andfor α =1/2 , 3/2, …. we have the maximal phasedependence. These limiting cases can be realized
numerically also for realistic cell geometry.
The emittance compensation in a RF gun is based on
the focussing of electrons inside a magnetic field.
Therefore the quotient of cell radius and cell length
defines the phase dependence of the focal distance and thephase dependence of the emittance.

Figure 2: Cavity shape and magnetic field distribution of
the TE mode.
case it is meaningful to minimize the emittance withrespect to this phase. The cell geometry and the field
distribution of the gun are given in Fig.1 and Fig. 2
respectively.
Fig. 3 shows the fields on the cavity axis.

CAVITY DESIGN AND RF FIELDS
As mentioned in the first section, the TM mode
frequency of our gun cavity is 520 MHz. At thisfrequency the beam energy of a 1½-cell cavity with
Epeak = 30MV/m is already greater 10 MeV. The cell radii
are determined by the TM frequency and the field
amplitudes on the cavity axis. We place the TE mode in
the second cell. After this the phase slippage of the TM
mode and the TE mode frequency define the width of thecells. As discussed in the previous section, the TE
frequency can be defined by different arguments. In thiscalculation the frequency of 1560 MHz is used. Thismode has the radial node number m = 2 and the field ratio
Bzmax(r=0)/Bsmax is 2.69. Furthermore, the integer value of
the TE/TM frequency ratio allows the operation of the RF
gun with the same TE - phase φo for each bunch. In thisFigure 3: Axis fields of the cavity.

FIELD AMPLITUDES
The magnetic surface fields of the TM and the TE
mode are perpendicular to each other. Therefore we haveto evaluate the vector sum of both surface fields tocompute the limiting field. Table 3 lists the maximal field
limits used in the calculations. They are clearly below thecritical limit. In Fig.4 the two surface fields and the sumof both fields are shown.
Table 3: Maximum axial and surface field values

Figure 1: Cavity shape and electric field distribution of
the TM mode.

572

field
Ezmax
Bzmax
Bsmax(TM)
Bsmax(TE)
Bsmax

unit
MV/m
mT
mT
mT
mT

value
57
363
130
118
130

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH008

TESLA-cavities have been combined to one section.
Typically for 1 nC bunch charge the reasonable laser
pulse length is in the order of Lt =20 ps regarding spacecharge effects arising just at the cathode. To mitigate theenhanced space charge at 2.5 nC the laser pulse length
could be further increased sacrificing some longitudinalemittance. First without the booster linac we have studied
the behaviour for Lt = 20 ps resulting in a minimumtransverse emittance of ~1.8 π mm mrad at a distance of~5.3 m behind the photocathode for Bzmax = 363 mT as
shown in Fig. 5.

Figure 5: Dependence of the projected transverse
emittance on the axial TE mode amplitude (position
behind cathode z = 5.3 m, laser spot radius 1.25mm).

Figure 4: Magnetic surface fields in dependence on thesurface coordinate s, Bs =(Bs _ TM )2 + (Bs _ TE)2 .

LASER PULSE SHAPE AND THERMALEMITTANCE

With these settings however one operates apart fromthe usual emittance compensation in the drift. Thus when
including the booster we observed that the beam can not
be matched according to the so-called invariant envelope(I.E.) [3]. Instead the beam is strongly focussed within the
linac due to RF-focussing and without measures tends toextend behind the focal point.

In a RF photo cathode gun the laser pulse determines
the bunch shape at the cathode. In the present calculations
a temporal flat top laser pulse profile up to Lt = 40 ps anda rise and fall time of 2 ps have been used. The radial
distribution is uniform. At a laser wavelength of 260 nm
the electrons leave the cathode with a thermal energy of
1 eV isotropically in the whole space. This seems to be a
set of realistic parameters [1].

RESULTS OF TRACKINGCALCULATIONS
Tracking studies using ASTRA [2] have been
performed for the gun cavity followed by a drift space
and a booster linac section comprising 3 x 4 1.3 GHz
standard 9-cell TESLA cavities to investigate emittanceconservation. A Simplex routine has been utilized for a
multi-parameter optimization. Hereby the transverse
emittance at the linac exit has been minimized by varying
the laser spot size at a given laser pulse length Lt and theoperational parameters of the RF gun (TM and TE mode)and booster cavities with Eacc = 20 MV/m in maximum
for the latter. To reduce the computation time four

FEL Technology

573

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 6: Evolution of the projected transverse rms
emittance (top) and rms beam size (bottom) through thelinac for Lt = 20 and 40 ps respectively (30000 particles).
The projected emittance can not be further minimized
but rather stays constant. This is illustrated in Fig. 6
showing the evolution of the projected transverse rms
emittance (top) and rms beam size (bottom) for Lt = 20.
However the projected emittance is largely deluted bymismatched fringe particles which are responsible for theoscillations of the projected emittance within the linac
cavities. Actually the slice emittance as the figure of meritamounts to only 1.1 π mm mrad in average.
We then tried to match the beam to the booster byfollowing more closely the I.E.. This necessitates to adjust
the electric field of the gun according to Bzmax to balance
the repelling and focussing forces. Thus a typicalemittance compensation accompanied by an emittanceoscillation with a double emittance minimum in the drift[4] can be produced. Holding the I.E. criterion in thismode of operation the minimum projected emittanceobtained for Lt =20 ps however is rather large (~4 π mmmrad). Moreover the accelerating fields in the first
TESLA-cavities would be in the order of Eacc = 40 MV/m.
However, the situation relaxes once the pulse length isfurther increased. This has been done using Lt =40 ps in anext step as shown in Fig. 6 as well. Here a projectedtransverse emittance of only 1.5 π mm mrad is achieved.
As more particles follow the I.E., the average slice
emittance is ~1.4 π mm mrad only marginally below the
projected emittance.
Table 4 and 5 summarizes the optimized parametersettings and achieved results at the booster exit (z = 24m)
for Lt = 20ps and Lt = 40ps respectively. Albeit the results
are not regarded as an overall optimum yet, the required
specifications of the BESSY FEL can be well fulfilled.
Table 4: Parameter settings for the photocathode laser, RF
gun (TM and TE mode) and booster cavities respectively
parameter settings
laser
flat toprise/fall time
spot radius
thermal energy
thermal emittanceRF gungun TM field (max.)
beam energy
magnetic TE field (max.)
peak surface fieldbooster cavities
acc. field (cavities #1-4)
acc. field (cavities #5-8)
acc. field (cavities #9-12)

574

unit

value

ps
ps
mm
eV
π mm mrad

20
2
1.2
1
0.69

40
2
1.35
1
0.77

MV/m
MeV
mT
mT

54.8
9.8
354
128

54.6
9.7
360
127

MV/m
MV/m
MV/m

10.5
19.9
17.6

7.5
20
17.4

Table 5: Achieved beam parameters with a bunch chargeof 2.5 nC at the exit of the booster linac (z = 24m)
achieved parameterslaser pulse length (z = 0)
normalized transverse
projected rms emitttanceaverage slice emittancetrans. rms beam size
long. rms beam size
average kinetic energy
long. rms emittancecorrelated energy spread

unit
ps

value
20
40

π mm mrad21.5

π mm mrad

1.1
1.45
2.7
218
1438
129

1.35
0.37
3.6
204
3250
305

mm
mm
MeV
keV mmkeV

DISCUSSION AND SUMMARY
For two different lengths of the laser pulse it has beenshown, that the design parameter of the injector for the
BESSY FEL can be obtained, using a 1½-cellsuperconducting RF gun. In the calculation a maximal
surface field of 130 mT has been assumed. This value
corresponds to accelerating field strength of ~28MV/m ina TESLA cavity. For cavity frequencies in the order of 1.3
GHz this value is standard, but the frequency of theaccelerating mode in the gun cavity is 520 MHz. For thisfrequency the maximal surface field, which can beobtained, is an open question.
In the present calculation the cathode has a flat surface,which is inside of the back wall of the cavity. In thissimple arrangement we have near the cathode no
focussing RF forces and possible wake fields from thecavity surface are absent.
In analogy to [6] we plan to place a Cs2Te cathode into
the superconducting cavity. For this material and λlaser =260 nm a quantum efficiency of 5% is realistic. In thiscase the bunch charge of 2.5 nC demands a laser pulse
energy of 0.24 μJ.

ACKNOWLEDGMENT
The authors thanks Dirk Lipka (BESSY), Klaus
Floettmann (DESY) and the members of the SRF gun
project group for many helpful discussions.

REFERENCES[1] I. Will, MBI Berlin, private communication.
[2] K. Flöttmann, http://www.desy.de/~mpyflo/.
[3] L. Serafini, J. B. Rosenzweig, Phys. Rev. E, Vol. 55,
June 1996, 7565.
[4] M. Ferrario et. al., SLAC-PUB 8400, March 2000.
[5] J.Sekutowicz et al., Phys. Rev. ST Accel. Beams 8,010701 (2005).
[6] D.Janssen et al., Nucl. Instr. and Meth. A507 (2003)
34.

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH009

CRYOMODULE AND TUNING SYSTEM OF THE SUPERCONDUCTING
RF PHOTO-INJECTOR*
J. Teichert#, A. Arnold, H. Buettig , R. Hempel, D. Janssen, U. Lehnert, P. Michel, K. Moeller, P.
Murcek, C. Schneider, R. Schurig, F. Staufenbiel, R. Xiang, FZ Rossendorf, Dresden, Germany,
T. Kamps, D. Lipka, BESSY, Berlin, Germany, J. Stephan, IKS, Dresden, Germany,
W.-D. Lehmann, SGE, Dresden, Germany, G. Klemz, I. Will, MBI, Berlin, Germany.

Abstract
The designs and a report on the progress in construction
and testing of the cryomodule and the tuning system for
the SRF gun are presented. The SRF gun project, acollaboration of BESSY, DESY, MBI and FZR, aims at
the installation of a CW photo injector at the ELBE linac.
The cryostat consists of a stainless steel vacuum vessel, awarm magnetic shield, a liquid N cooled thermal shield,
and a He tank with two-phase supply tube. A heater pot in
the He input port will be used for He level control. The
10 kW power coupler is adopted from the ELBE module.
A cooling and support system for the NC photo cathodehas been developed and tested. It allows the adjustment of
the cathode with respect to the cavity from outside. The
cryomodule will be connected with the 220 W He
refrigerator of ELBE and will operate at 1.8 to 2 K. The
static thermal loss is expected to be less than 20 W.
Two tuners will be installed for separate tuning of thethree TESLA cells and the half-cell. The tuners are dual
spindle-lever systems with step motors and low-vibration
gears outside the cryostat. Functionality, tuning range andaccuracy have been tested in cryogenic environment.

INTRODUCTION
Superconducting radio frequency (SRF) acceleration
technology is well established for electron linacs withconsiderable progress in acceleration gradient during thelast years [1]. The adequate SRF photo-injector was
already proposed in 1988 [2], but up to now such an
injector has not been operated at an accelerator. As
electron sources for SRF electron linacs, DC photoinjectors or thermionic injectors are in use for CW
operation or normal-conducting RF photoinjectors inpulsed mode. The RF photo-injectors deliver electron
beams of highest quality (short bunch length and lowtransverse emittance at high bunch charge). Its
combination with a superconducting cavity would further
allow CW operation. After a successful proof-of-principle
experiment with a half-cell cavity [3] a project for a SRF
photo injector has been launched in 2004. The goal of this____________________________________________* We acknowledge the support of the European Community-Research
Infrastructure Activity under the FP6 “Structuring the European
Research Area” programme (CARE, contract number RII3-CT-2003506395) and the support of the German Federal Ministry of Education
and Research grant 05 ES4BR1/8.
#
j.teichert@fz-rossendorf.de

FEL Technology

project, carried out in a collaboration of BESSY, DESY,
MBI and FZR, is to build a fully functioning SRF photoinjector for the ELBE accelerator. Beside the significant
beam quality improvement, the operation at ELBE willallow long term studies of important issues of SRF
injectors like low-temperature operation and lifetime ofphoto cathodes, or cavity quality degradation.
The design parameters of the SRF gun are presented inTable 1. The gun will be operated in three modes: thestandard ELBE FEL mode with 77 pC and 13 MHz pulse
repetition, the high charge mode for neutron physics at
ELBE and ERL studies (1 nC, 1 MHz), and the BESSY
FEL mode (2.5 nC, 1 kHz). A UV driver laser system forthese three operation modes is under development [4].
Beam parameter studies will be performed with a new
diagnostic beam line [5]. The ELBE mode is determinedby the two existing far infrared FELs which need 13 MHz
bunch repetition rate, as well as the maximum average
current of the ELBE accelerator. The high charge mode isessential for neutron physics experiments planned at
ELBE where time-of-flight measurements require 1 µs
pulse spacing without average current reduction. At thesame time, 1 nC is a typical bunch charge for new FEL
projects and state-of-the-art normal conducting RF photo
injectors (e.g. FLASH at DESY) where the beam
parameter should be measured and compared. It isplanned to study and optimize different emittancecompensation methods proposed for SRF guns, like adownstream magnetic solenoid, RF focusing with abacktracked and properly shaped photocathode, and RF
focusing with an additional TE mode [6] in a future
upgrade. For the soft x-ray BESSY FEL project [7] abunch charge of 2.5 nC is envisaged and the SRF gun will
be evaluated with respect to future application.

CRYOMODULE
The basic design for the SRF gun cryomodule wasadopted from the ELBE cryomodule [8] which contains
two 1.3 GHz TESLA cavities and is developed for CW
operation with 10 MeV per cavity at a beam current up to
1 mA. ELBE modules are in routine operation since 2001
at FZ Rossendorf and wide experience has gained forthese modules. The SRF gun cryomodule contains one 3½
cell cavity which consists of a half-cell with the normalconducting cathode in it and three acceleration cells withTESLA shape [9]. The envisaged acceleration gradient of
this cavity is 18.8 MV/m which corresponds to a

575

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Proceedings of FEL 2006, BESSY, Berlin, Germany

maximum axial peak field of 50 MV/m in the TESLA
cells. The geometry constant is 240 Ω and R/Q is 165 Ω.
For Q0 = 1x1010 and the gradient mentioned above a RF
power dissipation of 26 W is expected.

ELBE module. It contains a conical cold ceramic window
at 70 K in its coaxial part. The warm REXOLITE window
is in the waveguide.

Table 1: Gun design parameters and expected beamvalues for the planned operation modes
ELBE high charge BESSYmode
FEL
mode
RF frequency
beam energy
Operation
drive laser
Photocathodequantum efficiency
average current
pulse length
Repetition ratebunch chargetransverse emittance

1.3 GHz
9.5 MeVCW
262 nm
Cs2Te
>1 %
1 mA
5 ps
20 ps
13 MHz
[1MHz
77 pC
1 nC
1.5 µm
2.5 µm>2.5 %
2.5 µA
50 ps
1 kHz
2.5 nC
3.0 µmFig. 1 shows a section view of the SRF gun
cryomodule. The stainless steel vacuum vessel has acylindrical shape with 1.3 m length and 0.75 m diameter.
The vessel has flat plates on both sides and is designed as
short as possible in order to get a minimum length of thetransfer rod for cathode exchange, and on the beam line
side it is planned to install a solenoid magnet for
emittance compensation as close as possible. The He port
and the N2 port are on top on the right hand side. The
refrigerator delivers 4.5 K helium to the valve box, about
5 m before the cryomodule. There is the Joule-Thompson
valve for expansion. From the port the He flows through aheater pot and the two-phase supply tube into the chimneyof the He tank. For the cooling of the thermal shield,
liquid nitrogen is used. The 70 K shield consists of acylindrical Al sheet welded to two circular tubes filledwith N2. The liquid N2 tank in the upper part of themodule must be refilled after about 5 h from an outside
dewar. The liquid N2 is also used for the cooling of thephoto cathode stem. The photo emission layer, which is
Cs2Te, and the Cu cathode stem are normal conducting.
The heat load from the RF field into these parts, estimatedto be between 10 and 20 W, burdens the liquid N2 bath.
The cavity is passively protected against ambient
magnetic fields by means of a µ-metal shield, placed
between the 80 K shield and the vacuum vessel. The
shield is fabricated and its suppression of the earthmagnetic field was measured. The results are shown in
Fig. 2. In the region where the Nb cavitiy will be placed,
the residual magnetic field is below 1 µT which is thelimit during the cool-down [9].
The He tank is made of titanium. Three stainless steel
bellows are integrated for the two tuning systems and forthe manually tuned choke filter cell. The ten thin titanium
spokes support the He tank and allow the adjustment of
the cavity position. The spokes end in micrometer drives
and vibration dampers attached to the vacuum vessel. The
main power coupler is the 10 kW CW coupler of the576

Figure 1: Cut drawing of the SRF gun cryostat.

Figure 2: Measurement of the earth magnet field
suppression by the µ-metal shield.
From outside it is also possible to move the cathodesupport and cooling system which allows the adjustmentof the photo cathode with respect to the cavity. For thatreason, three rotation feed-throughs exist in the backsideplate of the vacuum vessel. Fig. 3 shows the design of thatsystem.
The main sources for the static heat leak are the coaxial
tube of the power coupler, the beamline vacuum tube andthe vacuum tube for the cathode exchange system (both
DN40), and the rotational drives of the two tuners. For allthese subsystems the design is similar to the ELBE
cryostat. Thus nearly the same static heat leak of less than
20 W can be expected.
The SRF gun will be installed in parallel to the existing
thermionic injector of the ELBE accelerator. The cryostat
will be connected with the existing 220 W He
refrigerator. A new helium transfer line with valve box
was assembled and tested in January 2006. Its design
allows the connection of the SRF gun cryostat without
warming up the other two ELBE cryomodules. The
cryostat can be operated down to 1.8 K but the standard

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany
operation temperature at ELBE is 2 K (31 mbar). In the
ELBE helium cooling system, the pressure stabilization is
performed with cold compressors located in the cool boxof the helium refrigerator. It will be performed for all
three cryostats together based on a pressure value in one
module. During operation of the two ELBE modules, itturned out that the common pressure stabilization worked
well for constant liquid helium flux to the modules. In
order to realize that, the total heat power from theelectrical heater in the module and the RF power
dissipation was hold constant by means of a feed-forward
control.

THPPH009

and the He tank. At the end, the ELBE tuner design was
modified essentially.
The tuner mechanism consists of a spindle with partly
left-hand thread and right-hand thread and two levers. Via
the threads and the lever system the rotational motion istransformed into a longitudinal motion performing thelength variation of the half-cell and the TESLA cells,
respectively. The use of two levers ensures that no axial
force is present on the spindle. The bearing point of theleverage system has no rotational parts. It consists of two
flexible links as it is shown in Fig. 4. The advantage is thelack of any hysteresis due to friction effects and bearing
clearance. The third flexible link is connected with amoving bolt which transfers the force to the parts of the
He tank joint to the end plates of the half-cell or the
TESLA cells. To allow the movement the He tank has
two bellows.

Figure 4: Lever and flexible link of the tuner.
Figure 3: The cathode alignment system.

TUNING SYSTEMSFor the SRF gun cavity a frequency tuning is needed
for the choke filter, the half-cell and the three TESLA
cells. The bandwidth of choke filter is comparably large.
Therefore a tuning during assembling in the warm stage issufficient. For the accelerating cells tuning is required
during operation. The half-cell on one hand and the three
TESLA cells on the other essentially differ in theirmechanical properties, especially in their stiffness.
Therefore it was decided to use two separate tuning
systems, one for the half-cell and one for the three
TESLA cells in common.
The tuner design is adopted from the ELBE
cryomodule dual spindle-lever tuning system [8]. Main
objectives are a sufficiently large tuning range, highresolution, a hysteresis-free and linear operation, long life
time and low cryogenic loss. But the requirements are lessrestrictive than for tuners in high-energy SRF linacs: Due
to CW operation a fast tuning for the compensation ofLorentz force detuning (LFD) with piezoelectric actuators
is not needed. This applies to active microphonics
compensation too, since for a bandwidth of about 100 Hz
and a moderate acceleration gradient up to about 20
MV/m, passive methods for microphonics reduction are
sufficient. Costs per unit and compactness are lessimportant too. On the other hand, the two tuners for the
SRF gun cavity have required a sophisticated mechanicaldesign due to many mechanical and cryogenic constraints
and the insufficient clearance at cathode side of the cavity

FEL Technology

The step motor driving the tuner spindle is outside thevacuum vessel. The fixed point is between the half-celland the first full cell where the star-like arranged plates of
the cavity are welded with the He tank. The motor motion
is transmitted by rotation feed-throughs and a two-stage
bellows coupling (the 70 K point is in between) to thespindle of the tuning system. The bellows compensate theshrinking offset and reduce the heat conduction. Bothtuning systems have the same design. They differ in thelever lengths only.
The frequency constants Δf/dL of the SRF gun cavity
were measured with the help of the warm tuning machinedeveloped at FZR [10]. The measurement results are 254
kHz/mm for the half-cell and 449 kHz/mm for the three
TESLA cells. These values belong to the change of the πmode frequency of the whole cavity, where the three
TESLA cells were unchanged in the first case, and thehalf-cell in the second. Simple numerical estimations withSUPERFISH assuming a smoothly and homogeneouschange of the surface contour give 674 kHz/mm for thehalf-cell and 625 kHz/mm for the TESLA cell tuning. The
large difference for the half-cell seems to be an effect of
the low stiffness of the end disk or of other weak areas
having low influence on the frequency.
For operating tests and parameter measurements a test
bench for the designed tuning system was built up. This
test bench consists of the liquid nitrogen dewar, theleverage of the tuner, a spring packet to simulate thecavity, and the equipment to produce the tuning force, toperform force and length measurements. The spring
packet was variable in order to simulate the half-cell andthe three TESLA cells, as well as to measure with577

THPPH009

Proceedings of FEL 2006, BESSY, Berlin, Germany

preload. For the three TESLA cells a spring constant of
9 kN/mm was taken [11]. The spring constant for the halfcell was assumed to be about three times higher. The
preloads were varied between zero and 9 kN. In
comparison to the final tuning systems the levers weremade of aluminium instead of titanium and the tests werecarried out with one lever only.
The results of the tuner test bench are summarized inTable 2. As expected, the tuning range became smallerwith 5 kN preload due do the elastic behaviour of theflexible link of the tuner. The hysteresis measured iscaused by the test bench mechanics itself. Fatigue effects
were not found.
Table 2: Measurements of the tuning ranges in the tuner
test benchtuning range for 2°
half-cell
TESLA cell
Lever range
tuner
tuner
without preload
436 µm450 µm
D = 0 N/mm
416 kHz247 kHzwith 5000 N preload
218 µm223 µm
D = 9000 N/mm
208 kHz122 kHz
Table 3 presents the properties of the two tuners for the
SRF gun including the test bench results. The limit in thetuning range is given by the maximum bending of theflexible links of ± 1.5°. The expected tuning ranges are
sufficient. By comparison, the tuning range in the ELBE
modules is 230 kHz [8]. The overall tuner resolution
given in the table are estimations taken from the ELBE
system. A complete 3D view of the SRF gun tuners withparts of the He tank and the cavity is given in Fig. 5.

Fig. 5: The two tuners of the SRF gun.

SUMMARY AND OUTLOOKIn the paper the design and the parameters of thecryostat and the cavity tuning systems for the 3½ cell SRF
gun are presented. Tests and parameter measurements ofthe tuners were carried out in a cryogenic test bench with
sufficient results. At present, the different subsystems ofthe cryostat are being assembled und checked. In autumn,
first vacuum and cryogenic test are planned. In parallel
the treatment and measurement of the niobium cavity is
carried out, following by the He tank welding. The

578

commissioning is envisaged with the cool-down and RF
tests beginning of 2007.
We would like to acknowledge the permanent supportof the ELBE crew (FWL) and the staff of the technicaldepartments (FWF) at FZ Rossendorf.
Table 3: Parameters of the SRF gun tuners
half-cell
TESLA
tuner
cell tuner
lever length
630.6 mm570.2 mmleverage
50.4
44.2
lever range
33 mm
30 mm
3.0°
3.0°
tuning range
0.7 mm
0.7 mm204 kHz404 kHzcavity frequency
178 kHz/mm 283 kHz/mm
constants Δf/dL
mechanical drive step
0.70 nm/step 0.62 nm/stepfrequency drive step
0.23 Hz/step 0.28 Hz/stepmechanical resolution
3 nm
frequency resolution
1 Hz
position of step-motors
warm, outside

REFERENCES[1] L. Lilje, et al., “High-Gradient Superconducting
Radiofrequency Cavities for Particle Acceleration”,
Proc. of EPAC 2006, Edinburgh, UK, 2006, p. 2752.
[2] H. Piel, et al., FEL 1988, Jerusalem, Isreal, 1988.
[3] D. Janssen, et al., “First Operation of aSuperconducting RF Gun”, Nucl. Instr. and Meth. A
507 (2003) 314.
[4] I. Will, et al.,” Photocathode Laser and its Beamline
for the Superconducting Photoinjector at the
Forschungszentrum Rossendorf”, this conference.
[5] T. Kamps, et al.,”Diagnostics Beamline for the SRF
Gun Project”, Proc. of FEL 2005, Stanford, USA,2005, p. 530.
[6] K. Floettmann, D. Janssen, V. Volkov, “EmittanceCompensation in a Superconducting RF Gun with a
Magnetic Mode”, Phys. Rev. Special Topics, AB 7
(2004) 090702.
[7] “The BESSY Soft X-ray Free Electron Laser”, TDR
BESSY March 2004, eds.: D.Krämer, E. Jaeschke,
W. Eberhardt, ISBN 3-9809534-0-8, Berlin (2004).
[8] J. Teichert, et al., “RF Status of Superconducting
Module Development Suitable for CW Operation:
ELBE Cryostats”, Nucl. Instr. and Meth. A 557(2006) 239.
[9] B. Aune, et al., “Superconducting TESLA Cavities”,
Phys. Rev. Special Topics, 3(2000) 092001.
[10] J. Teichert, et al., “.Progress of the Rossendorf SRF
Gun Project“, Proc. of FEL 2005, Stanford, USA,2005, p. 534.
[11] C. Pagani et al., “Improvement of the Blade Tuner
Design for Superconducting RF Cavities”, Proc. of
PAC 2005, Knoxville, USA, p. 3456.

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH012

DARK CURRENT COLLIMATION AND MODIFIED GUN GEOMETRYFOR THE EUROPEAN X-RAY FEL PROJECT
Jang-Hui Han∗ and Klaus Flöttmann, DESY, Hamburg, Germany

3GUN
0

10
5

8
size (mm)An rf field of 60 MV/m will be applied at the L-band
gun of the European X-ray FEL project. Such high rf gradient will allow to achieve a transverse emittance below
1 mm mrad for 1 nC electron bunches but will also produce a high dark current. The dark current generated in the
gun shows a comparable dynamics as the electron beams
because the same acceleration will be provided from thegun to the last acceleration module. The dark current fromthe gun might generate high radiation doses in the undulator and limit the long pulse operation of the SASE. To
minimize dark current before the first acceleration module,a modified design of a gun cavity and collimator is investigated. The beam dynamics for minimal transverse emittance is optimized with the present and the new designed
gun cavity and the resultant machine parameters are used
to understand the dark current behavior.

dark current seems to come from the boarder of the Cs 2 Te
film on the cathode plug [3]. The dark current has a larger
radius at the emission position and obtains a lower kinetic
energy through the gun than the beams. However, 1 nC
beams are focused over a longer distance due to the spacecharge force and the higher momentum than the dark cur-

10
15

6
4
2

Y (mm)

Abstract

20

0
0

0.5

1

25

1.5
z (m)

2

2.5

3

30
35

INTRODUCTION

40∗ jang.hui.han@desy.de

FEL Technology

45
0

10

20

30
X (mm)

4050

60(a) Dark current image and simulation
for the dark current from the cathode.
3GUN
0

4
3.5

5

size (mm)

3
10
15

2.5
2
1.5
1

Y (mm)The Free Electron Laser in Hamburg (FLASH) gun operates with a max rf field of about 44 MV/m at cathode. The
L-band Cu cavity with cylindrical symmetry is fed throughthe coaxial rf input coupler [1]. The photocathode is composed of a Mo cathode plug and a Cs 2 Te film on the plug.
The plug is a cylindrical rod with 16 mm diameter and theemissive film has typically 30 nm thickness and 5 mm diameter. The cathode has a high quantum efficiency (QE) of
the order of 1%. Such high QE relaxes the requirement forthe drive-laser producing photoelectrons from the cathode.
In August 2006, a long rf pulse of 800 μs has been applied into the gun cavity to produce 600 electron bunches
per rf pulse. The number of bunches was limited only by
the flat range of the rf pulse in the accelerator modules. In
the near future, the bunch train will be expanded to fill out
the rf pulse of the gun [2]. At the same time of the longrf pulse operation, the SASE lasing was also successfully
achieved with the 600 bunches.
One critical factor limiting the long bunch train operation is the dark current generated in the gun cavity. At theexit of the gun, the dark current is 0.2 ∼ 0.3 mA. Simulations of dark current trajectories show that only the darkcurrent emitted at the cathode area can escape from the gun
cavity and flow downstream. The dark current starting at
the cathode area is mostly released at an rf phase around90◦ , i.e. when the rf field is maximum. At the FLASH gun,dark current starting at the cathode has a similar size as theelection beams at the collimator position, 1.27 m downstream from the cathode (see Fig. 1). The inner ring-shape

0.5

20

0
0

0.5

1

25

1.5
z (m)

2

2.5

3

30
35
40
45
0

10

20

30
X (mm)

4050

60(b) Dark current and 1 nC beam image
and beam simulation.
Figure 1: Dark current and beam images taken at the screen
1.27 m downstream from the cathode. Machine parameters
for the nominal SASE operation are used. The simulationsin the small boxes have been made with ASTRA [4]. A
collimator is located at the same position as the screen. The
dark current from the cathode has a similar size as the 1 nC
bunch. Therefore, the dark current cannot be chopped withthe collimator efficiently.

579

Proceedings of FEL 2006, BESSY, Berlin, Germany

The XFEL gun will operate with 60 MV/m max rf field
for a lower beam emittance and 700 μs rf pulse length fora long bunch train [5]. The dark current generated in the
gun is an issue because the dark current might be very highdue to the high rf field. Extrapolating the measured darkcurrent level to gradients of 60 MV/m by means of theFowler-Nordheim equation yields dark current levels in themA range. This ignores conditioning effects. Moreover isa reduction of the dark current by improved cleaning techniques as dry-ice cleaning expected.
At FLASH a fraction of the dark current has a momentum as high as the electron beam [3]. As increasing the rf
field in the gun cavity, the optimum emission phase for thehighest momentum gain and the smallest transverse emittance is shifted toward 90 ◦ of the rf phase. At FLASHthe optimum emission phase is about 38 ◦ . When 60 MV/m
max field is applied to the FLASH gun cavity (type #1), theoptimum emission phase will be shifted to 45 ◦ . This meansthat a larger fraction of the dark current emitted around 90 ◦rf phase will overlap with the electron beam in the momentum spectrum.
In order to separate the momentum distribution of thedark current from the beam, the half cell of the gun cavity is elongated by 10 mm (type #2). The on-axis rf field
profiles of the two cavity types are shown in Fig. 2. The rf
field profile is calculated with SUPERFISH [6]. When thehalf cell is longer, the electrons have to start at an earlier
rf phase to gain the most effective acceleration through thecavity. The dark current starting around 90 ◦ will be too late
to be efficiently accelerated.

Beam dynamics
Machine parameters of the injector, including the gun
and the first acceleration module, are optimized for a minimum emittance (Fig. 3 and Table 1). When the half cellis elongated, the optimum emission phase is shifted toward580

type #1
type #2

40
20
0
-20
-40
-60
0

0.05

0.1

0.15

0.2

0.25

z (m)

Figure 2: On-axis rf field profile for two gun types.
0◦ . For cavity type #1, the optimum emission phase is 45 ◦ ,resulting in an rf field of 42 MV/m at cathode during emission. For cavity type #2, optimum emission phase is 31 ◦and the rf field during emission is 31 MV/m.
In photocathode rf guns, a strong rf field suppresses thebeam expansion due to the space charge forces during theemission of high charge density electron beams. Because
the emission field is lower in gun type #2, the initial beam
size at cathode need to be larger in order to reduce the spacecharge force.
The kinetic energy of the emitted electrons is assumed
to be 0.55 keV and an isotropic emission is assumed according to Ref. [7]. The kinetic energy of electrons emitted
from Cs2 Te cathode has been measured in laboratory condition with a very low electric field at cathode [8].
In a high rf field, a Cs 2 Te cathode changes its surface properties and the kinetic energy of the emitted electrons increases with the field strength [9]. For the caseof gun type #1, the kinetic energy of the emitted elec8
beam size for type #1
beam size for type #2
emittance for type #1
emittance for type #2

7
6
5

emittance (mm mrad)

XFEL GUN

60
rf field (MV/m)

rent. With the influence of the focusing solenoid, the size ofthe dark current and the beams are similar at the collimator(see the simulations in Fig. 1).
For a better efficiency, the collimator should be locatedmore downstream because the dark current is strongly overfocused. But, the collimator position is limited by the cryotank of the first acceleration module. The dark current
gets larger than beams as propagating downstream because
the dark current has a lower momentum than the beams.
This spreading dark current generates radiation doses at theaccelerator modules, the bunch compressor and the otherbeamlines. After the first acceleration module, the darkcurrent can get a kinetic energy of several tens MeV andpossibly produce neutrons and γ rays especially at the firstbunch compressor. Therefore, it is desirable to collimate
the dark current before the first module. This situation is,
however, significantly improved at the XFEL design parameters.

emittance (mm mrad) & size (mm)

THPPH012

4
3
2

1.8
type #1
1.6
1.4
type #2
1.2
1
0.8
0.6
0.4
0.2
0
-4 -3 -2 -1 0 1
z (mm)

2

3

4

1
0
0

2

4

6

8
z (m)

10

12

14

16

Figure 3: Rms beam size and normalized emittance evolution simulated with ASTRA. The simulation parameters are
summarized in Table 1. The transverse slice emittances at
z = 30 m are shown in the small box. The temporal profileof the electron bunches at z = 30 m is a hat-shape similar to
the initial distribution of the bunch, i.e. the temporal profileof the drive-laser.

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany
Table 1: Simulation parameters for two gun types.

a This initial distribution is determined by controlling thethree dimensional shape of the drive-laser at the cathode.
b Homogeneous distribution.
c Assuming the kinetic energy of emitted electrons to be
0.55 eV.
d Simulations include the acceleration with 8 × 9 cell
TESLA type cavities.
e 200 000 macro particles are used for the tracking simulation with ASTRA.
f At the center of bunch.
trons is 0.738 eV according to the emission model in
Ref. [9]. This kinetic energy rise and the field enhancement for photoemission increases the thermal emittance up
to 0.59 mm mrad. For the case of gun type #2, the kinetic
energy of the emitted electrons is 0.675 eV and the thermal
emittance is estimated to 0.69 mm mrad.

Dark current
With the machine parameters obtained with the beam optimizations, dark current has been simulated (Fig. 4). For
the two gun types, the same amount of dark current fromthe cathode is tracked with ASTRA. The inner structure of
the cavities and beam pipe with 35 mm diameter is considered as aperture.
When machine parameters for the beam optimization areused, the amount of the surviving dark current to the entrance of the first acceleration module is below 40% for
gun type #2 compared to the gun type #1 case. The over-

FEL Technology

count (arbitrary unit)

dark current
dark current with collimator
electron beam

0

1

2

3
4
5
momentum (MeV/c)

67(a) Gun type #1.
dark current
dark current with collimator
electron beam

count (arbitrary unit)

Parameter
Type #1
Type #2
Initial distributions of electronsa
transverseb
0.45 mm rms
0.55 mm rms
temporal (flat-top) 2 ps rise/fall and 20 ps fwhm
0.37 mm mrad 0.47 mm mrad
thermal ε cGunmax rf fieldat cathode
60 MV/m
60 MV/m
at full cell
54 MV/m
53 MV/memission phase45 ◦31◦
rf field at emission 42 MV/m
31 MV/m
max solenoid field 0.222 T
0.226 Tat 0.28 m
at 0.29 m
Acceleratord
max rf field
20 MV/m
20 MV/mstart of 1st module 3.43 m
4.05 mSimulation resultebunch charge
1 nC
1 nC
trans. projected ε0.60 mm mrad 0.64 mm mradtrans. slice ε f0.47 mm mrad 0.56 mm mrad
bunch length
2.05 mm1.95 mmmean energy
90.1 MeV
90.4 MeV
energy spread
1.19 MeV rms 1.12 MeV rms
long. emittance
302 mm keV
262 mm keV

THPPH012

0

1

2

3
4
5
momentum (MeV/c)

67(b) Gun type #2.
Figure 4: Simulated momentum spectra of dark current and
1 nC beam. The machine parameters for the beam optimization are used. The dark current surviving to the entrance of the first acceleration module is shown. Because
the emission phase of dark current is higher that the optimum emission phase, some part of the dark current stays
in the gun cavity for several rf cycles. When the dark current finally escape from the gun cavity, the dark current
can have certain definite momentum, appeared as spikes.
The dark current reduction by the geometrical collimator isshown as well.
lapping of the momentum distribution with the beam is significantly reduced, which is of great benefit for the darkcurrent collimator.

COLLIMATION IN THE GUN SECTION
In the gun section, two kinds of collimators can be used.
The first one is a geometrical collimator for different transverse sizes (Fig. 5). Dark current with lower momentumis strongly overfocused by the solenoid field which is optimized for the beam focusing. The overfocused dark current
is lost at the beam pipe. If a circular collimator is inserted
inside the pipe, the dark current with larger transverse size
can be cut out. Due to the cryo tank, a possible last position

581

THPPH012

Proceedings of FEL 2006, BESSY, Berlin, Germanymainsolenoid

drive−laser

buckingsolenoid
rf input
photocathode(Cs2Te)

11
00
00
11

coaxialcouplerlaser
mirrorhorizontal
steerergeometricalcollimator

momentumcollimator

rf cavity(copper, 1.5 cells)

Figure 5: Schematic of gun section. The light blue line shows the reference path of beams. The circular shape collimator
chops the dark current with larger transverse size. The elliptical shape collimator uses a difference in the momentum
distributions of beams and dark current. The first horizontal steerer projects the momentum distributions of beams anddark current to the horizontal axis.
of the collimators is 1.2 m upstream from the entrance ofthe first acceleration module. For gun type #1, the position
for the collimator is at 2.2 m. At that position, the electron
beam size is 1.13 mm rms (Fig. 3) and a collimator with
10 mm diameter can be applied. With this collimator, thedark current from the gun can be reduced by 66%. For gun
type #2, the position for the collimator is 2.8 m. The electron beam size will be 1.03 mm rms and a collimator with
10 mm diameter can be applied. With this collimator, thedark current current from the gun can be reduced by morethan 70%. Taking into account the high losses at the beam
pipe for gun type #2, the dark current behind the circularcollimator is only 30% for type #2 compared to type #1.
The second possibility is a momentum collimator. This
collimator is combined with a series of steerers and possibly has an elliptical shape with the major axis in the horizontal direction. If the first steerer kicks the beam and thedark current, the dark current with lower momentum is deflected more and can be chopped with a collimator. The minor axis length of the inner ellipsoid is determined by thebeam size and the major axis length is determined by thebeam size and the momentum distribution at the collimator
position. When the dark current lower than 6.2 MeV/c,i.e. 10% lower than the mean momentum of the beam,is cut out with the elliptical collimator, again 75% of thedark current is possibly reduced for gun type #2. For gun
type #1, 35% of the dark current is possibly reduced when
the dark current lower than 5.9 MeV/c, again 10% of themean momentum of the beam, is cut out.
The momentum collimator can be used to block the darkcurrent from the acceleration modules which might have amomentum of several tens or even hundreds MeV/c. Whenthe high energy dark current hits the Cs 2 Te cathode, theemissive film might be seriously damaged.

gun cavity, the dark current can be separated from the beamin the momentum spectrum. Collimators can be efficiently
used to chop the dark current with lower momentum before
the first acceleration module.

ACKNOWLEDGMENTS
The authors thank M. Krasilnikov and F. Stephan for
helpful discussions.

REFERENCES[1] B. Dwersteg, K. Flöttmann, J. Sekutowicz and Ch. Stolzenburg, “RF gun design for the TESLA VUV Free Electron
Laser”, Nucl. Instr. and Meth. A 393 (1997) p. 93.
[2] S. Schreiber, private communication.
[3] J.-H. Han et al., “Dark current and multipacting in the photocathode rf gun at PITZ”, in Proceedings of the 2005 PAC,
p. 895.
[4] http://www.desy.de/∼mpyflo/.
[5] http://xfel.desy.de/.
[6] J. H. Billen and L. M. Young, Poisson Superfish, LA-UR96-1834.
[7] K. Flöttmann, “Note on the thermal emittance of electrons
emitted by cesium telluride photo cathodes”, TESLA FEL
Reports 1997-01, 1997.
[8] D. Sertore et al., “Cesium telluride and metals photoelectron thermal emittance measurements using a time-of-flight
spectrometer”, in Proceedings of the 2004 EPAC, p. 408.
[9] J.-H. Han, “Dynamics of Electron Beam and Dark Current
in Photocathode RF Guns”, PhD thesis, University Hamburg, 2005.

CONCLUSIONThe XFEL gun requires an rf field as high as 60 MV/m
for 1 nC bunches with an transverse emittance below
1 mm mrad. But, such high rf field might generate very
high dark current. With elonging the half cell length of the582

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH013

IMPACT OF THE CATHODE ROUGHNESS ON THE EMITTANCE OF AN
ELECTRON BEAM
M. Krasilnikov*, DESY, Zeuthen, Germany.
Abstract
An RF photo injector for the European XFEL should
produce electron beams with normalized transverse
emittance under 1 mm mrad. In order to achieve this highperformance of the electron source the electric field at thephoto cathode has to be increased up to 60 MV/m. The
emittance budget of the optimized XFEL photo injector
contains a significant part of thermal (intrinsic) emittance.
A roughness of the cathode could lead to an additional
uncorrelated divergence of the emitted electrons andtherefore to an increased thermal emittance. The cathoderoughness has been modelled using an analytical
approximation and numerical simulations. The influenceof the roughness parameters and the increase of theelectric field have been studied.

z/h

&
v M

a)

1

The main goal of the Photo Injector Test facility in
Zeuthen (PITZ, [1]) is to optimize electron sources for
FEL injectors, including already existing (FLASH) andfuture (XFEL) facilities. Increasing the maximum
gradient at the photo cathode in the rf gun from 40 MV/m
to 60 MV/m is one of the main improvements towards
XFEL requirements. This implies (with taking into
account an optimum launch rf phase) an increasing of theelectric field at the photo cathode at the moment of theemission from 24 MV/m to 42 MV/m. The improved
normalized beam emittance in the injector is expected to
be under 1 mm mrad. Besides earlier suppressing of thespace charge effect in the rf gun the gradient increase also
leads to a significant increase of the contribution of initial(thermal) emittance in the total emittance budget.
The cathode roughness increases the intrinsic
divergence of the emitted electron bunch. A model with aperiodical roughness of the cathode is applied to study thegeometrical emission effect in dependence on roughness
parameters. A single bump model is used to study the
impact of the applied electric field on the initialemittance.

THE MODEL OF THE PERIODICSURFACE ROUGHNESS(1)

where 2h is the roughness depth and O 2S / k is theroughness period along the cathode surface. Let’s
consider first the case of the emission normal to thecathode surface, so M 0 (Figure 1a), what implies zero

&
n

-1
-4

-2

0

2

4 k*x

Figure 1: Periodic roughness, 2D (a) and 3D (b) models.
Transverse component of the electron velocity isvxv0[ sin(kx)1  [ 2 sin 2 (kx),(2)

kh , v0 is velocity of the emitted electron.

After corresponding integration over the roughness period
one can obtain an expression for the emittance induced by
the rough cathode surface

H x2 DVx 

p x2 | 2V x

eE0 §¨
1 ·¸ ,h  1
2¨
mc
1  [ 2 ¸¹©

(3)

where V x is an rms electron beam size at the cathode,px

vx / cis the normalized transverse momentum

1  v02 / c 2

and E 0 is the electric field at the cathode at the momentof the emission.

3D model, normal emission only
A cathode surface with periodic roughness is givenz h cos(kx) cos(ky ) ,(4)
where x  y isotropy is assumed (Figure 1b). Transverse
component of the electron emission velocity:[ sin(kx) cos(ky ). (5)v x v02
2
1  [ sin (kx) cos 2 (ky )  cos 2 (kx) sin 2 (ky )Transverse emittance induced by 3D rough cathodesurface (4) is
H x3 D

2D model, normal emission onlyb)0

where [INTRODUCTION

Consider a cathode surface given by the formulaz h cos(kx) ,thermal emittance from the non-perturbed (no roughness)cathode.

Vx p x2 | 2V x

eE 0
mc 2

h  I ([ ) ,

where
(6)
S
2 S
2
2
[
sin X cos Y
I ([ )dX
dY .
4S 2 ³S ³S 1  [ 2 sin 2 X cos 2 Y  cos 2 X sin 2 Y
One can show, that for the for same roughness parameters
3D

the emittance H x

is in a factor ~ 2 smaller than 2D
one, because the effective roughness depth ( ~ hI ([ ) ) in____________________________________________*mikhail.krasilnikov@desy.de

FEL Technology

583

THPPH013

Proceedings of FEL 2006, BESSY, Berlin, Germany3D/ H x2 D is shown in
Figure 2 as a function of the roughness parameter [ .

the 3D case is smaller. A ratio H x

3D

H0.76/H

2D

0.75
0.74
0.73
0.72
0.71

Thermal emittance growth H xth ,rough / H xth , 0  1 due to thecathode roughness is shown in Figure 3. From this plot
thermal emittance growth <30% corresponds to thecathode roughness with O ! 5h , for 10% growth O ! 12his required. Preliminary cathode plug roughness
measurements performed at INFN LASA (Milano) [4]showed that photo cathodes presently used at PITZ haveroughness with V ~ 10nm . In order to keep the thermal
emittance growth under 10% it is necessary to provide aroughness period over 100 nm.

Figure 2: Emittance from 3D surface (4) compared to 2D
case (1) vs. roughness parameter [ 2Sh / O .

60
40
20
0

2D model with emission distribution

0

yields a formula for the thermal emittance of the smoothcathode (no roughness assumed) [2]:H xth ,02 Ek
2  cos3 M m  3 cos M m .
mc 2
6 (1  cos M m )

Vx

(7)

Within an applied roughness model (1) a transverse
momentum of the electron emitted at angle M to the local
normal is given

2 Ek
(8)
 sin M cos T cos D  cos M sin D ,mc 2
where T is a local azimuth angle, D (x) is a roughsurface slope obtained from (1):(9)
tan D [ sin kx .
px

Applying triple integration to p x2 over M  [0; M m ] ,T  [0; S ] and over the roughness period [3] yields a
formula for the thermal emittance from the periodic roughsurface:Hth , rough
x

Vx
3

(10)
3

( 2  cos M m  3 cos M m ) cos D m  2(1  cos M m )(1  cos D m ),u
6 (1  cos M m )1 1  [ 2 . Obviously, that in the absenceof the roughness ( D m 0 ) the formula (10) is reduced towhere cos D m

0.25

0.2

0.15

0.1

14

16

18

20

10

20

6

15

25
8

15
10
6
20

8

4

6

10

0.05

8
0 124

8

10

40
35 30

20

2Ek
u
mc 2

8 10 12[=2S *h/O

for photoemission, which partially can include also a
surface roughness effect. A thermal emittance growth as afunction of roughness period and electron affinity isshown in Figure 4 with a contour plot.
9
8 95
805 0
75

Cs2Te photo cathode E A | 0.2eV , by a applying driving
laser with 262 nm wavelength Ek | 0.75eV . This model6

In practical case the electron affinity is affected bymany factors. It is well known that the quantum efficiency(QE) of the photo cathodes decreases with operation time;electron affinity increase due to the change of the cathodesurface status is one of the possible mechanisms
explaining QE degradation. On the other hand an appliedrf field lowers the electron affinity due to the Schottky
effect [5]. The electron affinity can be modelled as [6]:e3(11)E ph E0 ,E A NE A, 0 
4SH 0
where N is responsible for the increase with a time of theinitial affinity E A, 0 , E ph is a field enhancement factor

70

normal, where E A is the electron affinity of the emitting
material and Ek is the electron kinetic energy. For the4

Figure 3: Thermal emittance growth vs. roughness
parameter [ 2Sh / O . Ideal Cs2Te cathode parameters
E A 0.2eV , Ek 0.75eV have been assumed [2].

EA, eVIn the case of nonzero non-perturbed thermal emittancethere is an emission in a finite angle M , as it happens i.e.
by emission from the Cs2Te photo cathode. Using
approach described in [2], one assumes that electrons are
emitted isotropically in a cone with an angle
M m arccos E A Ek with respect to the local surface2

15[9=2 10
S *h/O

20

8

15

7

35
30
25

6

20

5

6
605

4

55
4 5 50

3

35 40
30
25

2

6
605

1

55
45 50

0

thermal emittance
growth, %

80

0.7

40

4
12

6
60

80

4

2

2
1

1

100

120

140

O, nm

Figure 4: Thermal emittance growth H xth ,rough / H xth ,0  1given in % as a function of roughness period and electron
affinity. For this plot h 10 nm , E k 0.75 eV is assumed.

the expression (7).

584

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Proceedings of FEL 2006, BESSY, Berlin, Germany

DEPENDENCE ON ELECTRIC FIELD
In order to study the dependence of the initial emittanceon the electric field during emission a model of single
bump can be used. A two-dimensional model of the bumpis described in [7]:

z
b

1

a2
1 ,
b  x2(12)2where parameters a and b are constants depending onroughness depth and width. Typical bump shapes areshown in Figure 5.
a/b=0.01

1.2
1a/b=10a/b=100

0.8
0.6

z/z(0)

0
-10

-8

-6

-4

-2

d § p x (mc) ·¨¸d (ct ) ¨© p z ( mc) ¸¹

0

2

4

6

x/b
10

8

e § Ex ·¨ ¸
mc 2 ¨© E z ¸¹

(15)

§ px ·1d § x·¨¨ ¸¸,¨¨ ¸¸22d (ct ) © z ¹
1  px  pz © pz ¹
with initial conditions:xn (t 0) xn 0 ; z n (t 0) z n 0 ;(16)
p xn (t 0) 0; p zn (t 0) 0.
Parameter u from (13) characterizes the location on thesurface from which an electron is emitted ( w 0 ):unb
xn 0
; u n n  u N N ; n 1...Nzn  b
(17)
zn0

0.4
0.2

THPPH013

a 2  b 2  u n2 b 

u n2  a 2  b 2  4u n2 a 2
2.

The last emission location u N can be defined from thecondition:

Figure 5: Rough cathode surface: single bump model(10). Upper curve corresponds to a b 100 .
The choice of equation (12) for the rough cathode surface
is motivated by the simple conformal transformation]2x  iz  ib  a 2  ib ,u  iw(13)

The electric field lines are shown in Figure 6.
15

10

0.01 

a2  b2  b(18)

It should be noticed that within this approach the spacecharge effect is neglected.
Shown in Figure 7 are typical numerical results of thelocal electron divergence p x /( mc ) as a function of theemission parameter u / u N at the moment in time whenelectrons reach the region of homogeneous field. At thisz-position the electric field varies along x-axis not morethan by 1%, it means that the field at this distance fromthe cathode does not “feel” the rough surface.

px/(mc), mrad

which maps the electric field of a plane capacitor onto thefield of the surface (12). An analytical expression for theelectric field can be obtained from the corresponding
conformal transformation
 iEo  >x  i y  b @ .
(14)
E x  iE z
>x  i y  b @2  a 2

0.01  z (0)

zN

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

20MV/m24MV/m36MV/m42MV/m46MV/mbump profilez, a.u.

0

0.1 0.2

0.3 0.4

0.5

0.6 0.7

0.8 0.9 u/uN
1

Figure 7: Local divergence as a function of u / u N for5various E0 . Roughness parameters: depth h | 20 nm ,width O
0

-8

-6

-4

-2

0
x. a.u.

2

4

6

8

Figure 6: Electric field lines of the bump (10).
Once the electric field magnitude Eo and the bumpparameters a and b are specified, the field profile isdetermined from (14) and particle position ( x, z ) andmomentum ( p x , p z ) can be numerically integrated intime according to

FEL Technology

10 nm ( a21 .52 nm; b 1.57 nm ).

An estimation of the emittance growth due to theincrease of the applied electric field could be done basedon the analysis of the electron divergence for various
roughness parameters. Emittance growth as a function of
the applied electric field in comparison to the case of
E0 24 MV / m is shown in Figure 8. Relative emittance
growth for various bump widths O has a slope of about
2 % ( MV / m) , so field increase up to 42 MV / m results in
a ~30% emittance growth.

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THPPH013

Proceedings of FEL 2006, BESSY, Berlin, Germany50%

H (E 0 )/H (24MV/m)-1

40%
30%
20%
10%

Emit.growth, lym=1nm

0%Emit.growth, lym=10nm-10%Emit.growth, lym=100nm

-20%
20

25

30

35

40

45 E0 , MV/m
50

Figure 8: Emittance growth as a function of the electricfield, compared to the emittance at E 0 24 MV / m .
Simulations based on the assumption of the neglecting
the space charge effect have been performed. Modellingthe space charge limited emission from the bumpy
cathode surface in the steady state regime [7] showed thatthe space charge may reduce the deterioration effect of
the surface roughness. But from the other hand thecathode roughness may result also in additional density
non-homogeneity of the emitted electron beam, which
could lead to degradation of the beam quality.

CONCLUSIONS AND OUTLOOKThe photo cathode roughness contributes to the initialemittance of the electron beam. Several models of thecathode rough surface have been used to estimate theeffect of the thermal emittance growth. Thermal emittance
growth induced by the cathode roughness has beenstudied for different roughness parameters, including
photo emission issues from a Cs2Te photo cathode.
Since one of the main improvement steps toward XFEL
requirements is an increase of the maximum rf gun

586

gradient from 40 to 60 MV/m, the impact of increasing
the field at the cathode has been studied. The model ofsingle bump has demonstrated that the increase of theelectric field at the cathode could result in a ~30% growthof the roughness contribution to the initial thermal
emittance.
Studies on the role of the space charge effect during
emission from rough cathode as well as more detailed
measurements of the cathode roughness have to be
performed in order to improve the understanding of thethermal emittance features.

ACKNOWLEDGMENTS
I would like to thank K.Floettmann, F.Stephan and PITZ
members for helpful discussions.

REFERENCES[1] A. Oppelt et al., “Status and first results from theupgraded PITZ facility”, FEL 2005, Stanford,
Aug.2005.
[2] K. Floettmann, “Note on the thermal emittance ofelectrons emitted by Cesium Telluride photo
cathodes”, TESLA FEL Reports 1997-01, 1997.
[3] J. Schmerge, private communication.
[4] D. Sertore, private communication.
[5] R.Gomer, “Field emission and field ionization”,
American Institute of Physics, New York, 1993.
[6] J.-H. Han, “Dynamics of electron beam and darkcurrent in phototcathode rf guns”, PhD thesis,
Hamburg University, 2005.
[7] Y. Lau, “Effects of cathode roughness on the qualityof electron beams”, J. Appl. Phys 61(1), Jan. 1987.

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH016

FIRST EXPERIENCE WITH THE MACHINE PROTECTION SYSTEM OF
FLASH
L. Fröhlich∗ , University of Hamburg and DESY, Hamburg, Germany
A. Hamdi, M. Luong, J. Novo, CEA-Saclay, Gif-sur-Yvette, France
M. Görler, P. Göttlicher, D. Nölle, D. Pugachov, H. Schlarb, S. Schreiber,
M. Staack, M. Werner, DESY, Hamburg, Germany
Abstract
The linac-based free electron laser facility FLASH 1 at
DESY Hamburg is designed to transport electron beams
with high average power of more than 50 kW. To protect
the machine from serious damage passive and active systems have been installed. This paper concentrates on thefast active machine protection system (MPS), that stops the
production of new bunches if hazardous machine conditions are detected. Furthermore, the results from the commissioning of the fast beam interlock system are presented
that has for the first time allowed to operate the accelerator
with macropulses of up to 600 bunches.

INTRODUCTION
The FLASH linac currently employs 40 superconducting
9-cell cavities distributed over five cryogenic modules toaccelerate an electron beam to an energy of up to 700 MeV.
The beam is guided through an undulator of approximately
30 m length to initiate a free electron laser (FEL) process
based on the SASE principle. The facility is now alternating between blocks of accelerator development and user
operation, supplying experimentators with pulsed radiationof high brilliance in the XUV wavelength range between
13 and 50 nm. [1]As typical for superconducting linacs, the transported
bunches are grouped in macropulses or bunch trains. The
viable rf pulse length limits the length of a bunch train to
800 µs. With the standard bunch frequency of 1 MHz anda macropulse repetition rate of 5 Hz, the power delivered
to the beam dump amounts to ∼3 kW. If the future option
for high duty cycle operation with 9 MHz/10 Hz is realized, this figure increases above 50 kW. Even on partial
loss of the beam along the linac, the induced heat load andradiation can cause substantial damage to accelerator components. Therefore, an active protection system is required
to ensure safe operation of the machine.

MPS ORGANIZATION
The machine protection system of the FLASH linac isa substantially enhanced version of the system used inphase 1 of the TESLA Test Facility [2]. Since the descrip∗ lars.froehlich@desy.de
1 Since April 2006, FLASH—Free Electron Laser in Hamburg—is the

new name for the VUV-FEL, part of the TESLA Test Facility TTF.

FEL Technology

Figure 1: Schematic of the FLASH linac. The depicted
elements include the five acceleration modules ACCn, thetwo bunch compressors BCn, and the main dipole magnets.
tion of the basic design in [3], the operational experience
gained during the commissioning of FLASH has led to anumber of changes that will be discussed in the following.

Detection Schemes
The detection of beam and darkcurrent losses in the
linac is based on two independent approaches. The FPGAcontrolled Toroid Protection System [4] measures the transmission by comparing the readings from charge monitors(toroids) in the injector and dump part of the machine, andgenerates alarms within less than 110 ns if one of several
configurable thresholds is exceeded.
The second system for fault detection is constituted bya set of 51 photomultipliers and 18 secondary emission
multipliers distributed along the machine. These beamloss monitors (BLMs) provide a bunch-resolved online display of electromagnetic shower intensities (Fig. 2). VMEbased alarm generators with a reaction time far below 1 µs
check whether user-defined thresholds for one or multiple
bunches, or for the integrated signal are exceeded. They
also generate an alarm on failure of the high voltage supply, or if a misconfiguration has been detected.
As the permanent magnets of the undulator are susceptiple to radiation, close monitoring of beam losses is required
to avoid degradation of the field quality. Therefore, the undulator section features the highest concentration of BLMs
in the whole machine, with 26 monitors currently in place
and another 12 to be installed until the end of the year.

Response to alarms
The purpose of any MPS is to detect situations which
may lead to damage of components, and to take appro-

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Proceedings of FEL 2006, BESSY, Berlin, Germany

BLM signal (a.u.)

0.3
0.2
0.1
0
600

650

700

750

800

850

900

t (µs)
Figure 2: Signal from a beam loss monitor behind the collimation section. At t = 700 µs, a part of one single bunch
is lost. The losses visible from 690–820 µs are caused by
darkcurrent from the gun.
priate counter-measures. These potentially harmful conditions can be classified into three main categories:
Fast Since the loss of a complete macropulse may alreadypresent a substantial hazard, a fast system must stop
the production of bunches within the train, i.e. on atime scale of few µs.
Intermediate For the major part of potential dangers, areaction between two macropulses is sufficient. Since
the time constants of all magnets employed at FLASH
are of the order of tens of milliseconds or more, thefailure of power supplies falls into this category.
Slow Even if moderate losses of darkcurrent or of few
bunches do not pose an immediate threat, they contribute to the deposited radiation dose, and may thus
cause damage over time scales of minutes or days.
This issue is of special importance for the undulator.
To guarantee an appropriate response to events on anyof these timescales, the FLASH MPS uses two independent subsystems: A network of Beam Interlock Concentrators for fast events, and a programmable logic control—theBeam Interlock System—for intermediate and slow events.

Beam Interlock Concentrators (BICs)
The function of the BIC modules is simply a fast logical
OR concentrating 16 alarm inputs to two outputs within aprocessing time of ∼50 ns, with a configurable mask thatallows to suppress any of the input channels. Ten modules
are currently in use, connected in a tree-like fashion as illustrated in Fig. 3. Most of the input channels are usedby the 69 BLM alarm signals, but also the TPS, the cavity
quench detection, and a fast vacuum shutter are connected.
When any of the inputs show an alarm, the top-level BICs
will switch off the injector laser to suppress the productionof new bunches in the gun, and cut the first acceleration
module off from rf power as a precaution against furthertransport of darkcurrent.

588

Figure 3: Organization of beam interlock concentrators.
BIC 3–10 collect alarms from various alarm generators andrelay them to BIC 1–2, which switch off the photoinjector
laser and the rf power of the first acceleration module.
Measurements have confirmed that the reaction time of
the BIC system to beam losses is below 4 µs. This time isdominated by cable delays, and it means that up to three
more bunches enter the machine after detection of the loss
at the standard bunch frequency of 1 MHz.

Beam Interlock System (BIS)
While the BIC system has been designed to guarantee
minimum response time to fast events, the emphasis for
the Beam Interlock System has been placed on flexibility.
The programmable logic control continuously monitors thestatus of critical components like magnet power supplies,
screens, collimators, and valves. It also checks the flow ofcooling water, and the compliance to temperature limits.
From the status of the main dipole magnets and of several valves, the BIS deduces an operation mode defining thebasic beam path through the machine according to Tab. 1.
As a simple protective measure, no beam is allowed if there
is no valid operation mode.
Furthermore, the BIS selects one of three beam modes asshown in Tab. 2. Besides defining the maximum allowed
number of bunches per macropulse, the beam mode also
determines whether the fast protection via the BIC systemis active. This policy allows the operation under charge loss
as long as only few bunches per macropulse are needed,which is necessary for tuning and for experiments using
the beam. While the operator can choose between shortand long mode, the BIS will automatically reduce to shortor single mode if obstacles like screens are moved into thebeam path, or if other conditions are met.
Apart from these general safety features, attempts havebeen made to limit the radiation dose deposited in the undulator with a special BIS routine. Due to the dense placement of BLMs in the undulator section, there is considerable overlap in their geometrical acceptances, and electromagnetic showers are usually observed on more than one
monitor. The BIS-BLM protection takes advantage of thisby counting the number of simultaneous BLM alarms in

FEL Technology

Table 1: List of operation modes with the required valve
and dipole magnet settings, and the maximum allowed
beam mode.
operation
mode
Gun
Analysis
BypassFEL

conditions
gun valve open, ACC1 valve closed,
D1IDUMP off
gun valve open, ACC1 valve closed,
D1IDUMP on
all valves open, D1BYP on, D1DUMP
on, D6DUMP off
all valves open, D1BYP off, D1ECOL
on, D6DUMP on

beam
mode
short
long
long
long

Table 2: List of beam modes with the maximum allowed
number of bunches per macropulse.
beam mode
Single
¿
Short
Long

nr. of bunches
230
no limit

BIC systemdisabled
disabled
activethe section. If 2 alarms are pending over 120 s, 4 over 30 s,
or 8 over 5 s, the beam is stopped and has to be restarted
manually via the control system. To allow tuning, the tolerances of this routine can be increased for 30 minutes.
Figure 4 shows the average dose rates in the firsttwo undulator segments measured with thermoluminescence dosimeters [5]. Since the activation of the BISBLM protection in September 2005, the dose rates havebeen predominantly below 10 Gy/day, indicating that—together with an overall improved understanding of orbit
and optics—the requirement of avoiding beam stops has
led to a reduction of losses.

OPERATION WITH LONG
MACROPULSESThe commissioning of MPS components relevant forlong pulse operation has been completed in August 2006.
The increase of the gun rf pulse length from 70 to 800 µs
led to the expected rise of darkcurrent losses in the bunch
compressors and in the collimation section by about an order of magnitude. By successive optimization of orbit andoptics, the beam losses could be reduced to a minimum,and operation of the FEL with 600 bunches per macropulse
was possible with minimal interference of the BIC system.
At an average energy of 20 µJ per photon pulse, the output
power during the test run has reached about 60 mW.
Imperfections of the rf regulation constitute the main
problem in setting up a stable transmission of long macropulses. Due to poorly compensated beam loading or transient behavior at the beginning of the rf pulse, the bunches
at the head of the macropulse can experience amplitudes
and phases of the accelerating field that deviate significantly from the designated values. For the first bunch, an

FEL Technology

avg. dose rate (Gy/day)Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH016

50
40
30
20
10
0
01/05 05/05

09/05

01/06 05/06

09/06

date
Figure 4: Average dose rates measured in the first two undulator segments.
energy deviation of 0.6 % with respect to the last bunchesof a 300 µs long macropulse has been measured after the
first acceleration module. This effectively enlarges the total
phase space occupied by the macropulse and thus reduces
the tolerance for jitter and drifts.

CONCLUSION AND OUTLOOKThe FLASH machine protection system reliably prevents damage of the accelerator due to beam losses, withthe total downtime of the linac caused by MPS failures andmisconfigurations amounting to only few hours. It is also
successful in limiting the slow accumulation of radiationdose in the undulator.
While the number of bunches per macropulse has been
limited to 30 during past accelerator runs, the recent commissioning of the beam interlock concentrator system withreaction times in the microsecond range now allows to operate the machine with bunch trains of up to 800 pulses.
We expect that future user experiments will benefit highlyfrom the improved duty cycle.

ACKNOWLEDGEMENTS
We wish to thank all members of the operation crew for
their outstanding commitment and support. The assistanceof the controls and low-level rf groups is greatly appreciated.

REFERENCES[1] V. Ayvazyan, et al., “First operation of a free-electron laser
generating GW power radiation at 32 nm wavelength”. Eur.
Phys. J. D, 37:297–303, November 2006.
[2] H. Schlarb, et al., “Expansion of the fast linac protection system for high duty cycle operation at the TESLA Test Facility”. EPAC’02, pp. 1966–1968. Paris, France, June 2002.
[3] D. Nölle, et al., “The beam inhibit system for TTF II”. DIPAC’03, pp. 62–64. Mainz, Germany, 2003.
[4] A. Hamdi, et al., “VHDL design and simulation of a fast
beam loss interlock for TTF2”. EPAC’04, pp. 2020–2022.
Lucerne, Switzerland, 2004.
[5] T. Vielitz, Hasylab, Hamburg, private communication.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

EXPERIENCE WITH THE PHOTOINJECTOR LASER AT FLASH
S. Schreiber,∗ , M. Görler, K. Klose, M. Staack, L. Fröhlich, DESY, Hamburg, Germany
I. Will, I. Templin, MBI, Berlin, Germany

Abstract
The photoinjector laser system of FLASH is a key element for the generation of high quality electron beams
required for a stable and reliable operation of the facility.
FLASH is the VUV and soft X-ray FEL user facility at
DESY. FLASH is based on superconducting accelerating
structures allowing to accelerate electron bunch trains of alength of up to 800 µs with a repetition rate of 10 Hz. Basedon the standard 1 MHz pattern, the laser provides to someextend a flexible bunch train structure. We report on operational issues and on the performance of the laser system
and its integration into the machine protection system.

INTRODUCTION
FLASH is a free electron laser user facility at DESY providing laser-like radiation from the VUV to the soft X-ray
wavelength regime.[1, 2] SASE free electron lasers require
an excellent beam quality, which is achieved with an injector based on a laser driven rf gun.[3] The electron beam isaccelerated with TESLA superconducting modules.
A high quantum efficiency photocathode [4] together
with a synchronized mode-locked laser system is used togenerate the electron beam structure typical for superconducting accelerators: some thousand bunches in a millisecond long rf pulse. High quantum efficiency cathodes allow
to use a laser system with moderate average power in the
Watt range.
The user facility FLASH has been realized by upgrading
the TESLA Test Facility (TTF) phase 1 FEL to phase 2.[5]The TTF phase 1 laser system [6] has also been upgradedto a partially diode pumped system as described in [7].
In this report we describe the running experience withthe laser system and its integration into the machine protection system of FLASH.

OVERVIEW OF THE LASER BASEDELECTRON SOURCEThe FLASH electron source is based on a laser driven
L-band 1+1/2-cell rf gun operated with a 5 MW 1.3 GHz
klystron. The rf pulse length is up to 900 µs, the repetition
rate 5 Hz, up to 10 Hz are possible.
The electron beam is generated by photoemission with a
Cs2 Te photocathode. With a forward rf power of 3.2 MW a
gradient of 42 MV/m on the cathode surface is achieved on∗ siegfried.schreiber@desy.de

590

Figure 1: Schematic overview of the laser system.
crest. High gradient on the cathode surface is required topreserve excellent beam quality. The cathode exhibit a highquantum efficiency in the range between 1 and 5 % for UV
laser light. The charge per bunch required is 1 nC whichtranslates into a laser pulse energy of not more then 0.5 µJ
per pulse. The design of the laser accounted for a QE of
0.5 % only, a bunch frequency of 9 MHz within the train
and an overhead by a factor of 4. With a conversion efficiency of 15 % from the IR to UV this asks for an average
power of 2 W in the infrared.

THE LASER SYSTEM
The laser design is based on a pulsed master oscillator
with subsequent amplification stages. Details of the systemlayout are described in [7], a schematic overview shows
Fig. 1.
The laser material chosen is Nd:YLF, lasing at a wavelength of 1047 nm. The material has together with a highgain a long upper-state lifetime of 480 µs, and exhibits
only a weak thermal lensing. This makes it suitable to produce pulse trains with milliseconds length. The oscillator
and preamplifers are end-pumped with laser diodes emitting at 805 nm with a maximum power of 32 W. The twomain amplifiers are flashlamp pumped.

The Pulse Train Oscillator
The pulse train oscillator (PTO) runs at 27 MHz synchronized to the master rf of the accelerator. It is a pulsed osciallator with the advantage of a much higher single pulse
energy of 300 nJ as compared to typical cw oscillators. The
master provides reference rf signals in the frequency of theaccelerator of 1.3 GHz and its harmonics 108, 27, and 9MHz. The synchronization to the rf is achieved using two

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 2: As an example, the air temperature measured at
the laser over a period of 3 days. The temperature reading
is within ±0.02◦ C.
acousto-optic modulators running at 27/2 = 13.5 MHz and
108 MHz resp., and an additional electro-optic modulator
powered with the amplified 1.3 GHz reference. The latterprovides synchronization to the required 1 ps level. The oscillator length is stabilized against temperature drifts with
two quartz rods. Quartz has a low temperature coefficientof expansion of 0.6·10−6 m/◦ C. At the same time, the temperature of the laser room is stabilized to ±0.02 ◦ C (Fig. 2).
Both measures provide the bases for an excellent phase stabilization of the laser pulses with respect to the rf. An active fast feedback loop could be omitted, only a slow feedback acting on the resonator length is implemented.
The phase jitter of the laser pulses in respect to the rf canbe estimated using the phase scan technique. The phasestability measured with this technique depends also on theperformance of the gun rf amplitude and phase regulation
system and therefore only gives an upper limit. The measurement results an rms phase jitter of 0.14 ◦ in respect to
1.3 GHz rf.[8] This translates in an timing stability of thelaser pulses of better than 300 fs rms.

Amplification
Selected pulses of the 27 MHz output of the PTO is
amplified with a chain of linear amplifiers, also based on
Nd:YLF, diode and flashlamp pumped.
A Pockels cell based pulse picker before amplification
runs at 1 MHz forming a pulse train with a length of 1.5 ms.
With the present high voltage driver (4 kV), up to 3 MHz
is possible. The train is amplified by two diode pumped
single pass amplifiers from 0.3 to 6 µJ per micro pulse.
A second pulse picker before the last amplification stage
has two functions. The diode pumped amplifiers produce
a transient at the beginning of the pulse train. The second
pulse picker choses the flat part of the train. The second
aim is to give the operator or user of the laser the possibility to remote control the number of pulses and to a certain
extend the bunch pattern. Details will be described later inthis report.
The final amplification to 300 µJ per pulse is performedby two flashlamp pumped amplifiers. They have alreadybeen used at the phase 1 laser system. They provide a
power over the pulse train of about 300 W or an average

FEL Technology

THPPH017

power of up to 3 W for 10 Hz repetition rate.
The pump diode lasers are running since their installation for more than 20.000 h without any visible degradation. The flashlamp life time is between 1 to 5·107 shots
and are routinely replaced every 40 days.
The infrared radiation (1047 nm) is doubled twice with
an LBO and a BBO crystal to the UV (262 nm). The energy
stability of a single micro pulse is between 1 and 2 % rms.
However, to maintain this stability, a frequent fine tuningof the BBO phase matching angle is required.

Transport Beamline
A variable attenuator consisting out of a Brewster angle polarizer together with a remotely rotatable half wave
plate. It allows to adjust the laser pulse energy according
to the electron beam charge required. It is also used for aslow charge feedback to compensate slow drifts in electron
charge.
Spent beams at various locations (PTO, Pockels cell,
LBO, attenuator) are measured with fast photodiodes andrecorded with a 1 MHz ADC giving additional information
to the operator.
A double pulse generator can be switched into the beamline doubling each micro pulse with a variable distance ofsome nanoseconds in order to accelerate double bunches inclose-by rf buckets. Refer to [9] for details.
In addition, the laser beam can be directed remotely to ajoulemeter to measure its energy. It is frequently used forquantum efficiency measurements. The laser pulse can also
be directed to a fast streak camera (Hamamatsu FESCA
200) to measure its longitudinal pulse structure. The pulse
length in the UV is measured frequently and is stable at
4.4±0.1 ps sigma.
The UV beam is transported from the laser hut to the rf
gun. The beamline has a length of 10 m. It is protectedwith tubes against dust and air turbulences. The beamline
needs five dielectric mirrors with a coating optimized for
262 nm. A remote controlled mirror box allows true linear
steering of the beam along the cathode. The last mirror in
the vacuum chamber guides the beam to the cathode. It is
manufactured of solid aluminum. Its surface is diamondturned and has a good optical flatness and a reasonable reflectivity of 90 %. We have chosen a solid metal mirror
for two reasons. Dielectric mirrors charge up when hit bydarkcurrent. Charging and discharging leads to cracks on
the mirror surface and influences the electron beam trajectory. Secondly, experiments supported by simulations haveshown, that the beam emittance is also effected.[10]The laser beam transport is based on the relay imaging
technique together with spatial filtering. A hard edge aperture downstream of the diode pumped amplifiers is consecutively imaged to the flashlamp pumped laser heads, to the
doubling crystals and finally to the cathode. This results
in a quasi flat laser pulse on the cathode which is further
sharpened by a hard edge iris aperture close to the gun.
The magnification of the telescope system is about 10 re-591

THPPH017

Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 3: Laser beam profile measured with a Ce:YAG
crystal at the ’virtual cathode’. A large laser spot (diameter
1 to 1.5 cm) is seen through an iris of 3 mm in diameter. Although interference fringes show up, the pointing stability
is much improved.

Table 1: Laser parameters. Most parameters are adjustable
and are set according to the requirements for the specificexperiment.
parameterlaser material
wavelength after conversion
output structure
train repetition rate
train length
micro pulse spacing
micro pulse longitudinal shape
micro pulse lengthtransverse profiletransverse size on cathodevalue
Nd:YLF262 nmpulsed trains
5 or 10 Hz
up to 800 µs *0.33 us to 800 µs *gaussian4.4±0.1 ps (sigma)
flat, with fringes
3 mm diam.**adjustablesulting in a large beam size of about 1 cm in diameter. The
iris is remote controlled and is usually adjusted to a diameter of 3 mm cutting a large portion of the laser beam. This
results in a roughly flat transverse profile. In addition andmost important, these measures reduce the pointing jitterby a large amount and contributes to the stability of theelectron source. However, interference fringes created by
the hard edge aperture could not been completely avoided.
The modulation is about 20 %. An upgrade is foreseen to
reduce the modulation (see [11]).
A so called virtual cathode is used to set-up and control
the transverse laser beam shape. A remote controlled mirror directs the laser beam onto a Ce:YAG crystal mounted
at a distance identical to the cathode position. Figure 3
shows an image of the laser beam on the virtual cathode.
Table 1 summarizes the main laser parameters.

592

Figure 4: Scope screen shot of a 40 kHz pulse train (green
trace, Nb. 4). In addition, the central part of the 27 MHz
train of the oscillator (PTO) (yellow, nb 1), and the 1 MHz
pulse train after the diode pumped preamplifiers (cyan,nb. 2) are shown.

BUNCH TRAIN PATTERN AND MACHINEPROTECTION
Experiments with FEL radiation often require different
electron bunch train pattern. The laser can provide to acertain extend a flexible bunch train pattern chosen by theoperator.
We use the Pockels cell based pulse pickers to vary thepattern of the laser pulse train. The Pockels cells may run
for 1.5 ms with a rate of up to 3 MHz, pulsed with up to
10 Hz.
An FPGA based controller has been developed. It takes
as an input the 9 MHz rf signal from the master oscillator
and the 5 Hz or 10 Hz trigger from the control system. The
controller produces the trigger gates which go to the Pockels cell drivers. The FPGA allows a flexible control on thenumber of pulses and the repetition rate, for example in addition to the standard 1 MHz, 250 kHz, 100 kHz, 10 kHz,and others are possible. As an example, Fig. 4 shows ascope screen shot of a 40 kHz pulse train.
The controller also serves as an interface to the machine
protection system (MPS).[12] Three beam modes are defined: a single pulse, short pulse, and a long pulse mode.
These modes are a machine safety measure, for instanceonly single bunches are allowed when screens are inserted
in the high energy part of the accelerator. Depending on
the mode, the controller limits the number of laser pulses
picked by the second Pockels cell, independent of the operator request. It also receives a fast beam stop signal from
the MPS, for instance when losses grow within a pulse
train. The stop signal suppresses further triggers to thepulse pickers. The reaction is immediate within some tensof nanoseconds.
For a safe operation of the laser, important operating

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Proceedings of FEL 2006, BESSY, Berlin, Germany
conditions are surveyed by an SPS based system. For instance, the system issues warnings and interlocks on overtemperature, water flow interruptions and so on. The overall system is controlled with a VME-crate based cpu integrated into the FLASH control system providing an interface to the operators. The cpu reads important laser parameters and drives for instance flashlamps, slow feedbacks ona shot to shot bases.

CONCLUSION
The photoinjector laser system has been upgraded bypartially replacing flashlamp pumped laser heads by diodepumped heads. The upgraded system has been put into operation at FLASH in February 2004 and providing beam
since then (for more than 20.000 h). The stability and reliability of the system is satisfactory, maintenance a routine
task. An FPGA based controller allows to drive the pulse
pickers with a variable pulse pattern and serves at the sametime as an interface to the machine protection system. The
laser is integrated into the FLASH control system providing informations about the status of the system and various
remote control options.

THPPH017[9] O. Grimm, K. Klose and S. Schreiber, EPAC-2006THPCH150, Proceedings of EPAC 2006, Edinburgh, UK, 2630 June 2006.
[10] M. Krasilnikov et al., DESY-M-04-03U Prepared for 9th
European Particle Accelerator Conference (EPAC 2004),
Lucerne, Switzerland, 5-9 Jul 2004.
[11] M. V. Hartrott et al., eConf C0508213 (2005) MOPP034[arXiv:/]Presented at the 27th International Free Electron Laser Conference (FEL 2005), Stanford, California, 22-26 August 2005.
[12] L. Fröhlich et al., ”First Experience with the Machine Protections System of FLASH”, FEL-2006-THPPH016, theseproceedings.

ACKNOWLEDGMENT
We like to thank our colleagues from the FLASH controls group for their support, mainly B. Petrosyan for
the interface to the doocs control system, J. Thomas and
O. Hensler for the motor drivers. We also thank M. Werner
for many fruitful discussions and his valuable help on theimplementing of the FPGA controller, and O. Grimm forhis kind help with the streak camera.

REFERENCES[1] V. Ayvazian et al., Eur. Phys. J. D 37, 297 (2006).
[2] S. Schreiber, “First lasing at 32-nm of the VUV-FEL at
DESY,” eConf C0508213, MOOB002 (2005),
Presented at the 27th International Free Electron Laser Conference (FEL 2005), Stanford, California, 22-26 August 2005.
[3] S. Schreiber, eConf C0508213 (2005) THPP038 [arXiv:/]
Presented at the 27th International Free Electron Laser Conference (FEL 2005), Stanford, California, 22-26 August 2005.
[4] D. Sertore, P. Michelato, L. Monaco, A. Bonucci, J. H. Han
and S. Schreiber, PAC-2005-MOPB009 Prepared for Particle
Accelerator Conference (PAC 05), Knoxville, Tennessee, 1620 May 2005.
[5] “SASE FEL at the TESLA Facility, Phase 2,” DESY-TESLAFEL-2002-01.
[6] S. Schreiber, D. Sertore, I. Will, A. Liero and W. Sandner,
Nucl. Instrum. Meth. A 445 (2000) 427.
[7] I. Will, G. Koss and I. Templin, Nucl. Instrum. Meth. A 541(2005) 467.
[8] E. Vogel, W. Koprek, P. Pucyk, EPAC-2006-TUPCH189,
Proceedings of EPAC 2006, Edinburgh, UK, 26-30 June 2006.

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SINGLE-SHOT LONGITUDINAL DIAGNOSTICS WITH THZ RADIATION
AT THE FREE-ELECTRON LASER FLASH
H. Delsim-Hashemi, J. Rossbach, P. Schmüser , Univ. Hamburg, Germany
O. Grimm, H. Schlarb , B. Schmidt, DESY, Hamburg, Germany
A.F.G. van der Meer, FOM, Nieuwegein, The Netherlands.
Abstract
The longitudinal charge distribution in the electron
bunches has a strong impact on the lasing process in a
Free-Electron Laser based on the principle of Self
Amplified Spontaneous Emission of radiation. For theultraviolet and soft X ray FEL FLASH at DESY, structuresin the range of ten to hundred micrometers play a crucialrole. The investigation of the longitudinal charge
distribution in the electron bunches on a bunch-by-bunchbasis is an important issue for optimizing the bunch
compression and improving the performance of themachine. This paper introduces a new tool for longitudinal
diagnostics based on THz spectroscopy of coherent
radiation. A novel spectrometer has been designed which
permits to analyze the radiation of single electron bunches
in a broad spectral range and with high resolution.
Preliminary measurements with this spectrometer arepresented.

Advanced bunch compression monitor
As it is described in reference [3], a multi stage
reflectance blazed grating spectrometer is used to study
bunch compression versus machine parameters. In thefollowing comes an example. It is known that the off-crest
phase φ in the first acceleration module ACC1 has a strong
influence on the longitudinal bunch profile that is obtained
when the bunches have passed the two magnetic chicanes.
Empirically it is found that the SASE efficiency depends
very critically on φ and reaches its maximum at φ ≈ −5oto − 6 . A phase scan around this value is shown in Fig.1.
The signal of the gas monitor detector (GMD), measuring
the pulse energy of the FEL light, exhibits a pronouncedomaximum at φ = − 5.7 with a width of ± 0.2 . The
coherent transition radiation intensities in various
wavelength channels are also plotted in Fig.1. The
remarkable observation is that the intensity for short
INTRODUCTION
wavelengths (20 to 75 μm ) exhibits a strong peak in the
FEL facilities in the VUV and X-ray regime require kA region of maximum SASE intensity while the intensity ofpeak currents which are usually achieved by several stages long wavelengths has a monotonic increase towards moreof bunch compression. The longitudinal charge negative phase.
distribution of the compressed bunches has to be measured
with high precision in order to fine-tune the off-crest phasein the accelerating section preceding the magnetic bunch
compressor chicanes and to optimize the SASE
performance. The existing interferometers operate in thescanning mode and determine the average pulse shape ofmany thousand bunches. They are intrinsically unable toyield information on single bunches. The new single-shot
spectrometer uses diffraction gratings as dispersive
elements and an array of pyro-electric detectors withmulti-channel readout. Exploratory measurements with thefirst stage, containing thirty channels will be presented.
oo

GRATING SPECTROMETER
The coherent radiation of the compressed bunches
subjected to a radiation process in the FLASH linac covers
a wide wavelength spectrum from the millimeter range
down to a few micrometers. Diffraction gratings are well
suited to disperse broad-band radiation to different
detection channels. The principles of grating based
spectrometers as tools for longitudinal diagnostic aredescribed in reference [1]. These principles are applied inseveral devices that are described in [2] and [3] or will be
explained in this paper.

Figure 1: Amplitude of the SASE FEL signal as a functionof the off-crest phase φ in the first acceleration module.
Also the intensity of coherent transition radiation forwavelengths of 20 ± 1μm , 40 ± 2μm , 75 ± 4μm andfor λ > 90 μm is shown. Distributions are individuallynormalized to a maximum value of 1.

594

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THPPH018

Spectrograph
Here a single shot spectrometer that gives the ultra
broadband spectra of coherent radiation on a shot to shotbasis is called spectrograph. As it was described in [1] aspectrograph is composed of three main components, onethat disperses the polychromatic radiation, one that
focuses the dispersed radiation to spatially different
coordinates dependent on wavelength without mix-up andthe detector system. The first two issues were covered andexplored in [2] and [3]. The most new achievement is thedevelopment of a fast 30 channel detection system basedon pyro-electric sensors, Fig. 2.

Figure 4: Recorded spectra by using a transmission gratingwith 2.5 lines per mm.

Figure 2: The 30 channel pyro line detector is equippedwith fast read out electronics and pyro sensors withbroadband smooth response function. The sensitivity is
about 300 pJ (5 times noise level) for 1μm < λ < 1mm, [4].
Two types of single stage spectrographs based on
Transmission Grating (TG) and Reflectance Blazed
Grating (RBG) have been successfully tested.
A TG base spectrograph can cover a rather large rangeof wavelengths in a single stage. It should be noticed thatwith a single stage TG spectrograph we will cover theentire interesting wavelength range from 50 to 300 μm ,with only two stages the spectra up to 1.8 mm could bederived, Fig. 3. Fig. 4 shows a sequence of 600 subsequent
single shot spectra.

Reflectance blazed grating have a limited free spectral
range of about a factor of two but offer much better
resolution and efficiency and can be staged [1]. From theprevious studies it is clear that the most relevant part ofthe spectra for the FLASH machine operation in SASE
mode is about 10 to 100 μm . One of the measured spectrain this regime is shown in Fig.5. A combined plot of
measured spectra on different regions, averaged overmany shots, is shown in Fig. 6.

Figure 5: About 900 subsequent shots measured with reflectance grating of 50 lines per mm during SASE operaFigure 3: The averaged combined spectra recorded by tion.
stages with 2.5 and 0.5 line per mm.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 7: Plotted is the variation of the spectra in one of
the stages of reflectance blazed grating spectrograph (withFigure 6: The averaged combined spectra recorded by
25 lines per mm) when phase of the first accelerating
different RBGs. Full coverage of interesting range of themodule changed over ~10 degrees. The peak coherent
spectra for FLASH electron bunches requires 5 stages ofradiation intensity corresponds to operational condition for
RBG base spectrograph.
optimum SASE.
Fig. 7 shows a series of single shot spectra in the
REFERENCES
wavelength range from 30 to 50 μm recorded while thephase of first accelerating module was changed by ~10 [1] H. Delsim-Hashemi et. al., Broadband single shot
spectrometer, Proceedings FEL2005.
degrees. The spectra shows a very pronounced peak at the[2]H.
Delsim-Hashemi et. al., Single-shot longitudinal
phase of operation for optimum SASE.
diagnostics with THz radiation, Proceedings FLS2006.
[3] H. Delsim-Hashemi et. al., Bunch compression
CONCLUSION
monitor, Proceedings EPAC2006.
We have demonstrated that single-shot wavelength- [4] B. Schmidt and H. Delsim-Hashemi, to be published.
selective spectroscopy of coherent radiation is possible.
The described spectrograph can give, on a shot to shotbasis, information on very short structures of the electron
bunches which is not possible by other techniques and canbe used for fast feedback systems.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH019

INVESTIGATIONS OF THE LONGITUDINAL BEAM PROPERTIES AT
THE PHOTOINJECTOR TEST FACILITY IN ZEUTHEN∗
J. Rönsch† , J. Rossbach, Hamburg University, 22761 Hamburg, Germany
G. Asova, J. Bähr, H.-J. Grabosch, S. Khodyachykh, S. Korepanov, M. Krasilnikov,
A. Oppelt, B. Petrosyan, S. Riemann, L. Staykov, F. Stephan, DESY, 15738 Zeuthen, Germany
D. Lipka, D. Richter, F. Marhauser BESSY, 12489 Berlin, Germany
A. Onuchin, Budker Institut of Nuclear Physics, Novosibirsk 630090, Russia.

INTRODUCTION
The main goal of PITZ is the test and optimization of LBand RF photo injectors for Free-Electron Lasers (FELs).
The demands on this photo injector are long bunch trains
with short bunches, a charge of about 1 nC and small emittances. The linac based FEL at FLASH incorporates a 1.5
cell RF gun capable of producing a high charge density,
followed by an acceleration section and a magnetic bunch
compressor. For an effective bunch compression detailed
studies of the longitudinal phase space after the gun and its
evolution behind the booster cavity have to be performed.
The new screen station (HIGH1.Scr2) is planed to beplaced about 5 m downstream of the photocathode andabout 1.5 m downstream of the exit of the booster cavity
in the PITZ2 setup [1] as shown in Figure1.
In the past, PITZ made good experience by using thefull cone of a Cherenkov radiator for bunch length measurements after the gun [2]. It will be discussed whether
a copy of screen station LOW.Scr3 can be used and which
modifications are necessary.

Screen Dimensions
For higher energies the beam size becomes smaller, butwhen the booster cavity is turned off the beam size increases. Simulations of transverse beam size at the positionof HIGH1.Scr2 were made to clarify the needed dimensions. Figure 2 (a) shows the simulated transverse beam
size at a gun and booster phase with maximum energy gain
for different solenoid currents, when the booster is turned
on. The smallest transverse beam size could be reached forabout 260 A. In Figure 2 (b) the simulated transverse beam
4

xrms
yrms

3.5
3

y [mm]The goal of the Photoinjector Test Facility at DESY in
Zeuthen (PITZ) is to test and optimise electron guns for
FELs like FLASH and X-FEL at DESY in Hamburg. In
2005 the setup was extended by a booster cavity. In order tomeasure longitudinal and transverse properties of the beamwith a momentum in the range between 4 to 40 MeV/c, aviewport after the booster cavity has been developed. It
contains several radiators. One of them is Silica aerogel
used as Cherenkov radiator for the measurement of the longitudinal electron distribution with a streak camera. Design
considerations are presented in this paper.

tors (aerogel, an optical transition radiator (OTR), quartz),
whose light is transported to the streak camera [3] and atapered empty tube, for beam passage without wakefield
production. The Silica aerogel (refractive index n = 1.03,
thickness th = 2 mm) is used as a Cherenkov radiator andthe pulse length is measured using an optical transmission
line [4] and a streak camera.
The new screen station (HIGH1.Scr2) and its elements
should be designed for electron energies in the range of 4
up to 40 MeV, so it can be used even if the booster cavity
is off. Planed elements are: a YAG-screen and an OTR for
the determination of the transverse beam size and positionof the electron beam using a TV camera, Silica aerogel anda further OTR for bunch length measurements as well as an
empty tube.

beamsize / [mm]Abstract

8
0.6
7
0.4

6

2.5

0.2

5

2

0

4

1.5

-0.2

3

-0.4

2

1
0.5

1

-0.6

0

SCREEN STATION FOR BUNCH LENGTH
MEASUREMENTS
Screen station LOW.Scr3 was designed for an electronenergy of about 5 MeV. It contains a YAG screen to determine transverse properties using a TV camera, three radia∗ This work has partly been supported by the European Community,
contract numbers RII3-CT-2004-506008 and 011935, and by the ’Impulsund Vernetzungsfonds’ of the Helmholtz Association, contract number
VH-FZ-005.
† jroensch@ifh.de

FEL Technology

200 220 240 260 280 300
solenoid current [A](a)-0.6 -0.4 -0.20

0.2 0.4 0.6
x [mm]

0(b)

Figure 2: Simulations of the electron beam size as a function of the solenoid current (a) and transverse beam properties at the screen station (b) for a gun and booster phasewith maximum energy gain and a flat-top longitudinal laser
distribution at 1 nC.
distribution are shown for 260 A and a gun and booster
phase with maximum energy gain.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 1: Planed setup of PITZ2. The screen station HIGH1.Scr2, LOW.Scr3 and DISP1.Scr1 are marked.

20
18
16
14
12
10
8
6
4
2
0

x rms, 40 MV/my rms, 40 MV/mx rms, 60 MV/my rms, 60 MV/m

y [mm]

beamsize / [mm]Results of simulations of the beam dynamics, when the
booster is off are shown in Figure 3. In this case the beam
size is almost 10 times higher than with the booster cavity
turned on.
8

8

6

7

4

6

2

5
4

0

3

-2

2

-4

1

-6

250

300
350
400
solenoid current [A]

-10

-5

(a)

0

5

10
x [mm]

0(b)

Figure 3: Simulated transverse electron beam size as afunction of the solenoid current for 40MV/m and 60MV/m
gradient (a) and transverse beam properties at the screen
station (b) for a gradient of 40MV/m in the gun and a phasewith maximum energy gain, a flat-top longitudinal laser
distribution at 1 nC, when the booster is turned off.
For measurements using the booster the beam size could
be very small, therefore both OTRs will have an effective
size of 20 mm × 20 mm. Using an OTR at an angle of 45 ◦with respect to the beam direction, backward radiation isemitted at 90◦ regarding the beam direction. A thin plate(about 300 µm) will be used as OTR, because of its better
optical quality and resistance compared to a thin foil. Two
different types of OTR screens are in use at FLASH [5]:• 350 um thick polished silicon (Si)• 350 um thick Si with an aluminium (Al) coating
The Si has a better thermal resistance than Al, and therefore
the pure Si screen stands a higher charge density (i.e small
beam with high charge) than Si coated with Al. On theother hand the Al emits about 2-3 times more photons thanpolished Si, i.e. the light yield is much better. That is why
we decided to use the Al coated Si plates.
Since there are no quadrupoles planed before this screen
station there is no possibility to reduce the beam size inthe case the booster is off. To catch the whole beam even598

when the booster is off the effective size of the YAG screen
should have the dimension size as the beam tube (diameter= 35 mm).

Bunch Length Measurement
The temporal resolution of the Silica aerogel used at
LOW.Scr3 was calculated to be 0.12 ps at a beam momentum of 4.5 MeV/c [6]. This value is very small compared to the resolution of the optical transmission line.
The temporal resolution of the optical transmission line
was determined with 1.15 ps when using an optical transmission filter of 550 nm with a bandwidth of 10 nm [7].
The bunch length measurements were typically done for a
streak camera slit width of 100 µm. The temporal resolution of a 100 µm slit was determined with about 1.75 ps forthe streak camera used at PITZ [2]. The resolution of thestreak camera C5680 is denoted by the producer with 2 ps
FWHM [3]. Therefore it is useful to increase the thicknessof the Silica aerogel in order to increase the number of photons, so one could reduce the slit width or the number ofpulses used for a measurement. The initial idea was to use
Silica aerogel with an index of refraction n = 1.03 and a
thickness of 5 mm. Cherenkov light is emitted under a certain angle depending on the average refractive index of theradiator (n) and the electron energy. It leaves the radiator
following Snells law. Figure 4(a) shows the emission angleof Cherenkov radiators with three different indices of refraction. For low energies the angle changes strongly withthe energy, but at higher energies it stays constant. Aerogel with n = 1.03 has an emission angle of up to 14.3 ◦ at
an electron beam momentum of 40 MeV/c, but the acceptance angle of the optical system from the screen station to
the streak camera is only ±11.8 ◦. Using an aerogel withn = 1.03 it is impossible to collected the whole Cherenkov
cone.
In contrast to Cherenkov radiator the optical transition
radiator emits the light within a certain angular distribution.
The angular distribution of transition radiation depends on
the particle energy and the angle of incident [8]. In Figure 4,(b) the angular distribution for a beam momentum of
40 MeV/c and 5 MeV/c electrons are shown. At 40 MeV/cbeam momentum most of the light is emitted within a small
angle. At smaller energies it becomes impossible to collect

FEL Technology

intensity [a.u.]

16oemission angle [ ]Proceedings of FEL 2006, BESSY, Berlin, Germany

14
12
10
8

0.7
0.6
0.5
0.4

Aerogel, n=1.008
Aerogel, n=1.02
Aerogel, n=1.03
θ (OTR)

6
4
2
0

40 MeV
5 MeV
5 MeV magnified

0.8

5

0.3
0.2
0.1
0
-50-40-30-20-10 0 10 20 30 40 o50
θ[ ]10 15 20 25 30 35 40
momentum [MeV/c]

(a)

(b)

Figure 4: The emission angle of OTR and the Silica aerogel radiators with different reflective indices as a functionof the electron momentum (a) and the angular distribution of optical transition radiation produced by 40 MeV and5 MeV electrons (b).
all the light by the used optical system. The red curve in
Figure 4 (a) shows the angle with the highest number of
emitted photons.
An aerogel with n = 1.02 and th = 7 mm (as well
as n = 1.008 and th = 15 mm) would lead to about thesame temporal resolution as an aerogel with n = 1.03 anda thickness of th = 5mm, but the number of photons islower, as shown in Figure 5.

THPPH019

LONGITUDINAL PHASE SPACEMEASUREMENTS
The longitudinal phase space after the gun at DISP1.Scr1(shown in Figure1) and its projection were measured for
different phases of the gun. In order to compare simulated (Fig.6 second row) and measured (Fig.6 first row)
longitudinal phase space the simulated one was tracked
through the dipole using matrix formalism. The verticalscale was converted into momentum scale after the correction of M56 [9] by shearing the distribution (Fig.6 thirdrow). Matrix element M 56 describes the influence of thedipole on the longitudinal distribution due to different particle momenta. The measured momentum distribution fits
very well with the distribution traced through the dipole(Fig.6 fourth row). Also the longitudinal distribution (Fig.6
fifth row) shows a rather good agreement. It is difficult tofind similarities with in the longitudinal phase space. The
longitudinal phase space changes completely after tracing
the particle though the dipole. In [10] it will be shown,how to design a dipole magnet in order to minimize thisproblem. Beside the influence of the dipole magnet the optical transmission line and the streak camera itself have an
influence onto the resolution as described in [7].

t_rms [ps]photons per electron

CONCLUSION
Aerogel n=1.008, d=15mm

16
14
12
10
8
Aerogel n=1.008, d=15mm

6

Aerogel n=1.008, d=9mm

4

Aerogel n=1.02, d=7mm

20

Aerogel n=1.03, d=5mm

510 15 20 25 30 35 40
momentum [MeV/c](a)Aerogel n=1.008, d=9mm

0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

Aerogel n=1.02, d=7mm
Aerogel n=1.03, d=5mm

510 15 20 25 30 35 40
momentum [MeV/c]

A screen station to measure longitudinal and transverse beam properties in the momentum range from 4 to
40 MeV/c was designed. One of the radiator is Silica aerogel used as Cherenkov radiator for the measurement of
the longitudinal electron distribution with a streak camera.
Even at 40 MeV/c Silica aerogel produces a higher photon
yield than OTR. Longitudinal phase space studies and improvements of the system are ongoing.

(b)

ACKNOWLEDGMENT
Figure 5: Number of photons (a) and resolution (b) of Silica aerogels with different indices of refraction and thickness’s as a function of the energy.
By mechanical reason the maximum usable thickness is
9 mm. The Budker Institut of Nuclear Physics (Novosibirsk) is producing Silica aerogel for PITZ, but only Silica aerogel with n = 1.008, 1.03 and 1.05 are produced
by default. A production of Silica aerogel with n = 1.02
would take a lot of effort. So we will start to use aerogel with n = 1.008 and 9 mm, which can be replaced later.
The main disadvantage of the refractive index n = 1.008 isthat the lower limit for the production of Cherenkov lightis at about 4 MeV/c and the photon yield changes strongly
within the beam momentum range from 4 to 6 MeV/c. The
advantage is that the Cherenkov light of bigger transverse
distributions can be transported and small misalignmentsof the optical transmission line does not lead to losses. The
number of photons produced by aerogel at 40 MeV/c is stilla factor of a few hundred higher compared to OTR.

FEL Technology

We would like to thank Lap Van Vu (DESY Zeuthen) for
the technical design and J. Kolbe for useful discussions andhints concerning the design and construction.

REFERENCES[1] A. Oppelt, PITZ2 Elements and Coordinates, http://wwwzeuthen.desy.de/∼apohl/pitz2/PITZ2-Schema.jpg(11.08.2006).
[2] D. Lipka, “Investigations about the longitudinal phase spaceat a photo injector for minimized emittance”, PhD Thesis
2004 Humboldt University Berlin.
[3] Hamamatsu, “Test report C5680-21, Serial No. 040168”.
[4] J. Bähr, D. Lipka, H. Lüdecke, “Optical transmission line forstreak camera measurement at PITZ”, Dipac Mainz 2003.
[5] K.Honkavaara private communication.
[6] D. Lipka et al, “Silica aerogel radiators for bunch length measurements”, Nuclear Instruments and Methods in Physics Research A 538 (2005) 597?607.

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Figure 6: Measurement (1st row) and simulation (2nd row) of the longitudinal phase space. The simulation was traced
through the dipole to show the expected distribution. The projections of the three distributions were compared to thedirect bunch length measurement (4th row) and momentum measurement (5th row). Black line is direct measurement,
red simulation, cyan projection of the phase space measurement and blue projection of the traced distribution. The results
were shown for gun phase with maximum energy gain +10 ◦ , +0◦ , -10◦ and -25◦ (from left to right).
[7] J. Rönsch et al, “Investigations of the longitudinal phasespace at PITZ”, EPAC Edinburgh 2006.
[8] K.Honkavaara, “Considerations of streak camera measurements for Photoinjector Test Facility (PITZ) in DESY
Zeuthen”, note, July 2000.

600[9] D. C. Carey, K. L. Brown, F. Rothacker, “Third-Order TRRANSPORT with MAD Input”, FERMILAB-PUB-98/310.
[10] S. Khodyachykh et al., Design of the Multipurpose Dispersive Section at PITZ, contribution THPPH020, FEL 2006.

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH020

DESIGN OF MULTIPURPOSE DISPERSIVE SECTION AT PITZ∗
S. Khodyachykh† , J. Bähr, M. Krasilnikov, A. Oppelt, L. Staykov, F. Stephan,
DESY, Zeuthen, Germany,
T. Garvey, LAL, Orsay, France, D. Lipk, BESSY GmbH, Berlin, Germany,
J. Rönsch, University of Hamburg, Hamburg, Germany.
Abstract
A detailed knowledge of the parameters of a highbrightness electron beam is of major importance for evaluating the performance of a free electron laser using thebeam. Therefore, a full characterization of the beam parameters is required during the commissioning of RF photo
injectors. As one important contribution to fulfill this task,a multi-purpose high energy dispersive arm (HEDA1) for
electron energies up to 40 MeV is presently under construction at the Photo Injector Test Facility at DESY in Zeuthen(PITZ). The dispersive section is designed such that it will
combine the functionality of 1) an electron spectrometer,
2) a device for characterization of the longitudinal phasespace, and 3) a transverse slice emittance measuring system. The HEDA1 consists of a 180◦ dipole magnet (CBend), followed by removable slit, a quadrupole magnet,
and a screen station with a read-out for the streak camera.
Design considerations and the detailed lay out of the highenergy dispersive section are presented.

INTRODUCTION
The Photo-Injector Test Facility at DESY in Zeuthen(PITZ) is an electron accelerator which was built byDeutsches Elektronen-Synchrotron (DESY) in collaboration with international partners with the goal to develop
and to optimize high brightness electron sources suitablefor SASE FEL operation.
The PITZ facility consists of a 1.5 cell L-band RF gun,a photo-cathode laser system, a normal-conducting booster
cavity and a diagnostic section. Being an operational machine showing pioneering results in achieving of highcharge low-emittance electron beams for electron bunchtrains [1], PITZ is still under development. The beam line
which has a present length of about 13 meters will be extended up to about 21 meters within the next two years.
Many additional diagnostics components will be added tothe present layout. Together with the deflecting cavity [2],the phase space tomography module [3] and the second
high-energy dispersive arm (HEDA2), HEDA1 will extend
the existing diagnostics system of the photo injector. The
scope of the present paper is the multi-purpose high energy dispersive arm (HEDA1). The dispersive section isdesigned to combine the functionality of (i) an electron∗ This work has partly been supported by the European Community,

contracts RII3-CT-2004-506008 and 011935, and by the ’Impuls- undVernetzungsfonds’ of the Helmholtz Association, contract VH-FZ-005.
† sergiy.khodyachykh@desy.de

FEL Technology

spectrometer, (ii) a device for characterization of the longitudinal phase space, and (iii) a transverse slice emittancemeasuring system.

SETUP
The layout of the dispersive section HEDA1 is schematically shown in Fig 1.
The heart of the dispersive section is a 180◦ dipole magnet having the bending radius of 300 mm. The bending
radius has been chosen as a compromise between the spacerequirements and momentum resolution on the one hand
and the ability of the spectrometer to operate within thelarge range of gun and booster parameters. Being deflected
in vertical plane, the electron beam enters the dispersivearm which goes below the main beam line parallel to it.
The dispersive arm includes a pumping port combined witha removable slit mask, a quadrupole magnet Q1 for the slice
emittance measurements, a drift space of 600 mm followedby two screen stations (for simplicity only one is shown)and by a beam dump. For measuring of the bunch charge an
integrating current transformer (ICT) is foreseen between
the two screen stations (not shown).
For the reasons described in the following sections additional components which contribute to the measurements
at HEDA are located in the main beam line. These are thequadrupole magnet Q2 and the screen station S2 placed upand downstream to the dipole magnet D, respectively.
The main advantage of the 180-degree spectrometeris the simplicity to reconstruct the momentum distribution [4]. One uses the screen S2 in the straight section andmeasures the contribution from the transverse beam sizeand divergence, which can be de-convoluted with the measured spectrum to obtain the pure momentum distribution.
This can be illustrated by comparing of the transport matrix MD (describing the transport of the electron beam between the position of the quadrupole magnet Q2 and thescreen S1 ) with the matrix MS which corresponds to thedrift between Q2 and the screen S2 . The matrices in thinlens approximation have the form⎛

−1
MD = ⎝ 00⎛−l1 − l2
−1
0

1 l1 + l2
1
MS = ⎝ 0
0
0

⎞
2ρ
0 ⎠
1
⎞
0
0 ⎠
1

(1)

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 1: Simplified layout of PITZ with the first high energy dispersive section.

LONGITUDINAL PHASE SPACE
Very important information for the understanding of thephoto-injector can be gained by studying the electron distribution in the longitudinal phase space, when the electron
momentum is measured as a function of its longitudinal position within the bunch. For this purpose one of the screen
stations will be equipped with an aerogel screen used as a
Cherenkov radiator and a read-out for the streak-camera.
Figure 3 (a) shows the results of numerical simulationof the longitudinal phase space using the code ASTRA [7]

602

(a)
(c)
(a − c)/adx (mm)booster phase (degree)where ρ is the bending radius of the dipole magnet and at the entrance of the dipole magnet. The particles werelengths l1 and l2 are defined in Fig 1.
tracked through the dipole using the matrix formalism,
The transverse coordinates of the i-th electron can be de- similar to that described in previous section, but using
scribed by a vector yi = (yi , yi , pi /p)T , where yi is theTable
6 × 6 transport matrix. The longitudinal phase space retransverse position, yi is the divergency and pi /p is the60
250
relative momentum. Assuming the electron with the coordinate y0 is transported through the spectrometer it will40
get the transverse coordinate on the screen S1 which is de200
scribed by the first component of vector y1 = MD y0 . The
20
shift of the particle with respect to the reference trajectory
150
is thus defined not only by the relative momentum of the0particle, but also by it initial transverse offset and diver100
gency. To exclude these two contributions one uses the-20measurements on the screen S2 where only initial coordinate and initial divergency define the position of the parti50-40
cle (compare M11 and M12 elements of matrices in Eq.1).
Moreover, by focusing the beam on the screen S2 with the-20 -100
102030
help of the quadrupole magnet Q2 one can control the resgun phase (degree)
olution of the momentum measurement.
Beam momentum and momentum spread depends Figure 2: The total beam size in dispersive plane on screenstrongly on the machine parameters. It is very sensitive S1 as a function of gun and booster phases.
to the RF phases of the gun and of the booster. Because of
the large dispersion of the dipole magnet the spot sizes on constructed on the screen S1 of the dispersive section after
the screen S1 are expected to be very large, especially in the drift having the length of a 1 m is shown in Fig. 3 (b). A
cases of far off-crest RF phases. Figure 2 shows the depen- correction of the influence from the matrix element M56 [6]dence of the vertical beam size on the screen S1 as a two was applied in Fig. 3 (c). Figure 3 (d) shows the momendimensional function of the gun and booster phases. The tum distribution as a projection of Fig. 3 (a) in red and 3 (c)aperture of the quadrupole magnet Q1 (80 mm) defines the in blue.
A comparison of the initial and the reconstructed values
transversal acceptance of the dispersive section. Thus, usof
mean momentum p, momentum spread prms and lon◦ing HEDA1 measurements within the range of −35...35
gitudinal
emittance l are shownin table 1. Theof booster phases will be possible in single shot. For larger
off-crest phases a scan of dipole current will be used.
Table 1:Initial and reconstructed values of mean momentum, momentum spread and longitudinal emittance.
< p > (MeV)
18.311118.3109−0.0009%

prms (keV) l (π keV mm)
36.6
75.99
49.0
105.0833.8%
38.3%

results in Fig. 3 and table 1 were done without quadrupole.
These results could be improved by applying deconvolution with known beam size at S2 . However, this procedure unnecessary complicates data analysis comparing to
the method discussed below.
The simulations were repeated using a quadrupole triplet
4.5 m downstream the photocathode in order to focus the

FEL Technology

18.35
18.30

18.40
18.35
18.30

18.25

18.25

18.20

18.20

18.15
0

5
10
z (mm)

-15

-10

18.35
18.30
18.25
18.20
18.15
-10

-5

-5

0

0

5
10
z (mm)

180

before dipole

160
140

after dipole

18.22

18.20

18.20
18.18
-10

pmean (MeV)
18.3105
18.3104−0.0005%

18.22

40

18.20

20

18.18

prms (keV)
36.54
36.59
0.16%

l (π keV mm)
75.72
76.11
0.5%

The use of a quadrupole triplet brings a remarkable improvement to the measurements of the longitudinal phasespace. Both, the longitudinal phase space and the momentum distribution are reproduced with very good agreement.
The differences between the simulated and reconstructedvalues of the momentum spread and longitudinal emittance
reduces by using of the triplet from about 35% down to lessthan one per cent.
In order to save some space in the main beamline, we
studied the possibility to exchange the quadrupole triplet
with a single quadrupole magnet. Indeed such replacement
almost does not decrease the accuracy of the longitudinal
phase-space reconstruction. Figure 5 shows a comparisonof the momentum measurements. The differences between
the simulated and reconstructed mean momentum, momentum spread and longitudinal phase space are still within
1 %.

-10

18.16
-15

-5

0

5
10
z (mm)

0

5
10
z (mm)

(b)

18.30

18.24

Table 2: Initial and reconstructed values using a quadrupole triplett

18.16
-15

5
10
z (mm)

18.32

60

beam onto screen S1 (at position 6.5 m). The results areshown in figure 4 and table 2.

0

18.34

18.26

(d)

-5

(a)

80

Figure 3: Longitudinal phase space obtained with thequadrupole magnet Q2 being off: longitudinal phase space(a), reconstructed longitudinal phase space at S1 (b), reconstructed longitudinal phase space at S1 after correction of
M56 (c), momentum distribution (d).

FEL Technology

18.24

18.22

18.28

(c)

(a)
(c)
(a − c)/a

18.26

18.24

100

18.15 18.2 18.25 18.3 18.35 18.4
p (MeV/c)

18.30
18.28

120

0

18.32

18.26

18.16
-15

5
10
z (mm)

18.34

18.28

(b)
Intensity (a. u.)p (MeV/c)

(a)
18.40

-15

18.30

p (MeV/c)

-5

18.32

18.35

18.3

18.25

18.2

-10

-5

0

5
10
z (mm)

18.15
-15

-10

-5

(c)
(d)
Figure 4: Longitudinal phase space obtained with thequadrupole triplet placed on the position of Q2 being on:
longitudinal phase space (a), reconstructed longitudinal
phase space at S1 (b), reconstructed longitudinal phasespace at S1 after correction of M56 (c). For a comparison reconstructed longitudinal phase space at S1 [as (c)]but with a single quadrupole instead of a triplet.

TRANSVERSE SLICE EMITTANCEMEASUREMENTS
The functionality of the HEDA can be enhanced with asetup that allows us to measure the transverse emittance ofthe electron beam at different longitudinal positions along
the bunch. The so called slice emittance is providing better
understanding of the physics of a photoinjector, particulary
the emittance compensation and conservation principles. It
is also an important parameter for the SASE FELs since
the slice emittance and slice peak current define the gainof the SASE FEL process. Using proper phasing of thebooster cavity we can obtain linear correlation between the
momentum and longitudinal distribution of the electrons in
Intensity (a. u.)

-10

18.34

18.18

p (MeV/c)

-15

18.15

THPPH020
p (MeV/c)

18.40

p (MeV/c)p (MeV/c)p (MeV/c)

Proceedings of FEL 2006, BESSY, Berlin, Germany

180
160
140
120
100
80
60
40
20
0

18.15 18.2 18.25 18.3 18.35 18.4
p (MeV/c)

Figure 5: Simulated momentum distribution (black) compared to its reconstruction in the dispersive arm with thesingle quadrupole Q2 (red), quadrupole triplet (green) andwithout quadrupole (blue).

603

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Proceedings of FEL 2006, BESSY, Berlin, Germany

the bunch. Afterwards one applies the standard quadrupole
scan technique and measures the emittance for different
momentum/time slices of the bunch.
A setup similar to that in [8] will be implemented. A slit
at the dipole exit selects the necessary slice from the energy
chirped beam. This slice is scanned with the quadrupole Q1
focusing in a plane orthogonal to the dispersion plane of thedipole, the beam distribution will be observed on screen S1 .
Due to the short distance between the quadrupole and thescreen the beam size tends to become very small during thescan. For the correction of this the quadrupole magnet Q2
with fixed strength placed before the dipole will be used(see Fig.1). The experimental setup was simulated with

Figure 7: Deviation between the result from the simulated
measurement and the slice emittance distribution obtainedwith ASTRA.
Figure 7 shows the deviation between the result from thesimulated measurement and the slice emittance distribution
obtained with ASTRA. The average deviation is 21 % but
for some slices it can reach up to 66 %. Further improvement of the measuring accuracy can be reached by taking
into account the space charge during the reconstruction.
Figure 6: Slice emittance distribution at the dipole entrance. The solid line gives the value for the projected emittance.
ASTRA [7] in attempt to verify the technique and to optimize the setup. For the simulations presented here, a gun
gradient of 60 MV/m and a phase of maximum acceleration in the gun, the current in the main solenoid was 385 A,
and a booster phase of +70 degrees were chosen. This corresponds to a projected emittance of 1.6 mm · mrad (seeFig. 6), a mean momentum of 17 MeV/c and an RMS momentum spread of 1.4 MeV/c.
The electron bunch was separated in ten longitudinalslices which were scanned with ten different quadrupole
strengths. The distribution is fited to a quadratic equation(2) where the corresponding beam parameters are obtained.
22·x20 +2·M11 M12 x0 ·x0 +M22·x2
x2s  = M11
0  (2)

Here x2s  is the beam size coresponding to the particularstrength of the quadrupole magnet, M11 , M12 and M22
are the elements of the transport matrix, functions of the
quadrupole strength, x20 , x0 · x0  and x02  are the initial
beam parameters that need to be found. The corresponding
value for the emittance then is calculated using Eq. 3.

 2
(3)
εn = βγ · x20  · x20  − x0 · x0  .
Here x20  and x20  are the rms dimensions of the beam in
the so-called trace phase space and x0 · x0  is the correlation between both.

604

ACKNOWLEDGEMENTS
Besides the funding agencies mentioned on the first pageof the present paper the authors would like to thank S. Riemann, H.-J. Grabosch (both DESY) for valuable discussions. Without brilliant ideas of our engineers the realization of this work would not be thinkable.

REFERENCES[1] F. Stephan, Status and perspectives of photo injector developments for high brightness beams, proceedings of teh workshop on the Physics and Applications of High Brightness
Electron Beams. Erice, Italy, 2005.
[2] S. Korepanov et al., Design Consideration of the RF Deflector
to Optimize the Photo Injector for PITZ, Proceedings of the
FEL2006, Contribution THPPH021.
[3] D.J. Holder et al., A phase space tomography diagnostic for
PITZ, Proceedings of EPAC 2006.
[4] D. Lipka, Spectrometer design for the SRF Gun, BESSY
Note SRFgun-BESSY-003-12-2004, 2005.
[5] D. Lipka et al, Silica aerogel radiators for bunch length measurements, Nucl. Instr. Meth. A 538 (2005) 597.
[6] J. Rönsch et al., Measurement of the longitudinal phase spaceat the photo injector test facility at DESY in Zeuthen (PITZ),
Proceedings of DIPAC 2005, Lyon.
[7] K.Floetmann, ASTRA, http://www.desy.de/ mpyflo.
[8] X. Qiu et al., Demonstration of emittance compensation
through the measurement of the slice emittance of a 10 picosecond electron bunch, Phys. Rev. Let. 76 No. 20 (1996)
3723.

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH021

DESIGN CONSIDERATION OF THE RF DEFLECTOR TO OPTIMIZE THE
PHOTO INJECTOR AT PITZ*
S. Korepanov#, S. Khodyachykh, M. Krasilnikov, A. Oppelt, F. Stephan, DESY-Zeuthen, Germany
V. Paramonov, INR, Moscow, Russia.
Abstract
In order to optimize photo injector for Free Electron
Laser (FEL) applications, a detailed characterization of
the longitudinal and transverse phase space of the electron
beam provided by the Photo Injector Test Facility at
DESY in Zeuthen (PITZ) is required. In the paper we
present design considerations of the RF deflecting cavity
for transverse slice emittance and longitudinal phasespace measurements.

V%

Deflecting voltage

YB

zs

z

LB

INTRODUCTION
The main research goal of PITZ is the development ofelectron sources with minimized transverse emittance [1].
The current setup at PITZ permits us to measuretransverse emittance averaged along a bunch using theEmittance Measurement System (EMSY) [2]. With theuse of an RF deflector it is possible to analyse theslice transverse emittance. Adding a dispersive arm
the longitudinal beam phase space can be completely reconstructed.
At PITZ2 the application of an RF deflector is planned.
The deflector position is about 9 m from the gun. The
next 3.5 m space is taken by a tomography module, which
will be used for transverse phase space measurements. At
about 15.5 m a spectrometer based on dipole magnet ispositioned.
In Fig. 1 the effect of the RF deflector is illustrated: theRF deflector voltage is null in the longitudinal centre of
the bunch and gives a linear transverse deflection to thebunch itself. The maximum displacement of the edge slice
YB can be estimated by the expressionYb

S  f RF  L  LB  VA
cE /e,(1)where fRF is the frequency of the deflecting voltage, VA is
the peak transverse voltage, L – drift space after the
deflector, and E is the beam energy in eV units [3].
The resolution length Lres can be estimated as the bunch
length LB divided by the number of slices Nslices which canbe resolved at the screen. And the number of the slices is
YB divided to transverse beam size VB.

Lres

LB
N slices

LB  V B
YB

VB c E /e
S  f RF  L  VA___________________________________________* This work has been partly supported by the European
Community, contracts RII3-CT-2004-506008 and 011935, and by
the ‘Impuls- und Vernetzungsfonds’ of the Helmholtz Association,
contract VH-FZ-005#
sergey.korepanov@desy.de

FEL Technology(2)L

Figure 1. The principle of the RF deflector work.
For the prospect beam parameters at PITZ2 (Table 1)
the possible resolution length is limited by the transverse
size of the screen ( < 36 mm) and minimum transverse
beam size (VB ~ 1.6 mm). That gives the maximum
number of the slices about 20 and the longitudinal
resolution length about 0.4 mm (1.3 ps).
Table 1. PITZ2 beam parameters.
bunch charge
1 nC
max. long. momentum
32 MeV/cmin. norm. emittance (rms)< 1 S mm mradtransverse beam size on< 0.4 (1.6) mm
screen in tomography
module, rms (full)
full longitudinal beam size
8 mm (27 ps)
pulse frequency
1-9 MHz
repetition rate
10 Hz

RF DEFLECTORSFor PITZ2 diagnostics we have reviewed three kinds of
RF deflectors. Two of them are steady wave resonatorsand one is a travelling wave cavity. We analyzed electron
beam parameters after passing the cavity and compared
the results for the different deflectors.

Steady wave cavities
We have chosen the well known cavity which is a disk
loaded waveguide [3]. It has five cylindrical cells. We
scaled it to the frequency 1.3 GHz, Fig.2a. This cavity

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Proceedings of FEL 2006, BESSY, Berlin, Germany

from the deflector. In the table Q is unloaded quality
factor, “Field build up” is the time which field needs toreaches about 99% of there maximum value [5].

BEAM DYNAMICS

a)b)

Figure 2. General view of “classical” cavity (a) and“Paramonov” cavity (b).
operates with TM11 mode. Another steady wave cavity is
a new one designed by V. Paramonov. The shape of thestructure is shown in Fig.2b. It operates in TE11 mode.
More details about this cavity are given in [4].

Beam dynamics simulations have been performed forcomparing the cavities presented above. For our
simulations we use a beam with the parameters: averageenergy 32 MeV, energy dispersion 140 keV, transverse
beam size about 0.7 mm, transverse emittance - 0.9 S mm
mrad. The beam is passing through the deflector and isobserved at the points of screens positions in the
tomography module and in the dispersive section after the
dipole.
Longitudinal momentum distributions

Longitudinal momentum distributions
1800

1800

1600

1600

1400

1400
1200

1200

Travelling wave cavity

1000

a)

1000

The third cavity is based on LOLA-IV - transverse
deflecting cavity [5], Fig.3. We have adapted it for our
beam: scaled it from 2.856 GHZ to 1.3 GHZ and changed
length from 3.6 m to 0.7 m. It has 9 cells and two
additional cells for coupler and load.

c)

800

800

600

600

400
400

200
200
0
3.185

0
3.185
3.19

3.195

3.2
3.205
Pz, eV/c

3.21

3.2

3.21

3.215

3.22
x 10

Pz, eV/c

7

3.19

3.195

3.2
3.205
Pz, eV/cPz, eV/c

3.21

3.215

3.22
x 10

7

1800
1600
1400
1200
1000
800

RF

b)

600
400
200
0
3.185

3.19

3.195

3.205

Pz, eV/c

3.215

3.22
x 10

7

Figure 4. Longitudinal momentum distribution.
Red line corresponds to the initial distribution (before
deflector).Blue line is the distribution for the beam
passed through a)“classic” cavity, b) “Paramonov”
cavity, c) traveling wave cavity.
Deflection

Figure 3. Travelling wave cavity based on LOLA-IV.
In the Table 2 we compare the deflector parameters
for two operations regimes - to analyse the longitudinal
phase space at a distance of about 6 m from the deflector
in the dispersive arm and – to observe the beam at thefirst screen in tomography module at a distance of ~ 2 m
Table 2. Deflector parameters.
Classic cavity
Frequency 1.3
GHz2Distance,m
1.8
VA, MV
Q
21000
PRF, MW2
Fieldbuild up, ~20
Ps

606“Paramonov” Travelling
cavitywave cavity

1.3

1.3

1.3

1.3

1.3

6

2

6

2

6

0.6
1.8
21000 15000
0.12 0.17

0.6
15000
0.02

1.8
19000
9.1

0.6
19000
1.01

~20

~20

~0.2

~0.2

~20

For correct longitudinal phase space measurements inthe dispersive arm we have to minimize distortion of thelongitudinal momentum distribution during passing thedeflector. We compared the longitudinal momentum
distribution on the dispersive arm screen for the different
deflectors. In Fig.4 momentum distributions for the threevariants of the deflectors are compared with the initialmomentum distribution (before deflector). One can not
see large difference between these three cases. The
estimated resolution of the method is about 25keV/c. Thisvalue we can roughly resolve from the presented
distributions. The rise or fall edge in the initialmomentum distribution is about a few keV. They aretransformed to the edges with the width of about 25 keV.
The transverse slice emittance measurements require
high similarity of the initial longitudinal charge
distribution to the transverse charge distribution (along
deflecting direction) after deflector. This requires a lineal
dependence of the deflecting voltage to the position inside
the bunch. The requirement is provided by a quite large
RF wave length (230 mm) in the cavities in comparison
with the bunch length (8 mm). Beside that the cavity has
to generate a minimum distortion in the transverse

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany
120
100

80

DISSCUSION OF THE RESULTS

60

All presented cavities can be used for the beam phasespace analysis. We have considered their advantages anddisadvantages. The main differences are between steadywave and travelling wave cavities. The first one request
less RF power (see Table 2) and is easy in control. But thetravelling wave cavity gives us a possibility to analyse asingle bunch in a bunch train. We plan to work with thebeam bunch repetition frequency up to 9 MHz (period~0.11 Ps). Because of short filling time in travelling wave
cavity (0.2 Ps) we can “take” a single bunch and direct it
to a screen and distort 1-2 other pulses in the train only.
This possibility is important for the analysis of the beam
parameters fluctuation in the train from bunch to bunch.
Also we can make the beam monitoring during tuning thebeam. We decided to use the travelling wave cavity in
combination with the tomography module for the
possibility to analyse single bunches.

80

40

60
40

20

a)

c)

20
0
-0.01

-0.005

140

0
0.005
0.01
Z(scaled), Y, m

0.015

0.02

0
-0.01

0
0.01
Z(scaled), Y, m

0.02

120
100
80
60
40

b)

20
0

-0.01

0
0.01
Z(scaled) , Y, m

0.02

Figure 5. Charge distributions.
Red line corresponds tothe initial longitudinal
distribution (before deflector). Blue line is the transverse
distribution in the deflected direction for the beam passed
through a) “classic” cavity, b) “Paramonov” cavity, c)
traveling wave cavity.
direction (perpendicular to deflected direction). This isnecessary for correct emittance measurements. In Fig.5
we compare the longitudinal charge distribution of theinitial beam and transverse charge distribution for the
beam passed through deflecting cavity. We add a special
gap (0.4mm) in the initial distribution in our simulations.
That helps us to estimate the resolution length byobserving the gap in the transverse distribution of theTransverse momentum distribution
600
500
400
300
200
100
0
-3

-2

-1

0
Px, eV/c

1

2

3
4

x 10

Figure 6. Transverse momentum distribution(perpendicular to deflect direction). Red line –initial distribution (before deflector), blue line –distribution for the beam passed throughtraveling wave cavity
deflected bunch. One can see that all cavities provide
transverse bunch charge profile (corresponds to deflected
direction) similar to the initial longitudinal charge profile.
Because of the 100 % degree of the modulation in the
final distribution we can estimate that the resolution
length for these measurements is about the gap width (0.4mm).
Thetransverse
momentum
distributions(perpendicular to deflection direction) practically are notchanged in the deflector. An example of the transverse
momentum distribution before and after the deflector isshown on Fig.6 for the travelling wave cavity. The
simulations show minimal influence from the deflectors
to transverse beam parameters (perpendicular todeflection direction).

FEL Technology

THPPH021

DIAGNOSTIC COMPLEX FORLONGITUDINAL SLICE TRANSVERSEEMITTANCE MEASUREMENTS
The layout of the prospect system for slice emittancemeasurements is shown in Fig.7. It contains a deflecting
cavity, a tomography module and four kickers. The beam
is matched by quadrupoles on the entrance of thetomography section so that D and E functions are
periodically repeated from screen to screen [6]. That
permits us to analyse the beam more easily. The bunch
deflected in the RF cavity in vertical direction is deflectedby the kicker in horizontal direction to the screens. The
screens are located off axis. The kicker pulse duration isless 100 ns with rise(fall) time about 10 ns. That permits
to observe deflected bunches only. The few bunches
which are distorted in deflecting cavity by the rising or
falling RF field don’t hit the screens and are lost in the
beam line. All other bunches are passing through thetomography module and accepted at the beam dump.
tomography module
matching
Screen1
QQ

Q

DC
K

Q

Q

Q

K

K

Screen2

Screen3

Screen4

Q

Q

Q

Q

Q

K

~5m

Figure 7. Prospect diagnostic for longitudinal slice
emittance measurements.
Q – quadruple; K – kicker; DC – deflecting cavity
The layout of diagnostics for longitudinal beam phasespace measurements is shown in Fig.8. After tomography
module downstream we plan to set dispersive section. The
distance between the deflector and the screen in thedispersive arm is about 6 m. Bunches are deflected by adipole magnet and are analysed on the screen. During the607

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Proceedings of FEL 2006, BESSY, Berlin, Germany

dispersive arm operation the magnets in the tomography
module will be off.
~6m

Q

DC
K

Q

Q

K

Q

Q

K

Q

Q

Q

Q

K

Dispersive arm
ScreenFigure 8. Prospect diagnostics for longitudinal beamphase space measurements.

CONCLUSION
The deflectors reviewed in this paper satisfy therequirements for the beam diagnostic at PITZ2. We
consider to use the travelling deflecting cavity due to its
additional possibility to analyse single bunches in a bunchtrain. We expect the possibility to measuretransverse slice emittance with ~20 slices in the
tomography module. For longitudinal phase spacemeasurements in the dispersive arm we estimate theresolution as ~25 keV/c.
The authors would like to thank D.J. Holder and B.D.
Muratori for their work under the tomography module
analysing.

REFERENCES[1] F.Stephan, D.Kraemer, I.Will and A.Novokhatski,
Proc. FEL2k, Durham, USA, August 2000
[2] V.Miltchev
etal.,“Transverse
Emittance
Measurements at the Photo Injector Test Facility at
DESY Zeuthen (PITZ)”, DIPAC, 2003
[3] D.Alesini,
C.Vaccarezza,“Longitudinalandtransverse phase space characterization”, SPARCRF-03/003, INFN/LNF, Frascati, 2003
[4] V.Paramonov, et. al. “Effrctive standing-wave RF
structure for charged-particle deflector”, LINAC,
2006, (to be published)[5] O.H.Altenmueller, et.al., “Investigations of traveling– wave separator s for the Stanford two-mile linear
accelerator”, The rev. of Sci. instr., Vol.35(4), 1964
[6] D.J.Holder, et. al., “A phase space tomography
diagnostic for PITZ”, EPAC2006, Edinburgh, UK

608

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH023

TUNING, CONDITIONING, AND DARK CURRENT MEASUREMENTS
OF A NEW GUN CAVITY AT PITZ∗
A.Oppelt† , K.Abrahamyan, O.Aldrian, G.Asova, J.Bähr, G.Dimitrov, H.-J.Grabosch,
L.Hakobyan, J.Ivanisenko, S.Khodyachykh, S.Korepanov, M.Krasilnikov, B.Petrosyan,
R.Spesyvtsev, L.Staykov, F.Stephan, F.Tonisch, DESY, 15738 Zeuthen, Germany
F.Marhauser, D.Richter, E.Weihreter, BESSY, 12487 Berlin, Germany
K.Flöttmann, J.H.Han, C.Martens, R.Meyer, V.Miltchev, DESY, 22603 Hamburg, Germany
O.Kalekin, Humboldt University, 12489 Berlin, Germany
P.Michelato, L.Monaco, D.Sertore, INFN Milano, 20090 Segrate, Italy
J.Rönsch, University of Hamburg, 22761 Hamburg, Germany.
Abstract
In December 2005, a new gun cavity for the Photo Injector Test Facility at DESY in Zeuthen (PITZ) was tuned withthe help of a specially designed tuning device. The tuning
procedure and its results as well as RF measurements will
be presented. Meanwhile, the cavity was installed in the
PITZ facility and conditioned. Dark current measurementswith different cathodes were performed and are described.
Comparisons to former measurements are made.

INTRODUCTION
The photo injector test facility at DESY in Zeuthen (PITZ)
was built in order to test and optimize electron sources
for Free Electron Lasers and Linear Colliders. One of themain tasks is to prepare gun cavities for subsequent use at
FLASH and XFEL. Up to now, three gun cavities have been
built by DESY and another one is in production. They aredesigned for a peak power of 4.5 MW and an average heatload of 50 kW [1]. In order to reach higher power levels,
two further guns with improved cooling will be built towards the end of 2006.
After the production of the first gun cavity, prototype No.1,
a water-to-vacuum leak was found. It was figured out thatthe used copper did not fulfill the specifications. The leak
was repaired with a kind of glue, but an installation at
FLASH was not recommended. Therefore, this gun wasused for high power tests at PITZ after the commissioning of a 10 MW multi beam klystron in June 2005 [2]. The
conditioning towards higher peak and average power ended
suddenly with the break-up of the old water-to-vacuum leak
which appeared at a gradient of about 57 MV/m [3]. Meanwhile, the cavity was again repaired and is available forfurther tests.
Frequency measurements after the gun production showeda frequency difference from the goal frequency of 1.3 GHz(detuning) of 615 kHz, see Table 1. This detuning is caused∗ This work has partly been supported by the European Community,
contract numbers RII3-CT-2004-506008 (IA-SFS) and 011935 (EUROFEL), and by the ’Impuls- und Vernetzungsfonds’ of the Helmholtz Association, contract number VH-FZ-005.
† presenting author: anne.oppelt@desy.de

FEL Technology

by the brazing and cannot be calculated. Thus, the gun wasmechanically tuned and the dimensions of the cells havebeen corrected in the design of the next gun cavity.
Gun cavity prototype No.2 was nevertheless showing alarge detuning, probably due to the different copper quality.
The gun was used in the PITZ1 phase until Nov.2003 andwas installed at FLASH after a complete characterization
at PITZ [4] where it is in operation since February 2004.

Table 1: RF measurements results of all three existing
DESY cavities before tuning. The detuning was calculated
for an operation temperature of 43◦ C under vacuum (measurement at 23◦ C in air).
Gun cavity prototype No.
Frequency detuning (kHz)
Field flatness Ehalf /Ef ullMode spacing 0-π-mode (MHz)

1
616
0.90
5.3

2
1207
0.97
5.2

3.1
632
0.94
5.2

The third gun cavity (prototype No.3.1) has been built in
2003. In order to avoid the complicated tuning procedurethat was necessary for the previous guns, the cell’s dimensions have been corrected again. In addition, the gun has
special tuning knobs that allow modifying the resonance

Figure 1: Photograph of gun cavity prototype No.3.1.

609

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Proceedings of FEL 2006, BESSY, Berlin, Germany

frequency by up to 300 kHz. However, after some firstrf measurements of the resonance frequency in September
2004, it became clear that the tuning knobs cannot be used:
the measured detuning was too large (Table 1).

or pulled some ten microns and the deformation was surveyed. The use of the tuning tools left partly visible signatures in the material, but mostly not to recognize whentouching. Figure 3 shows an example of the marks fromboth tuning tools.

TUNING OF THE NEW GUN CAVITY
In order to shift the frequency and to correct the field profile, a new tuning device has been developed. It consists ofa stable girder on which the gun is placed, and two tools
for deforming the cavity walls: a tuning stamp for pushing the cathode wall at the cathode plane, and a tuning
clamp for pulling the coupler-facing wall of the full cell.
For frequency measurements a small tapered coupler has
been built by BESSY. Thus the system became much easier to handle compared to the large and heavy coaxial coupler used in the beamline installation. A bead pull setup forfield profil measurements can be easily mounted to the tuning device. Figure 2 shows a photograph of the complete
setup.

Figure 3: Marks in the copper material from the tuning
stamp (left; a circular mark around the cathode hole) andfrom the tuning clamp (right; two imprints in the couplerside wall).

Normalized E-Field

As result of the tuning, the resonance frequency is reachedat the design operation temperature of 54◦ C, while thefield flatness Ehalf /Ef ull was measured to be about 1.06,
see Figure 4. This means, the field at the cathode is 6%
higher than in the full cell. According to simulations, thisis a good compromise between high average accelerating

1,1
1
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
-250

-200

-150

-100

-50

Normalized E-Field

Relative Position z [mm]
1,1
1
0,9
0,8
0,7
0,6
0,5
0,4
0,3

Figure 2: Photograph of the tuning device with the gun
cavity, the BESSY test coupler, the bead pull setup, and thetuning tools: the clamp (mounted) and the stamp.
In November 2005, the new tuning device was used for the
first time. Gun cavity No.3.1 was tuned in several consequent steps. Each time the cavity walls were pushed

610

0,2
0,1
0
-300

-250

-200

-150

-100

Relative Position z [mm]Figure 4: Field distribution in the gun before (top) and after(bottom) tuning. The cathode field is finally 6% higher than
the field in the full cell.

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

DARK CURRENT STUDIES
After the tuning, the new gun cavity was installed in the
PITZ beamline and conditioned up to the full FLASH specifications: 3.5 MW peak power, 900 µs pulse duration,and 10 Hz repetition rate, corresponding to an average
power of 31.5 kW [3].
Extensive dark current studies started in April 2006 andcontinued during the summer. The measurements weredone for one Cs2 Te cathode (used for beam operation in2005 and 2006), and for four Mo cathodes (with opticalpolished surface, used for gun conditioning). One of the
Mo cathodes (cathode 80.1) has a hole pattern on its surface [5]. It was foreseen to serve for dark current generation studies but the corresponding pattern was not foundin the dark current images. An example of such an image
is displayed in Figure 5: it shows the YAG screen signalof dark current emitted by this specially prepared cathode80.1.

Figure 6: Topview of two of cathodes in the cathode chamber: Mo cathode 80.1 with the special hole pattern (left)
and Cs2 Te cathode 58.1 (right).
produced 2002 without magnets is higher than the currently
measured level. In order to understand the origin of thisdifference - the cavity or the photo cathodes or both - moredetailed studies are necessary. One possible reason is a difference in the emitted dark current spectrum, as presented
in [3]. At fixed magnet settings it can lead to a different effective aperture (due to the gun itself, the coupler, and thefollowing beamline) and thus to a different detected darkcurrent level downstream the gun.
Dark Current (µA)

gradient and maximum gradient at the cathode for spacecharge compensation. The quality factor of the cavity was
also determined: Q0 = 24200.
Using the new tuning device, the tuning procedure was verysmooth and comfortable. Therefore, it was decided to doa re-tuning of cavity No.1 which was tuned in 2001 for an
operation temperature of 35◦ C. But during the high power
tests in 2005 it was found that the lower temperature limitof the cooling water system limits the reachable average
power at such a low operation temperature. The goal of thetuning was thus to increase the operation temperature. As
a result of the re-tuning, an operation temperature of 50◦ C
was obtained while keeping the field flatness constant at avalue of about 1.05.

THPPH023

10 3
10 2

Gun2, cathode 44.1 (Cs2Te)
Gun2, cathode 69.1 (Mo)
Gun3.1, cathode 58.1 (Cs2Te)
Gun3.1, cathode 53.1 (Mo)10

1

Imain= 0A
20 22.5 25 27.5 30 32.5 35 37.5 40 42.5 45
Gun Gradient (MV/m)

Figure 7: Dark current without solenoids produced with
two gun cavities for different cathodes at PITZ.

Figure 5: Dark current from cathode 80.1 on a YAG screen.
Figure 6 displays a photograph of the cathode 80.1 as well
as a picture of cathode 58.1 (Cs2 Te).
Figure 7 shows the measured dark current level withoutsolenoid magnets (Imain = Ibucking = 0 A) as functionof the gradient at the cathode for two different guns: cavity prototype No.2 (data from 2002) and cavity prototype
No.3.1 (data from 2006). For each gun, one distribution isshown for Mo and one for Cs2 Te. The dark current level

FEL Technology

Dark current measurements at different gradients have been
performed as function of the currents in the main and thebucking solenoids. Examples for such 2D dark current
measurements are shown in Figure 8: the dark current emitted by cathode 75.1 (Mo) was recorded for all combinationsof Imain and Ibucking at three different gradients.
Taking the maximum entry in such a 2D dark current distribution, one obtains the maximum dark current level emitted
by a certain cathode at a defined gradient. Figure 9 shows
the resulting distribution for gun cavity No.3.1 with cathode 53.1 (Mo) and cathode 58.1 (Cs2 Te). In addition to thedata from 2006, an old result from the PITZ1 phase (spring2003) when using gun cavity No.2 is drawn for comparison. The level of the emitted dark current is approximately
equal, at least for the Cs2 Te cathode.
Finally, the maximum dark current of all Mo cathodes usedin gun cavity No.3.1 is shown in Figure 10. The maxi-

611

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Dark Current (µA)

Figure 8: 2D scans of dark current emitted by Mo cathode 75.1 for all combinations of Imain and Ibucking at different
gradients: 35 MV/m, 40 MV/m, and 3543 MV/m (from left to right). Note the different color coded scale.
400
350
300
250
200
150
100
50
0

by using the new tuning device. Therefore, the device canbe also used for the tuning of further new cavities which
are planned to be used at PITZ.
Nevertheless, the dark current level produced by the cathodes needs to be further decreased. In order to do so, moredetailed studies of the dark current emission are necessary
as well as improvements on the photo cathodes themselves.

Gun2, cathode 31.1 (Cs2Te)
Gun2, cathode 34.1 (Mo)
Gun3.1, cathode 58.1 (Cs2Te)
Gun3.1, cathode 53.1 (Mo)

SUMMARY AND OUTLOOK
30

32

34

36

38

40

42

44

Gun Gradient (MV/m)

Figure 9: Maximum emitted dark current with two gun cavities for different cathodes.

Dark Current (µA)

mum amount of dark current is comparable for the analyzed cathodes, even if the emitted spectrum was different,
as reported in [3].
350300

cathode 53.1 (Mo)250

cathode 80.1 (Mo)200

cathode75.1 (Mo)150

cathode 35.1 (Mo)

A new gun cavity (prototype No.3.1) has been built, tuned,and commissioned at PITZ. The results of the tuning andextensive dark current measurements have been presented
in this paper. Comparisons with formerly taken data wasdone. The gun is currently used for beam measurements at
PITZ. After its full characterization, it will be dismounted
from the beamline in autumn 2006 in order to be available
as spare gun for the FLASH user facility. For PITZ, a new
gun is currently in preparation (prototype No.3.2).

REFERENCES[1] K.Flöttmann et al., RF gun design for the TESLA VUV Free
Electron Laser, NIM A 393 (1997) 93-95.
[2] A.Oppelt et al., Status and first results from the upgraded
PITZ facility, FEL 2005, Stanford, Aug.2005.

100[3] A.Oppelt et al., Status of the PITZ facility upgrade, LINAC
2006, Knoxville, Aug.2006.

50
0
30

32

34

36

38

40

42

44

Gun Gradient (MV/m)

Figure 10: Maximum emitted dark current from the Mo
cathodes used in gun cavity No.3.1.

[4] F.Stephan et al., Recent results and perspectives of thelow emittance photo injector at PITZ, FEL 2004, Trieste,
Sept.2004.
[5] L.Monaco et al., dark current investigations of FLASH andPITZ RF guns, EPAC 2006, Edinburgh, June 2006.

From all dark current studies done with the new gun cavity
it can be concluded that this cavity produces about the sameamount of dark current as the former used cavity (prototype
No.2). This means that there is no influence on the darkcurrent from the tuning marks which have been produced

612

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH025

DESIGN OF THE CAVITY BPM FOR FERMI@ELETTRA
P. Craievich∗ , D. Castronovo, M. Ferianis, ELETTRA, Trieste, Italy
M. Poggi, Laboratori Nazionali di Legnaro, INFN, Legnaro, Italy
Abstract
High resolution Beam Position Monitors (BPM)
are fundamental diagnostics for a seeded FEL, like
FERMI@ELETTRA, as they allow to measure the electron
beam trajectory non destructively and on a shot-by shot basis. Cavity BPMs provide the required sub-micrometer resolution relying on the excitation of the T M110 dipole mode
when the beam passes through the cavity off axis. For theseeded FEL FERMI, we adopted a pair of cavity BPMs
located upstream the modulating undulator to measure theelectron beam trajectory at the sub-micrometer level. In
this paper we first discuss the requirements for such a cavity BPM including those for the beam based alignment.
The scaling from an X-band design to the final C-band design is presented. The resolution to stay below one micrometer has been cross-checked, both analytically and numerically. The losses of the common mode T M010 havebeen also checked, leading to the final dimensions whichkeep the losses at the level of the X-band cavity BPM.

INTRODUCTION
An accurate measurement of the transverse beam position is an important issue throughout all the machine; inthe undulator sections, the position and angle of the electron beam at the entrance is a fundamental parameter to bemeasured in order to match it to the seed laser trajectory to
maximise the interaction, laser to beam. In order to provide
the required single shot resolution for the position measurement two cavity BPMs have been adopted in front of themodulator. According to the FERMI layout based on two
undulator sections (FEL-1 and FEL-2), two pairs of cavity
BPMs will be located in front of each FEL. The design ofthis cavity BPM is based on a previous development [1, 2].
It is a resonant pill-box cavity where the information on
beam position is encoded in the amplitude and phase variations of the dipole mode (T M110 ) with beam transverse
position, as measured on the two ports located on opposite
sides of the cavity. A scaling from X-band to C-band ofcavity BPM has been performed. We evaluated by meansof analytical and numerical models that the resolution at
C-band remains below 1 micron. In the scaling process
we paid attention at the losses in the common mode: thenew dimensions have been set to get same losses as for the
X-band common mode. Using previous analysis we have
fixed geometrical dimensions for a 3-D model of the cavity
BPM and coupling waveguide used to extract the signals
excited by electron bunch. Here we present results of the∗ paolo.craievich@elettra.trieste.it

FEL Technology

simulations obtained by means of Microwave Studio 3-D
code [3].

BACKGROUND
The cavity BPM is essentially a pill-box cavity; the analytical formulas for a cylindrical cavity with circular section without beam pipe are an upper limit to estimate beamlosses and RF parameters. From a theoretical point of viewthe energy losses experienced by a charge q when passing
through a cavity are: ΔU110 = q 2 k110 x2 and ΔU010 =q 2 k010 for T M110 and T M010 modes respectively. The
loss factors are defined as k110 = (ω110 /2)(R/Q)110 and
k010 = (ω010 /2)(R/Q)010 . ω110 and ω010 are the resonant frequencies of dipole and monopole modes. The ratio
R over Q is defined for the two modes as:
R
Q

110

=

R
Q

010

|Vz (x)|2110
x2 2ω110 U110

(1)

|Vz (x)|20102ω010 U010

(2)=where |Vz (x)|2110 and |Vz (x)|2010 are the squared voltages
for each mode seen by a charge particle when it flies along
the longitudinal axis at some offset x (x=0 for monopole).
U110 and U010 are stored energy in cavity for the T M110
and T M010 modes respectively. The ratio R over Q of agiven mode can be also theoretically computed for a cavity
without beam pipe.

Dipole mode T M110
R
Q

110

=

2LJ1 ( ab11 x)2 T 2π0 ω110 b2 J0 (a11 )2 x2(3)

where L is cavity gap, b is the cavity radius, 0 is the permeability of the vacuum, J0 is the 0th order Bessel functionof the 1st kind, J1 is the 1st order Bessel function of the 1stkind, with its first zero a11 = 3.832 and T is the transit time
factor defined by:


110 L
sin ω2c0(4)
T =ω110 L
2c0

being c0 the speed of light. It is worthwhile to mention
11
x; furthermore R over Q
that for small x, J1 ( ab11 x) ≈ a2b
and also k110 become independent from x. The loss factor
k110 , as a function of the cavity gap L and of the resonant
frequency of T M110 , is plotted in figure 1. In general fora small cavity gap, the transit time factor T is almost equal
to 1, but from figure 1 we can see that in the X-band range613

Proceedings of FEL 2006, BESSY, Berlin, Germany

and with a cavity gap longer than 15mm, approximately,
there is a reduction of the loss factor due to influence of T.
120
Cavity Gap
3 mm

100
2

k110 [V/nC/mm ]

10 mm
15 mm

80
60
40
20

2

4

6

8
fr [GHz]

10

12

14

Figure 1: Loss factor of the dipole mode T M110 versus
cavity gap L and resonant frequency.

Monopole mode T M010
R
Q

010

=

LJ0 ( ab01 x)2 T 2π0 ω010 b2 J1 (a01 )2(5)

where a01 = 2.405 is the first zero of the Bessel function J0 and T defined as above. For the monopole mode
the R over Q is calculated on longitudinal axis (x=0) where
J0 ( ab01 x) = 1. The loss factor k010 as a function of cavity
gap L and resonant frequency of T M010 is shown in figure
2. The energy lost in the T M010 mode produces undesirable wake fields and has to be minimized in the design.
We can see from figure 2 that, using a lower resonant frequency, we can increase cavity gap L without increasing
the value of the loss factor.

BPM RESOLUTION
As presented in [1, 2] it is possible to design the coupling
waveguide to selectively couple out to the T M110 mode
but not the T M010 mode. Without the contamination of themonopole mode, the intrinsic BPM resolution is limited by
the signal to thermal noise ratio of the system. For a given
coupling coefficient, the external signal voltage on matched
impedance Z0 for a charge q is:ω110
k110 x(6)
Vext = q Z0
Qext
√ The thermal noise voltage of the BPM is given by N =Z0 kTk Δf where k is the Boltzmann’s constant, Tk thetemperature in Kelvin and Δf = f110 /Qext is the bandwidth. The upper limit of resolution can be achieved whenthe external signal Vext is equal to the thermal noise N for:
1
kTk
xmin =(7)q 2πk110
Assuming a charge q = 0.8nC and Tk = 300K, infigure 3 we plot the BPM resolution with respect to theresolution at X-band as a function of resonant frequency of
dipole mode T M110 . As a reference case for an X-band
design we have assumed a pill-box cavity without beampipe, with gap length L = 3mm and cavity radius b =14.7mm. In table 1 we report the parameters for the Xband cavity used as reference.
40
Cavity gap
35

3 mm
10 mm
15 mm

30
Xmin / Xmin,X−band

THPPH025

25
20
15
10

3000
2500

5

3 mm
10 mm
15 mm

0
2

4

6

8
f [GHz]

10

12

14

r

Figure 3: Resolution of the cavity BPM with respect tothe resolution of an X-band cavity BPM versus its resonant
frequency.

1500

k

010

[V/nC]

2000

Cavity gap

1000
500
0
2

3

4

5
6
fr [GHz]7

8

9

Figure 2: Loss factor of the monopole mode T M010 versus
cavity gap L and resonant frequency.

614

Table 1: Loss factors and resonant frequencies for X-band
cavity BPM without beam pipe used as reference.
f110
k110
xmin
f010
k010
[GHz] [V /nC/mm2 ] [nm] [GHz] [V /nC]
12.4
49.7
0.14
7.8
907.6

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH025

SCALING OF THE CAVITY BPM
At X-band frequencies the mechanical tolerances are
more stringent than at lower frequencies. Considering also
the requirement on the minimum beam pipe radius, being
equal to about 10mm in the undulator region, we have
explored the achievable performance adopting a scalingat frequencies lower than X-band. In fact, dipole mode
T M110 will be coupled away into the beam pipe if its
resonant frequency is higher than the lowest cut-off frequency of the beam pipe. Assuming a beam pipe radiusof 10mm, the beam pipe cut-off frequencies are: 8.8GHz
and 11.5GHz, respectively for the T E11 and T M01 circular waveguide modes. Considering the available C-band
hardware together with the above motivations, a resonant
frequency of 6GHz (C-band) for the cavity BPM (radiuscavity b = 30.4mm) has been selected. From figure 3,
we can see that the resolution at C-band is still within an
acceptable range. Looking at figures 2 we can increase
the cavity gap up to about L = 10mm without increasing losses in T M010 mode if compared to the losses in the
X-band cavity. Assuming a charge q = 0.8nC, at room
temperature, in table 2 are reported the parameters for Cband BPM cavity.
Table 2: Loss factors and resonant frequencies for C-band
BPM cavity without beam pipe (cavity radius b = 30.4mm
and gap length L = 10mm).
f110
k110
xmin
f010
k010
[GHz] [V /nC/mm2 ] [nm] [GHz] [V /nC]
6.0
8.3
0.35
3.8
684.9

Figure 4: C-band cavity BPM with its four coupling waveguides and reference cavity.
Table 3: Comparison between numerical obtained bymeans of CST MWS and analytical results for C-band
BPM.
analytical numerical
unit
f110
6.0
5.7
[GHz]
(R/Q)1100.44
0.39[Ω/mm2 ]
k110
8.3
7.0
[V /nC/mm2 ]
Q0
8400
f010
3.8
4.0
[GHz]
k010
685
523
[V /nC]
unloaded Q factor of the cavity with new dimensions. Figure 5 shows the dipole Qext as a function of the distance
between beam axis and bottom of the waveguide.

C-BAND CAVITY BPM
6

FEL Technology

10

dipole Qext

Preliminary numerical simulations by means of CST
MWS[3] were done on a 3-D model with beam pipe to havea comparison with previous analytical treatments. For 3D model we have adopted the following dimensions: b =30.4mm, L = 10mm and beam pipe radius a = 10mm.
Table 3 shows results from analytical and numerical calculations and we can observe that the analytical one without beam pipe is a good estimation of cavity BPM withbeam pipe for both dipole and monopole modes. We haveadopted as waveguide the commercially available standard
WR137 with internal dimensions of 34.85×15.80mm2 . To
couple this waveguide to the cavity we have left unchanged
the width while we have used a transition to 6mm for theheight. This standard works in the frequency range of
5.85-8.20 GHz thus we have fixed the resonant frequency
at 6.5GHz decreasing the radius of the cavity to 26.4mm.
Figure 4 shows the 3-D model of the C-band cavity BPM
where we can observe the waveguide transition to the standard WR137.
The external voltage in eq. 6 depends on Qext = Q0 /βwhere β is the coupling coefficient and Q0 = 8530 is the

5

10

4

10

10

11

12

13
14
15
16
17
distance wg to beam axis [mm]1819Figure 5: Qext of the dipole mode as a function of distanceof the bottom of waveguide to beam axis.
The waveguide is always under coupled to the cavity andfor distance below 13 mm the Qext remains about constant.
We have fixed the distance between waveguide and beamaxis at 12 mm thus β = 0.1 and Qext = 10500. In this615

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Proceedings of FEL 2006, BESSY, Berlin, Germany

situation we only have a loss of 0.9 dB in the external voltage with respect to a critical coupling β = 1. In figure 4
the reference cavity is also indicated. The cavity will be
used to provide the reference signal in the RF electronics
and is designed to resonate at 6.5 GHz approximately with
T M010 mode. The external coupling is foreseen by meansof an antenna placed on the cavity lateral side.
A prototype C-band cavity BPM is being designed andcold test are foreseen. Table 4 shows dimensional and RF
parameters of the C-band and reference cavity prototypes.
From the mechanical point of view, we are faced with somechallenges. First of all the required machining tolerance
was fixed to ±10μm for cavities, waveguides and their relative positioning. An important item is to decide how tobuild the BPM and reference cavities from bulk copper.
One idea is to divide in two parts the whole geometry along
the longitudinal symmetrical plane. The first part consistsof half cavity together with waveguides, as shown in figure 6 [4], and second part consists of the other half cavity without waveguides. Both parts will be milled with theprofile of the cavity and waveguides and subsequently thebeam pipes, cavity and waveguides are brazed together. So
the challenge concerns the brazing process and in particular to find the best brazing material. During the process
it is important not to pollute the copper nor to deform theconstruct. This last item must be investigated through additional numerical simulations.
Table 4: Collections of the dimensional and RF parametersof the C-band cavity BPM and reference cavity.
C-band cavity BPM
Cavity gap
10mm
Cavity radius
26.4mmBeam pipe radius
10mm
Coupling WG
34.85 × 6mm2
Distance WG to beam axis 12mm
WG standard
WR137
Resonant frequency
6.5GHz
Unloaded Q factor
8530
External Q
10500
Coupling coefficient
0.1
Reference cavity
Cavity gap
10mm
Cavity radius
17.6mmFigure 6: Preliminary technical drawing of the cavity
BPM [4].
fixing dimensional parameters for a C-band prototype ofthe cavity BPM.

REFERENCES[1] R. Johnson et al., “Cavity BPMs for NLC”, BIW 2002, Upton, NY, May 2002.
[2] Z. Li et al., “An X-band Cavity for a high precision beam
position monitor”, DIPAC 2003, Mainz, Germany, May 2003.
[3] CST Microwave Studio, http://www.cst.de.
[4] Cinel Strumenti Scientifici, http://www.cinel.com.

CONCLUSION
In this paper we have explored a possible scaling of thecavity BPM presented in [1, 2]. For our considerations, wehave used a model of a pill-box without beam pipe and haveshown that a scaling from X-band to C-band frequencies ispossible without loss of resolution. In addition, we havedone simulations on a 3-D model to validate the analyticaltreatment and we have analyzed the position of the coupling waveguide to the cavity. These studies have allowed

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DESIGN OF A TWO-STAGE LASER PULSE SHAPING SYSTEMFOR FEL PHOTOINJECTORS∗
M. B. Danailov, A. Demidovich, R. Ivanov (ELETTRA, Basovizza, Trieste).
Abstract
This paper presents an approach for photoinjector laser
pulse shaping which combines the two main pulse
shaping techniques, namely acousto-optic dispersive filter(DAZZLER) and Fourier-based 4-f system. The
DAZZLER is inserted between the seed mode-locked
oscillator and the amplifier and is used for preliminary
shaping in the infrared, while the final pulse shape andduration are determined by a 4-f dispersive system
positioned after the harmonic conversion to UV.

INTRODUCTION
Temporal pulse shaping is one of the most important
requirements to photoinjector lasers needed in the
majority of FEL projects. The laser pulses commonly
requested for excitation of the photocathode are in the UV(around 260 nm) and have flat-top shape of duration in
the 5-10 ps range. Recently, more complex pulse shapes
like ramps have been shown to be advantageous andproposed for implementation [1,3], indicating that thepulse shaping scheme must offer flexibility in generating
different shapes. In principle, there are two main
ultrashort pulse shaping techniques, namely 4-f type
Fourie shaping [4] and acousto-optic dispersive
modulator (DAZZLER) based [5] shaping. As it will beshown below, the use of one of these only is unlikely toallow reaching the required performance. The main
complication comes from the fact, that the pulse shape isneeded in the UV, and the required pulse energy is quite
high, while pulse shaping is easy to do at low pulse
energy in the IR. In the paper we describe a hybrid
scheme proposed for the FERMI photoinjector, which
utilizes both methods, one in the infrared and the other in
UV. The paper starts with brief introduction to theultrashort pulse shaping basics and notation, which isimportant for understanding the analysis and resultspresented later on. The specific problems related tophotoinjector laser pulse shaping and the proposed opticalscheme are discussed in the next section, followed bysimulations and preliminary experimental results of flattop and increasing ramp pulse generation.

PULSE SHAPING BASICS
As mentioned above, there are different laser pulse shapesthat can be used to optimize the photoinjector (and overall
FEL) performance. Here we will mostly refer to two ofthem, namely flat-top and increasing ramp, however thetechniques used allow in principle to generate any desired
pulse shape. To make the discussion of the pulse shaping____________________________________________∗

This work has been partially supported by the EU Commission in the
Sixth Framework Program, Contract No. 011935 EUROFELFEL Technology

schemes clearer, we will very briefly introduce somebasics of the pulse shaping theory.
Assuming that the light field can be factorized into spatial
and time dependent part, the electric field of the latter canbe written as:

E(t)=1/2 [I(t)]1/2 exp{i[ω0t-ϕ(t)]}+ c.c. ,(1)where ω0 is the central frequency , I(t)1/2 and ϕ (t) are thetime dependent temporal amplitude and phase. For
simplicity in the following equations the c.c. part will beomitted. The quantity

E(t)= I(t)1/2 exp[-iϕ(t)](2)

is referred to as the complex amplitude in the time
domain. In the frequency domain, the pulse field can be
represented in a similar manner:

E(ω)=1/2 [S(ω)]1/2 exp[-iψ(ω)] ,(3)

where S(ω) is the spectral intensity of the light pulse. As
it is known, the time and frequency domain field
representations are linked by a Fourier transform relation:∞

E(t)=(1/2π) ∫ E(ω)exp (iωt) dω

(4).

−∞

Most of the known methods for shaping of ultrashortpulses are based on this relation, they implement
manipulation of the spectral amplitude or phase (or both)of the pulse, which in turn leads to the required
modulation in the time domain. The output pulse shape isgiven by the convolution of the input pulse and theimpulse response function of the modulating function:∞

Eout(t)= ∫ Ein(t`)h(t-t`) dt` ,

(5)

−∞

where h(t) can be calculated from its complex frequency
transfer function by:∞h(t)=(1/2π) ∫ M(ω)exp (iωt) dω.

(6)

−∞

The complex transmission function M(ω) can bepresented as:
M(ω)=[MI(ω)]1/2 exp[-iΦ(ω)],(7)

and the phase transmission is commonly expanded in
Taylor series :Φ(ω)=Φ(ω0)+Φ(1)Δω+(1/2!)Φ(2)Δω2++(1/3!)Φ(3)Δω3+…

(8)

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Proceedings of FEL 2006, BESSY, Berlin, Germany

where Φ(i) is the i-th derivative of the phase evaluated at
ω0 and are usually called i-th order dispersion. While thefirst and second terms in (9) represent only a constant andan overall time shift of the pulse, the third and higher
order terms may lead to significant pulse shape changes
even if the spectral amplitude[MI(ω)]1/2 remains
constant. In principle, if one could design a frequency
filter with a prescribed optical frequency transmissionfunction, any desired pulse shape (with temporal
resolution limited by the inverse bandwidth of the input
pulse Ein(t)) can be generated. In reality, it is quitedifficult to produce optical filters with complex frequency
transmission functions defined with high precision. As
will be shown later, some specific shapes, like flat-tops,
however, can be produced by use of interference filter.
The first technique which solves in a general way thepulse shaping has been known for more than a decade [4]: the spectral components of the input pulse are spatiallyseparated by a dispersive element (e.g. diffraction grating), and then manipulated in the spatial domain by using a
modulator with spatially dependent transmission, placedin the Fourier (focal) plane of a lens, as shown on Fig.1.
A second lens and grating recollimated the pulse spectral
components, so the output pulse has again a spatiallyindependent pulse shape that can be calculated using
Eq.6. By proper choice of the modulator the techniqueallows to use both amplitude and phase modulation. It is
worth noting that large second order phase terms (i.e large
linear chirp) can be produced even without the use ofmodulator in this scheme, by just shifting the grating withrespect to the focal plane of the lens.

M(x)x

f

f

f

f

Figure 1: 4-f Fourier shaping system
A newer and very powerful technique for pulse shaping is
the so called DAZZLER introduced by P.Tournois [5] andcommercially available from Fastlite (France). In thismethod, also based on Eq.6, the spectral components are
not separated spatially, the optical pulse travels in an
acousto-optic modulator where a longitudinal acoustic
wave is present. By shaping the acoustic wave frequency
and amplitude, the spectral components of the opticalpulse are diffracted out of the crystal at different positions(and therefore with different delay) and with different
efficiency. In this way, the deviated part of the incoming
pulse can be time modulated with very good precision.

618

DISCUSSION
The basic gun laser specs in the case of Copper
photocathode are relatively well agreed. It is usuallyaccepted that about 0.5 mJ of pulse energy in the UV(wavelength around 260 nm) has to be provided in orderto obtain about 1 nC of charge.
Both techniques presented above allow in principle toobtain pulses with the required shape for thephotoinjector. When flat-top is concerned, someexperimental results with Dazzler have been presented in[6].The Dazzler has the obvious advantage of flexibility
and compactness. It is provided with computer control
allowing both amplitude and phase modulation. However,it has the following limitations:- wavelength resolution of the high resolution model isabout 0.3 nm. For this reason the bandwidth of the input
pulse should be about 10 nm or higher in order to obtainhigh fidelity amplitude shaping;-if a single pass is used, the maximum second orderdispersion that can be provided by the Dazzler allows to
generate pulses of up to 4 ps, which is not enough in mostcases. A two pass geometry can be used for having ~10
ps long pulses, however in this case the insertion loss ,even at maximum diffraction efficiency, is above 90%
which does not seem to be practical;-the Dazzler can be used only in IR. Fastlite announced
recently a UV version, however it is not suitable for thetask considered here (allowed power levels andwavelength resolution can not be met)
- maximum peak power limitation in the IR does notallow to use the Dazzler after the amplifier. For thisreason it has to be placed between the seed oscillator andlaser amplifier.
On the other hand, the 4-f based shaping can be useddirectly in UV, if a proper modulator is found. At present,
the only available option is a piezo-deformable mirror [7]with a dielectric coating. Liquid crystal modulators likeare only available down to 350 nm, which is not enoughfor our photoinjector case. There are two main limitations
to be taken into account:- the use of deformable mirror allows to obtain only phasemodulation- the obtainable phase curvature is limited by the limit ofabout 8 micron for maximum mirror deformation, so thedeformable mirror alone will not be enough for obtaining
large phase gradients, it can rather be used as a tool forcompensating slow phase curvature errors.

PROPOSED LAYOUT
Fig.2 presents a layout of the hybrid shaping setup
proposed for the FERMI photoinjector. Input seed pulses
with a bandwidth of about 12 nm at 780 nm are generated
by a mode-locked Ti:Sapphire laser. The IR pulse shaping
is done by a DAZZLER inserted before the amplifier
stages. The Dazzler is implemented primarily for
producing the desired spectral amplitude shape (e.g.
super-gaussian like) , and in addition for compensation of

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

phase

THPPH026

Pulse shape control
Figure 2: Proposed two-step shaping setup

third-order phase distortions
due to the grating
compressor of the amplifier. Usually this compressor isused for exact compensation of the chirp introduced by
the stretcher. In our scheme it is also used for adding asecond order dispersion by detuning with respect tomaximum compression point. In this way, the pulse
duration at the entrance at the harmonic generation
crystals can be adjusted to an optimum value whichallows to have high enough harmonic efficiency whilestill keeping high order nonlinear effects (e.g. self-phasemodulation) at low. Such a safe peak power level isreported to be in the order of 10-20 GW/cm2 for BBO.
We note that our approach gives an additional degree of
freedom for adjusting this level.
The final pulse duration and shape is then controlled by adispersion based system working in the UV. Two versionof this system are under consideration. The simpler one isjust a two-pass grating stretcher used for adding a secondorder phase needed to obtain the exact pulse duration (seethe simulation later on). This version will be used in case
the DAZZLER alone allows good enough compensationof all phase distortions. If it appears that an additional
high order spectral phase compensation is needed after
the harmonic generation, the UV shaping will include also
a deformable mirror in a modified 4-f arrangement.
In order to illustrate better the described scheme, on
Figs.3 and 4 we present the results of a simple simulation

Figure 3: Input spectrum for the simulation (blue dots)
and modulated spectrum after Dazzler (red solid line).

FEL Technology

Figure 4: Pulse profiles after compressor in the IR(redsolid line), after THG (blue dots), after UV stretcher (bluesolid).
of pulseshaping which generates the pulse shape(increasing ramp) requested for the FERMI ‘long bunchcase’ [3].
The simulation is done starting with a transform-limited
Gaussian pulse at 800 nm having 12 nm of FWHM
bandwidth (dashed blue line on Fig.3). The spectrum
shown in red line is obtained after amplitude filtering by
the Dazzler. In addition, it is assumed that the lattercompletely compensates the residual third-orderdispersion of the system. The pulse shape shown by blueline on Fig.4 corresponds to the amplifier output, where asecond order dispersion of about 60000 fs 2 has been
introduced by detuning the compressor. Assuming thatthe third harmonic generation is performed in sufficiently
thin BBO crystals , so GVM and spectral acceptanceeffects can be neglected, the UV pulse shape (dashed blueline) is proportional to the third power of the IR one. The
final shape and duration, shown by solid blue line are
obtained by adding only an additional second orderdispersion from the UV grating stretcher. We note that
this stretcher will inevitably add also a third orderdispersion term on the order of 100 000 fs3 , which is inprinciple possible to compensate in advance by theDazzler, so it has not been taken into account into theabove presented simulation. As mentioned above, in case
the DAZZLER compensation is not sufficient the odd
dispersion terms will be cancelled by the use of
deformable mirror.

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PRELIMINARY EXPERIMENTAL
RESULTS

1.0

Most of the components of the above presented setup
have already been tested at Elettra. Here we will briefly
summarise some of the results. The DAZZLER has been
installed and tested using a femtosecond Ti:Sapphireoscillator at 780 nm. On Figure 5, two typical flattop
pulse shapes are presented: phase only polynomial
modulation (blue line) and amplitude super-gaussian
modulation. In both cases, the pulses were additionallystretched by the use of grating stretcher. The pulse
measurement is done by cross-correlating the shaped
pulse with a part of the input 100 fs long pulse.

AMPLITUDE (a.u.)

0.8

0.6

0.4

0.2
0

1

2

3

4

5

6

TIME (ps)Figure 7: Increasing ramp generated by the Dazzler withpure amplitude modulation

1.0
0.8
0.6
0.4
0.2
0.0
0

1

2

3

4

5

6

TIME (ps)Figure 5: Flat-top pulses generated by the Dazzler; blue
line: phase modulation, red line: amplitude modulation
It is important to mention here that the fact that amplitudefiltering plus stretcher added second order dispersion
works well indicates a simpler method. The amplitudefiltering can be performed by the use of an interference
filter. Indeed, we demonstrated this by the use of acommercial filter (Spectrogon), centered at 780 nm. There

1.0

data velocity = 1ps/s

FWHM=12.8ps

0.9
INTENSITY (a.u.)

AMPLITUDE (a.u.)

THPPH026

is some freedom to detune the filter transmission curve
position and shape by tilting and to obtain a nearly perfectsuper-Gaussian spectrum. As a result, after stretching , a
flat-top pulse can also be obtained, as shown on Fig.6.The
price to pay for the simplicity is that there is no control onphase, this might not be a problem if the UV partcontains the deformable mirror.
On Fig. 7 we show a ramp type pulse profile [3] obtainedon the same setup by using the Dazzler in amplitude
modulation mode. We note that the cross-correlator
scanning in this setup was starting from the back of thepulse, so the pulse front is on the right of graph and theramp is increasing, as requested.

CONCLUSIONSThe setup described above is in principle capable ofproducing arbitrary pulse shapes in UV, especially in theversion containing deformable mirror. The two basic
techniques have been already tested at low power atElettra, and a high energy version including the UV partis to be completed and tested in a few months time. Thereis still some freedom to choose the exact system and laser
pulse parameters in order to obtain the required shapeswith high fidelity.

0.8

REFERENCES

0.7[1] C. Limborg-Deprey, Proc.27th FEL Conf.(2005), 418.
[2] O.J. Luiten, M.J. Van der Wiel, 27th FEL
Conf.(2005) ,paper WEOB003.
[3] G.Penco et al, Proc.EPAC 2006, to be published[4] A. M. Weiner, J. P. Heritage, E. M. Kirschner, J. Opt.
Soc. Am. B 5, (1988). 1563
[5] P. Tournois, Opt. Comm. 140 (1997), p.245 .
[6] C.Vicario et al, Proc.EPAC 2004, p.1300[7] J.Gardino-Mejia et al, JOSA B 21 (2004), 833.

0.6
0.5
0.4
0.3
0.2
0.1
0.0
0

2

4

6

8

10 12 14 16 18 20 22 24 26

TIME (ps)Figure 6: Flat-top pulse generated by the use ofinterference filter as an amplitude filter.

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THPPH027

RAMPING LONGITUDINAL DISTRIBUTION STUDIES FOR THE
FERMI@ELETTRA INJECTOR
G. Penco∗ , M.Trovò, Sincrotrone Trieste, Trieste, Italy
Steven M. Lidia, LBNL, Berkeley, California, USA.
Abstract
In the FERMI Linac optimization studies it comes out
the request to have at the exit of the photoinjector a linear
ramp in the current distribution along the bunch as alternative option with respect to the flat-top. This requirement istranslated in the photoinjector optimization in a big issue.
In fact the longitudinal bunch profile at the exit of the photoinjector is affected by the strong non linearity of the spacecharge fields at the cathode and in the drift between the gun
and the first booster. The knowledge of the space charge
fields at the cathode plays in important role in finding the
optimum driven laser pulse shape. At this purpose an analytical description of the space charge fields produced by abunch with an arbitrary current distribution at the cathodeis provided. Space charge codes (GPT [1] and ASTRA [2])have been used to evaluate the evolution of several ramping
profiles from the cathode to the entrance of the first booster
and the results are presented in this paper.

charged bunch the longitudinal space charge field on axis,
inside and outside the bunch, at a distance z from the bunch
tail is given by the following equation [4]:EzSC (z) =where H(z) is
H(z) =Q
H(z)2π0 R2

(1)

 2
z 2
R
+
−
L
γL

 z  2  R 2 z   z +− 1 −  +   (2)
L
γL
L
L


1−

and Q is the total bunch charge, L the bunch length, R thebunch radius. For simplicity γ = 1 is assumed.
As example the figure 1 shows the field EzSC (z) versus z(normalized with respect to the bunch length L) for a nominal 1nC bunch, with a radius of 1mm and a bunch lengthof 3mm. The flat-top current distribution at the cathode is

INTRODUCTIONLONGITUDINAL SPACE CHARGE FIELD
ON AXISIn order to solve this problem, the longitudinal spacecharge fields on axis at the cathode was investigated, since
it is mainly responsible for blowing out the particles, especially in case of high peak current. In case of a uniformly∗ giuseppe.penco@elettra.trieste.it

FEL TechnologySC

Ez (z) (MV/m)

4

In the optimization of the high brightness RF photoinjector a great effort is usually spent to produce an electron
bunch as much as possible uniformly charged distributed.
This is a precise requirement coming from the optimization of the emittance compensation in the injector and in
the bunch transport through the linac, especially in presence of bunch compressors. By the other hand it has been
demonstrated that the strong non-linearity of the linac sections longitudinal wakefields can be compensated by providing at the exit of the photoinjector a linear ramping electrons distribution instead of a flat top [3]. This requirementtranslates to the photoinjector optimization as a large perturbation due to the strong nonlinearity of the space charge
fields at the cathode and in the drift between the gun and thefirst booster. To produce a ramped current bunch, a special
initial profile has to be found that evolves along the injector
to produce the final desired shape.

2
0
-2
-4
-0.5

0.0

0.5
z/L

1.0

1.5

Figure 1: Longitudinal space charge field on axis of abunch just extracted from the cathode; Q=1nC, R=1mm,
L=3mm
deformed by this space charge field into a parabolic distribution after several centimeters, suggesting that a linear current distribution would suffer a strong degradation before
entering into the relativistic regime. Thus the drive laser
pulse should be shaped according to a non-linear distribution pattern. Eq.(1) has been generalized for an arbitrary
longitudinal current density distribution ρ(z) at the cathode[5], obtaining: Lz − zρ(z  )dz −
EzSC (z) =20(z  − z)2 + R20|z  − z|z − z(3)621

Proceedings of FEL 2006, BESSY, Berlin, Germany

Eq.(3) represents a useful analytical instrument toquickly predict the evolution and distortion of an arbitrarycurrent profile. For example figure 2 shows the longitudinal space charge field on axis inside a bunch with respectively a linear and a quadratic ramping in the current
distribution (image charge not included). Electrons in thehigh charge density region are pushed backwards during
the bunch propagation because of the strong repulsive electric field and this modifies the starting bunch profile.

0
0.0

0.2

0.4

0.6

0.8

1.0

2

0
-2

1
-4
0
0.0

0.2

0.4

0.6

z/L

z/L

(a)

(b)

0.8

1.0

Figure 2: Longitudinal space charge field on axis of a linear(a) and parabolic (b) ramping charged bunch just extracted
from the cathode having different radius; Q=1nC, L=3mm.
Cathode plate is in z=0.
Figure 2a shows that a linear ramp charge distribution
samples an almost quadratic longitudinal space charge field(Figure 2a). Thus one can easily expect a large deterioration of the initial ramping current profile while propagating
through the injector. Multiparticles codes trackings of linear ramp profiles similar to figure 2a have confirmed the
expectation and figure 3 shows the bunch current profileat the exit of the injector: the initial linear ramp has been
destroyed and the bunch presents a parabolic-like charge
distribution.

Current (Amp)

60
40
20
-2

Current (Amp)

1

2

80

300
250
200
150
100

60
40
20

50
0
-1

0
z (mm)

(a)

1

2

-2

-1

0
z (mm)

12(b)Figure 5: A fourth-degree polynomial distribution at thecathode (a) and at the end of the photoinjector (b).

60
40
20

-2

-1

0
z (mm)

1

2

Figure 3: Resulting profile at the exit of the injector in caseof an 800pC-bunch with a linear ramp at the cathode.
Also a quadratic ramp, like Figure 2b, is strongly modified during the transport between the cathode and the first
booster section, but the linearity of the space charge field
at least in the middle of the bunch helps in preserving thelinear ramp in about 70% of the bunch (see Figure 4).

622

0
z (mm)

Several initial current distributions have been studied inorder to find the best one which linearizes as much as possible the space charge field experienced by electrons within
the bunch and which evolves into the desired longitudinal
profile. A fourth-degree polynomial distribution (see Figure 5) has been found to be an interesting solution that offers flexibility in compensating the high orders contributions of the space charge field and that increases the bunch
fraction sampling a linear space charge field.

-2

80

-1

Figure 4: Resulting profile at the exit of the injector in caseof an 800pC-bunch with a quadratic ramp at the cathode as
Figure 2b.

Current (Amp)

-4

sc

1

Ez (z) (MV/m)sc

Ez (z) (MV/m)

-2

3
2

Normalized Charge distribution

20

Normalized Charge distribution

3
2

80

Current (Amp)

THPPH027

The current distribution plotted in Figure 5a has been
considered as the baseline ramping distribution for the
medium bunch case assuming a large efficiency in the laser
pulse shaping process [6]. However in a conservative scenario even a quadratic distribution could be used without
severe drawbacks.
A large charge density close to the cathode surface increases the image charge field and this should be considered in the generation of a ramping charge distribution. The
effect of the image charge at the cathode can be easily included by adding the field EzSC (−z) to the formula 3.
As example the space charge field with and without the image charges effects in case of a parabolic ramping charged
bunch is shown in figure 6: the electrons close to the cathode sample a space charge field two times the value obtained without considering the image charges. In the optimization process and in the multiparticles trackings the

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany
1.0

0

0.8

Current (Amp)

Laser intensity (a.u.)

image charge effects have been included.

Esc (MV/m)

THPPH027

0.6
0.4

80
60
40

0.2
20

0.0
-6

-4

-2

0
2
z (mm)

4

6

-2

(a)

-5

-1
0
z (mm)

1(b)

Figure 7: The “double peaks” charge distribution at thecathode (a) and at the end of the potoinjector (b).

-10

-15
0.0

0.2

0.4

0.6

0.8

1.0

z/L

Figure 6: Comparison between the Longitudinal spacecharge field on axis with (continuous line) and without(dashed line) the image charges effects; Q=1nC, L=3mm

EMITTANCE COMPENSATION AND
OPTICS MATCHING ISSUESFEL Technology

Figure 8: Top view of the evolved “double peaks” option.
The initial charge distribution is translated into a transversal charge density.

αX

slice. These modulations in α and β affect not only thematching with the linac optics, but they can be even sourcesof microbunching instabilities when the bunch propagates
through the chicanes, leading finally to enlarge the bandwidth of the FEL output radiation [7]. A different result is

60

slice emit (mm mrad)

2.0

50

1.5
1.0

40

0.5

30

0.0

20

-0.5

10
-2

-1

0

βX

Because of the non-uniform charge distribution of theramping regime, it is very difficult to find an injector parameter set-up that completely satisfies the invariant envelope equation, performing perfect emittance compensation
for all slices. Since each slice contains a different amountof charge, each slice evolves in a particular and unique way
in the gun-booster drift when the injector parameters are
fixed. In order to minimize the projected emittance at theend of the injector an average parameters setting should befound, taking in account also the slice parameters behavior along the bunch. Studies were carried on by tracking
several initial laser shapes with GPT and ASTRA. A crucial role has been played by the coefficients of the quadratic
ramp chosen at the cathode. For example an attractive solution is to consider a quadratic profile with “double peaks”,
as showed in figure 7a. The small peak electrons are pushedforwards by the space charge field and this partially compensates the backwards spreading of the high peak electrons, increasing the linearity and the width of the ramping fraction of the bunch (figure 7b). In addition the headof the bunch presents a hard edge, instead of a smoothing
falling edge. By the other hand, finding the optimum focusing condition is an issue in this case. In fact in order tocompensate the emittance contribution of the high charge
fraction of the bunch, the solenoid strength has been increased, leading to an overfocusing of the bunch core andhead, as showed in the top view of figure 8.
Figure 9 shows the slice analysis concerning the emittance and the Twiss parameters for this case. The overfocused electrons in the middle of the bunch have evena higher slice emittance, around 1.4mm mrad. This ovefocusing has consequences also in the optics parameters:
Twiss parameters suffer a very large oscillation slice by

1

Z (mm)

Figure 9: Slice analysis of the emittance, αX and βX parameters for the double peaks solution.
obtained starting with a profile similar to figure 5a, which
presents at the end of the injector a trasversal distribution
showed in figure 10. The slice analysis have been performed as well and the results are reported in figure 11. In
this case the slice emittance has a ramping behavior very
similar to the ramp in the charge distribution, and no bunch

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Proceedings of FEL 2006, BESSY, Berlin, Germany
to the behavior of the slice optics parameters. In fact tracking results have revealed that large modulation of the slice
α and β functions can be an issue in the bunch propagation through the linac chicanes. Finally great attention has
to be paid in the choice of the coefficients of the quadratic
ramp, in order to reach the best compromise between theachievement of the linear ramp at the end of the injector
and emittance and optics functions slice behavior.

REFERENCES[1] S.B. Van der Geer et al.,“General Particle tracer Overview”,
http://www.pulsar.nl/gpt/index/html.

Figure 10: Top view of the evolved profile of figure 5a.
fraction is overfocused. By the way in correspondence ofthe high charge density the space charge field leads to increase the transversal dimension, as showed in the plot inside of figure 11. Also the slice β and α functions are very
high in correspondence to the high charge density, but they
are quite constant in the remainder bunch fraction and thisconstitutes a great improvement for the linac matchingαX
2.0[4] M.Ferrario et alter, “HOMDYN Study for the LCLS RF
Photo-Injector”, LCLS-TN-00-04.
[5] G. Penco, “Longitudinal Space Charge Field at the CathodeIn Case of a Non Uniform Bunch”, ST/F-TN-06/03 (2006).

[7] S. di Mitri and E. Allaria, private communication.

60
1.5
1.0

40

βX

slice emit. (mm mrad)[3] A.Zholents at al., “Study of the electron beam dynamics
in the FERMI@ELETTRA linac”, Proc. of the EPAC 2006
Conf., Edimburgh (GB).

[6] M.Trovò, G.Penco, S.Lidia, “Further Studies in the
FERMI@elettra photoinjector optimization”, this conference.

80

2.5

[2] K. Flöttman, ASTRA User’s Manual,https://www.desy.de/˜mpyflo/Astra dokumentation.

0.5
20

0.0
-0.5
-2

-1

0
Z (mm)

1

2

Figure 11: Slice analysis of the emittance, αX and βX parameters for the propagated bunch of figure 5a.

CONCLUSION
The linac requirement to have a bunch with a linear current ramp at the injector exit has been translated in studying
the best current distribution at the cathode that evolves inthe desired profile. An analytical description of the longitudinal space charge field on axis helps in predicting the evolution of an arbitrary current ramp before running the multiparticles space-charge codes. A quadratic current ramp at
the cathode constitutes a good option to have at the end of
the injector a reasonable large ramping bunch fraction.
Emittance compensation scheme has been showed to be anissue since each slice evolves in an unique way. Optimization of the injector parameters has to aim not only to minimize the projected emittance, but also to avoid overfocusing and slice emittance blowing-up, paying attention also

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH028

FURTHER STUDIES IN THE FERMI@ELETTRA PHOTOINJECTOROPTIMIZATION
M. Trovò∗ , G. Penco, Sincrotrone Trieste, Trieste, Italy
S. M. Lidia, LBNL, Berkeley, California

In the framework of the FERMI@elettra project weare presently studying an electron beam configuration satisfying the bunch energy distribution requirements coming from the FEL photon production system.
The
multi-particle tracking results concerning the photoinjector, which include the RF gun and the first two accelerating
sections, are presented in this paper. We describe two possible electron bunch configurations which satisfy the FEL
operation modes. Both injector configurations match thelinac requirements for a ’ramped’ current profile at the exitof the photoinjector. Sensitivity studies and time and energy jitter estimations are presented for both cases.

INTRODUCTION
Several configurations of the electron bunch delivered to the undulator chain by the linac accelerator havebeen considered in the optimization study process for
the FERMI@elettra project. After considerations of performance optimization in the remainder of the FERMI
linac [1], a new type of laser excitation at the photocathode,consisting in a ramped current distribution, is proposed.
In particular, the linac studies show that the accelerating
structure wakefield and chicane CSR effects require an initial electron beam distribution with a quasi-linear head-tailramp in the instantaneous current in order to produce a’flat-flat’ beam profile (i.e. uniform in current and energy)
at the entrance of the FEL undulators. This linac requirement translates to photoinjector in the problem of finding a
special laser shape that extracts from the cathode a bunchthat evolves along the gun machine section (mainly a drift
at low energy), producing the desired output profile. In thispaper two possible ’ramped’ bunch solutions are presented.
These two FERMI photoinjector configurations are suitable
for the machine operation in the so called medium and longbunch modes [2].

Table 1: Main beam parameters required at the exit of injector in the two studied configurations.
Parameters
MediumLong
E
95 MeV
95 MeVQ
800 pC
1 nC
Ipeak A
80 A
100 A
Lb (FWHM)
8 ps
10 ps
proj.
<1.5 μ m
1.5 μmslice<1.0 μm <1.0 μm
σE (uncorr.)<2 keV<2 keVquasi-linear head-tail current ramp in the bunch an unconventional shape of the laser pulse has to be introduced. In
the simulations performed so far a transverse cylindrical
distribution (top hat with 1mm edge radius) has been usedwhile a time-varying intensity is used to produce the variation in instantaneous current along the bunch. This particular shaping is achievable with the appropriate design of thedrive laser optical system [4].

Medium bunch case
The first case (so called medium bunch case) requires
from the photoinjector a bunch charge of 800pC and a current profile, in the ramped part, with a length of about 8ps.
1.0

Intensity (arb.units)

Abstract

0.8
0.6
0.4
0.2
0.0
-4

PHOTOINJECTOR CONFIGURATIONS
For the FERMI@elettra project two machine operating modes are proposed that provide at the undulator entrance two different bunches in term of length and peakcurrent [3]. These two mode require the gun to provide
two different beams, presented in Table 1. To produce a∗ mauro.trovo@elettra.trieste.it

FEL Technology

-2

0

2

4

Emission time (ps)Figure 1: Longitudinal laser pulse shape: temporal intensity modulation.
Figure 1 shows the shape chosen for laser pulse intensity [2]. The curve is a Fermi-edge (with 7ps FWHM, 0.5ps
of rise/fall time) multiplied by a polynomial (0.26 + 0.05 ·t + 0.012 · t2 + 0.008 · t3 + 0.0019 · t4). A bunch generated

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Proceedings of FEL 2006, BESSY, Berlin, Germany

by such a laser pulse propagates in the FERMI Gun machine section producing the output current profile shown in
Figure 2.

Current (A)

80
60

1.5

20
97

96

15

-4

1.0

0
time (ps)

Slice energy spread (keV)

slice emittance (mm mrad)

2.0
Energy (MeV)

THPPH028

4

10

0.5

5

40
0.0

20

0
-6

-4

-2

0

2

4

6

Slice position along the bunch (ps)

0
-2

0

2

4

6

Time (ps)Figure 2: Current profile of the output bunch (head on theleft).

100
6

0.8
100
0.6

0.4

0.2

80
60
40
20
0

-6

-4

-2

0

2

4

6

-6

Emission time (ps)

4

60

3
40
2

Energy (MeV)

proj (mm mrad);5

laser pulse. Figure 5 shows the laser shape chosen for thelong case. The curve has FWHM of 10ps and the slope isdriven by polynomial as 35 + 10 · t + 1.5 · t 2 . The output
current profile is also shown and it reaches a peak currentof 100 A. The useful bunch part (from head to the currentdrop) is about 10ps and this satisfies the linac requirements(Table 1).

0.0

80

s

X (mm)

Because of the highly non-linear charge distribution of
the ramped profile, it is difficult to find an injector parameter configuration that completely satisfies the invariant
envelope equation, performing perfect emittance compensation for all slices. Since each slice contains a different
amount of charge, it evolves in a particular and unique way
in the gun drift. Thus an average setting has been foundthat minimizes the projected emittance at the exit of thephotoinjector (see Figure 3), which reaches 1.39 mm mrad.
In the core 80% of the bunch particles the emittance is reduced to 1.21 mm mrad.

Figure 4: Slice emittance and slice energy spread at the injector exit for the medium bunch case calculated at the exitof the photoinjector machine section. Plot inside: Longitudinal phase space. Bunch head is to the left.

Current (A)-4Intensity (arb.units)

-6

-4

-2

0

2

4

6

Time (ps)Figure 5: Longitudinal laser pulse shape: temporal intensity modulation on the left. Output current profile on theright.

20

0

0
4

6

8

6

100

5

s

2

X (mm)

e

1

80

Z (m)

Long bunch case
The second, or “long bunch”, case represents the configuration with higher bunch charge (1 nC) and longer drive

626

40
2
20

1

e

The slice analysis of the bunch at the injector exit, see
Figure 4, shows that the slice emittance is affected by thecurrent ramp and presents an head-tail increase from 0.7 up
to 1.1 mm mrad.

60
3

Enegy (MeV)

Figure 3: Transverse normalized emittance, radial spot dimension and energy along the photoinjector beamline forthe medium bunch regime.

proj (mm mrad);

4

0

0
0

2

4

6

8

Z (m)

Figure 6: Transverse normalized emittance, radial spot dimension and energy along the photoinjector beamline forthe long bunch regime.

FEL Technology

THPPH028

140
14

97.5

120

97.0
12
96.5
10

96.0
-1

0

1 2mm

8

Bunch length
1.0

6
4

0.5

-1

0

1

# Counts

1.5

Slice energy (MeV)

2.0

silce energy spread (keV)

slice emittance (mm mrad)

Proceedings of FEL 2006, BESSY, Berlin, Germany

100
80
60
40

2

20

0

0

2mm

1.1

Slice position along bunch

Figure 7: Slice emittance and slice energy spread at the injector exit for the long bunch case calculated at the exit of
the photoinjector machine section. Plot inside: Longitudinal phase space. Bunch head is to the left.

1.2

1.3

1.4

1.5

1.6

Emittance (mm mrad)
Figure 8: Projected transverse emittance jitter at the injector exit obtained by randomly sampling input injector parameters.
120
100# Counts

Figure 6 shows the evolution of the transverse beamemittance, spot size and beam energy in this case. A final
projected emittance of 1.33 mm mrad is achieved. Similarly to the medium bunch case The slice emittance alsopresents an head-tail ramp (see Figure 7).

80
60
40

SENSITIVITY AND JITTER STUDIESThe time of flight, the energy, the energy spread and theemittance at the end of the injector have been identified
as the main output parameters whose shot to shot variation should be quantified, as well the slice properties of thebunch. To identify the main sources of variation for eachof these, a single-parameter sensitivity study has been performed for the two cases, with results shown in Table 2.
The time of flight is sensitive to gun parameters, while theemittance is more effected by a solenoid variation.
By randomly sampling each injector parameter within a
specified tolerance range fixed by present technology (seeTable 3), one thousand injector cases have been tracked(with 50000 particles), obtaining a statistical evaluationof the expected jitter. Results are presented in Table 4.
Figures 8 and 9 show the jitter distributions for the emittance and the time of flight and their histograms. The
gun solenoid has been neglected in this analysis due to thehigh stability (10 −5 ) provided by DC power supplies. The
bunch time of flight jitter is about 300 fs at the injector
exit and, linked to the energy jitter, it is propagated throughthe whole machine [5]. This effect becames an issue inthe synchronization in the undulators between bunch and ashort seed laser.
In order to consider the optical matching between the injector and the linac, an analysis of the jitter in the Twiss parameters has been also carried out on the same ensemble ofbunches. The results are reported in Table 4. The average
αx and βx are respectively -0.09 and 18m for the medium
case (0.77 and 21m for the long), but the jittered outputs are
spread out with a standard deviation respectively of 0.15

FEL Technology

20

28.072028.0725

28.0730

28.0735

Time of fligth (ns)Figure 9: Electron bunch time of flight jitter at the injector
exit obtained by randomly sampling input injector parameters.
and 2.1m (0.26 and 6.3m for the long case). This should betaken into account for the finalization of the optics matching.
Parameters
RF injection phase
Laser time jitter
Gun Eacc
SOA Eacc
SOA RF phase
ChargeLaser spot size
Laser pulse length (FWHM)

Tolerances
0.1 deg
200 fs0.25%
0.25 %
0.1 deg4%4%5%Table 3: Tolerance budget for the injector parameters.

Further analysis
A further analysis of the injector output bunches fromthe jitter simulations has been implemented. Polynomial
fittings of the longitudinal phase space and current bunch

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Table 2: Minimum parameters variation, for the medium bunch and long bunch (in parentheses) cases, providing a fixedvariation of the outputs, indicated in brackets in the first row. The average slice emittance <  slice > is calculated over all
the slices. n/s = not sensitive.
ΔI (1%)
1.5 (2.2)
0.47 (0.6)
0.65 (1.0)
20 (n/s)
6.2 (n/s)

Parameters (variation)
Gun Bsol (%)
Gun Eacc (%)
Gun RF phase (deg)SOA Eacc (%)
SOA RF phase (deg)ΔT (100fs)> 10 (10)0.13 (0.15)
2.8 (0.3)
2.0 (2.0)n/s (n/s)

σE (10keV)
1.1 (5)0.12 (0.17)
0.8 (0.28)
3.9 (1.1)
0.1 (0.22)

ΔE/E (0.1%)
n/s (n/s)
0.96 (1.6)
3.8 (1.8)
0.21 (0.2)
1.9 (0.7)

proj (10%)
0.2 (0.8)
0.33 (0.5)
0.5 (2.9)n/s (n/s)n/s (n/s)< slice > (10%)
2 (1.2)4.3 (0.9)
4.8 (4.6)n/s (n/s)n/s (n/s)

100

Table 4: Simulation results of the output jitter for the
medium and long bunch cases.
Arrival Time (fs)Peak Current (%)
Energy (%)σE (keV)
Emittancex (%)αxβx (m)

RMS jitter
medium
351
2.4
0.17
42
13.1
0.15
2.1

RMS jitter
long
266
3.3
0.17
24
6.3
0.26
6.3

80
70
60
50
40

-1.5mm -1.0

-0.5

0.0

0.5

1.0

1.5

Bunch length

Figure 11: Twelve polynomial curve fits (fourth order),randomly sampled in the thousands performed, of the current profile of bunches simulated for the long ramped case.
Bunch head is on the left.

97.5

Energy (MeV)

Current (A)Output parameter

90

97.0
96.5
96.0

-1.5mm -1.0

-0.5

0.0

0.5

1.0

1.5

Bunch length

Figure 10: Twelve polynomial curve fits (fourth order),randomly sampled in the thousands performed, of the longitudinal phase spaces of bunches simulated for the longcase. Bunch head is on the left.
profile have been performed for each simulated case. Figure 10 shows twelve fourth order polynomial curve fits of
the longitudinal phase spaces of the bunches simulated forthe long case, while Figure 11 shows the current profile
cases. The curves show the synchronous bunch core (3mm)
while the bunch tails are neglected.
After fitting all simulation results, a statistical analysis of
the fit coefficients has been performed [6]. These statisticalcharacterization can be used to reconstruct analytically the
injector output particle distribution with respect to the jitter.

CONCLUSION

lutions for the FERMI@elettra FEL operation with respect
to the “standard” flat-top distribution despite the slight projected emittance increase. The jitter studies have shownthat time jitter remains a critical parameter for seeded machine FELs and it will drive the future improvements in theperformance of the laser and RF systems.

REFERENCES[1] A. Zholents et al., “Study of the electron beam dynamics
in the FERMI@ELETTRA linac”, Proc. EPAC 2006, Edinburgh, UK.
[2] G. Penco et al., “Optimization Studies of the
FERMI@ELETTRA Photoinjector”, Proc. EPAC 2006,
Edinburgh, UK.
[3] S. D. Mitri, “How to obtain high quality electron bunches
in presence of normal conductiong Linac Wakefields”, Proc.
this conferece.
[4] M. B. Danailov et al., “Design of a Two-Stage Laser Pulse
Shaping System for FEL Photoinjectors”, Proc. this conferece.
[5] P. Craievich et al., “Jitter Studies for the FERMI@ELETTRA
Linac”, Proc. EPAC 2006, Edinburgh, UK.
[6] G. Penco, M. Trovò and S. Lidia, Technical Note ST/F-TN06/11.

Injector optimization of the medium and long bunchramped cases have been described. The ramped current
distributions have been presented as possible interesting so-

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH029

THE DIAGNOSTICS OF THE FERMI@ELETTRA BUNCH COMPRESSORS
M. Veronese*, S. Di Mitri, M. Ferianis, Sincrotrone Trieste, Trieste, Italy
Abstract

Table 1: Fermi@Elettra parameters

Bunch compressors (BC) are key components of theseeded FEL FERMI@ELETTRA. A complete set up of
non destructive diagnostics is foreseen to provide therequired stability for the production of sub-psec electron
bunches. Main task of these diagnostics is to provide theerror signals to the feedback systems used to stabilize theenergy and the peak current of the electron bunch which
are crucial parameters for optimum FEL operation. The
different operation regimes foreseen for FERMI [1] callfor a flexible set-up, for both the bunch compressors andthe associated diagnostics. In this paper we present the
adopted diagnostics for the measurement of position,energy and energy spread; both “energy” BPM, inbetween bunch compressors (BC), and optical transition
radiation (OTR) screen plus wire scanner have been
adopted. The design of a relative bunch length monitor
needed for the determination of the optimal compression
and for peak current stabilization is presented as well. The
scheme is based on non-invasive techniques, namely thedetection of the coherent synchrotron radiation (CSR)
from the last bending of the BC plus the coherent
diffraction radiation (CDR) from a downstream slit.
Finally, a technique for the bunch phase measurement ispresented.

INTRODUCTION
The FERMI FEL, presently under construction at the
Elettra Laboratory, is based on a seeded HGHG scheme.
Two FEL undulator chains FEL1 and FEL2 are foreseen
according to the needs of the FERMI scientificcommunity, to lase in two adiacent UV spectral regions(100-40nm and 40-10nm) with different pulse lengths.
The FERMI layout has been described in detail in [1], its
main parameters are presented in Table 1. High charge(~nC) electron bunches are produced in a RF photoinjector, with bunch length (LB) of about 10psecFWHM.
The acceleration is provided by normal conducting Sband RF structures and the bunch compression isachieved by two magnetic chicanes. Up to now, two mainbunch regimes have been studied: the “medium bunch”(LB=600fsFWHM) optimized for the FEL1 operation andthe “long bunch” (LB=1.4psFWHM) which is best suited for
FEL2. High quality beams (low emittance, low energy
spread, high current stability and high energy stability)
are needed to obtain high quality FEL output radiation.
Non-standard diagnostics and instrumentation suitable tofully characterize and monitor the beam during themachine operation have to be developed according to thespecific beam parameters and machine requirements.
___________________________________________*E-mail: marco.veronese@elettra.trieste.it

FEL Technology

Parameter

FEL 1(medium bunch)

FEL 2(long bunch)

Wavelength

100-40 nm

40-10 nmElectron Beam Energy

1.2 GeV

1.2 GeV

Bunch Charge

0.8 nC

1 nC

Peak Current

800 A

500 A

Bunch Length(FWHM)

600 fs1400 fs

Energy Spread (slice)

100 KeV

100 KeV

Norm. emittance(slice)

1.5 mm mrad

1.5 mm mrad

Repetition Rate

10-50 Hz

50 Hz

Photon Pulse Length(FWHM)≤ 100fs~ 1000 fs

BUNCH COMPRESSORS
Bunch compressors are used to produce high peak current
electron bunches needed to obtain GW peak power FEL
radiation generation. Several aspects have to beconsidered to avoid beam quality degradation (e.g. CSR
induced emittance dilution). In particular, the stabilisationof the peak current and the energy in the chicane areneeded to guarantee the long term stability of the FEL
output [2]. The bunch compression is obtained with twomagnetic chicanes located at the nominal energies of 220
MeV (BC1) and 600 MeV (BC2) respectively. This
design allows for both single and double compression
schemes, with a total compression factor ranging from 2
up to about 100 [3].

DIP2 BPM

BPM

Ring
El. DIP1
θCollimator

Wire
Δx Scanner

Screen

DIP3

DIP4

CSR

Ring
El.

CDR

Figure 1: Bunch Compressor Diagnostics layout.
The conceptual scheme is the same for BC1 and BC2, butsome components are adapted according to the different
bunch parameters. In Fig. 1 the bunch compressor scheme
is sketched together with the foreseen diagnostics. The
main parameters of BCs for a double compression scheme
are summarized in Table 2.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Table 2: Fermi bunch compressors parameters.
Parameter

BC1

BC2

4

4

Magnetic length

0.5 m

0.5 m

Distance DIP1-DIP2

2.5 m

2.5 m

Distance DIP2-DIP3

1m

1m

Distance DIP3-DIP4

2.5 m

2.5 m

Nominal DIP angularrange

66.8 :77.2 mrad53.1:77.5 mrad

Commis. DIP angularrange

50 : 80 mrad

50 : 80 mrad

Linac phases ranges

L1=-42° : -20°

L1=-42° : -20°
L2,3=-20° : -10°

Number of magnets

From Table 2 it can be seen that even if the bending
angles are quite small they span over a wide relative
range [3]. This fact, together with the dispersion and theenergy spread, has a deep impact on the electron beam
parameters in the chicanes (see Table 3) and on theirmeasurement.

width of at least 150mm is needed to allocate the wide
electron beam (±3σ beam size of 35mm) and its
displacements. Taking in account a beam transversely
centred at Δx=200 mm, the rms energy stability requiredby the FEL (ΔΕ/Ε=0.1%) will translate in terms of rm
displacement variations to 200 μm (at nominal BC1
operating conditions). To correctly operate the feedback
system, the resolution of the position measurement has to
be at least four times better than the value we want tostabilize within, which means that a single shot resolutionof 50 μm is needed. This is a very tough value to be met
on a 150mm chamber width and with a beam size of
35mm. Therefore, we plan to put the second and the third
dipoles of the chicanes and all the related diagnostics on atransverse high precision translator stage. This will allow
us to reduce the vacuum chamber transverse size to about
60 mm and thus to use an “energy BPM”. Anotherpossible approach to the problem has been proposed at
DESY; it is based on the measurement of the relative timedifference between two pulses generated in a transverse
strip-line arrangement [4]. Its applicability to Fermi will
be evaluated in the near future.

Energy Spread Measurement

We will now discuss the diagnostics according to themeasured parameter: energy, energy spread, bunch arrivaltime, relative bunch length.

The energy spread is a crucial parameter for the machine
operation and it has to be carefully monitored. It will bemeasured by means of a wire-scanner on multi shot basis
and by an OTR screen plus a CCD camera, shot by shot.
Both techniques are destructive and the measurements
will be performed during the commissioning and,periodically, during the operation to check the long term
stability of the energy spread. As depicted in Fig. 1, in
between the wire-scanner and the OTR screen, we plan toinstall a collimator. With this geometry the energy spreadof the beam can be measured upstream and downstreamof the collimator and its effect can be followed step bystep. The energy spread can be directly extracted from themeasurement of the transverse size of the beam since thedispersion in the middle of the chicane is known anddominates the beam size. The needed resolution isdifferent for the two bunch compressors. For BC1 theminimum δE/E is 2.3% which will reflect in a 28 mm
beam size (±3σ beam). The needed relative resolution isestimated to be 2%, which means 0.56 mm, in terms ofspatial resolution. For BC2 the energy spread will besmaller and it will have a small operation range. Then fora 0.95% δE/E will reflect in a ±3σ beam size of 10 mm
and to appreciate the changes in energy spread we willneed to have a 1% relative resolution which means 100
microns spatial resolution. This resolution level can beachieved with an OTR screen plus a CCD detector, higher
resolutions will be achieved by the wire-scanners [5].

Energy Measurement

Bunch Arrival Time Measurement

The transverse displacement of the beam centroid (Δx of
Fig.1) spans, for the BC1 and BC2 ranges, overapproximately 100mm. If we consider building the BCs
with a wide vacuum chamber, then for that chamber a

The bunch arrival time measurement will be provided bya new kind of diagnostics. The concept has been proposed
at DESY [6] and will make use of the optical pulses fromthe ultra stable timing distribution system [7] to measure

Table 3: Main beam parameters at BC1 and BC2.
Parameter

BC1

BC2

Energy Range

220 : 260 MeV

580 : 615 MeV

Rel. En. Spread

2.3 : 2.7 %0.97 : 1.05 %Beta (βx)

16 m (z=31 m)

23 m (z=98 m)

Dispersion (Dx)0.165 : 0.255 m

0.155 : 0.24 m

Transverse
displacement (Δx)

0.165 : 0.255 m

0.155 : 0.24 m

28 : 44 mm

10 : 15 mm

1.4 mm

2.0 mmEnergy Spread
Beam size ±3σ
Betatron
Beam size ±3σ

In particular, in the area between DIP2 and DIP3, where
all diagnostics will be located, the beam size is expected
to be dominated by the dispersion.

DIAGNOSTICS

630

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany⎛ C −1 ⎞ ⎛ σ φ ⎞
⎟
+⎜
⎟ ⎜
⎜
⎟
⎝ C ⎠ ⎝ c0 k RF ⎠
2

2

2

⎛1⎞
+ ⎜ ⎟ Σ i2
⎝C ⎠

0.0

(1)

As can be seen from Eq. 1 the coupled measurement of
the jitter at the entrance and at the exit of the chicane
initial will give us the RF contribution of the timing jitter.

Relative Bunch Length Measurement
The needs for peak current stabilisation push to develop a
non-destructive relative bunch length monitor, so that its
signal can be fed to the feedbacks systems that will keep
the peak current stability acting on the phases of the RF
accelerating sections. For this purpose we will develop
power monitors based on the detection of coherent
synchrotron radiation (CSR) [8] and coherent diffraction
radiation (CDR) [9]. We plan to implement a redundant
system based on the detection of the CSR emitted fromthe last dipole of the chicanes and on the detection of the
CDR emitted from a slit placed downstream the chicane.
Coherent radiation is emitted from short electron bunches,in the case of a Gaussian bunch where σz is the sigma of
the distribution, it is emitted at wavelengths longer thanroughly 2πσz. For electron bunches with psec and subpsec duration the coherent emission is in the mm/sub-mm
wavelength spectral range. An overview of the related
physics can be found in [10]. The CSR spectral angular
distribution of a N-electrons bunch can be related to thespectral angular distribution of a single electron as shownin Eq. 2.

[

]

2
d 2I
2 d I
= N + N ( N − 1) F (ρ (t ))dvdΩ N −el .
dvdΩ 1−el .

2.0Intensity (arb.units)-12

3.0x100sec

MEDIUM BC2

0

200

400
sec

-15

600 800x10

1

2

3 4
sec

5 6x10-12

LONG BC2

0.0

1.0
sec

2.0x10-12

Figure 2: Longitudinal electron distributions at BC1 exit(red) and BC2 exit (blue) for the “medium bunch” (left)
and the “long bunch” (right).
The code implements a full Liénardt-Wiechert potential
formalism, and makes a tracking of a single electron
through an arbitrary magnetic field. In the calculation both
velocity and acceleration terms are included as well as thefinite dimensions of the dipoles, the contributions of both
3rd and 4th bending magnets and the shielding effects ofthe vacuum chamber walls (in a parallel perfectly
conducting planes approximation). Some results of thesesimulations are shown in Fig.3 for the CSR emission fromthe last bending magnet of BC1 for the “medium bunch”
and in Fig.4 for the “long bunch” case. Plotted are theangle integrated spectral intensity distributions, for a
detector (30x30 mm) placed 150 mm downstream the last
bending of BC1 and normal to the edge radiation direction
centred 25 mm away from the straight beam path.

(2)

Where F(ρ(z)) is the Fourier transform of the longitudinal
normalized bunch distribution ρ(t). From Eq. 2 we can seethat the total N-electron CSR angular distribution is thesum of the incoherent synchrotron radiation of N electrons(∝ N) and a coherently enhanced term (∝ N2). The
frequency behaviour of the coherently enhanced term
depends on the square of the Fourier Transform of ρ(t). As
the bunch gets shorter the F(ρ) get spectrally broader andthe emitted power increases. To evaluate the emission
properties (spectral distribution and intensity) we havecomputed the CSR spectra angular distribution in two
steps. In the first we have calculated F(ρ), by means of the
FFT of the bunch profile coming from Elegant simulations(shown in Fig. 2). In the second, to calculate the single
electron spectral-angular distribution, since the circular

FEL Technology

1.0

LONG BC1

Intensity (arb. units)

2

MEDIUM BC1Intensity (arb.units)⎛r σ ⎞
Σ 2f = ⎜⎜ 56 A ⎟⎟⎝ c0 A ⎠motion approximation is not sufficient in our case, wehave used a numerical code written by O.Grimm at DESY.
Intensity (arb.units)

the bunch arrival time relative to the optical clock pulse.
This technique is non-destructive and it has shown so far
a resolution better than 100fs. Two devices, one at theentrance and one at the exit of each chicane, will be
installed. The signal from the device at the entrance of
BC1 will provide a direct measure of the total initial jitterfrom the injector.

THPPH029

Figure 3: Expected spectral distribution of the radiation
extracted from the 4th dipole of BC1 for the “mediumbunch.
These results suggest that, for the CSR emitted from thebunch compressors of FERMI the Gaussian bunch plus
circular motion approximations [8] might not be
sufficient. They also indicated that the choice of the631

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Proceedings of FEL 2006, BESSY, Berlin, Germany

frequency range for the detectors has to be done withspecial care for narrowband detectors. Moreoverconsidering both BC1 and BC2 the core of CSR emission
is in a critical spectral region (between 10GHz and 1THz)
for the detectors.

space requirements. This led us to choose a screen radius“a” of 60 mm and an angular acceptance of 0.2 rad. The
effect of the hole radius has to be considered, for CDRemission, the smaller the hole radius is, the better. On theother side the higher is the radius, the smaller is theimpact of the CDR emitter on the beam dynamics. CDR
Spectral distributions calculated with a rectangular
distribution approximation of the longitudinal bunch
profile are shown in Fig. 5 for two extreme cases: BC1“long bunch” and of BC2 medium bunch for different
values of the hole radius.

Figure 4: Expected spectral distribution of the radiation
extracted from the 4th dipole of BC1 for the “long bunch”.
In this region the detection of CSR can be done by RF
diodes or pyrodetectors. The diodes have higher
sensitivity in the sub-THz range, but are limited at about
600GHz while pyrodetectors offer a wider operation
range starting from about 150GHz. We plan to use thepyrodetectors for their flexibility and ease of use, but RF
diodes may be employed especially for the case of “long”
bunch in BC1. The total energy per pulse emitted in the
spectral range from 10 GHz to 1THz is of about 10μJ for
the “medium bunch” and of about 4μJ for the “longbunch”. In the spectral range of the pyrodetector (e.g.
Coherent/Molectron P4-42) the energy per pulse isrespectively of 1.5μJ and 0.3μJ. In this case a simple
estimate gives us a sensitivity of 0.04% sufficient to fulfil
the 2% of the feedback requirements (to obtain 10%
current stability). Other factors should also be considered:
the efficiency of the radiation collection, the absorption
and reflection from air and from the vacuum window.
A second coherent radiation source, a CDR source (e.g.
an OTR screen with a small aperture) will be installed
immediately downstream the bunch compressors. It ismeant to add redundancy to the CSR system. We have
performed some calculations to evaluate its application to
FERMI diagnostics. Our calculation started from the
CDR description given in [11] for a relativistic electron
beam. Here γ is the Lorentz factor of the electrons passing
through a hole of radius “b” in a circular screen of radius“a”. It is worth saying that the infinite screen
approximation is satisfied if a > λγ. For FERMI BC1“medium” bunch we can consider: λ=3 mm and γ=430
then the condition becomes a > 1.3 m. This shows that alarge screen and a large detector angular acceptance aredesirable to avoid low frequency intensity suppression.
On the other hand a compromise has to be found to meet

632

Figure 5: CDR spectral distributions for “medium bunch”
at the exit of BC2 and the “long bunch” at the exit of BC1
for values of b=0, 1, 5 mm.
The calculation indicates that, for the “long” bunch at
BC1 a quite large hole can be used without loosing too
much in intensity, while the hole size effect is more
important in the case of the “medium” bunch in BC2.

ACKNOWLEDGMENTS
We would like to thank O.Grimm for providing his code,
P. Craievich, M. Cornacchia, M. Dunnig, J. Travish, J.
Wu and P. Krejcik for fruitful discussions. And F. Rossi
for his help with Matlab simulations. This work has been
partially supported by the EU Commission in the Sixth
Framework Program, Contract No. 011935 – EUROFEL.

REFERENCES[1] M. Cornacchia, et al. EPAC 06, 145, (2006).
[2] J. Wu, et al. PAC 05, 1156, (2005).
[3] S. Di Mitri, ELETTRA, ST/F-TN-06/09, (2006).
[4] K. Hacker, et al. EPAC 06, 1043, (2006).
[5] K. Wittenburg, Tesla Report 2000-18 (2000).
[6] F. Loehl, et al. EPAC 06, 2781, (2006).
[7] M. Ferianis, et al. FEL 05, 134, (2005).
[8] J. Wu, et al. PAC 05, 428, (2005).
[9] E.Chiadroni, et al. EPAC 06, 1127, (2006).
[10] O. Grimm, EPAC 06, 1040, (2006).
[11] S. Casalbuoni, et al. TESLA Report 2005-15 (2005).

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Proceedings of FEL 2006, BESSY, Berlin, Germany

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MAIN HIGH VOLTAGE SOLID STATE GYROTRON POWER SUPPLY
60kV / 80A *G. Taddia, M. Pretelli#, L. Rinaldi, V. Rossi, L. Sita, O.C.E.M. SpA, San Giorgio di Piano, Italy
T. Bonicelli, P.L. Mondino, EFDA CSU Garching, Germany
D. Fasel, EPFL/CRPP Lausanne, Switzerland
R. Claesen, M. Santinelli, ENEA Frascati, Italy.
Abstract
This paper will describe the preliminary design of a 4.8
MW Main High Voltage Power Supply, rated 60kV/80A,
especially conceived to supply the voltage between
Cathode and Collector of a Gyrotron. A full solid statetechnology, named SWM (Stair-Way Modulation) for thefull scale Electron Cyclotron (EC) Test Facility at CRPP,
Lausanne. The ITER EC system may also make use of asimilar system, in alternative to the present baseline
design based on naturally commutated thyristor
converters and series high voltages solid state switches.
The 60kV output is reached by adding more than 120
high voltage modules in series connection, with ad hoc
control criteria to allow a regulation at full performancesin the range of 45kV-60kV, a square wave modulation
and a fast switch-off in less than 10us.Components
choices and simulations of the system will be highlighted
in order to demonstrate the fulfilments of the technicalspecification before the manufacturing stage. Thissolution can be extended to several applications in theHigh Voltage domain and is aimed to enhance thereliability, decrease costs, provide redundancy, plug-in
modularity, component de-rating and component
standardization.

solid state BPS has now been completed [2] and installed
at ENEA Frascati. For the new EC Test Facility in
Lausanne, EFDA is now procuring, on behalf ofEuropean Commission, both power supplies (MHVPS
and BPS). The results of a competitive tendering showedthat the above described modular topology was
economically convenient beside yielding some important
technical advantages.

OUTLINE SPECIFICATIONS
The performance specifications are listed in Table 1:
Table 1: Main Performance Specifications
Description

Value

Duty Cycle

8 / 24 hours

AC input Voltage

20kV / 50Hz (±10%)Nominal Output Voltage-60 kV DC

Output Voltage range-1 kVDC < VDC < 60kVDC
regulation
atfull
performances -45kV to –60kV

INTRODUCTION

Nominal Output Current

80 A

The ITER Heating and Current Drive (H&CD) system,
includes the installation of an Electron Cyclotron system
based on CPD type Gyrotrons (170GHz). This type of RF
sources requires two power supplies, one Main High
Voltage Power Supply (MHVPS) between cathode andcollector (typically V = 50 ÷ 60kV, 80A) and an
Acceleration Power Supply, which, with the MHVPS,
establishes the voltage between body and cathode,typically 80 ÷ 100 kV. The modulation frequency
specified in the ITER reference design is 1 kHz but in thedevelopments on-going in Europe, 5 kHz are considered
for the stabilization of Neoclassical Tearing Modes(NTM). The continuous developments of solid state
devices, available for both higher voltages and higher
switching frequencies, have highlighted several
advantages of the fully static solutions which could
conveniently replace the more traditional systems basedon vacuum tubes (e.g. tetrodes). On the basis of theabove considerations, OCEM has performed a conceptual
study of a Solid State Body Power Supply (BPS) [1] for
ENEA Frascati, with support from EFDA. The first fully

Modulation freq.(ON/OFF)

5kHz___________________________________________*Work supported by European Fusion Development Agreement#
physics@ocem.com

FEL Technology

Output Voltage Accuracy:
StaticReproducibility
Dynamic transient
Ripple<± 1% of VDC nominal<± 0.5% of VDC nominal<± 1500V<± 2%@600Hz, <±0.5%
for higher frequencies

Voltage Settling time

<15us

Shutdown time

<10us

Max Energy delivered to
the load in case of arc

10J

Protection Transm. delay<1us

Measurement Accuracy
Voltage

Current
Measurement Bandwidth+/-0.1% in DC+/-0.2% at 10kHz+/-0.3% at 50kHz<± 1% of nom. value≥500kHz633

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Proceedings of FEL 2006, BESSY, Berlin, Germany

MHVPS TOPOLOGY
The preliminary design of the MHVPS is based on aseries connection of elementary power modules which do
not require direct series connection of semiconductors.
Each module, is provided with its own DC power supply
so that the voltage is evenly shared during normal
operation. The total output voltage is hence controlled by
the number of switched-on modules in quantization stepsof voltage. This topology, together with an ad hoc control
strategy developed by OCEM, the Multi Pulse Width
Modulation (MPWM), has been named Stair-Way
Modulation (SWM). This type of modulation has theadvantage of an averaged power distribution among all
the modules, with a consequent minor stress of the maintransformers. Also the achievement of a high bandwidthis not related to the increasing of the switching frequency
of only a few modules. In a SWM system the maximum
switching frequency of each module remains equal to all
the modules. This leads to reach a very high value of
bandwidth, according to the constraints due to theparticular specifications. The overall system also foresees
a level of modularity in a redundant and fault tolerant
configuration. Hence, in case of fault of a single module,
the faulty module can be easily excluded from the main
circuit, ensuring continuous operation.
The MHVPS consists mainly of the following blocks:• Input circuit breaker with a protection relay, toconnect the P.S. to the medium voltage grid
(20kV, 50Hz, three-phase) through a soft startequipment.
• Multi Secondary Transformer system, to adapt
the input voltage from the grid to the voltage
required by the downstream parts, with the proper
insulation level.
• Power modules in series connection, to transformthe 50 Hz supply voltage from the transformer
system in a regulated DC voltage.
• Control electronics, to provide regulation,
protection and interface.
The main parts of the MHVPS are described in thefollowing subsections.

Multi Secondary Transformer System
Due to the design constraints (mainly the 120kVdc
insulation voltage, the reduced available space on the
installation site and the requested very low harmonic
content in the input current) the transformer system isbased on two cast-resin transformers, made of several
secondary, each feeding one power module.
The secondary coupling of these two transformers iseither of the star type or of the delta type, in order toobtain an overall primary current from the grid with low
harmonics. Finally, soft-start devices are integrated
between the transformers and the main grid.

Power Modules
The general scheme diagram of the power module isshown in Figure 1.

634

The switched-on power modules, controlled by amodulation index, determine the total output voltage. By
using this technique and a proper switching strategy, themodulation can be performed in order to obtain the
L
Lin

+HV

soft-startanddisconnection

+

R

Vout

RC
Q1

Driver

L

Vac

C1

-

C2
R
Q2

Driver-HV

Control circuits

Command

StatusFigure 1: General schematic of a Power Module.
desired value of output voltage within the specification
requirements. The Module is ON when the switch Q2 isclosed and Q1 is open; a voltage step of -Vdc is added tothe total output voltage. The Module is OFF when theswitch Q2 is open and Q1 is closed; the module isbypassed. The two switches Q1 and Q2 must be never ON
simultaneously. Using this structure it is relatively simple
to perform a fast switch-off: there is enough time tosimultaneously open the series switches (Q2) of each
module, and then to close all the parallel switches (Q1);this operation can be very fast, in the order of 2-3 us.
Each module has an output L-R filter, which is aportion of the total output filter seen by the load. The
filter has been conceived for:• smoothing the output voltage ripple;• limiting the di/dt and the peak current during thearc;• obtaining a correctly damped overall system;
Calculations show that in order to minimize the energy
delivered to the system it is necessary to consider an
additional resistor of some ohms (4 ohms) in series withthe load; this will permit to dissipate a portion of theenergy before that this energy is delivered to the
Gyrotron. The module is designed for an output voltageof 560V. This leads to a series connection of more than
120 modules with the consequence of a relatively highcomplexity of transformer and cabling. However thecomponents mounted on each module can be low voltage
devices, with an advantage in terms of cost andavailability. Moreover, each stair of voltage is lower than
the allowable peak to peak ripple, leading to have anadditional degree of freedom in the dimensioning of theoutput filter.

Control Electronics
The control electronics has been designed to performthe following functions:• measurement of the output voltage and current;• regulation: to keep the output voltage at thedesired value and within the allowed fluctuations;

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Proceedings of FEL 2006, BESSY, Berlin, Germany•

protection: to guarantee an effective protection incase of internal faults or external overloads;• interface: to communicate with the main control
system and to allow the local or remote commandof the power supply.
The user interface, data log and Ethernet connections
are based on commercially available electronics, withcustom designed software. The regulation system (fully
digital, based on an high performance FPGA card)
determines the number of modules that must be ON ineach time interval, providing a proper "rotation" in themodule sequence. This allows to equally share thestresses among the modules. During commutations, with aproper modulation strategy for the semiconductor
switches, the switching frequency seen by the load isequal to the frequency of the single module multiplied by
the number of modules. This allows an high output
switching frequency (seen by the load) with the advantage
of a relatively low switching frequency seen by thecomponents of the modules.
In steady state, when the output voltage is between an
acceptable range around the set value, the algorithm
foresees a lock modulation input that stops the switchingof the modules and the rotation. This prevents an
unnecessary power dissipation.

Components Choice
After a careful market inspection, the main standard
components have been chosen. The IGBTs is a
VCES=1200V / IC=140A @80°C (IC=200A @25°C) device
based on the SPT technology which offers a goodcompromise between the VCE_ON and the switching speed(switching losses). The size of the IGBT was chosen also
looking at its overload behaviour: it has a short circuit
capability of 1000 pulses at ten times IC and self limiting
current capability to 6•IC. The IGBT driver choice wasmade looking firstly to its delays which are extremely
small. The input DC filter topology is an LC-parallel
damped filter. The damping is chosen to avoid excessive
over-voltages during power connection or load

THPPH030

disconnection and to limit the filter peak output
impedance to less then 0.5 Ohm.

PRELIMINARY SIMULATIONS RESULTS
The preliminary simulations for the MHVPS have been
performed by considering the overall system which will
be installed in Lausanne and which include the CPD
Gyrotron, the BPS and MHVPS in order to verify theadequate compatibility of the MHVPS to the alreadydesigned BPS now under construction.
The model of the whole system has been developed
using Pspice and Matlab/Simulink. Figure 2 shows thestep up of the whole system simulation (with Simulink):
the ramp up of the MHVPS current and voltage are shownin the first and third rows respectively. In the second row
the switch-on of the BPS is simulated. This leads to theincrease of the Body to Cathode Voltage up to the
maximum value 100kV, as shown in the fourth row.
In Figure 3 it is sketched how the MHVPS and theoverall system behave during the required 5kHz
modulation. The first two rows show the commands given
to the BPS and MHVPS for starting the modulation; both
power supplies start modulating as specified, and thevoltage patterns can be observed in rows 3 (BPS) and 4(MHVPS). The total output voltage between Body andCathode is the result shown in row 5 (100kV peak). Last
row is the MHVPS current which shows a promising
behaviour of the overall system during the 5kHz
modulation.
Finally, Figure 4 reports a simulation of the overallsystem in case of an arc between Cathode and Collector.
The arc is simulated by adding in the Simulink model a
voltage generator of 100V. At 200 us the arc occurs andBody to Cathode voltage collapses by leading to anincrease of the amount of charge in the Gyrotron (fifthrow). The 0,1 limit value depicted in the fifth row,
represents the amount of charge delivered to the load and,considering an arc voltage of 100V, corresponds to the
maximum value of energy that could be delivered as pertechnical specification (10 Joules). However it can beobserved how safe is kept this limit.

Figure 2: Simulation of the Step up of the whole system (MHVPS+BPS+Gyrotron)

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 3: Simulation of the 5kHz Modulation

Figure 4: Simulation of the Step up of the whole system with an arc between K-C at 200us

CONCLUSIONSThis paper has described the preliminary design of a 4.8
MW Main High Voltage Power Supply, rated 60kV/80A,
especially conceived to supply the voltage between
Cathode and Collector of a Gyrotron. This topology has
been chosen for the EC Test Facility at CRPP, Lausanne(CH). Similar systems could be adopted for ITER, which
includes the installation of an Electron Cyclotron system
based on CPD type Gyrotrons (170GHz) in alternative tothe present baseline design.
The first simulations have demonstrated the correct
behaviour of the MHVPS not only as a stand alone
modulator but as part of a complete system which will be
installed in Lausanne, and which include the MHVPS, the
BPS and the CPD Gyrotron. Three main situations havebeen depicted in the simulation sketches: the step-up and636

the steady state, the 5kHz ON/OFF modulation and the
behaviour of the system in case of an arc between
Cathode and Collector. The first results are very
encouraging and the design phase can enter into a further
final detail before entering the manufacturing stage. The
installation of the overall system in Lausanne is foreseen
to be starting by September 2007.

REFERENCES[1] T. Bonicelli et alia, “High Frequency/High Voltage
Solid State Body Power Supplies for CPD
Gyrotrons”, SOFT’02, Helsinki, September 2002, p.
543-548.
[2] G. Taddia et alia, “High Voltage Solid State Gyrotron
Body Power Supply”, 14th Joint Workshop on
Electron Cyclotron Resonance Heating, Santorini,
May 2006, p 95.

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH031

COMMISSIONING OF THE SPARC PHOTO-INJECTOR∗
M. Bellaveglia, D. Alesini, S. Bertolucci, M. E. Biagini, R. Boni, M. Boscolo,
M. Castellano, E. Chiadroni, A. Clozza, L. Cultrera, G. Di Pirro, A. Drago, A. Esposito,
M. Ferrario, L. Ficcadenti, D. Filippetto, V. Fusco, G. Gatti, A. Gallo, A. Ghigo,
S. Guiducci, M. Incurvati, C. Ligi, M. Migliorati, A. Mostacci, L. Palumbo,
L. Pellegrino, M. Preger, R. Ricci, C. Sanelli, F. Sgamma, B. Spataro,
F. Tazzioli, C. Vaccarezza, M. Vescovi, C. Vicario (INFN/LNF);
A. Bacci, I. Boscolo, F. Broggi, S. Cialdi, D. Giove, M. Mauri,
A. Rossi, L. Serafini (INFN/Milano);
M. Mattioli, P. Musumeci, M. Petrarca (INFN/Roma1);
L. Catani, A. Cianchi, S. Tazzari (INFN/Roma2);
A. Perrone (INFN /Lecce);
L. Giannessi, M. Quattromini, A. Renieri, C. Ronsivalle (ENEA/FIS);
J. Rosenzweig (UCLA)
Abstract
The SPARC project [1] is born to perform R&D activity
headed to realize SASE-FEL experiments at 500nm andhigher harmonic generation. The project foresees the realization of a high brightness photo-injector able to produce a
150 ÷ 200M eV electron beam to drive FEL process inside
a dedicated 12m long undulator. The machine is going to
be assembled at LNF and its final configuration is made upof an RF gun, driven by a Ti:Sa laser, injecting into three
SLAC type accelerating sections. Nowadays we are working in a photo-injector test phase, aiming to characterize themain hardware components and to investigate the behaviorof the e-beam dynamics in the first meters of drift. To dothis we utilize the emittance-meter, a home designed diagnostic device placed just after the RF gun, able to move 1.2
meters along the longitudinal axis to measure beam parameters. In this paper we report a more accurate descriptionof the project, the status of the single systems constituting
the machine and the most important results we obtained in
the e-meter phase.

INTRODUCTION
The commissioning of the SPARC photo-injector isstarted at Frascati INFN laboratories and we are operating in a gun test phase, before installing the accelerating
sections. In this phase, laser, radiofrequency, timing, control system and beam diagnostics are installed and working
in the SPARC bunker. We performed a characterization of
the beam at the gun exit with the home-designed movable
emittance-meter [2] and a spectrometer. A picture of the
hardware installed in the bunker is reported in figure 1. The
most significant results are reported in table 1 that shows
the two investigated main beam configurations.
∗ Work supported by the EU Commission in the 6th FP, contract no.
011935 EUROFEL and contract no. RII3-CT-2003-506395 CARE.

FEL Technology

Table 1: Main beam configurations
Low charge
High charge
Charge
200pC
900pC
Emittance
0.8mm mrad 2.2mm mrad
Energy5.65M eV
5.55M eV
Energy spread
1%
2.6%
Pulse length
8ps
12ps

PHOTO-INJECTOR STATUS
In the following paragraphs we will give a short description of the main systems constituting the machine.

Figure 1: Picture taken in the SPARC bunker

RF and timing system
The SPARC RF system is mainly constituted by two RF
chains and its scheme is reported in figure 2 together withthe synchronization system layout [3]. The power sources,
shown in figure 3(a), are the 45 MW peak, 2856 MHz
klystrons TH2128C. The klystron n.1 presently feeds only
the RF gun with 3µsec pulses and it is designed to feed also
one accelerating section via a 3dB waveguide coupler andan RF deflecting cavity for beam diagnostic purposes.
The RF gun, reported in figure 3(b), was successfully
conditioned without relevant problems and we fed into it
more than 10M W of RF power that corresponds to an

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Proceedings of FEL 2006, BESSY, Berlin, Germany

(a)

(b)

Figure 4: (a) transverse laser spot on the cathode and (b)UV pulse longitudinal shape
Figure 2: RF system layout

Figure 5: Cathode QE before (left) and after (right) laser
cleaning(a)(b)

Figure 3: Installed RF hardware: (a) modulators andklystrons and (b) RF gun
accelerating electric field of about 120M V /m. Klystronn. 2 and its waveguide distribution lines are now under
test and they will feed two high gradient accelerating sections through an energy compressor that allows to obtain a
60M W - 0.8µsec RF pulse.
The timing distribution system is installed and it provides the 79.33M Hz reference to lock the laser system to
the RF oscillator using a home-designed frequency divider
board. It also furnish the 10Hz repetition rate signal tothe machine, synchronous with the external line and to the2856M Hz internal distribution.
The synchronization diagnostic is working with goodand stable performances and the time jitter from each location of the machine (relative to the main oscillator) is
displayed in the control room monitors. Also an RF phasefeedback system was implemented to correct slow drifts
due to temperature. The observed time jitter of the accelerating field inside the gun is 250f s RMS and the laser oscillator time jitter is 350f sRMS .

Laser system
Beam dynamics simulations defined the SPARC laser
system [4] specs in order to obtain 2mm mrad emittanceat 100A. The laser is a 10Hz CPA Ti:SA, TW system produced by Coherent. At the laser exit a THG and an UV
stretcher produce the required wavelength (266nm) andpulse duration (2 ÷ 10ps). To manipulate the time profilean acousto-optic programmable dispersive filter is installed

638

before the amplifier.
The pulse profile is flat in time and gaussian in transverse plane (with 1mm spot size) and an image of the spot
is shown in figure 4(a). We are using a cross-correlator toinvestigate the longitudinal behavior of the UV pulse and atypical observed shape is reported in figure 4(b). The optical transfer line is designed to increase the pointing stability, to easily change the spot dimension and to compensate
the 72◦ incidence distortions.
A laser cleaning on the cathode was performed and it
has given good results, increasing the quantum efficiency
from 3.75 · 10−5 to 6 · 10− 5 and improving the emission
uniformity as can be seen in figure 5.

Control system
The control system is perfectly working and it is ready to
be extended to the SPARC full configuration. The SPARC
main server with a RHEL3 operating system, is in a LTSP
configuration so that the consoles are identical disklessworkstations. The photo-injector device drivers are installed in industrial PCs placed in the bunker. The layout of
figure 6 report the SPARC protected 1Gbit/s LAN architecture. Two machines form a connecting bridge from thefront-end industrial PCs to the control room consoles:• the data server: it accepts a request of informationfrom the consoles and send them the data read fromthe proper industrial PC. The data can be software
variables (that identify the controlled devices), sampled signals, images or information about the status of
the computer itself;

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An exhaustive description of the measurements taken using these items is given in the next section.

BEAM MEASUREMENTS
Charge vs phase
First of all we report the charge relative to the gun RFphase measurement (phase scan) that allow us to choose
day by day the optimal phase for the electron extraction andto collect information about the accelerating gradient andthe quantum efficiency. Moreover this kind of measurement permit us to obtain a rough estimation of the beam
duration. Picture 8 report some phase scans performed indifferent photo-injector working points.
Figure 6: Control system architecture• the command server: it elaborates the queue coming from the consoles and, once identified legal commands, it delivers them to the front-end PCs to control
the photo-injector devices.

Diagnostics
Beam diagnostic devices are placed along the photoinjector as shown in figure 7 and reported in table 2.
The main diagnostic tool is the home-designed emittancemeter, able to move 1.2m along the longitudinal axis andto study the first meters of beam propagation, where spacecharge effects and plasma oscillations dominate the electron dynamics.

Figure 8: Charge vs phase in three different beam configurations

Energy and energy spread

Figure 7: Photo-injector actual layout

Table 2: Diagnostic elements
Distance from
cathode [cm]60
85 ÷ 200220
250 ÷ 300
250 ÷ 300
350

DeviceMeasurement

Faraday cup,
CROMOX screen
E-meter (slits,
YAG screen, CCD)
aerogel + streak
cameraFODO cell,
dipolespectrometer(Yag + CCD)
BCM

charge, beam
centeringemittance, beam envelope
and parameters

FEL Technology

beam duration
beam conditioning
before spectrometerenergy andenergy spreadbeam charge

A spectrometer and its transport line (constituted by a
FODO cell) are placed at the end of the diagnostics chain
to measure energy and energy spread. We performed thesemeasurements in low and high charge configurations asfunction of the launching phase as shown in figure 9. The
difference both in maximum energy and energy spread between the low and high charge case are due to longitudinal space charge effects (including the image charge at thecathode) and to the wakefield effects in the long bellows.
The presence of the emittance-meter allowed us to perform some special energy spread measurements inserting aslit in the bunch orbit and selecting a beam slice in different longitudinal locations. In fact, as shown in picture 10,
we ‘froze’ the beam evolution under the longitudinal spacecharge and wakefield effects at different points along thebeamline.

Bunch length
A longitudinal diagnostic, based on Cherenkov radiation
produced by the beam passing through a 5mm thick aerogel slab with index of refraction n = 1.017, was installedwith the main purpose of studying the photo-injector response to hundreds femtosecond long laser pulses created639

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Proceedings of FEL 2006, BESSY, Berlin, Germany

(a)

(b)

Figure 9: Energy (a) and energy spread (b) for low and highbunch charge

Figure 12: Emittance measurement with relative simulated
curvesFigure 10: ‘Slit’ energy spreadby the Ti:Sa laser system [5]. A field-lens narrow band
filtering optical system delivers the Cherenkov light to theentrance slit of a 2ps resolution Hamamatsu streak camera
enabling pulse length measurements (see figure 11).

Figure 13: Phase space reconstruction

CONCLUSIONSThe SPARC photo-injector commissioning was started
and a good characterization of the electron beam at the exitof the gun has been performed with the emittance-meter.
In particular measurements show that the beam brightness
required to drive a SASE-FEL experiment was achieved.
The linac installation phase will begin at the end of thissummer with the commissioning of the accelerating sections and the second RF power line. Moreover it is planned
to use a SPARC-like system as photo-injector for the future
SPARX X-ray FEL experiment [6].

Figure 11: Bunch length measurements with streak camera

REFERENCES[1] D.Alesini et al., IEEE Cat. N. 05CH37623C, (2005) 1327.

Transverse dynamics
Using the emittance-meter we were able to characterize
the emittance as function of the longitudinal coordinate andto observe clear indications of emittance oscillations driven
by space charge forces in the drift downstream of the RFgun, in agreement to what expected from our theoreticalmodel and numerical simulations. Figure 12 reports two
set of measurements compared with numerical simulation.
The algorithm used to calculate the emittance was designed
also to reconstruct the phase space and good results wereachieved (see figure 13).

640

[2] L. Catani et al., ‘Operational experience with the emittancemeter at SPARC’, these proceedings.
[3] A. Gallo et al., ‘The SPARC RF Synchronization System’,
PAC’05 proceedings, Knoxville, May 2005, p. 1024.
[4] C. Vicario et al., ‘Commissioning of the Laser System for
SPARC Photoinjector’, EPAC’06 proceedings, Edinburgh,
June 2006.
[5] M. P. Dunning et al., ‘Optimum beam creation in photoinjectors using space-charge expansion’, these proceedings.
[6] D. Alesini et al., ‘Status of the SPARX FEL project’,
EPAC’06 proceedings, Edinburgh, June 2006.

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH032

FREE ELECTRON LASER TRIGGERED PHOTO-CATHODE
E. Sabia, A. Dipace, ENEA, C.R. Portici (Napoli), Italy
G. Dattoli, ENEA, C.R. Frascati (Roma), Italy.
Abstract
The possibility of realizing a FEL triggered
photocathode has been proposed long time ago and theadvantages have been pointed out. In these devices the
FEL can be exploited to extract electrons from a
photocathode to provide a high quality e-beam. The
device becomes even more appealing if photothermoionic cathodes can be exploited in two different
phases. In the first the electrons are extracted from thecathode working as thermoionic and are used to drive a
FEL oscillator, the FEL light is then used to flash thecathode which operates as a photo thermal assisted
device. We comment on the possibility of using FEL
triggered photocathodes to produce high quality e-beams
for SASE or oscillator FEL devices. The use of the samee-beam driving the photocathode and the FEL makes thesystem naturally free of any synchronization problem
arising when an external laser is used. Examples ofinterplay between the generation of electron and opticalbursts are also investigated.

LINAC

RF gunM1

Thermoionicemission+

Undulator
interaction

Photoelectric
emissionM2

Fig.2: Layout of the “hybrid FEL oscillator”.

In this paper we will consider a thermal dispenser
cathode [3], with good photoelectric quantum efficiency,
initially operating in the thermoionic mode and heated ata sufficient temperature in order to have enough e-beamcurrent to allow FEL operation, radiation is then feedback to the cathode to switch it on the photo-assisted
mode.

THEORETICAL MODELINTRODUCTION
In previous investigations it has been shown that FEL
radiation can be exploited to trigger a photocathode gun[1], [2]. In this paper an extension to an “hybrid device”
has been considered: in such a device, sketched in Fig. 1,2
a thermoionic gun produces an e-beam driving a FEL
oscillator, the FEL radiation can be backward sent toilluminate the thermoionic cathode in order to exploit a
different operating regime, i.e., a thermally assisted
photoemission. Such a feedback mechanism, with aproper choice of the parameters, can enhance the e-beambrightness despite a modest increase of the transverse
emittance.

UNDULATOR

Under a number of assumptions and proper
approximations that will be explained in the following, asemi-analytical model has been developed to take into
account the interplay among the oscillator intra-cavity
radiation growth, the temperature rise due the photonic
incident energy loss in the cathode material and theelectron current extracted. It has already been shown thatthe round-trip evolution of a FEL oscillator can be written
as [4]:

I =I
n 0[(1−ηcl )(1+G)]nI(1)
1+ 0 [[(1−ηcl )(1+G)]n −1]
IE
where n is the round trip number, G the maximum

small signal gain, ηclthe total cavity losses, I 0

theinitial seed and I E the intra-cavity equilibrium intensity
given byIE =1
( 2 + 1)⎛⎜⎜ 1 η− η G − 1⎞⎟⎟ 2 Ng
P
cl

⎝

cl

⎠

e

(2)

0

with N being the number of undulator periods, g 0
Energy loss incathodeFig. 1: Block diagram of “hybrid FEL oscillator”.

FEL Technology

the small gain coefficient and Pe the e-beam power.
In the previous relations (1) and (2), the quantities
I 0 , g 0 , G, Pe are no longer constant but, due to thefeed-back mechanism, they are updated at each round
trip.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

The temperature rise due to the photonic incident
energy loss in the cathode can be evaluated using theAnisimov heat equations [5], [6] which relate the electron
to the lattice temperature. As suggested in [3], for timescale characteristic of laser pulse in the range 1ps-1ns, asteady state approximation of the Anisimov equation canbe considered, which implies that the electron and lattice
temperature are equal. Moreover, under the assumption ofa laser pulse with a uniform spatial profile and a constant
power of duration τ (microbunch duration) [7], at a
power level such that neither melting nor vaporization
occure, and by considering the heat to be generated at thesurface of the cathode, we get:(1 − η − R )I λτ
ΔT =

(3)

2κρcvτ

where η is the photoelectric quantum efficiency, κ ,ρ , cv are the thermal conductivity, the density and thewhere q is the photoelectric extracted charge and σ zis the length of the bunch.
We can estimate the amount of emittance increase byrelating it to the illuminating power. An example of therelevant behaviour is given in Fig. 3.
1.2

1

emittance (mm.mrad)

THPPH032

0.8

0.6

0.4

0.2

specific heat of the cathode material respectively, R thecathode reflectance, τ the laser micro-pulse duration, I λ⎛ e ⎞ ⎛ U ((hν − φ ) / kT ) ⎞J = (1 − R )⎜⎟⎟ + J RLD⎟ I λ ⎜⎜⎝ hν ⎠ ⎝ U (μ / kT ) ⎠(4)

J RLD = AT 2e −φ / kT

(5)

where A is the Richardson constant, R the cathodereflectance, hν the incident photon energy, k theBoltzmann constant, T the electrons temperature, μ the
chemical potential, φ = Φ − 4QF the barrier height, Φthe cathode work function,

4QF the Schottky barrier

lowering due to the image charge Q , F the product of
the electric field gradient between cathode and anode andthe electron charge and finally U is the FowlerDuBridge function [8], [9].
It may be argued that since the cathode is operated asthermoionic and photocathode there is a detrimental effectdue to the increase of beam emittance (both transverseand longitudinal). The emittance increase can be
estimated following the recent analysis by Bazarov andSinclair [10]. In their scaling law the transverse emittanceis related to the extracted charge and bunch length :⎛ε [mm mrad] = q [nC] ⋅ ⎜⎜ 0.73 +⎝642

0.15 ⎞⎟σ z [mm] ⎟⎠
2.3

(6)

0

40

80

120

160

round trip number
Fig.3: Emittance increase vs. round trip number (in red
the photoelectric contribution, see Eq. 6, in black the total
emittance) [mm mrad].
It is evident that with increasing number of reflections
the emittance grows (we have assumed quadraticcomposition for the different emittance contributions) but
the increase of current is larger and the net effect is anincrease of the e-beam brightness. We must however notexceed the reflections to avoid effects of power
overloading which may create a too large emittancedegradation as shown in Fig. 4. It may also be argued thatthe Bazarov-Sinclair scaling holds for an optimized
system and therefore the previous estimation may be
optimistic.
1 . 10e-beam brightness (A m-2 rad-2)

the power laser density to the cathode.
The electron current density extracted from the cathode,using the Richardson approximation, can be obtained as asum of 2 contributions: one proportional to the laser
intensity, the other to the Richardson-Laue-Dushmanncurrent density for thermoionic emission [3]:014

1 . 1013

1 . 1012

1 . 101 . 108

9

1 . 1010

1 . 1011

1 . 1012

1 . 1013

power density (W/m2)
Fig. 4: e-beam brightness [A mdensity [W m

−2

−2

rad

−2

] vs. power]

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH032

RESULTS AND DISCUSSION

length Lc of the resonator cavity. The system is designed

A preliminary analysis of the device has beendeveloped using the parameters listed in Table 1 and 2

in such a way that for the first 3 round trips the intracavity radiation grows according to the Eq. 1 withconstant parameters ( I 0 , g 0 , G , Pe ), then Eqs. 1, 2, 3, 4
and 5 are fully coupled.
In our example we have considered 153 round trips
which ensure, as already remarked• Increase of the bunch current.
• Increase of the e-beam brightness despite a modest
increase of the transverse emittance (this last point
deserves however a dedicate analysis including thecontributions from the longitudinal and transverse
shapes of the optical bunch).
In Fig. 5, 6 and 7 the time evolution of cathodetemperature, e-beam current density and laser intensity
are shown respectively.

Table 1: FEL oscillator
laser wavelength

500 nmλuundulator wavelength

2.8 cmN

number of undulator periods

100γe-beam energy

305.8

σε

relative energy spreadre-beam radius

I0

Input seed

τe-beam micropulse duration

3 ps

τM

e-beam macropulse duration

10 μs

n

round trip number

153

δ

distance between RF gun and

20 m

10

−3

8.9 10−3

1 W/cmm
2

mirror M 1 (see Fig. 2)

Lc

resonator cavity length

ηcltotal cavity losses

4%

mirror M 1 transmissivity

2%

T1

10 m

0.01

relative temperature increase

λ

1 .10

3

1 .10

4

1 .10

5

1 .10

6

1 .10

7

1 .10

8

1 .10

9

1 .10

10

1 .10

11

1 .10

12

0

50

100

150

200

round trip number
Table 2: Dispenser cathode characteristics

Sc2O3 in matrix of W
Φwwork functionφeffective barrier height

1.68 eVdinter-electrode distance

1 cm

thermal conductivity

1.78 W/cm°K

density

19.3 g/cm3

cv

specific heat

0.13 J/g°K

Tin

temperature operation before
first illumination

1300 °K

Relative temperature increase vs. round trip

1.8 eV10e-beam current densityκρFig. 5:
number.

10

10

8

7

6

0

40

80

120

160

i

round trip number
The example we have considered is a FEL oscillator inwhich the distance between the cathode and the first
semitransparent mirror M 1 (see Fig. 2) is 2 times the

FEL Technology−2Fig. 6: E-beam current density [A m ] vs. round trip
number.

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laser intensity (W/m2)

THPPH032
1 . 1013

1 . 1012

1 . 1011

1 . 1010

1 . 109

1 . 108

1 . 107

1 . 106

1 . 105

1 . 104

Proceedings of FEL 2006, BESSY, Berlin, Germany[6] N.A. Papadogiannis, S.D. Moustaizis, J.P. GirardeauMontaut, J. Phys. D: Appl. Phys. 30,2389 (1997).
[7] J.H. Bechtel, J. Appl. Phys., 46, 1585 (1975).
[8] R.H. Fowler, Phys. Rev. 38,45 (1931).
[9] L.E. DuBridge, Phys. Rev., 43,727 (1933).
[10] I.V. Bazarov and C.K. Sinclair, Phys. Rev. Special
Topics-Accelerators and Beams 8, 03402-1 (2005).
[11] E. Sabia, G. Dattoli, A. Dipace and G. Messina,
submitted to J. Appl. Phys.

0

50

100

150

round trip number−2

Fig. 7: Laser intensity [W m ] vs. round trip number.

CONCLUSIONS
A different possibility has been discussed in a previous
paper [11] in which a hybrid SASE FEL has been
considered: the radiation inside the undulator may becollected with a mirror (if we consider radiation in thevisible) and sent back to the cathode. This has not a feedback on the radiation and it is just an external passive
device. We must underline that for this device theradiation grows from the noise and the optical spectrum
may be dominated by spikes and energy fluctuations, thus
inducing dangerous effects which may strongly affect thequality of the e-beam itself. On the contrary, the use of theresonator cavity, acting as an active feed back on the
optical field, may eliminate all the problems due to theshot noise, and the length of the optical pulse can also beeasily controlled as well as other problems due to thetransverse distribution.
It is worth noting that the technique we have considered
can be exploited for higher harmonics of the radiation. It
is indeed well known that along with the fundamental
higher order harmonics are generated in the optical cavity.
The harmonic power is not stored in the cavity but it isemitted shot after shot. The harmonic radiation too can be
exploited to irradiate the cathode. This different operation
will be more deeply examined in a forthcoming
investigation.

REFERENCES[1] G. Dattoli, L. Giannessi, and L. Serafini, J. Appl.
Phys., 93,1 (2003).
[2] G. Dattoli, L. Giannessi, A. Renieri, A. Marino, and
L. Serafini, Appl. Phys. B: Photophys. Laser Chem.
B55, 446 (1992).
[3] K.L. Jensen, D.W. Feldman, M. Virgo, P.G. O’Shea,
Phys. Rev. Special Topics, 6, 083501 (2003).
[4] G. Dattoli and P.L. Ottaviani, Opt. Commun. 204,283 (2002).
[5] S.I. Anisimov, B.L. Kapeliovich, T.L. Perelman, Zh.
Eksp. Teor. Fiz., 66,776 (1974) (Engl. Transl. 1974
Sov. Phys.-JETP,39,375).

644

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH033

SUB-PICO-SECOND TRIGGER SYSTEM FOR THE
SCSS PROTOTYPE ACCELERATOR
Yuji OtakeA), Hirokazu Maesaka A), Takashi Ohshima B), Naoyasu HosodaB),
Toru Fukui B), Toru Ohata B), Tumoru Shintake A)A)
RIKEN, Harima Institute 1-1-1 Kouto, Sayo-tyou, Sayo-gun, Hyogo, 679-5148, Japan
B)
Japan Synchrotron Radiation Research Institute (JASRI/SPring-8)
1-1-1 Kouto, Sayo-tyou, Sayo-gun, Hyogo, 679-5198, Japan .
Abstract
To verify the feasibility of X-FEL using an 8 GeV linac,
the 250 MeV SCSS prototype accelerator was built at
SPring-8. A sub-pico-second time jitter was set as adevelopment target for the timing system of the prototype
accelerator, because of its beam pulse width of several
pico-seconds. This jitter value had a possibility to beachieved by the present technology. In accordance withthe target, we developed a very low-noise reference
signal source that generates 238 MHz and 5712 MHz RF
signals for acceleration, a master trigger VME module
having output pulses synchronized to 238 MHz, and a
trigger delay VME module synchronized to 5712 MHz.
The time jitters of the delay module are less than 700 fs,
and the SSB noise of the 5712 MHz reference signal
source is less than -120 dBc at 1 kHz offset. These values
are sufficient for our present requirement. A beam energy
variation of 0.06% was achieved by the timing system.
The beam stability based on AM noise theory in the FEL
linac is discussed based on the above data.

INTRODUCTION
The SASE (Self Amplified Spontaneous Emission) XFEL project at RIKEN HARIMA Institute is now underway.[1] The important component of the project is anaccelerator, having an energy of 8 GeV, which comprises
a 500 kV thermonic electron gun, a 238 MHz subharmonic buncher, a 476 MHz booster, a 2856 MHz
booster and 2856 MHz accelerating structures, 5712 MHz
accelerating structures with an accelerator field of 32
MV/m, and in-vacuum undulators. To evaluate thefeasibility of X-FEL, a 250 MeV prototype accelerator,
including the main key elements of the above-mentioned
linac (not a full number of the elements), at SPring-8 wasconstructed by November, 2005, and is under beam
testing to generate SASE VUV-FEL.
To generate a stable VUV laser in the prototype linac,
an accelerated electron beam with a pulse width of lessthan 1 ps should pass through an orbit within one hundred
micrometers for the undulator section having a length of
12 m.[2] The energy stability of the beam is in the order of
10-4, and the timing jitter of the trigger pulses toaccelerator instruments is less than 1 ps were required toarchive the orbit and the stable beam pulse width in abunch compressor, which means the constant peak currentof the beam to generate stable laser light. Therefore, we
employed a timing jitter and a drift of less than 1ps, asdevelopment targets. This is because the beam energy

FEL Technology

variation of 10-4 corresponded to a phase change of about
1 deg. (about 500 fs) in 5712 MHz RF acceleration at the
crest point. For the present, in the case of the prototype
accelerator, these targets are sufficient for generating andamplifying 60 nm light with about a 1 ps pulse width. In
accordance with the targets, we have developed thetiming system of the prototype accelerator as shown in
Fig. 1. In this system, the final time jitters and drift of theaccelerated electron beams, which are directly connectedto the energy variation, are decided by thesynchronization accuracy of the trigger delay, and the
SSB noise of RF instruments, such as a signal source. The
long-term drift of the timing is reduced by a feedback
control. Therefore, to decrease the SSB noise and torealize a less than 1ps time jitter were set as the main
purposes of our instrument development to make thesystem. This paper describes how to realize these
purposes.

TIMMING CONTROL SYSTEM
System Configuration
The configuration of the timing system of the SCSS
prototype accelerator is shown in Fig. 1. The timing
system comprises a master trigger VME module
synchronized to a 238 MHz RF signal and alsosynchronized to a commercial AC of 60 Hz, a very lownoise signal oscillator to generate 238 and 5712 MHz RF
signals as a time reference, a 10 W RF amplifier toamplify the RF signals for signal transmissions, RF signal
distributors, a trigger transmission system using 100 Ωdifferential cables with LVDS (Low Voltage Differential
Signaling), and trigger delay VME modules synchronized
to both acceleration RF signals of 238 MHz and 5712
MHz.

Master Trigger VME Module
The circuit configuration of the master trigger VME
module is shown in Fig. 1. The module comprises a
FPGA including 24-bit counters of eight channels, which
are driven by a 238 MHz clock signal. The output pulse isalso resynchronized by a fast flip/flop working by the 238
MHz clock to reduce the time jitters. The main functionof the modules is to generate a trigger pulse train from 1
Hz to 60 Hz for activating the accelerator components,
such as the klystron modulators. The pulses are alsosynchronized to a commercial AC line, and distributed tothe components.

645

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Proceedings of FEL 2006, BESSY, Berlin, Germany
VME Master
Trigger Module
AC 100V

1 - 120 Hz
Synchronization

Pulse Repeater

Balanced Line
100 ohmtransmission

50 ohm line
Single End

AC 5V FPGA D F/F
DQ
CK

10 V
Trigger Pulse Train

BufferN Divider

From Master
Oscillator

BufferMasterOscillator

5712 MHz RF Signal

External 60Hz
Sinusoidal Wave

-10 dB238 MHz RF Signal-10 dB
8 Way Power Divider

10 W Amp

Trigger Delay Unit

Level Converter

10 dBmInput Pulse

Pulse Input, PECL Level
CK
D

CK

24 bitCounter FPGAx 8 ch.

BufferControl

Buffer

D Q

INV.

CK
D Q

AMP

8 Channels
Trigger Pulse

Inhibit, 8 Channels
Hardware Control

or
To instruments such as
the klystron modulator.

10V, TTL, NIM Levels
Pulse Output Selectable

Fig. 1. Trigger system of the SCSS prototype accelerator.
Low Noise Signal
Divider F/F 1/2 F/F 1/6 F/F 1/2
Source10MHz 2856 MHz
5712 MHz 2856 MHz 476 MHz

signal source uses the frequency-dividing method, a very
low-noise power supply (-150 dBV), and the above238 MHz mentioned PLL connection. The other important function
is to decrease the effect of the environmental temperaturearound the master oscillator. For achieving this function,a temperature controller using a heater to eliminate thetemperature variation within +/- 0.1 oK was employed.
Sinusoidal

2x

60Hz
Trigger

Band Pass
Filter5712 MHz

Wave
2856 MHz5236 MHz

2380 MHz

Fig. 2. Circuit diagram of the master oscillator. The
signal source uses frequency dividing, a very low-noise
power supply and the PLL connection between the 10
MHz and 2856 MHz sources to achieve a low noise.

Master Oscillator
The master oscillator, which generates 238, 476, 2380,
2856, 5236, and 5712 MHz stable RF signals, is a timereference source. The circuit configuration of theoscillator is shown in Fig. 2. It comprises a very stablereference generator (stability of 10-11) of 10 MHz, which
has a low-noise characteristic in the frequency region
below 1 kHz measured from 10 MHz, a 2856 MHz signal
generator having a low noise characteristic in thefrequency region over 1 kHz measured from 2856 MHz, afrequency doubler instrument to make 5712 MHz from2856 MHz, and frequency dividers to generate the abovementioned frequency signals. Both low-noise signal
generators are connected by a PLL (Phase Locked Loop)circuit to make the very low SSB (Single Side Band)power noise over the whole frequency range, as shown in
Fig. 3. The noise level is -140 dBc at 1 MHz measured
from 2856 MHz. The most important feature is that the646

SSB noise Power (dBc)

Divider

Divider
PLL

5712 MHz
-60
5236 MHz
-70
2856 MHz-80
2380 MHz-90
476 MHz-100
238 MHz
-110
-120
-130
-140
-150
-160
1.E+0 1.E+0 1.E+0 1.E+0 1.E+0 1.E+0
1
2
3
4
5
6

Frequency (Hz)Fig. 3. SSB noise power spectrum of the master oscillator.
The decreasing noise level at individual frequencies is
proportional to the dividing ratio.

Differential trigger pulse transmission system
Our trigger system employs a trigger-pulse repeater
including the function of a differential trigger pulse
transmission of LVDS to reduce the influence of noise.
The twisted-pair cable to transmit LVDS has acharacteristic impedance of 100 Ω to easily adapt to theusual 50 Ω circuit without any signal reflection. The
temperature dependence of its electrical length is about
100 ppm, which does not exceed quarter wavelengths of

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

Time Jitter (fs)

238 MHz under the conditions of the usual temperature
variation for a day and a length of several ten meters usedin the prototype accelerator. The repeater, as shown in Fig.
1, can interconnect between the other two repeaters
separated by more than 10 m. One port of the repeater isinput from the previous repeater, and the other port is
output to the following repeater. The repeater also has afunction to distribute 8 trigger pulses of LVPECL (Low
Voltage Positive Emitter Couple Logic) from the mastertrigger module to the trigger delay VME modules.
660
650
640
630
620
610
600
590
580
0

20

40

60

80

Temperature (deg.)
Fig. 4. Measurement result of the time jitters of the trigger
delay unit. The jitters (rms) are less than 1ps, which satisfies our requirement. The temperature dependence of thejitter is very low.

Trigger delay unit
The trigger delay unit is the main instrument of our
trigger system, and the VME module, as shown in Fig. 1.
The circuit of the module comprises a FPGA having 8
counters with 24 bits driven by the 238 MHz RF signal,
fast flip/flops, and a temperature controller using a heater
to stabilize the temperature of the flip/flips circuit within+/- 0.1 oK. The output pulses of the FPGA are
resynchronized by fast flip/flops working by the 5712
MHz signal to realize sub-picosecond time jitters referredto the acceleration RF. The outputs of the delay unit havea voltage level of LVPECL to decrease jitters. A jittersmeasurement used to evaluate the module was carriedout; Fig. 4 shows the result of the measurement to a 5712
MHz signal dependent on the temperatures. The resultshows that the jitters are about 700 fs (rms). In addition, adelay time change of the unit dependent on thetemperature was about 400 fs/ oK (rms).

Level converter
The accelerator comprises many instruments,
equipping such various trigger voltage levels as TTL,
NIM, and 10V, for historical reasons. However, theoutput of the delay unit is LVPECL. Therefore wedeveloped an eight-channel level converter to change
from the output voltage level of the delay unit to the input
levels of the instruments (Fig. 1).

RF distribution and 10 W RF amplifier
To drive the VME modules related to the trigger
system (Fig. 1), the RF signals generated with the master
oscillator must be transmitted. This signal transmission

FEL Technology

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guarantees synchronization of the whole accelerator
system to achieve the stable generation of FEL light.
Phase-stabilized RF cables having an electrical lengthvariation of 5 ppm/oK were employed to transmit suchsignals as 5712 MHz for about more than 20 m. By
considering the RF loss of the cables, RF amplifiers,
having PLL, ALC and 10 W outputs were used. The
amplifier was cooled by water to stabilize the temperature
within +/- 0.5 oK. For distributing many RF signals of
about 1 mW to drive the trigger instruments, RF
distributors handling the 238 MHz and 5712 MHz signals
were developed. The phase variation of the distributor
dependent on the temperature was decreased by suchdesign work as choosing an RF divider with a low
thermal effect. The thermal phase variation of theamplifier and the distributor were 0.8 deg./oK and 0.28
deg./oK at 5712 MHz without PLL.

SUMMARY AND DISCUSSION
In the SCSS prototype accelerator, we finally obtained
a fruitful result: a beam energy stability of less than
0.06 % at the exit of the S-band accelerating structure (at50 MeV). This accelerated beam almost stably drove a
SASE of 53 nm in the undulator section. The measured
time jitter of the accelerated beams to the acceleration RF,
which was directly connected to the energy variation, wasless than 340 fs (rms). The measured jitter of the delay
unit was about 700 fs (rms). These jitter values satisfied
our requirement.
These jitters were mainly determined by the rise timeof a pulse of the synchronization clock for the delay unit
and the SSB noise of the RF signal. To realize the subpico-second jitters, we employed a clock signal of 5712
MHz, and very low-noise signal sources of 238 MHz and5712 MHz.
The influence of the SSB noise on the beam energy
variation and the time jitters of the beams is not veryclear. Therefore, we want to discuss the verification of
the SSB noise effect to the beam energy stability in the
prototype accelerator. The effect, that is the time-domain
voltage variations, of the SSB noise to an RF pulse in an
accelerating structure is calculated by integrating the SSB
noise amplitude for a certain frequency band width.[5] In
general, a carrier signal including SSB noise is expressed,
as shown in Fig. 5-A, and as the rotating vector of thenoise at the top end of the carrier wave vector. The AM
and FM modulations generated by the SSB noise are an
equivalent. To calculate the energy variation of the beamcaused by the amplitude and phase variation on a CW RF
signal, the integration span on the frequency axis of the
SSB noise graph is from less than 1 Hz to several more
figures of the frequency corresponding the filling time ofan accelerating cavity. If this integration span is applied
to the calculation in the case of our accelerator with the5712 MHz RF pulse of 2 μs (fp = 0.5 MHz) width, thetime-domain noise level on the pulse increases by more
about 7 digits compared to the noise level of -140 dB at fp
in Fig. 3. In this calculation, the voltage variation on the647

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pulse is near 0.1%. This value should be over estimated,
if the other noises generated by the accelerator
components are taken into account of. We can not explain
the present beam energy stability of 0.06%. For thesereasons, the frequency span of the integration should be
limited to the case of pulsed RF acceleration.
In this paper, we do not consider a beam energy
variation below a reputation frequency of 60 Hz in our
accelerator, because it can be eliminated by feedback
control. Here, we consider the SSB noise components
around fp, which do not change the base level of the RF
pulse, and only change the amplitude of the pulse. This
SSB noise effect to the beam energy change is assumed
as shown in Fig. 5. In the case of the frequency
components over fp, (Fig. 5-C), the effects of the noise,
which is expressed as odd functions ( fh2 ---) mixed on the
RF pulse, are cancelled by integration of the accelerating
force, when the beam passes through in the accelerating
structure. However, the even components (fh1,, fh3 --- fhn ),like Fig. 5-C, are not cancelled, and have an influence on
the energy variation, which is inversely proportional to
the frequency. In the lower frequency components,
measured from the RF pulse frequency, fp, the effect of
the noise components to the pulse decreases in proportion
to the frequency, because of a constant pulse width. The
slope of the amplitude variation of individual frequency
components (fl1,, fl3 ---- fln ) of the noise within the pulse
width decreases in proportion to the frequency, as shownin Fig. 5-B.
The integration of the SSB noise to estimate the effect,
N(t), to the beam energy variation could have a factor of
1/2, which corresponds to the influence of the evenfunctions, and the weight functions reflecting the above
mentioned frequency dependence. By an assumption
based on the above-mentioned discussion, we canconsider the flowing equations. In the case of a higher
frequency, f, than fp, the equation is11)
N (t ) = ∫ w( f ) N SSB ( f )df
f ≥ fp .
2
At a frequency lower than fp, the equation is2)
N (t ) = ∫ w(1 / f ) N SSB ( f )df
f < fp .
The equations are integrating the SSB noise, NSSB(f),times the weight functions, w(f or 1/f), having a linear
peak shape like Fig. 5-D. For describing the abovementioned method by another way, we can also consider
applying the square window function (RF pulse) in atime-domain to the SSB noise, to calculate FFT.[6]The RF amplitude and phase variations in theaccelerating structure of the prototype accelerator were
estimated by integrating the 5712 MHz noise spectrum ofFig. 3 with the weigh functions described in Fig. 5-D.
The result of the integration for a frequency span between
1 Hz and 1 MHz was that the amplitude variation was
0.01% and the phase variation was 0.06 deg (about 30 fs).
These values were ten-times smaller than the values thatwere integrated without the weight functions. From theseresults, we can explain the 0.06% energy variation of the
prototype accelerator with the noise caused by the othercomponents by using the above-mentioned method. The
30 fs time variation is enough for our requirement.

REFERENCES[1] SCSS X-FEL Conceptual Design Report, 2005.
[2] Dr. T. Tanaka, private communications.
[3] M. Cohlus et al., Bunch Compression
Stability Dependence on RF Parameters,
Proc. The 27th FEL conf., 250-253, USA, 2005.
[4] SCSS X-FEL Conceptual Design Report, pp 8189,2005.
[5] S. Goldman, Frequency Analysis, Modulation andNoise, DOVER, pp 211-215, 1967.
[6] T. Koshikawa, Introduction of Signal Analysis,
Kindai Kagakusya pp25-30, 2001, in Japanese.
Higher ferequency compornentsof the SSB noise than RF pulse width.

Lower ferequency compornentsof the SSB noise than RF pulse width.

Electron Beame. g. 2 μs pulse width

fl1
fl2
fl3
fl4
fln
AmplirudeIm

SSB noise of
the signal
sourceAmplirudeRe

RF pulse

T0,or f0
RF pulse in
the accelerating
structure.

RF pulse
fh1
fh2
fh3
fhn

The slopes of amplitude variations of
the individual frequency components
fl1,, fl3 ---- fln of the noise within
the pulse width decrease to be proportional
to a frequency.
Because the RF pulse width is constant,the effect of each SSB noise component is decreasein the frequency reagion below the RF pulse width.

The even mode of one frequency componentof the SSB noise has the effect to an electronenergy gain variation in the accelerating
structure.
The even components fh1,, fh3 ---- fhn do
not cancel, and the effect is inversley
proportionanl to a frequency.
The odd mode of one frequency componentof the SSB noise is canceled out druing
an electron acceleration in the accelerating
structure.
Weight functions(Correspond to the square window ina time domain for integration on
Amplirude
the frequency axis.）

Frequency

The SSB noise of the siganl source.

Fig. 5. SSB noise effect on the RF pulse in the accelerating structure.

648

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH034

LASER PULSE LENGTH DEPENDENCE OF BEAM EMITTANCE OF
PHOTOCATHODE RFGUN
H. Dewa, T. Asaka, H. Hanaki, T. Kobayashi, A. Mizuno, S. Suzuki, T. Taniuchi, H. Tomizawa,
and K. Yanagida, SPring-8, 1-1-1 Kouto, Sayo-cho, Sayo-gun, Hyogo-ken 679-5198, Japan
Abstract
Laser pulse length and laser shape should be optimized
to minimize the beam emittance of photo-cathode RF-gun.
A 3-D particle tracking simulation predicted the smallest
beam emittance could be obtained with the square laser
pulse length of about 20 ps. To examine the effect of thelaser pulse length to beam emittance, the square laser
pulse of 10 and 20 ps was generated with laser pulse
stacking of 2.5-ps micro pulses and each beam emittance
was measured at the low beam charge of 0.4 nC/pulse.
The measured beam emittance was not significantly
different each other.
Then beam emittance was measured at the higher beam
charge of 1.0 nC/pulse. The minimum beam emittancewith 20-ps laser pulse was 2.3 mmmrad with 0.8mm x
1.0 mm elliptical laser profile. Although we also tried tomeasure the beam emittance with 10-ps laser pulse, thebeam charge of 1.0 nC could not be generated at the samelaser spot size due to probably space charge limit. The
measured beam emittance for 20-ps laser pulse wassmaller than the minimum beam emittance 3.0 mmmrad
for 10-ps laser pulse measured under different laser
condition, especially micro pulse of 1.0 ps and laser spot
diameter of ø 1.0 mm.
Although we could not compare the laser pulse 10 ps
and 20 ps at the equivalent conditions in high charge
region, these experimental results would indicate at least
the possibility of using long laser pulse about 20 ps tominimize the beam emittance for beam charge around 1.0
nC.

INTRODUCTION
The electron source for several XFEL projects [1-3]requires very low emittance beam as low as 1 mmmrad.
To minimize the beam emittance of a photocathode RFgun, the laser pulse shape should be optimized threedimensionally. The transverse shape could be modified
with a microlens array [4] or a deformable mirror (DM)[5]. As well as the transverse shape, the longitudinal
shape can be also modified with a spatial light modulator[5,6] or pulse stacker described in this paper. Beamemittance of 1.2 mmmrad for 1 nC/pulse has alreadyrealized by J. Yang et. al. with square 9-ps laser pulse [6].
So far, we demonstrated transverse shape optimizationand low emittance beam generation of 1.7 mmmrad at
the electron charge of 0.1 nC [5]. The beam emittance athigh charge was, however, much larger, because the laser
pulse length is too short (5 ps) and the diameter was 1mm(top hat) and therefore the charge density was too high.

In this paper, we tested longer laser pulse of 10-ps and20-ps square generated with laser pulse stacker to get low
emittance in high charge region. Three stages of pulse
stacking generated 20-ps pulse from eight micro pulses.
The purpose introducing longer laser pulse is to keep thelaser beam size small but decrease the charge density. The
small beam size contributes to decreasing the initialemittance, and small charge density to the space charge
effect. Therefore, long laser pulse is effective especiallyin high charge region. A 3-D particle tracking simulation
predicted smaller beam emittance could be obtained withthe laser pulse length of about 20 ps at 1nC/pulse as
shown in Fig. 1. It also predicted electron bunch length
can keep around 10 ps with both 10 and 20-ps laser pulse
length due to bunch length compression in the RF cavity.

Figure 1: Beam emittance of the photo cathode RF gun
for 10 and 20-ps laser square pulse length calculated witha 3-D particle tracking simulation. In the calculation, thelaser spot diameter was 1.6 mm (top hat) and the
maximum electric field on the cathode was 135 MV/m.

LASER PULSE STACKING

dewa@spring8.or.jp

Pulse stacker is composed of sets of half-wave plates
and polarizing beam splitter cubes. The fully s-polarised
pulse laser is rotated to 45 degrees polarised pulse with ahalf-wave plate. It is divided into an s-polarized pulse andp-polarised one with a polarizing beam splitter. The ppolarized pulse is delayed with an optical delay line andthen combined with the s-polarized pulse after anotherpolarized beam splitter. Finally, as shown in Fig. 2, thelaser pulse of 2.5 ps was stacked with optical delay ateach stage to generate longer square pulse. With threestages, we can obtain 20-ps square pulse.
The polarizing beam splitter cubes used in the first andsecond stage is optical contact type (produced by Showa
Optronics) considering the high power density of the UV
laser. The polarizing beam splitter used in the third stage
is bonded with optical cement, because the power density

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Proceedings of FEL 2006, BESSY, Berlin, Germany

is lower at the stage. The diagram of the optical system isshown in Fig. 3.

Setting of optical delay lines
After setting the origins of three micrometers, theposition of these micrometers are determined by simple
calculation. For example, if the pulse length is 20 ps, themicrometer positions are set as follows,
Position for 1st stage: origin - 1.5mm
Position for 2nd stage: origin - 0.75mm
Position for 3rd stage: origin - 0.375mm.

Figure 2: Timing chart of pulse stacking

Figure 3: Optical system of laser pulse stacker(three stages)

PULSE LENGTH CONTROL
Finding the origins of optical delay lines
To generate long pulse without any timing gap oroverlap, origins of the optical delay lines must determinedwith a precision less than 1 ps. The origin is defined here
as the position of micrometer in the delay line such thatthe s-polarization and p-polarization pulses reach thecathode at the same time. The way that determines theorigin is as follows. The energy of the electron pulse wasmeasured for two laser pulses divided by each stage of thepulse stacker. The energy of the electron beam ismeasured as beam position on a profile monitor after abending magnet downstream the RF-gun cavity. To
eliminate the positioning jitter and short time drift, thebeam positions were measured for 5000 times. The
micrometer for p-polarized pulse was tuned as these twoelectron beam pulses come to the same position on the
profile monitor after 3-5 times iterations. The timing
precision of the origin was about 0.5 ps estimated fromthe position jitter distribution.

650

The stacked laser pulse was finally checked by the beamenergy distribution on the profile monitor with
illuminating all eight micro pulses. The energy
distribution of the beam is shown in Fig. 4. At an
optimum phase (85 degree), the beam focuses on the
profile monitor. When RF phase is 44 degree, the energy
dispersion was made purposely larger to evaluate stacking
pulse structure. The uniformity is not ideal but there are
not any gaps and strong hot spot in the distribution.
Therefore, the eight micro pulses are thought to be
stacked properly. The incomplete uniformity mainly
comes from the insufficient flatness of energy among thelaser micro pulses.

Figure 4: The energy distribution on the profile monitor
for the 20-ps laser square pulse at different RF phase.
Top: RF phase at 85 degree (3.52 MeV @center),
Bottom: RF phase at 44 deg (3.29MeV @center)
The information of the pulse length of the micro pulse
can be also obtained from this measurement. When the
micro pulse was around 1.5 - 2.0 ps, five strong spots
were observed on the profile monitor as shown in Fig. 5.
These spots come from overlapping on the edges of two
micro pulses. Not all energy spots are seen on the profile
monitor, because of small screen. The number of the spot
was found to be totally seven when the RF phase was
moved.

Figure 5: The energy distribution on the profile monitor
for the 20-ps laser pulse, when the micro pulse is around
1.5 -2.0 ps.
Simulation results of the energy distribution for micropulse lengths of 1.5 ps and 2.5 ps are shown in Fig. 6.

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany
There are seven spots for the case of 1.5 ps, while there is
not any strong spot for the case of 2.5 ps.

THPPH034

beam splitter of the third stage could not divide the twopulses ideally because it is bonded with optical cement
and the energy loss of p-polarization pulse is larger athigher intensity.
There is a difference in total pulse energy to get thesame charge of 0.4 nC; 70.4 μJ for 20 ps and 96.6 μJ for
10 ps. This is due to both of the Schottky effect and spacecharge limit. These effects is not theoretically calculated
but can be understand from the facts that four micropulses in 10-ps pulse individually generate increasing
charge of 0.12, 0.16, 0.16, 0.17 nC, but generate only 0.4
nC with all four pulse at the same time.

Setup of Beam emittance measurements

Figure 6: Simulated of the energy distribution for micropulse length of 1.5 ps (Top) and 2.5 ps (Bottom).

BEAM EXPERIMENTS
Laser distribution and electron beam charge
The laser pulse energy of eight (20 ps) and four (10 ps)
micro pulses was tuned by the angle of half-wave plates
to get the beam charge of 0.4 nC and energy flatness. The
results are shown in Fig. 7.

The electron beam generated from the RF gun was
accelerated to 26 MeV with a 3m-long accelerating
structure. The beam emittance was measured with quadscan downstream the accelerating structure [7].
When we operate quad scan to measure the beamemittance, the beam size must be measured at theresolution of the order of 10 μm. To realize the fineresolution, we adopted a profile monitor with a thinscreen and high resolution CCD camera. The screen is analumina fluorescence sheet (Desmarquest AF995) withthe thickness of 0.05 mm. The CCD camera is 1.3-megapixels camera (SONY XCD-SX910). It has a 1/2-inch
CCD chip with 1280(H) x 960 (V) pixels, and each pixel
size is 4.65 x 4.65 μm2. To get a large depth of field, weused a telecentric lens of 1/4 magnification. The estimatedresolution of the image is about 20-30 μm. Only center
quadrupole magnet of the triplet quadruple magnet wasused to focus the beam on the screen with quad scan. The
setup of the quad scan measurement is shown in Fig. 8.
CCD camera

1290
100

F

100

200
100

100

D

F

screenunit:mmFigure 8: Setup of quad-scan measurement.
The emittance measurement was automatically executedin about 5 minutes if the measurement points were lessthan 15. The automatic measurement system wasprogrammed with Labview 7.1 and Vision developing
module (National Instruments Co.).

Figure 7: The laser pulse energy and electron beam
charge of micro pulse for 20-ps (Top), and 10-ps pulse
structure (Bottom).
The 20-ps pulse was generated with pulse stacker ofthree stages, and 10 ps with first two stages. The energy
flatness for 20 ps is worse than 10 ps. The polarizing

FEL Technology

Beam emittance measurements
Beam emittance for 10 and 20-ps laser pulse wasmeasured in low charge region of 0.4 nC/pulse. The
current of solenoid coils were optimized to get minimum
beam emittance. The laser shape was elliptical (0.8 mm(H) x 1.0 mm (V)). In this experiment, the optimization of
DM could not executed because the CCD of laser profiler

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Proceedings of FEL 2006, BESSY, Berlin, Germany

was damaged. The results of the quad scan are shown in
Fig. 9. The emittance of both beam were almost same, 3.2
mmmrad for 20 ps and 3.3 mmmrad for 10 ps.

Figure 9: Measured beam emittance for 10-ps and 20-ps
laser pulse at the beam charge of 0.4 nC/pulse.
Next, the beam emittance was measured in case of highcurrent beam. The beam current of 1.0 nC was generated
for 20-ps pulse but only 0.6 nC beam current could be
generated for 10-ps pulse at the same laser spot size,
though the laser power was high enough. It may be due tospace charge limit. After further optimizing parameterssuch as solenoid current, RF phase and half-wave plates,
the measured minimum emittance of the beam for 20-ps
laser pulse was 2.3 mmmrad as shown in Fig.10.

Figure 10: Measured beam emittance for 20-ps laser pulse
at the beam charge of 1.0 nC/pulse.

652

DISCUSSIONLong laser pulse of 20 ps generated with a pulse stacker
was tested, and low emittance beam of 2.3 mmmrad was
generated successfully without optimization of lasertransverse profile with DM. No large difference wasfound between 10 ps and 20 ps in the low charge region.
It is very important that the beam current for 10 ps could
not reach 0.7 nC if the laser beam size was small even if
the laser pulse energy was increased high. This effect may
limit the initial emittance of the beam in high charge
region. Long laser pulse of 20 ps is thought to have an
advantage in generating high charge with small initial
beam size.
Of course, the pulse charge of 1nC could be generated
if the laser spot size was large enough. However, themeasured beam emittance for 20-ps laser pulse wassmaller than the minimum beam emittance 3.0 mmmrad
for 10-ps laser pulse at 1.0 nC/pulse measured under
different conditions of micro pulse length at 1 ps and laser
profile modified with DM to a flat circle of ø1.0 mm [8].
The possibility of 20-ps laser pulse to get low emittancehas been confirmed by these results. Next, the splittercube of the third stage in pulse stacker will be exchanged
to that bonded with optical contact. Then micro laser
pulses should be tuned to get flat longitudinal distributionof electron beam. Further experiments to pursue smaller
beam emittance will be planed with simultaneoustransverse and longitudinal laser profile optimization.

REFERENCES[1] “Linac Coherent Light Source (LCLS) Conceptual
Design Report”, SLAC-R-593, April 2002.
[2] “TESLA Technical Design Report, PART V, The XRay Free Electron Laser”, ed. G. Materlik and
Th.Tschentscher, March 2001.
[3] “SCSS X-FEL Conceptual Design Report, RIKEN,
May 2005.
[4] H. Tomizawa et. al., “Reduction of electron-beamemittance with shaping both spatial and temporalprofiles of UV laser light source for photo-cathodeRF gun“, Proceedings of EPAC 2002, Paris, June
2002, pp. 1819-1821.
[5] H. Tomizawa et. al., “Status of SPring-8 photocathodeRF gun for future light sources“, Proceedings
FEL2005, Stanford, August 2005, pp138-141.
[6] J. Yang et. al., “Low-emittance electron-beamgeneration with laser pulse shaping in photocathoderadio-frequency gun“, J. Appl. Phys. Vol 92, pp.
1608-1612.
[7] H. Dewa et. al., "Photocathode RF gun designed asingle cell cavity", Proceedings of EPAC 2004,
Lucern, July 2004, pp. 411-413.
[8] H. Tomizawa et. al., “Automatic minimization ofelectron beam emittance with three-dimensionallyshaping laser pulse for a light source of rf gun“, Proc.
of the 2nd Annual Meeting of Particle Accelerator
Society of Japan, Sendai, Japan, 2-4 August 2006,(2006) pp. 16, (in Japanese).

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH035

DESIGN STUDY ON HIGH- TC SUPERCONDUCTING
MICRO-UNDULATOR
T. Kii, H. Zen, N. Okawachi, M. Nakano, K. Masuda, H. Ohgaki, K. Yoshikawa, T. Yamazaki.
Institute of Advanced Energy, Kyoto University, Uji, Japan.
Abstract
Design study on a new type of high critical temperature(TC) superconducting micro-undulator was carried out. In
this work, we introduce staggered array type microundulator using high TC superconducting material.
Transverse magnetic field was measured with YBa2Cu3O7
bulk superconductors at 77 K. The maximum transverse
magnetic field strength was about 0.5 mT, whenlongitudinal magnetic field of the strength in the range of
2 mT to 15 mT was applied.

HIGH TC SUPERCONDUCTING
UNDULATOR

Design of high TC superconducting undulator
To obtain transverse periodic magnetic field in a shortperiod, we introduce following micro-undulator as shownin Fig. 1.

INTRODUCTION
A micro-undulator or short period undulator will be auseful device for a compact FEL device and/or a shortwavelength FEL.
When a high energy electron beam moves in the
periodic magnetic field, resonant wavelength emitted
from the undulator λR is written by following well-known
equations.

λu ⎛ K 2 ⎞⎜1 +⎟2γ 2 ⎜⎝2 ⎟⎠(1)e ⋅ B0 ⋅ λu
≈ 93.36 B0 ⋅ λu
2π ⋅ m0 c

(2)

λR ≅
K=

Here, λu is the undulator period and γ is Lorentz factor,
K is the undulator parameter, e is the charge of theelectron, B0 is the maximum transverse magnetic fieldstrength of the undulator, m0 is the electron mass and c isthe speed of light. To obtain shorter wavelength radiation,
undulator period should be short or electron energy
should be high. Thus, if the λu is limited, high energy
electron beam is required for short wavelength FEL suchas X-FEL. In other word, if a short period undulator
realizes, high energy electron is not required. Moreoversince the FEL gain increases as the number of period of
undulator increases, the short period undulator will haveadvantage.
However, if we need K=1 for short period undulator of
5 mm, B0 should be almost 2 T. Thus, to realize micro
undulator or short period undulator, strong transverse
magnetic field is required.
___________________________________

Fig. 1. Conceptual drawing of the high TC SC undulator.
High Tc bulk superconducting materials are stacked in
the solenoid. First, these superconducting pieces arecooled down below the critical temperature TC. Then, asolenoid field is applied. As a result, density modulationof the magnetic field is produced, and thus the periodictransverse magnetic field is generated on the electron
beam axis. To realize shorter period, in vacuum structureis planned. If we can control the magnetic field precisely,
extreme good electron beam confinement can be realized[1].
If a perfect Meissner state is kept in a high magnetic
field strength of several T, excellent performance will be
realized. Unfortunately, Meissner region is typicallylimited below the lower critical field of several hundred
mT, but superconductivity is left up to the higher criticalfield of 100 T. Thus we tried to measure the transverse
magnetic field above lower critical field.

Expected performance
We have estimated performance of the undulator forfollowing applications.
1) Compact IR device2) Ultra short wavelength FEL
3) THz device
If such short period undulator with high transverse
magnetic field is applied for 1) compact IR FEL device,required electron energy will be less than 15 MeV as
shown in Fig. 2. Therefore a very compact IR system canbe designed.

#

kii@iae.kyoto-u.ac.jp

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Proceedings of FEL 2006, BESSY, Berlin, Germany
1000

30

λ und = 5mm
K=1

900
800
λ FEL [μm]λFEL[μm]25λund = 5 mm, K = 1.0
λund = 3 mm, K = 1.0
λund = 3 mm, K = 0.5

20
15

700

λ und = 2mm
K=1.0

600
500

λ und = 5mm
K=0.6

400

10

300
λ und = 5mm K=1.0
λ und = 5mm K=0.6
λ und = 2mm K=1.0
λ und = 2mm K=0.6
0.4
0.6
Ee [MeV]

200

5

100

0

5

10

15

20

0
0.2

Ee[MeV]

Fig. 2. Expected wavelength for short period undulator
with several tenth MeV electron beam.
For application to 2) ultra short wavelength FEL, thedevice is also fascinating as shown in Fig. 3. The FEL
wavelength of 1 Å will be achieved with 3 GeV electron
beam. It is expected that the whole system could becompact, because the length of the undulator and theaccelerator will be shortened compared to present
configurations of such X-FEL systems.
0.2
λ und = 5 mm, K = 1.0

λ FEL[nm]

0.15

0.1

λ und = 2mm
K=0.6
0.8

1.0

Fig. 4. Expected wavelength for THz device.

EXPERIMENT
To confirm the proposed micro-undulator, a preliminary
experiment has been performed. In this work, YBa2Cu3O7(YBCO) ceramic was selected as the high TC
superconducting materials, because it is easy to obtain,
and Tc is higher than the boiling point of liquid nitrogen.
Presintered YBCO powder made by Furuuchi Chemical
Corporation was used for sample fabrication. Test peaces
were made as following. The powder was pressed into
disks and sintered in an oxygen-containing atmospherefor 12 hours at a temperature of 900° C, and annealed for
48 hours at a temperature of 500° C. Diameter of the test
pieces was 27 mm and thickness was 2.5 mm.
Superconductivity of the test pieces were checked by the
Meisner effect and pinning effect using small permanent
magnet on the cooled test material. Schematic drawing of
the superconducting test piece is shown in Fig. 6.
27 mm

0

2.5 mm

0.05

2000

4000
6000
Ee[MeV]

8000

10000

Fig.3. Expected wavelength for GeV class electron beam.
A simple configuration consisted of an electron injector
and the proposed micro-undulator will provide 3) the THz
radiation as shown in Fig. 4. This system could generate
an intense THz radiation with a variety of operation mode,
in CW, because we can use a CW electron injector.

654

Fig. 5 Schematic drawing of the YBCO test piece.
Transverse magnetic field produced by the cooled
ceramics was measured with a dipole magnet and a 3Channel Gaussmeter Model 460, manufactured by Lake
Shore Cryotronics, inc. Experimental setup is shown in
Fig. 6.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

4 mm
Dipole magnet

YBCO ceramic

LN2 cryobath
Thermal insulator

Dipole magnet
Side view

Top view

Fig. 6 Experimental setup.
Test piece was cut into two ‘D shapes’ for thetransverse magnetic field measurement. The test pieces
were cooled down to 77 K in a LN2 cryobath. Aftercooled down below the critical temperature, they weremoved into the gap of the dipole magnet. Longitudinalmagnetic field of the strength in the range of 2 mT to 15
mT was applied. The magnetic field strength wasmeasured using a Hall probe. The measured strength was
about 0.5 mT, and did not depend on the amplitude of thelongitudinal magnetic field.

THPPH035[2] T. Harada; K. Yoshida, “The effects of Pr-doping on
the critical current density in YBa2Cu3O7-δ”, Physica
C: Superconductivity and Its Applications 383 (2002)
48-54.
[3] S. Sasaki, “The possibility for a short-period hybrid
staggered undulator”, Proceedings of 2005 Particle
Accelerator Conference, Knoxville, Tennessee (2005)
982-984.
[4] M. Morita, et al, “Development of Oxide
Superconductors - High Tc Bulk Superconductor,
QMG, and Its Magnetic Applications -”, Nippon
Steel Technical Report No. 93 January 2006 (2006)
18-23.

DISCUSSION
Transverse magnetic field was successfully generated
with YBCO test pieces, but the magnitude was very small.
Let us discuss on the small transverse magnetic fieldstrength. Although the upper critical field strength for the
YBCO is high, the lower critical field is about 1 mT. Thus,
the magnetic vortex lines penetrate into thesuperconductors. As a result the enough transverse
magnetic field was not produced.
To overcome this problem, strong pinning center
should be introduced. Then the penetration of the vortex
lines would be suppressed. Doping of Praseodymd[2] isplanned to introduce pinning center and increase criticalcurrent density.
Although, zero-field cooling is introduced in this work,
filed cooling is also considerable to produce transverse
magnetic field. If the each superconducting pieces withstrong pinning center are cooled in the strong solenoid
field, each pieces work as strong permanent magnet ofseveral T after the solenoid field is turned off. Such strong
permanent magnet would increase the performance ofhybrid staggered undulator [3]. Although the peak fielddepends on the trapped magnetic field by thesuperconducting pieces, recently typical trapped field isgreater than 2T [4], thus the peak field of greater than 1T
is expected.

ACKNOWLEDGEMENT
This work was supported by the Grant-in-Aid forYoung Scientists (A) by the Ministry of Education,
Culture, Sports, Science and Technology of Japan.

REFERENCES[1] J. Kitagaki, et al, “A design study on electron beam
confinement in a staggered array undulator based on
a 3D code”, Nucl. Instr. Meth. A475 (2001) 613-616.

FEL Technology

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Proceedings of FEL 2006, BESSY, Berlin, Germany

DESIGN STUDY OF RF TRIODE STRUCTURE
FOR THE KU-FEL THERMIONIC RF GUN
K. Masuda#, K. Kusukame, T. Shiiyama, H. Zen, T. Kii, H. Ohgaki, K. Yoshikawa, T. Yamazaki,
Institute of Advanced Energy, Kyoto Univ., Gokasho, Uji, Kyoto 611-0011, Japan
Abstract
A coaxial rf cavity with a thermionic cathode on its
inner rod has been designed to be adopted in a 4.5-cell rf
gun in order to minimize the inherent back-bombardmentof electrons onto the cathode. Dependences of the backbombardment power and the output beam properties on
the axial mounting position of the coaxial cavity havebeen studied using a 2-dimensional simulation code. Withan optimal mounting position and phase of ~90 kW rf
input fed into the coaxial cavity have shown significant
reduction of back-bombardment power of over 80 %. It
has also shown a lower longitudinal emittance and ahigher peak current of the output beam than theconventional rf gun, while the transverse emittancedegradation is reasonably acceptable.

degradations or rather enhancements, the beam extraction
phase from the rf triode should be considered in adopting
it to the 4.5-cell gun, because an off-crest beam injection
to the successive cells would lead to a degradation in the
output beam transverse emittance due to an increased rf
contribution to the emittance growth. In this work, weinvestigated both the input rf phase and axial mounting
position of the coaxial cavity with respect to the main
accelerating cells.

INTRODUCTION
Thermionic rf guns have advantages against
photocathode ones, such as low cost, high micropulse
repetition rate (high averaged current), and easy operation,
which make them well suited for FELs. They however
suffer from back-bombardment of electrons onto thethermionic cathode which eventually leads to an output
beam energy drop and limits the macropulse duration [13]. The back-bombardment effect is seen significant in the
4.5-cell rf gun (Fig. 1 and Table 1) for the KU-FEL linac
because of its original design, i.e. a high coupling
coefficient, large number of cells, small aperture between
the cells. Some countermeasures are applied, such as theuse of transverse magnetic fields [4,5] and the temporalcontrol of the rf input for compensating time-varying
beam-loading [6-8] with limited successes. The
macropulse duration achieved so far is 4 μsec at most fora limited beam output of ~80 mA [8], while a longer
duration and a higher current would be desired for the
FEL operation.
Numerical studies so far have suggested that the rf
triode structure could potentially reduce the backbombardment power drastically (~80 - 99%) [9,10].
Especially the use of a metal grid for the rf cutoff has
shown numerically over 99% reductions of the backbombardment power without degradation in the output
beam properties, by simulations on neglect of the beam
scattering by the grid [10,11]. In this work, weinvestigated an rf triode without a grid for comparison,since the use of a grid is practically undesirable unless it
is necessary in terms of the back-bombardment reduction
and/or the output beam characteristics.
Also, though the beam properties at the 1.6-cell [9] andthe half-cell [10] exits have shown reasonably acceptable___________________________________________#

masuda@iae.kyoto-u.ac.jp656

Figure 1: A simulation snapshot showing electrons’ radial
positions and energies along the longitudinal position, andthe on-axis cavity field. The blue dots indicate backstreaming electrons. A 2mm φ thermionic cathode with a
30 A/cm2 current density is located at z = 0, and the cavity
voltage is 10 MV to yield 7.6 MeV output.
Table 1: Beam properties by the simulation on neglect of
the back-bombardment effect. Only the electrons within
an output beam energy spread of ΔEk/Ek,max = 3 % aretaken into account.
at the gun exit
29.00 pC
charge, ΔQ
peak current, Ipeak
10.00 A
1.20 π mm mrad
normalized rms emittance, εr,n37.00 psec keVlongitudinal rms emittance, εzat the 1st cell exit
6.60 %
energy spread, ΔEk1/Ek1,max
29.00 pC
charge, ΔQ1
peak current, I1,peak
10.40 A
0.53 π mm mrad
normalized rms emittance, εr1,n1.80 psec keVlongitudinal rms emittance, εz1

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

COAXIAL CAVITY DESIGN
Figure 2 shows the coaxial cavity geometry to beinstalled in the rf gun instead of the conventional cathode,and the fundamental (2856 MHz) eigenmode pattern by a2-dimensinal eigenmode solver [12]. The outer radius islimited up to ~15 mm due to the cathode mount geometry
in the rf gun. We set it as the maximum, 15 mm tominimize the coupling coefficient, β, between the coaxial
cavity and the backside coaxial waveguide from which an
rf power is to be fed. The rf cutoff is ensured by a drift
tube of 4 mm in diameter and 5 mm in length between the
coaxial cavity and the successive half cell.
Figure 3 shows particles’ snapshots by a 2-dimensional

THPPH036

particle-in-cell simulation code [13] for three different
coaxial inner rod geometries on which the same
thermionic cathode (2 mmφ, 30 A/cm2) as is used in theconventional diode rf gun shown in Fig. 1. The code canreproduce the required rf input, Pin, for a given rf voltage,
Vo, taking into account the beam-loading effect [3,13].
In the design (a), the beam tends to hit the drift tube
due to radial forces by both the rf and the space charge.
The geometry (b) shows a good beam transport becauseof a reduced radial rf field, while at the same time thelarger inner rod diameter increases β, leading to a higher
Pin requirement for a fixed V0. Finally, the designrefinement in (c) meets both the requirements, showing agood beam transport and an acceptably high field with amoderate Pin below 100 kW, the maximum available
power in our experiments scheduled in the near futere.

BACKBOMBARDMENT AND BEAM
PROPETIES BY THE TRIODE RF GUN

Figure 2: An eigenmode pattern in a coaxial cavity with athermionic cathode on its inner rod, to replace the cathodein the conventional diode rf gun.

In the simulations in the triode rf gun, we varied theaxial mounting position, z0, of the coaxial cavity withrespect to the main accelerating cells in the 4.5-cell rf gun(see Fig. 4), as well as the rf voltage, V0, and phase, Δφ01,
in the coaxial cavity. The cavity voltage in the main
accelerating 4.5 cells is fixed as 10 MV throughout.
As seen in Fig. 4, the 1st half cell geometry is slightly
changed as the z0 varies, so that its resonant frequency,
quality factor and shunt impedance remain unchanged.
The back-bombardment effect is neglected, i.e. thecavity voltages and the cathode current density are kept
constant until periodically steady-state solutions.

Back-Bombardment Power and Beam
Properties at the First Cell Exit(a)Figure 5 and 6 show back-bombardment power onto the
2 mmφ cathode, Pback, bunch charge, ΔQ1, and transverse
normalized rms emittance εr1,n at the 1st half cell exit. For
comparisons, they are normalized by those in theconventional diode rf gun listed in Table 1. Electrons

(b)

(c)
Figure 3: Eigenmode patterns and particle snapshots inthe coaxial cavity, comparing three different geometricaldesigns of the coaxial inner rod. Peak electric fieldstrengths on the cathode (E0), and required rf input (Pin)are shown for a fixed peak cavity voltage, V0 = 30 kV.

FEL Technology

Figure 4: Eigenmode patterns of the 1st cell for two
different mounting positions (z0) of the coaxial cavity. In
the conventional diode rf gun (see Fig. 1 and Table 1) thecathode is located at z = 0.

657

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Proceedings of FEL 2006, BESSY, Berlin, Germany

normalized Pback1

0.1

V0 = 30 kV

z0=0-6z0=0-8V0 = 10 kV

z0=-10z0=-120.01
1.2
φ1, head [π rad]εr1, n

10

ΔQ1

1

1.0

conventional rf gun

0.8

εr1, n

0.1

0

30

60

90

120

150

180

210

240

270

Δφ01 [deg.]

Figure 5: Back-bombardment power (Pback), bunch charge
and transverse normalized rms emittance at the 1st cell
exit (ΔQ1 and εr1,n) divided by those in the conventional
diode rf gun (see Table 1), as functions of Δφ01 and V0 forz0 = -4 mm.
within an energy spread of ΔEk1/Ek1,max = 6.6 % are takenin account in the ΔQ1 and εr1,n, since they are foundcontribute to an acceptable output beam energy spread of
ΔEk/Ek,max = 3 % for the case of the conventional diode rf
gun shown in Fig. 1 and Table 1.
As seen in Fig. 5, a lower V0 results in a lower ΔQ1 andlarger εr1,n without significant reduction of Pback. Thus V0
is fixed as the maximum, 30 kV hereafter.
In comparison with the use of a metal grid instead forthe rf cutoff [10], the existence of zero-field region in
between the cathode and the 1st half cell is found result inhigher Pback, while the reduction of Pback by the present rf
triode is still significant.
In Fig. 6, regardless of the phase control by z0, φ1,head isfound far ahead of the crest for Δφ01’s where the Pback
reduction is over 90 % (called operational mode (I)hereafter).
At a lower Δφ01, however, a local minimum of Pback isfound, which is seen to reach 80 % reduction for z0 = –6,–8 and –10, and is also seen to shift in terms of Δφ01 as z0
decreases. Thus Pback at φ1,head = 1 π rad (crest) decreases
with decreasing z0 as shown in Fig. 7. This operationalmode (II) is not seen in the grid-based rf triode [10],which corresponds virtually to z0 = ~ –1 mm.
Note that, in the conventional rf gun, φ1,head is 0.94 πrad, slightly ahead of the crest as shown in Fig. 6, because
the rf voltage and corresponding output energy of 7.6

normalized ΔQ1 and εr1, nnormalized ΔQ1 and εr1, nz0=0-4 mm

V0 = 20 kV
0.01

658

0.1

10

ΔQ1

1

0.1

0

30

60

90

120

150

180

210

240

270

Δφ01 [deg.]

Figure 6: Pback, ΔQ1 and εr1,n divided by those in theconventional diode rf gun, and bunch head phase throughthe 1st cell exit (φ1,head), as functions of Δφ01 and z0 for V0= 30 kV.

normalized Pback , ΔQ1 and εr1, nnormalized Pback

1

10

εr1, n

ΔQ1

1

Pback
0.1

-12

-10

-8
z0 [mm]-6-4

Figure 7: Pback, ΔQ1 and εr1,n divided by those in theconventional diode rf gun for Δφ01 where φ1,head = 1 π rad,as functions of z0 for V0 = 30 kV.
MeV is higher than the nominal value of 5 MeV.
Nevertheless we usually operate the gun at a higher
energy, since it results in a lower beam emittance.

FEL Technology

normalized Ιpeak

Proceedings of FEL 2006, BESSY, Berlin, Germany1
z0=0-4 mm
z0=0-6z0=0-8z0=-10z0=-12

0.1

0

30

60

normalized εr,n and εz

10

εr,n

90

120

150

180

210

240

270

1

the output beams at optimal Δφ01’s and z0’s in terms of
Ipeak/er,n2 for the modes (I) and (II), together with theoutput by the conventional diode rf gun.
The off-crest beam injection in the mode (I) is found toresult in larger emittances than the mode (II) in exchangeof higher peak currents. It should be noted that the mode(I) greatly reduces the rf contribution to the transverse
emittance growth, i.e. the beam is obviously seen narrowin the phase space in Fig. 9(b), because of the optimal
beam injection phase into the 2nd full cell. In comparison
with the conventional rf gun, though the rf contribution isseen much reduced in the mode (II), transverse emittanceis rather degraded by the radial rf field nonlinear to theradial position, i.e. the phase space distribution is seen
bent much in Fig. 9(b). In the longitudinal emittance,
improvements are seen in both modes (I) and (II).

CONCLUSIONS

z0=0-4 mm
z0=0-60.1

z0=0-8εzz0=-10z0=-12

0.01

0

30

60

90

120

150

180

210

240

270

Δφ01 [deg.]

Figure 8: Dependences of the output beam properties on
Δφ01 and z0.

(a)

(b)

(c)

Figure 9: Transverse phase space distributions of theoutput beams by (a) the conventional diode gun, the triode
gun with (b) z0 = –10 mm, Δφ01 = 100 deg. (mode (II)),and (c) z0 = –6 mm, Δφ01 = 120 deg (mode(I)).
Table 2: Comparisons of back-bombardment powers andoutput beams’ properties between the conventional diodeand the triode rf guns.
Pback Ipeakεr,nεz[kW] [A] [π mm mrad] [psec keV]conventional
21.0 10.0
1.2
37.0
diode rf gunz0 = –10 mm,
04.3 04.9
6.3
04.0
Δφ01 = 100 deg.
z0 = 0–6 mm,
01.6 26.0
9.1
18.0
Δφ01 = 120 deg.

Output Beam Properties
Figure 8 shows output beam properties for Δφ01’s andz0’s where the reduction of Pback is found over 80 % in Fig.
6, in both modes (I) and (II). Figure 9 and Table 2 show

FEL Technology

THPPH036

The present rf triode structure has shown significant
reductions of the back-bombardment power, and reduced
longitudinal emittances and enhanced peak currents of theoutput beam. The optimal axial position of the coaxial
cavity with respect to the main cells has shown a greatly
reduced rf contribution to the transverse emittance growthby controlling the beam longitudinally with respect to the
rf. Transversely, however, the present design yields alarger beam radius, eventually leading to a transverse
emittance growth due to the contribution by the nonlinear
radial rf fields. Though the transverse emittancedegradation is reasonably acceptable, the wehnelt
configuration and/or optimal control of the rf voltages
should be considered in order to induce radial beamfocusing to minimize the output transverse emittance.

REFERENCES[1] C.B. McKee, et al., Nuclear Instruments and Methods
in Physics Research A 304 (1991) 386.
[2] T. Kii, et al., Nuclear Instruments and Methods inPhysics Research A 475 (2001) 588.
[3] K.Masuda, et al., Nuclear Instruments and Methods
in Physics Research A 483 (2002) 315.
[4] T. Kii, et al., Proc. 9th Intnl. Conf. Synchrotron
Radiation Instrumentation, May 2006, in press.
[5] C.B. McKee, et al., Nuclear Instruments and Methods
in Physics Research A 296 (1990) 716.
[6] T. Kii, et al., Nuclear Instruments and Methods inPhysics Research A 507 (2003) 340.
[7] F. Li, et al., Nuclear Instruments and Methods inPhysics Research A 407 (1998) 332.
[8] T. Kii, et al., Proc. FEL2005 (2006) 584.
[9] K. Kanno, et al., Japanese Journal of Applied Physics
41-1 2002 62.
[10] K. Masuda, et al., Proc. FEL2005 (2006) 588.
[11] K. Kusukame, master thesis Kyoto Univ., 2006 (inJapanese).
[12] K. Masuda, et al., IEEE Transaction on Microwave
Theory and Techniques 46-8 (1998) 1180.
[13] K.Masuda, Ph,D. thesis Kyoto Univ, 1997.

（

）

659

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Proceedings of FEL 2006, BESSY, Berlin, Germany

MAGNETIC FIELD MEASUREMENT OF UNDULATORIN KU-FEL
M. Nakano, N. Okawachi, H. Zen, T. Kii, K. Masuda, H. Ohgaki#, K. Yoshikawa, T. Yamazaki
Institute of Advanced Energy, Kyoto University, Gokasyo, Uji, 611-011, Japan.
Abstract
An FEL system (KU-FEL) covering wavelengths from4 to 13 μm is under construction at Institute of Advanced
Energy, Kyoto University. The magnetic field of theundulator in KU-FEL has been measured. Measured
magnetic field showed demagnetization in thedownstream part of the undulator. By using the measured
data, we have estimated the optimal parameters of boththe electron beam and the optical cavity to enhance the
FEL gains for the first lasing. In this optimized condition,
though FEL gains decreased by a few % but, FEL powers
were not much decreased, compared with those for thedesign field. Saturated FEL in 6-12 μm is expected fromthe recent studies in the macropulse width of the electron
beam from the RF gun.

INTRODUCTION
KU-FEL system for bio/chemical researches in 413μm is under construction [1]. Figure 1 shows aschematic view of the system. The system consists of a
4.5 cell thermionic RF gun, a 3-m accelerator tube, aHalbach type undulator and an optical cavity. The RF gun
and the accelerator tube have been installed andaccelerated an electron beam up to 40 MeV. The
undulator and the optical cavity will be installed within
this year.
In parallel with the construction, in order to estimate
the high FEL gains for the first lasing, we have optimized
parameters of electron beam and optical cavity based on
original design parameters of our undulator (shown in
Table 1) [2]. However, demagnetization was anticipatedsince the undulator had been used for lasing experiments
under the cooperation of FELI and University of Tokyo[3]. Then, we measured the magnetic field of theundulator. By using the date, we have optimized
parameters of electron beams and the optical cavity andcalculated realistic FEL gains and powers.

MEASUREMENT OF MAGNETIC FIELD
The magnetic field of the undulator was measured invertical and horizontal direction, using a Hall probe
manufactured by F. W. BELL. The probe was driven by
moving stage that run on a stepping motor (Fig. 2 ) andwas moved on the central axis of the undulator by 1 mmstep. Specification of the measurement device is shown in
Table 2. Figure 3 shows the measured magnetic field of
the undulator. The undulator error (shown in Fig. 4) is#ohgaki@iae.kyoto-u.ac.jp

660

Fig. 1 . Schematic view of KU-FEL.
Table 1: Parameters of the original designed
undulator of KU-FEL
Length1.6 m
Period40 mm
Number of period
40Gap
26 - 45 mm
Maximum magnetic field
0.25 - 0.045 T
K-value
0.95 - 0.17

Fig. 2: Measurement device for magnetic field.
Table 2: Specification of measurement device
Moving stage
Motor
Resolution
Operation range

Stepping motor
0.01 mm2m

Gauss meter
Resolution
Stability of temperature

0.10%
0.040 %/K

defined by following : Error = 1- Bp,exp/Bp,ideal, where
Bp,exp is the peak magnetic induction from fitting themeasured date to sinusoidal function and Bp,ideal is thepeak value of the design magnetic field. Thus, the error ispositive when there is demagnetization. The initial andend peak of the measured magnetic field of the undulator

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH037

78 in Fig.4. The gap is narrower (25.5 mm) than theoriginal design, because we have modified the undulator
in order to make the gap variable. Thus, the maximum
value of peak magnetic field and K-value are 0.26 T and
0.99, respectively.

Fig. 3: Measured magnetic field of the along thecentral undulator axis.

Fig. 6: Calculated spectrum of spontaneous radiation.

BEAM TRAJECTORY AND
SPONTANEOUS RADIATION

Fig. 4: Undulator error as a function of peak number.

Evaluation of beam trajectory and spontaneousradiation is an effective method to verify the measurementof the magnetic field. At first, We calculated electron
beam trajectories at 30 MeV with the measured magnetic
field and the designed field by using SRW [4]. Verticaldisplacement of the electron beam in the undulator shownin Fig. 5 (a) is 2 mm so that overlap between electron
beam and laser is too poor. In order to compensate this,
we are going to set a steering magnet before the undulator.
The beam trajectory thus deflected at an angle of 1.4 mrad
is shown Fig. 5 (b). Figure 5 (c) shows a beam trajectory
calculated from the designed field. Fig 6 shows calculated
spectra of spontaneous radiations. The radiation intensity
calculated from the measured magnetic field is reducedby 9 %, and the spectrum is shifted to longer wavelengthand shows asymmetric distribution, compared with thatfrom the design field.

FEL GAIN CALCULATION

Fig. 5: (a) and (b) is horizontal trajectories calculated
from the measurement without and with deflection at
the entrance of the undulator, respectively. (c) is ahorizontal trajectory calculated from the design.
is not considered as peak number: the number of peakfield is 79. Figure 3 and Fig. 4 clearly show ademagnetization in the downstream part, peak number 70-

FEL Technology

We previously reported on FEL gains based on
designed magnetic field of undulator (Table 1) [2]. On theother hand, by using the measured magnetic field insteadof the designed one, FEL gains have been recalculated toestimate realistic gains, which will be compared in thefollowing.
The axial symmetric 3D code TDA3D [5] was used to
calculate FEL gain and saturation. In addition, theundulator period was forced to be 39. This is because thenumber of peak magnetic field for TDA3D is defined as
double of the undulator period while the undulator period
in KU-FEL is 39.5.
At the 180-degree arc between the accelerator tube andthe undulator shown Fig. 1, we can control the electron
beam parameters for the optimization. Among the661

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Table 3: Fixed parameters of electron beam
Peak current
40 A
Normalized emmitance in x
11 πmm-mrad
Normalized emmitance in y
10 πmm-mrad
Energy spread
0.50%
Table 4: The optimized beam parameters
Beam energy (MeV)25
30
35
Beam size in x (mm)0.65 0.60 0.55
Beam size in y (mm)0.33 0.36 0.36
1.9 2.0 1.9
Twiss parameter αx000Twiss parameter αyTable 5: Optimized optical parameters
Beam energy (MeV)25
30 35
Rayleigh range
0.40 mBeam waist position
0.60 mWavelength (mm)12.3 8.6 6.3
Out coupling (%)
4.0 2.5 0.8
Diffraction loss (%)
5.6 6.0 7.0
Total loss (%)
9.6 8.5 7.8
electron beam parameters, a peak current, a transverse
emittance, and an energy spread, which are evaluated by
PARMELA [6], are fixed (Table 3) during the calculation.
The other electron beam parameters, electron beam sizes
and Twiss parameters, are optimized to obtain the
maximum FEL gains in three electron beam energies, 25,
30, 35 MeV. Electron beam sizes are RMS values. Twiss
parameter αy is set to zero due to the natural focusing of
the undulator field. Table 4 shows the beam parametersoptimized to the measured magnetic field of the undulator.
Optimization of the parameters of the optical cavity isalso essential to enhance the FEL gains. We also
optimized the optical parameters, Rayleigh range andbeam waist position, for three electron beam energies.
Table 5 shows the optimized optical parameters. The
optical cavity of the KU-FEL system has been designed
taking into account the diffraction loss and the out
coupling. The laser field is assumed to be the Gaussian in
the calculation optical loss. The out coupling hole is 1
mmφ located at the upstream mirror. As the result, thecurvature of upstream mirror is calculated to be 2.58 m
and that of downstream mirror is 1.92 m. Table 5 also
shows the diffraction loss and out coupling of thedesigned optical cavity. From the setup condition of the
optical cavity, shown in Fig. 7, the beam waist position is
not at the center of the undulator but is shifted to
upstream in order to reduce the diffraction loss at
upstream chamber (30 mmφ). FEL gains with
optimization of both of electron beam and of opticalcavity are shown in Table 6. The realistic FEL gains arelower by a few % than those based on the design
magnetic field distribution.
By using the above optimized conditions, we haveestimated the evolution of the FEL power with the662

Table 6: Comparison of the optimized FEL gains of
the measurement with those of the design
Beam energy (MeV)
25 30 35
Gain of design undulator (%)
89 65 49
Gain of real undulator (%)
87 64 49

Fig. 7: Undulator and optical cavity in KU-FEL. L1 is
1.605 m, L2 is 2.70 m, R1 (the curvature of M1) is 1.92m, and R2 is 2.58 m.

Fig. 8: FEL power as a function of pass number in eachbeam energy.
TDA3D modified to take into account the successive
development of the laser power after round-trip. The
optical loss is subtracted from the FEL gain in each pass.
Figure 8 shows that FEL power from the measured
magnetic field decreases by about 5 %.Then the numbersof round-trips necessary for saturation increase by about
round-trips to reach gain saturation by 0.2 μm, comparedwith those from the design ones.
The injector in KU-FEL is a thermionic RF gun whichhave a disadvantage of back bombardment, so thatmacropulse duration has been restricted to 4 μs. However,since we have estimated macropulse duration is up to 8 μs[7], FEL saturation in each energy is expected.

SUMMARY
The measurement of the magnetic field of the KU-FEL
undulator has been carried out. The electron beam
trajectory in the undulator and the spontaneous radiation
have been evaluated with measured magnetic field. The
beam displacement is about 2 mm for 30 MeV electron
beam. However, it can be reduced to 0.2 mm with asteering magnet placed just before the undulator. By using
the measured magnetic field, the beam parameters and the

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany
optical parameters were optimized to obtain the maximum
FEL gain. Calculation of FEL gain and FEL gain
saturation have been performed. Although FEL gains
show a few % decrease and thus the times to reach FEL
saturations with the measured magnetic field are slightly
longer than these with the design field, FEL saturation is
expected in the wavelength region of from 6 to 12 μm.

REFERENCES[1] T. Yamazaki, et al., Proc. Free Electron Laser Conf.
2001 (2002) ΙΙ−13.

FEL Technology

THPPH037[2] T. Fukui, et al, Proc. Free Electron Laser 2005
(2006).
[3] E. Nishimura, et al., Nucl. Instrum. Methods,
A341(1994) 39.
[4] O. Chubar, et al., Proc. of EPAC98, p.1177, 1998.
[5] J.S. Wurtele T.M. Tran. Computer Physics Comm.,
Vol.54, p.263, 1989.
[6] L. M. Young, James H. Billen : LA-UR-96-1835(2002).
[7] N. Ohkawachi, et al., “Production of electron beamwith constant energy by controlling input power intoa thermionic RF gun”, in these proceedings.

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PRODUCTION OF ELECTRON BEAM WITH CONSTANT ENERGYBY CONTROLLING INPUT POWER INTO A THERMIONIC RF GUN
N. Okawachi, M. Nakano, H. Zen, T. Kii#, K. Masuda, H. Ohgaki, K. Yoshikawa, T. Yamazaki,
Institute of Advanced Energy, Kyoto University, Uji, Japan
Abstract
A thermionic RF gun is compact and economical, but it
is difficult to produce electron beam of pulse width longer
than a few μsec with constant energy owing to inherent
back-bombardment effect. In this work we tried to keep
beam energy constant in macro pulse duration by feeding
modulated RF power. We also tried to perform transient
analysis with equivalent circuit taking into account the
back-bombardment effect in macro pulse duration in thecases of the W cathode and the LaB6 cathode. We foundthat the degradation of the peak energy could be kept
below 100 keV in the macro pulse duration of 8.0 μsec
and 8.2 μsec, respectively.

INTRODUCTION
It is necessary for the development of an FEL to
improve the source of electron beam, and a thermionic RF
gun is suitable for a compact and economical FEL system.
However a back-bombardment effect degrades the beamenergy during the macro pulse. In a previous work, wereported the preliminary result of improvement of athermionic RF gun [1]. In this work we tried to reducebeam energy degradation due to the back-bombardment
effect by feeding modulated RF power into a thermionicRF gun. In addition, we have performed a self-consistenttransient analysis which took into account the backbombardment effect during macro pulse duration by using
an equivalent circuit model and a thermal conduction.

EXPERIMENTAL SETUP
Fig.1 shows the experimental setup. The cathode is of
6-mm diameter made of porous tungsten impregnatedwith barium. RF power fed into the RF gun is controlled
by remotely adjusting the reactors in the pulse forming
network (PFN) with stepping motors. This experiment
was performed varying the beam current drawn from the
RF gun and input RF power in both the cases a flat input
RF and a modulated RF waveform power.
The profiles of the electron beam current were
measured with current transformer (CT) and Faraday cup(FC). The energy spectrum of the electron beam wasanalyzed with a bending magnet, beam slit and CT.

________________________________________#

kii@iae.kyoto-u.ac.jp

664

Figure 1: Experimental setup.

METHOD OF ANALYSIS
Back-bombardment effect depends on both the cavity
voltage in the RF gun and the cathode current density. We
performed a transient analysis in the RF gun taking into
account the time evolution of the beam loading dependingon the cavity voltage and the cathode current density byusing an equivalent circuit model and a thermal
conduction model. The beam loading was calculated fromthe cavity voltage and the cathode current density which
was calculated from the thermal conduction in thecathode taking into account the stopping power of theback streaming electron in the cathode.

Analysis of the cathode current density
The energy distribution of the back-streaming electrons
was calculated by using the results of the particle
simulation code PARMELA [2]. From this result the heat
quantity given to the cathode by the back streaming
electron with various energy was calculated. In thiscalculation we assumed that the cathode consisted of thin2000 disks.
In order to evaluate the effect of the back streaming
electrons on the time evolution of the cathode temperature,
we used following quasi empirical formula of the TIO [3]:[]a (γ − 1) ⎫a ⎧⎪ ln 1 + a 2 (γ − 1)
⎪
3
−
R= 1⎨
(1)
⎬
a5
a
ρ ⎪
1 + a (γ − 1) ⎪
2
4
⎩
⎭
1.209
−4
a1 = 2.335 A / Z
a2 = 1.78 × 10 Z
−4
a3 = 0.9891 − (3.01 × 10 Z )−2
a4 = 1.468 − (1.180 × 10 Z )FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

0.109
2
2
a5 = 1.232 / Z
γ = ( E + m 0c ) / m c0where, R is the stopping range of the electron in m, A is
the mass number of the absorber material, Z is the atomic
number of it, E is the kinetic energy of electrons in MeV,
ρ is the density of the absorber material in kg/m3.
Equation (1) is applicable to the 0.3 keV – 30 MeV
electrons. With this equation, stopping power dEb/dz was
obtained. Here, we used the values of ρ = 19250 kg/m3, A= 183.85, Z = 74 assuming that the cathode material was
made of W alone..
The time evolution of the temperature was calculated ineach disks of the cathode, and the time evolution of thecathode temperature was calculated by using the equation
below,
2
∂T
∂ T
cρ V
=λ
+ Qb ( z , t )
(2)
2
∂t
∂z
where, c is the specific heat, ρ is the density, V is thevolume, T is the temperature, λ is the thermal
conductivity of the cathode, z is the distance from thecathode surface, Qb(z, t) is the heat quantity from the backstreaming electrons. Here, we used the values of c = 130
J/kg/K, λ = 174 W/m/K.

Figure 2: Thermal conduction model.

THPPH038

Figure 3: Equivalent circuit model.

RESULT
Experimental result
We have succeeded to keep the peak energy of theelectron beam constant in 4 μsec by feeding a modulated
RF power into a RF gun. Fig. 4 shows the flat RF power
waveform and the modulated RF power waveform fed
into a RF gun. Fig. 5 shows the beam current waveform
whose peak energy is 8.6 MeV at CT2. Fig. 6 shows thetime evolution of the peak energy in macro pulse duration.
As shown in Fig. 5 feeding modulated RF power into a
RF gun was an effective way to extend the macro pulse
duration and to increase the beam current. As shown in
Fig. 6 the beam energy which had been degraded in thelatter part of the macro pulse duration was kept constantby feeding modulated RF power.

Figure 4: Input RF power waveform.

The cathode current density was obtained from the time
evolution of the cathode temperature calculated above.
The relationship between the cathode temperature and thecathode current density used in this analysis was obtainedby the results of the cathode performance test of Heat
Wave Labs, Inc.

Analysis of the cavity voltage in the RF gun
The cavity voltage in the RF gun and the reflecting RF
power were calculated with the equivalent circuit model
shown in Fig. 3. In this circuit, the RF power source wasexpressed by a source ig, the RF gun was expressed by
LCG resonant circuit, and the beam loading was
expressed by an admittance Yb. The conductance and thesusceptance of the electron beam were calculated fromthe cavity voltage and the cathode current density byusing the particle simulation code KUBLAI [4]. Thus thebeam loading was calculated.

Figure 5: Beam current waveform.

Figure 6: Peak energy @ CT2.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Result of calculation
In order to confirm the validity of calculation model,
experimental and calculated reflecting RF power
waveforms were compared. Fig. 7 shows the measured andreproduced reflecting RF power waveform when a flat RF
power was fed. Fig. 8 shows them when a modulated RF
power was fed. Experimental and calculation results agree
very well.

We estimated how long time the peak energy of theelectron beam could be kept constant by using our KUFEL 4.5 cell RF gun. The calculation was performed inboth cases of W cathode and LaB6 cathode. We used thevalue of ρ = 4700 kg/m3, A = 94.75, Z = 40, c = 122
J/kg/K, λ = 147 W/m/K and the relationship between thecathode temperature and the cathode current density was
obtained by the results of the cathode performance test of
KIMBALL PHYSICS INC, in the case of LaB6 cathode.
Fig. 10 shows the time evolution of the cavity voltageof W and LaB6 when a flat RF power was fed,
respectively. The degradation of the cavity voltage of
LaB6 was a little smaller than that of W.

Figure 7: Reflecting RF power waveform.

Figure 10: Comparison of W with LaB6.

Figure 8: Reflecting RF power waveform.

Fig. 11 and Fig. 12 show the time evolutions of thecavity voltage when an optimized modulated RF power
was fed. The input RF power was 8 MW at the beginningof the macro pulse and the controlled range was 1.6 MW
and the initial current density was 2.28 A/cm2 in eachcalculations. We found that the degradation of the peakenergy could be kept below 100 keV in the macro pulse
duration of 8.0 μsec when the cathode was W, 8.2 μsec
when the cathode was LaB6.

As shown in Fig. 9, there was a relationship between
the cavity voltage (Vc) and the peak energy of the electron
beam (E), and the peak energy could be kept constant bykeeping the cavity voltage constant.

Figure 11: Expected time evolution of thecavity voltage (W).

Figure 9: Time evolution of the cavity voltage
and the peak energy.

666

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THPPH038

REFERENCES[1] T. Kii, et al, Proceedings of the 27th International
Free Electron Laser conference, (2005) pp584-587.
[2] L. M. Young, James H. Billen : LA-UR-96-1835(2002).
[3] M. J. Berger and S. M. Seltzer, STOPPING POWER
AND
RANGESOF
ELECTRONSANDPOSITRONS (2nd Ed.),NBSIR (1982).
[4] K. Masuda, Development of numerical simulation
code and application to Klystron efficiency
enhancement, Ph. D Thesis, Kyoto University, (1998).

Figure 12: Expected time evolution of thecavity voltage (LaB6).

SUMMARY
It was confirmed in experiment that feeding modulated
RF power into a RF gun was effective on the reduction of
the degradation of the beam energy.
By the calculation in this work, the experimental results
were reproduced well. Moreover, the degradation of thepeak energy of the electron beam could be kept below
100 keV in the macro pulse duration of 8.0 μsec when thecathode was W, 8.2 μsec when the cathode was LaB6.

FEL Technology

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Proceedings of FEL 2006, BESSY, Berlin, Germany

EXPERIMENTAL STUDY ON EFFECT OF ENERGY DISTRIBUTION
ON TRANSVERSE PHASE SPACE TOMOGRAPHY
H. Zen#, H. Ohgaki, K. Masuda, T. Kii, T. Shiiyama, S. Sasaki, N. Okawachi, M. Nakano,
K. Yoshikawa, T. Yamazaki
Institute of Advanced Energy, Kyoto University, Gokasho, Uji, Kyoto, 611-0011, Japan.
Abstract
Effect of energy distribution of electron beam ontransverse phase space distroiion obtained by the use of
tomographic method is described. Experimental phasespace distribution of electron beam with low energy-tailhas weak and scattered halo, which does not appear in thecase of the beam without the tail. The result is consistent
with the result of previous simulations. An iterative
elliptical analysis is proposed to extract the beam
parameters of main component from distorted phase space
image. It was shown in simulation that the method could
extract the beam parameters of main component fromdistorted image. And then, the method was applied toexperimental results. As the results, the vertical andhorizontal emittances at the upstream and downstream ofenergy filter are agreed well.

INTRODUCTION
It is indispensable to measure not only emittances but
also phase space distributions of electron beams toevaluate and optimize the performance of electron guns.
Transverse phase space tomography [1] is powerful
method especially for non-Gaussian beam, because themethod directly reconstructs the phase space distributionof electron beams. However, the assumption of monoenergy is essential for the method. Thermionic rf guns
inherently produce electron beams which have large
energy spread (about 10 to 15 percent) and low energy tail,and the energy distribution distorts measured phase space
distribution obtained by tomographic method.
We have evaluated the effect of energy distribution on
the tomographic method by numerical simulations [2]. It
was found that the signals of low energetic electrons arereconstructed as weak and scattered signals on wide
region of reconstructed phase spaces, and those signals
lead to large errors in beam parameters. On the other hand,
it was also found that the energy spread of main
component have no large effect on the method even if theenergy spread is 15 percent.
The effect was evaluated by comparison of thereconstructed image from the upstream and that from thedownstream of an energy filtering section. Furthermore
for the beam just after the gun, we introduced an ellipticalanalysis to remove the effect of low energy tail in order toobtain correct beam parameters at the gun exit by the
tomographic method.

EXPERIMENTAL SETUP

Figure 1: Experimental arrangement.
Figure 1 shows the experimental setup. A dispenser
cathode of disk shape with 6 mm diameter is mounted in
the first half cell of our 4.5 cell RF gun. To reduce backstreaming electrons [3], transverse magnetic field wasapplied with a dipole magnet located just before the rf
gun [4]. The beam profile monitor (BPM) consist of afluorescence screen (Cr doped Al2O3) and a CCD camera,
and its spatial resolution is 0.05 mm.
Dog-leg section in Fig. 1, which consisted of two
dipole magnets, a slit, and a quadrupole triplet, worked as
an energy filter and its energy resolution is about 5
percent.
The quadrupole magnet 1 (Q1) and the BPM1 are used
to measure the phase space distributions at the upstreamof the energy filter, and the Q6 and BPM3 are used tomeasure them at the downstream.
Beam parameters in the experiments are shown in Table
1, and the energy distribution obtained with bending
magnet 1 (B1) and Faraday cup 2 (FC2) is shown in Fig.
2. Unfortunately signals of FC2 of low energy tail (lessthan 7 MeV) were too weak to be separated from theelectric noise. However, the existence of low energy tailhas been predicted in the previous simulation for our rf
gun [2].
For tomographic reconstruction, we used orderedsubset expectation maximization algorithm [5] whose
advantage is that there is no artefact on reconstructed
images.

___________________________________________#

heishun@iae.kyoto-u.ac.jp668

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THPPH039

Table 1: Beam parameters in experiments

Charge ΔQ/ΔE [a.u.]

Macro pulse duration
Total charge
Charge per bunch
Peak Energy@ BPM1@ BPM3
1.6 μ sec
1 μ sec
300 nC
100 nC
66 pC
35 pC
9.2 MeV

1.2
1.0

(a)
(b)
Figure 3: Phase space distributions at the entrance of Q1(dashed lines indicate the regions where electrons can
exist and are calculated from experimental geometry). (a)Horizontal and, (b) vertical.

0.8
0.6
0.4
0.2
0.0
0 1 2 3 4 5 6 7 8 9 10Energy [MeV]

Figure 2: Measured energy spectrum of the electron beamat the exit of gun (dashed lines indicate the energy
acceptance of dog-leg section).

RESULTS OF EXPERIMENTThe results of experiments are shown in Fig. 3 and 4.
Before reconstruct the Q1 result, background signals weresubtracted. At the Q1 entrance horizontal and verticalnormalized emittances are evaluated as 82 and 44 π mm
mrad, respectively, while those are 12 and 6.9 π mm mradat the Q6 entrance.
There are weak and scattered signals in Fig. 3 where
the electron beam had a low energy tail, while suchsignals are not seen in Fig. 4. It is consistent withprevious numerical studies that the phase space
distributions for the beam with low energy tail areseverely distorted.
In Fig. 3, the region between dashed lines indicateswhere electrons can exist and the region is calculated
from aperture of the gun exit (4 mm in diameter) and the
distance between the gun exit and Q1 (27.5 cm). The
signals in outside of the region are miss-reconstructedsignals due to difference from assumed energy at least.
Therefore, it was shown in experiment that the signals
from low energy tail are reconstructed as weak andscattered signals. We can not obtain correct phase space
distributions by using tomographic method if low energy
tail is contained in an electron beam.

REMOVAL OF LOW ENERGY SIGNALS
Amount of low energy electrons produced by athermionic rf gun is much fewer than amount of electrons
included in main component, and low energy electrons
are reconstructed wider and weaker than true distribution.
So intensity of low energy electrons on reconstructed
phase space is much weaker than intensity of electrons
included in main component. However, the emittancecalculation is strongly affected by the tail. Therefore, weneed to remove the weak signals which are originatedfrom low energy electrons to obtain correct beam
parameters by the tomographic method.

FEL Technology(a)(b)
Figure 4: Phase space distributions at the entrance of Q6
measured by tomographic method, (a) Horizontal and (b)vertical.

Procedure of Iterative Elliptical Analysis
To remove the weak signals produced by low energy
electrons automatically, we introduced an iterative
elliptical analysis (IEA) [6]. The procedure is:
I : Calculate <x2>, <x’2> and <xx’> from reconstructed
phase space distribution.
II : Draw ellipse defined by Eq. 1 on reconstructed
phase space.

x'2 x 2 + 2 xx' xx'+ x 2 x' 2 = 9ε 2

(1)

Eq. (1) represents the 99 percent ellipse of Gaussian
distributions.
III: Calculate <x2>, <x’2> and <xx’> from reconstructed
phase space distribution only in the ellipse.
IV : In the same way with step II and III, draw ellipse
using newly calculated <x2>, <x’2> and <xx’> in stepV : Repeat step III and IV until <x2>, <x’2> and <xx’>
sufficiently converge.

Simulation of Iterative Elliptical Analysis
Reliability of IEA was examined by using numericalsimulation. We gave the Gaussian-shaped phase space
distribution with the energy distribution shown in Fig. 5
as original distribution and simulated the experiment of
tomographic method. In this simulation, space charge
effect was neglected, since it was not significant for ourthermionic rf gun. As the result of the simulation, a
distorted phase space distribution was reconstructed (Fig.
6). Although weak and scattered signals exist in the figure,669

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Proceedings of FEL 2006, BESSY, Berlin, Germany

strong signals in the center are looked similar to theoriginal phase space distribution (Fig.5).

ΔQ/ΔE [a.u.]

1.2
1.0
0.8
0.6
0.4

Application of IEA to Experimental Result

0.2
0.0
0

The result of IEA applied to the Fig.6 is shown in Fig. 7.
The normalized emittance and Twiss parameters graduallyconverged to 3.9 π mm mrad, α = 3.0 and β = 2.8 m,
respectively as iteration number increased. The beam
parameters of original distribution were normalized
emittance = 3.3π mm mrad, α = 2.9 and β = 2.8 m. Since
each error in beam parameters is less than 20 percent, thismethod is reliable.

2

4

6

8

10

Energy [MeV](a)(b)
Figure 5: Original distribution of numerical simulation,(a) phase space distribution (normalized emittance = 3.3 π
mm mrad, α = 2.9 and β = 3.1 m), (b) energy spectrum.

IEA was applied to experimental results at the entranceof Q1 and the results are shown in Fig. 8. A center core ofreconstructed phase space distribution was successfully
obtained and beam parameters sufficiently converged. As
results of application of IEA, measured horizontal andvertical emittances were 5.4 and 4.7 π mm mrad,respectively.

Figure 6: A result of numerical simulation (normalized
emittance = 10 π mm mrad, α = 1.5 and β = 1.4 m).
(b)Norm. Emittance [π mm mrad]

(a)

100
Twiss Parameters

180

β [m] 0.32 60
0

-1

3.0

β [m]

2.8 8

2.0
1.5
1.0

10

6
Emittance
3.9
0 1 2 3 4 5 6 7 8 9
Number of Iteration

4
2

670

Emittance
5.4 0
510 15 20 25
Number of Iteration

(c)
50
1

40

β [m]

0.24 30

0

α

-1

20
-0.72

Emittance(b)
Figure 7: Result of IEA applied to simulation result, (a)phase space distribution (normalized emittance = 3.9 π
mm mrad, α = 3.0 and β = 2.8 m), (b) convergence ofemittance and Twiss parameters.

-0.87 20

Norm. Emittance [π mm mrad]

2.5

0

12
α

Twiss Parameters

Twiss Parameters

3.0

Norm. Emittance [π mm mrad]

(a)
3.5

40

α

0

5
10 15 20
Number of Iteration

10

4.7 0
25

(d)
Figure 8: Results of IEA applied to experimental results.
(a) Horizontal phase space distribution of horizontal
direction. (b) Vertical phase space distribution. (c) and (d)convergence of horizontal and vertical beam parameters,
respectively.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

The IEA was also applied to experimental results at the
Q6 entrance and measured emittances of horizontal andvertical directions at the Q6 entrance were 7.4 and 4.3 π
mm mrad, respectively. Measured emittances of verticaldirection at the Q1 and Q6 entrance agreed well. However,
emittances of horizontal direction did not agree well. The
reason of this disagreement was the non-zero horizontal
dispersion in the Dog-leg section.
Reliability and an ability of IEA were confirmed bothin simulation and experiment. We are now planning to do
more experiments under various conditions of the gun inorder to evaluate the accuracy of IEA quantitatively.
Comparison of transverse phase space distribution withthe slit methods will be useful, since the methods are notsuffered from energy distribution.

SUMMARY
To study the effect of energy distribution to transverse
phase space tomography, experimental results at the
upstream and downstream of the energy filter werecompared. As the result, the low energy electrons arereconstructed as weak and scattered signals, which are
predicted by previous numerical investigation.
To remove the signals from low energy electrons, IEA
was introduced and examined. By a numerical simulation,

FEL Technology

THPPH039

the validity of the analysis was shown. IEA was applied
to experimental results at the upstream of energy filterand compared with the experimental results at thedownstream of the filter. The emittances of verticaldirection at the upstream and downstream of energy filter
agreed well, although horizontal ones were not due to nonzero horizontal dispersion in the Dog-leg section.
Consequently, reliability and an ability of IEA wereshown both in simulation and in experiment.

REFERENCES[1] C.B.McKee, et al., NIM A358, 1995, p.264.
[2] H.Zen, et al., Proc. of FEL2005, 2006, p.592.
[3] T.Kii, et al., Proc. of FEL2005, 2006, p.584.

[4] T.Kii, et al., NIM A507, 2003, p.340.
[5] H.M. Hudson, et al., IEEE. Trans. Med. Imaging, 13,1994, p.601.
[6] H.Zen, et al, “Transverse phase space measurement
using tomographic method”, conference proceedingsof SRI2006, in press.

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STUDY ON FOCUSING PROPERTY OF NEW TYPE WIGGLER
AND SASE-FEL EXPERIMENT AT THE ISIR, OSAKA UNIVERSITY
S. Kashiwagi#, R. Kato, Y. Kon, T. Igo, G. Isoyama,
Institute of Scientific and Industrial Research, Osaka University, Ibaraki, Osaka 567-0047, JapanS. Yamamoto*, K. Tsuchiya and H. Sasaki
Institute of Materials Structure Science, KEK, Tsukuba, Ibaraki 305-0801, Japan*School of Advanced Sciences, The Graduate University for Advanced Studies,
Tsukuba, Ibaraki 305-0801, Japan.
Abstract
We have developed a new type of wiggler based on theedge-focusing wiggler for free electron laser (FEL) andself-amplified spontaneous emission (SASE) in theinfrared region at the Institute of Scientific and Industrial
Research (ISIR), Osaka University. The strong focusing(SF) scheme is adopted for the new wiggler in order tokeep the beam size small along whole the wiggler. The
wiggler consists of four FODO cells for double focusing.
A gain length and SASE output power for the strong
focusing wiggler were numerically estimated using the
1D FEL model and Genesis code. Measuring the electron
beam size in the wiggler at different wiggler gaps
performed the experimental study on focusing property of
the new type wiggler. We are conducting experiments togenerate SASE in the infrared region and to measure its
characteristics, using the strong focusing wiggler and ahigh intensity single bunch electron beam. We havemeasured the wavelength spectrum of SASE in the
wavelength region between 220 and 50 µm using a
grating monochromator and a Ge:Ga detector. The second
harmonic and the third harmonic peaks of SASE werealso observed in the spectrum measurement.

INTRODUCTION
We are conducting experiments of FEL and SASE witha high intensity electron beam in the infrared region at
ISIR L-band linear accelerator, Osaka University. Whilethe beam experiment are performing, we have developed
a new type wiggler, named the edge-focusing (EF)wiggler, which produces the strong transverse focusing
field incorporated with the normal wiggler field [1]. To
demonstrate its principle and evaluate the performance,
the first model wiggler has been fabricated. It is
experimentally confirmed that a field gradient of 1.0 T/m
is realized along the beam axis in the EF wiggler. The
details of the model wiggler were reported in previous
conference [2-3]. The EF scheme has been applied to thewiggler being used for FEL and SASE in the far-infrared
region at the ISIR L-band linear accelerator, to make thegain length of SASE shorter by keeping the beam size
small along whole the wiggler. Before replacing of the
wiggler, the wiggler was a conventional Halbach-type#

shigeruk@sanken.osaka-u.ac.jp672

wiggler and we changed its magnet parts with new ones.
We, therefore, hold the wiggler parameters same as
before. In order to meet a wide range of the electron beamenergy and the wiggler gap, we adopt the strong focusing
scheme using the EF wiggler. Focusing and defocusing
elements are composed of permanent magnet blocks withthe edge angle and they are alternately inserted in magnet
arrays of the wiggler. The strong focusing wiggler has
been fabricated and the magnetic field has been measured
at KEK. In June 2005, the strong focusing wiggler
installed to the FEL system at ISIR L-band linear
accelerator [4].
After the installation of the strong focusing wiggler, we
resumed to conduct the experiment to generate SASE in
the far-infrared region. In the beam experiments, afocusing property of the strong focusing wiggler is alsostudied by measuring the beam sizes using screen
monitors in the wiggler at different gaps.

STRONG FOCUSING WIGGLER
In this section, the developed strong focusing wiggler is
described shortly. The edge-focusing wiggler is basicallya Halbach type wiggler made only of permanent magnet
blocks, but their shapes are not rectangularparallelepipeds. The field gradient on the permanent
magnet with edge is approximately proportional to theedge angle φ and hence the focusing force can be easilyadjusted with the edge angle. A polarity of the field
gradient can be decided by choosing positive or negative
angle of edge against to beam trajectory. In the strong
focusing scheme, the electron beam is focusedalternatively in the vertical and the horizontal directions
to obtain focusing in the both directions using a sequenceof focusing and defocusing elements separated by drift
spaces, which is called the FODO lattice. Parameters of
the FODO lattice were optimized to meet therequirements of our experiment and the parameters of thestrong focusing wiggler are listed in Table 1. The
permanent magnet used is NdFeB (NEOMAX-38VH,
NEOMAX Co.) with Br = 1.22 T and the peak magnetic
field of the EF wiggler is 0.39 T at the minimum gap of
30 mm. The number of FODO cells in the wiggler is fourand the cell length is 0.48 m. The number of cells is afactor of the number of wiggler periods, 32. Focusing
elements are single wiggler periods with the edge angle of+5° and defocusing ones are those with –5°, and they are

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Proceedings of FEL 2006, BESSY, Berlin, Germany
5
beam size (mm)Table 1: Main parameters of the SF wiggler
Block sizes
90x20x15 mm3Magnet materials (Coating) Nd-Fe-B (TiN)
Period length
60 mm
Number of periods
32 periods
Total length
1.938 mPeak magnetic field
0.39 T (gap 30mm)
Number of FODO cells
4 cells
Length of FODO cell
0.48 mEdge angle±5 °Field gradient±3.2 T/m

Beam focusing of the strong focusing wiggler
The envelope of beam sizes in horizontal and verticaldirection for the strong focusing wiggler and a planar
wiggler were calculated with an electron beam of 10 MeV,a normalized emittance of 150π mm mrad in transverse
directions and a peak wiggler field of 0.392 T. Figure 1
shows the calculated beam envelopes and the solid line
and dashed line show the strong focusing wiggler and theplaner wiggler, respectively. In the horizontal direction,
the beam envelope of the strong focusing wiggler
alternatively changes along the wiggler and the average
beam size (σ) in the wiggler much smaller than that of theplanar wiggler. On the other hand, the vertical beam sizes
for the both type of wigglers are almost same. The FODO
lattice of the strong focusing wiggler slightly distorted
due to the natural focusing of the wiggler. The average
beam size for the strong focusing wiggler (σSF) and theplanar wiggler (σPL) are 1.41 mm and 1.69 mm
respectively, when the average beam size in the wiggler
assumed to be σ horizontal ⋅ σ vertical . Transverse charge
density of the beam, which is a square of the average
beam size, in that of the strong focusing is about 30%
higher than that of the planar wiggler. The gain length(Lg) for each wiggler is estimated from the above average
beam sizes by 1D FEL model using Eq. 1.
(1)

where λu and ρ are period length of the wiggler and FEL
parameter. Here, the bunch charge and the length of theelectron beam are assumed to 30 nC and 30 ps (FWHM),

FEL Technology

32
1
Edge-focusing wiggler
0

0.5

1
z(m)

1.5

2

beam size (mm)5NUMERICAL ESTIMATIONλu
4 3π ⋅ ρ

Planar wiggler

40

separated by 3 normal wiggler periods. Longitudinallymagnetized blocks are added at both ends of the strong
focusing wiggler in order to compensate for the horizontal
shift of the oscillatory beam orbit due to the fringing
magnetic field at the ends. Thus the total length of the SF
wiggler is 1.938 m.
In the field measurement, the peak magnetic field was
0.392 T and peak magnitude of field gradient at focusing
and defocusing elements was about 3.2 T/m at the wiggler
gap of 30 mm. The results of measurements were good
agreement with the numerical calculations.

Lg =THPPH040

4
3

Planar wiggler

Edge-focusing wiggler

2
1
0

0

0.5

1
z(m)

1.5

2

Figure 1: The envelopes of beam size in horizontal(upper) and vertical (down) directions for the strong
focusing wiggler and a planar wiggler.
corresponds to the peak current of 1.0 kA. The derived
the gain length of the strong focusing wiggler and theplanar wiggler are 0.152 m and 0.163 m respectively,
therefore the gain length of the strong focusing wiggler isabout 7% shorter than that of the planar wiggler. From thedifference of the gain length, it can expect 2 times large
gain of FEL can be obtained by using the strong focusing
wiggler.

SASE output power
SASE output power of the strong focusing wiggler andthe planar wiggler are estimated using Genesis code [5].
The beam parameters of electron beam are same in above
calculations. Figure 2 shows SASE radiation power along
the wigglers. In this figure, the red and the blue lines are
SASE radiation power of the strong focusing wiggler andthe planar wiggler, respectively. At 10MeV, the beam size
is kept small in the strong-focus wiggler and the SASE
power of strong focusing wiggler is 5~6 times higher thanthat of planar wiggler.

BEAM EXPERIMENTThe beam experiment was conducting using the L-band
linear accelerator at ISIR, Osaka University. ISIR L-band
linac consists of an electron gun, three-stage subharmonic buncher (SHB) system, pre-buncher, buncher,
3m-long accelerating structure and the experimental beamlines. The electron beam with peak current of 17 A and apulse duration of 5 ns was produced with a thermionicgun. The electron beam was injected into the SHB systemcomposed of two 1/12 and one 1/6 SHB cavities for theaccelerating frequency of 1.3 GHz to generate a highintensity single bunch beam, and then it was accelerated
to 10.3 MeV in the linac. The electron beam was

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5

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4

Proceedings of FEL 2006, BESSY, Berlin, Germany

Strong focusing wiggler

POWER (W)

1000
100
10
1

Planar wiggler
0.1
0.01

0

0.5

1
z(m)

1.5

2

Figure 2: SASE radiation power along the wiggler.
(Red line: Strong focusing wiggler, Blue line: Planar
wiggler).
transported to the strong focusing wiggler via theachromatic beam transport line as shown in Fig. 3. The
peak magnetic field and K-value of the strong focusing
wiggler were 0.353 T and 1.4 at the wiggler gap of 32
mm. Twiss parameter and the emittance were measured
using a quadrupole scan technique with a 100 µm
thickness phosphor screen monitor at the exit of theaccelerating structure. The normalized transverse beamemittance was ~170π mm mrad with a bunch charge of 30
nC and an energy spread of 3.0 % (FWHM). The beam
injection condition and an orbit of electron beam weretuned using quadrupole magnets and steering coils at thebeam transport line for FEL experiment. The unnecessaryenergy part of the electron beam was collimated by anenergy-slit located at the dispersion section of thetransport line and the energy width of the slit was about
2 %. Therefore, the net charge per bunch passing throughthe wiggler was about 20 nC. The experimental

arrangement is shown schematically in Fig. 3. SASE
radiation by the single bunch beam passing through the
wiggler was reflected with a mirror (MP1) at downstream,
and led to a far-infrared monochromator in themeasurement room via an optical transport line. The
optical transport line and the monochromator were
evacuated together with a rotary vacuum pump. The low
vacuum in the optical transport line and the high vacuumin the beam transport line were separated by a 0.2 mm
thick, 20 mm in diameter synthetic diamond window,
denoted by W1 in Fig. 3. The monochromator is a crossCzerny-Tuner type with a plane reflective grating, whose
braze wavelength is 112.5 µm. The monochromator canbe used in the wavelength region from 50 to over 240 µm.
The wevelength resolution of the monochromator isalmost constant over the range and approximately 1.5 µm
for a slit width of 6 mm. The monochromatized light was
detected with a Ge:Ga photo-conductive detector cooledwith liquid-helium.

EXPERIMENTAL RESULT
Beam size measurement in the wiggler
We measured the transverse beam size in the wiggler
using three screen monitors, denoted by F3, F4 and F5 in
Fig. 3, at different wiggler gap with 10.3 MeV electron
beam. In Fig. 4, the solid circles with the solid lines show
horizontal beam size and the open circles with the dashedlines show vertical beam on each screen monitors at
different wiggler gap from 30 to 50 mm. The horizontal
beam sizes on the all screens slightly change; but they
were almost constant at different wiggler gap. The
vertical beam size on the F4 and F5 periodically change at
different wiggler gap. It seems that the variation of thevertical beam sizes come from the changing of the natural
focusing, which is strongly depend on the magnetic fieldstrength of the wiggler. The strength of natural focusing is
proportional to the square of the peak magnetic field andFigure 3: Schematic layout of the ISIR L-band linac and the FEL system. SASE radiation is deriver to the grating
monochromator and Ge:Ga detector using optical mirrors.
674

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Proceedings of FEL 2006, BESSY, Berlin, Germany
3
F4(Y)Beam size (sigma) [mm]

2.5
F5(X)
2
F3(X)
1.5

F5(Y)

F4(X)

1
0.5
F3(Y)
0

28

32

36

40

44

48

52

gap [mm]Figure 4: Measured horizontal (X) and vertical (Y)beam size using three screen monitors, denoted by
F3, F4 and F5 in Fig. 3.
the strength of the edge focusing is only proportional tothe peak magnetic field in the simple model of the
wiggler composed of alternating bending magnets withthe edge angle. Furthermore, as reported previous FEL
conference [4], we have observed the peak field decreases
to one-third with wiggler gap from 30 to 50 mm, whereas
the field gradient decreases only by 56 % in the magnetic
field measurement. The field gradient of the edgefocusing wiggler is kept at different wiggler gap. At thiscondition of electron beam, the natural focusing is strong
and the edge focusing effect cannot be observed clearly.
The measurement results were compared with thecalculated beam size in the wiggler. In vertical direction,
the periodically variation of beam sizes are large different,
since the electron beam was injected into wiggler with notmatching conditions. We will continue the study on thefocusing property of the strong focusing wiggler at
different condition of electron beam energy using thebeam profile monitors.

Result of SASE spectrum measurement
Figure 5 shows a wavelength spectrum of SASE in the
wavelength range from 50 to 240 µm with 1µm step. The
closed dots and the error bar show the average values ofintensities and a standard deviation, respectively, of five

Detector output [mV]30
25

3rd harmonic(74µm)

20

2nd harmonic(~110µm)

fundamental(218µm)

15
10
5
0
50

100

150
Wavelength [µm]200

THPPH040

highest intensities in thirty successive optical pulses foreach wavelength. As reported in Ref. [6], the total
sensitivity of the measurement system, including thesensitivity of the detector, the efficiency of themonochromator, the transmission efficiency of the opticaltransport line, was calibrated over the wavelength range
from 50 to 200 µm using a blackbody radiator. We havenot measured the sensitivity of the measurement system
above 200 µm. In Fig.5, the plotted intensities are,therefore, signal intensities from the detector and theintensities at different wavelengths are not calibrated.
Although the second and the third harmonic peaks arecomparable in signal intensity to the fundamental one dueto the higher sensitivity of the measurement system
around 100 µm wavelength, the fundamental peak is
actually strongest. The intensity ratios of the second andthe third harmonic peak to the fundamental one areroughly estimated from the extrapolation from theprevious calibration data to be 1/35 and 1/10, respectively.
The measured spectral width of the fundamental peak
was about 1.75 %, which is slightly smaller than thosepredicted value (1.9 %) by the 1D FEL model (Eq. 2).
9ρ
(2)
dw =
2π 3 ⋅ N W
We can expect that the FEL parameter (ρ) in the actual
experiment is smaller than the predicted one due to that
the Twiss parameter of the electron beam are different
with matching condition at the entrance of the wiggler
and the beam size is larger than optimum one. We willconduct to study on SASE about the spectral width andthe angular distribution of the higher-harmonics and thestatistically fluctuation of SASE output power.

ACKNOWLEDGEMENTS
The authors would like to thank Messrs. S. Suemine andT. Yamamoto for the help of accelerator operation. This
research was partly supported by the Joint Development
Research at the High Energy Accelerator Research
Organization (KEK), 2006-15, 2006 and The Ministry of
Education, Culture, Sports, Science and Technology(MEXT), Grant-in-Aid and for Young Scientists (B),
17740144, 2005-2006.

REFERENCES[1] G. Isoyama et al., Nucl. Instr. and Meth. A 507 (2003)
234[2] S. Kashiwagi et al., Nucl. Instr. and Meth. A 528(2004) 203[3] S. Kashiwagi et al., Proceedings of the 2004 FEL
Conference (2004) pp458-461.
[4] S. Kashiwagi et al., Proceedings of 27th International
FEL Conference (2005) pp199-202[5] http://pbpl.physics.ucla.edu/~reiche/index.html[6] R. Kato et al., Nucl. Instr. and Meth. A 507 (2003)
409-412.

Figure 5: Wavelength spectrum of SASE in the wavelength
range from 50 to 220 µm.

FEL Technology

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Proceedings of FEL 2006, BESSY, Berlin, Germany

LONGITUDINAL PHASE-SPACE MEASUREMENTS
OF A HIGH-BRIGHTNESS SINGLE-BUNCH BEAM
R. Kato#, S. Kashiwagi, T. Igo, Y. Kon, G. Isoyama
ISIR, Osaka University, Ibaraki, Osaka 567-0047, Japan
A measurement system of the longitudinal phase-space
distribution of electrons using the combination of an
optical transition radiation profile monitor and a streak
camera are currently under development at ISIR, Osaka
University. The energy spectrum is measured usingtransition radiation in a preliminary experiment. It isfound that the OTR monitor has a higher momentum
resolution than the momentum analyzer system usuallyused.

INTRODUCTION
We are conducting experimental studies on SelfAmplified Spontaneous Emission (SASE) in the infrared
region using the L-band linac at the Institute of Scientificand Industrial Research (ISIR), Osaka University [1-3].
The performance of SASE-FEL strongly depends on
beam parameters, such as a longitudinal beam profile,bunch charge, the transverse emittance and an energy
profile. A correlation between longitudinal positions ofelectrons in a bunch and their energies has a crucial effecton the temporal evolution of the optical pulse of SASE.
Several types of methods are extensively under study toevaluate the longitudinal phase-space profile of theelectron beam [4-7]. Among them, a combination of
Cherenkov radiation and a streak camera was used in Ref.
5 and a combination of synchrotron radiation and a streak
camera in Ref. 7.
In order to measure the electron distribution in thelongitudinal phase-space, we use a combination of an
optical transition radiation (OTR) monitor and a streak
camera together with a bending magnet. Since thebending magnet produces momentum dispersion in theelectron beam, electrons diverge in the horizontal
direction. The OTR radiator is placed in the lower courseof the beam line from the bending magnet and it works as
a converter from electrons to photons. The horizontal
intensity distribution of photons is proportional to themomentum distribution of electrons, provided that thebeam size of the electron beam due to the transverse
emittance is negligibly small compared with themomentum distribution. By means of an appropriate
optical system, the intensity distribution of photons on the
OTR radiator can be focused on the horizontal slit of thestreak camera. When the temporal sweep of the camera isturned on, a streak image reproduces the electron
distribution on the longitudinal phase-space.
Advantages of using OTR are as follows: (1) theradiator is a simple metallic plate or foil, which produce
no vacuum degradation by irradiation, (2) since the___________________________________________#

kato@sanken.osaka-u.ac.jp676

emission process is a very rapid phenomenon at a flat
surface, the temporal resolution is expected to be high, (3)the number of photons is proportional to the incident
electron number without intensity saturation. Furthermore,
if a very thin organic film vapour-deposited with metal isused as an OTR radiator, a quasi-non-destructive monitor
will be realized [8].
Compared with Cherenkov radiation or synchrotron
radiation, on the other hand, the intensity of transition
radiation is lower and the photon yield in the visible
region is of the order of 10-2 photons per incident electron[9]. The L-band linac, however, can produce a highintensity single-bunch beam typically with charge of 30
nC, so that a detectable number of photons is expected.
We recently began the feasibility study of thelongitudinal phase-space monitor with OTR. In thiscontribution, we will present preliminary experimental
results of the energy spectrum measurements with OTR.

PROPERTIES OF TRANSITIONRADIATION
Transition radiation is produced by relativistic charged
particles when they traverse the boundary surface of two
media with different dielectric constants. When a charged
particle of the velocity βc, energy γ and charge e passes
across a metallic surface in a vacuum, the radiationenergy per unit solid angle dΩ and unit frequency dω isgiven by [10]:e2d 2W
sin 2 θ,=R 2dωdΩ
4π c (1 − β cos θ )2

(1)

where R is the reflection coefficient of the metal and θ theangle of emitted photons with respect to the electron

1

Intensity [arb. units]

Abstract

E=30MeV

20MeV

0.5

10MeV

0
-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Emission angle [radian]Figure 1: Angular distribution of the transition radiation.

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH041

ISIR L-Band Linac

PB

GUN
SHBs

Accelerating
Structure

BuncherBM
QM

OpticalTransport
Line

OTR

QM WS

QM

QM

QM

AM

Beam Dump

BM QM Undulator BM

Shielding Wall
Streak Camera

Figure 2: Schematic layout of the ISIR L-band Linac and FEL beam line. GUN: Electron gun, SHBs: Sub-harmonic
Bunchers, BM: Bending magnet, QM: Q-magnet, AM: Analyser magnet, WS: Wire Scanner Monitor.
beam axis for the forward radiation and the direction of
specular reflection for the backward. The angular
distributions of the emitted radiation for electron energies
obtained with our linac are shown in Figure 1. The
emission angle of the maximum intensity is expressed by
θ≅

1.

γ

(2)

The peak intensity of transition radiation for 10 MeV
energy is one-tenth of that for 30 MeV, and the emission
angle for 10 MeV increases three times wider than that for
30 MeV. We, therefore, have to broaden the acceptanceangle of the photon detection system in order to make useof the transition radiation as a longitudinal phase space

Figure 3: Configuration of the OTR radiator.

FEL Technology

monitor for lower energy electrons.

EXPERIMENTAL SETUP
Figure 2 shows a schematic layout of the L-band linac.
The linac is equipped with a three-stage sub-harmonicbuncher (SHB) system composed of two 1/12 and one 1/6
SHBs in order to produce an intense single-bunch beamwith charge up to 91 nC/bunch. For single-bunch
operation, the electron beam with a peak current up to 28
A (typically 18 A in our experiments) and a duration of 5
ns is injected from a thermionic gun (EIMAC, YU-156)
into the SHB system. After being compressed to a singlebunch, the electron beam is accelerated to 10 – 30 MeV in
the 1.3 GHz accelerating tube. The electron beam istransported via an achromatic beam transport line to thewiggler for the FEL system.
The OTR radiator, which converts electrons to photons,
is placed at a position 320 mm downstream from the firstbending magnet as shown in Figure 3. The screen is analuminium plate having sizes of 55 × 40 × 1.6 mm3, and it
is tilted vertically by an angle of 45° with respect to the

Figure 4: The OTR image of the beam profile
measured using a CCD camera. The horizontal
direction is the bending orbital plane of the electron
beam. Left side of the image is lower momentum one.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Momentum dipersion [%]
-4

-2

0

2

Momentum dipersion [%]
4

-4

0.5

0
-20

0

1

Intensity [arb. units]

Intensity [arb. units]

1

-2

-10

0

10

20

Horizontal position [mm]Figure 5: Momentum profile of the electron bunch
obtained by integrating the OTR image in a vertical.
bending orbital plane, so that backward transition
radiation is emitted in the vertical plane. The first mirrorof the optical transport system is a concave mirror and it
is placed the focal length away from center of the radiator,
so that OTR image on the radiator, which diverges in thehorizontal direction, is mostly included in the depth offield of the first mirror.
At first we have used a CCD camera, instead of thestreak camera, for directly observing the OTR image. The
camera (TAKEX, FC300M) is a progressive shutter
camera and works with 659(H) × 494(V) pixels in 1/3
inch. A macro lens (Canon, J6X11) with a lens aperture of
40 mm was used for focusing. The camera was placed at a
distance of 210 mm from the OTR radiator. In thisconfiguration, an acceptance angle is approximately ± 0.1
radians, which is sufficient to capture the radiation
emitted by the 20 – 30 MeV electrons.

2

4

Mov.Ave.(OTR)
Ana.Mag+FC

0.5

0
-20

-10

0

10

20

Horizontal position [mm]Figure 6: Momentum profiles of the electron bunch.
The solid line is the momentum profile measured withan analyzer magnet and a faraday-cup current monitor.
The dashed line is the profile obtained by moving
average of the OTR profile within a ± 0.5 % width.
magnet slit is estimated approximately to be 1 %. It turns
out that the OTR monitor has a higher momentum
resolution than the momentum analyzer system usually
used.

SUMMARY
In order to measure the longitudinal phase-space profileof the electron beam, we are developing the measurement
system consisted of an OTR radiator, a bending magnet
and a streak camera. As a preliminary experiment, themomentum spectrum is obtained from the OTR profile,and the momentum resolution of the new system is
evaluated. We are now preparing for the longitudinal
phase-space measurement experiments.

EXPERIMENTAL RESULTS

ACKNOWLEDGEMENTS

An experiment is conducted with a single-bunchelectron beam of 26.6 MeV energy. The normalized
emittances are 165 π mm mrad in the horizontal direction
and 160 π mm mrad in the vertical direction. A measured
OTR image is shown in Figure 4. The horizontal and thevertical scales are 0.085 mm/pixel. Figure 5 shows themomentum profile of the electron bunch obtained byintegrating the image in a vertical. Since dispersion
function η is 0.4 m at the position of the OTR radiator,
momentum resolution of the measurement system isestimated to be 0.02 %/pixel. Using the resolution, themomentum spread of the OTR profile was evaluated to be
0.4 % (full-width half-maximum). Figure 6 shows amomentum profile measured with a momentum analyzer
magnet and a faraday-cup current monitor. The spectrum
width of the profile is 1.6 %. The dashed line in Figure 6
shows the profile obtained by moving average of the OTR
profile within a ± 0.5 % width. Since the both profiles
have a similar width, the resolution of the analyzer

The authors express their sincere thanks to Mr. T.
Yamamoto for his technical contribution and Mr. S.
Suemine for his support of linac operation. This researchis partially supported by Japan Society for the Promotionof Science (JSPS), Grant-in-Aid for Scientific Research(C), 18540273, 2006.

678

REFERENCES[1] R. Kato et al, Nucl. Instr. and Meth. in Phys. Res. A
445 (2000) 164.
[2] R. Kato et al, Nucl. Instr. and Meth. in Phys. Res. A
475 (2001) 334.
[3] R. Kato et al, Nucl. Instr. and Meth. in Phys. Res. A
483 (2002) 46.
[4] A. Doria et al., Nucl. Instr. and Meth. in Phys. Res. A
475, (2001) 296.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH041[5] J. Rönsch et al, “Longitudinal Phase Space Studies at
PITZ”, FEL’05, Stanford, August 2005, p.552,
http://www.jacow.org.

[8] T. Asaka et al, "Development of the quasi-nondestructive beam screen monitor", 27th Linear
Accelerator Meeting in Japan, (2002).

[6] H. Loos et al, “Experimental Studies of Temporal
Electron Beam Shaping at the DUV-FEL
Accelerator”, FEL’05, Stanford, August 2005, p.632,
http://www.jacow.org.

[9] L. Wartski et al, IEEE. Trans. Nucl. Sci. NS-20(1973) 544.

[7] S. Zhang et al, “Temporal Characterization ofElectron Beam Bunches with a Fast Streak Camera at
the JLab FEL Facility”, FEL’05, Stanford, August
2005, p.640, http://www.jacow.org.

FEL Technology[10] M. Jablonka et al, “Beam Diagnostics Using
Transition Radiation Produced By A 100 MeV
Electron Beam”, PAC’91, San Francisco, May 1991,
p.1534.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

A COMPACT LOW EMITTANCE DC GUN EMPLOYING SINGLECRYSTAL CATHODE OF LaB6*
K. Kasamsook#, K. Nanbu, M. Kawai ,K. Akiyama, F. Hinode, T. Muto , T. Tanaka, M. Yasuda,
H. HamaLaboratory of Nuclear Science, Tohoku University,
1-2-1 Mikamine, Taihaku-ku, Sendai 982-0826, Japan
Abstract
Development of an electron gun capable of producing
low emittance is in the interests of further applications ofhigh brightness electron beam such as Smith-Purcell FEL[1] for example. A prominent point of this DC gun is that
operation high voltage is very low (50 kV). Since a higher
beam current of the macropulse is required in general, acathode should have higher current density, while thesmaller size of the cathode is preferred for lower
emittance. Consequently we have chosen single crystal
LaB6 as the cathode, which can provide higher current
with good homogeneity emission. Some numericalcalculations have also been performed. There are somegood agreement in calculated results between them.
Numerical calculations show a normalized rms emittanceis expected to be less than 5 S mm mrad. A state-of-theart electron source will possibly open new scientificopportunities in the many fields.

INTRODUCTION
Nowadays, the demand for high-brightness electron
gun has increased dramatically to achieve many
applications in the field of electron beam technolygy. The
low emittance DC electron gun at LNS is one of thecandidates. This DC electron gun has no grid which
would degrade beam emittance. The cathode is made ofmaterials with the low work function, and heated to 1700
- 1900 K for producing electrons. We have employed thecathode voltage of -50 kV with respect to grounded anodeand variable pulse duration from 1 to 5 Psec. This low
voltage choice can make the entire system to compact.
The schematic diagram of DC gun power supply is shownin Fig.1. In spite of such low voltage, the emittance canbe reduced to very small because of a very short distance
between the cathode and the anode. In order to produce
low emittance beam, the cathode size should be small, sothat the higher current density is required. Such highcurrent density can be realized by some cathode materials
such as single crystal LaB6 [2] or CeB6 [3].The design
parameters and the drawing of the low emittance DC
electron gun are shown in Table 1 and Fig.2, respectively.

Figure 1: The schematic diagram of DC gun power
supply.
Table 1: Design parameters of electron gun.
Beam energy

50 keV (Max.)

Peak current>300 mA

Pulse width (FWHM)

1-5 Psec

Repetition rate

300 pps (Max.)

Normalized emittance<10 S mm mrad.

Normalized thermal
emittance

0.25 S mm mrad**theoretical
1.75 mm.

Cathode diameter

Cathode___________________________________________*Work supported by KEK grant for accelerator science.
#kasam@lns.tohoku.ac.jp

680

Figure 2: The low emittance DC electron gun.

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THE LOW EMITTANCE DC GUN
LaB6 cathodeThe normalized rms thermal emittance of electrons
emitted from a hot cathode is followed by equation (1):H n,rmsrc
2k BT
mo c 2(1), 

where rC is the cathode radius, kB is Boltzman's constant,
m0 is electron rest mass and T is the cathode absolutetemperature. From the above relation, in order to obtainthe small emittance less than 1 S mm mrad required for an
example, the X-ray FEL application, the diameter of thecathode must be in the range of a few mm. On the other
hand, high emission density (~12 A/cm2) is required to
produce a several hundred miliampere peak current fromthe small surface. The LaB6 or CeB6 can emit such an
intense current over long lifetimes. A single crystal ispreferable for obtaining low emittance because of its
extremely flat surface with low porosity after surface
material evaporation. The emission density is more
uniform because the crystal orientation is the same over
the whole surface. In recent years, single crystal LaB6
cathodes are widely used for scanning electron
microscope (SEM) and superior stability has been
demonstrated. So, we decided to use a single-crystal LaB6
cathode with a flat crystal surface shown in Fig.3. The
diameter of our LaB6 cathode is 1.75 mm. The 300 mA
peak current will be produced when the cathode is heatedto ~1900 K at vacuum level of 10-8 torr or better. The
theoretical thermal normalized emittance is 0.25 S mm
mrad.

Figure 3: The assembly of single-crystal LaB6 cathode.

High-voltage power supply
A high voltage DC thermionic gun uses a heatedcathode to produce electrons, which are then initiallyaccelerated with a DC pulse voltage. A low energy
electron gun high-voltage power supply was developedfor 0~-50 kV with 300 mA a peak current, a pulse widthof 1-5 Psec, and pulse droop 0.1%, respectively. The
wehnelt voltage can be adjusted from 0~-1 kV. In
addition, a floating bias voltage can be applied between

FEL Technology

THPPH042

the cathode and the wehnelt to optimize the electric field
for achieving the lowest emittance. In the case of theheater power supply, we use 1 Vdc and 12 A maximum
current to feed the LaB6 cathode.
The high-voltage power supply was tested by loadingat an electron gun system to generate an electron
beam.The beam current was measured by the Faradayplate. The cathode was heated up to ~1800 K and thecurrent, 200 mA, was measured in the test chamber byapplying 10 W of heater power. So, one of reasons toachieve peak current, 300 mA, is that we have to increase
the absolute temperature of the cathode. Up to now, thecathode has been operated for 1000 hours without failure.
Fig. 4 shows the measurement waveform of theaccelerating voltage and beam current.

Figure 4: The measurement waveform of the accelerating
voltage and beam current.

NUMERICAL CALCULATION RESULTS
We performed a computer simulation using 2
dimensional simulation code [KUAD2 v2.21] developed
by Kyoto University [4,5] for 50 keV, 300 mA beam
current and 15 mm cathode-anode distance in simple
model. As shown in Fig.5, the beam trajectories diverge
too much including the emittance growth due to spacecharge, which would result in a rapid increase in beam
spot size. Nevertheless, the normalized emittance fromthe anode exit still has a small value (4 S mm mrad) at thelongitudinal position far from the anode. Fig.6 shows themacro-particle distribution and the phase space
distribution at the position 200 mm from the cathode. In
addition, the simulation result shows electric field near
the cathode surface is very sensitive to the emittance
growth, which means the mechanical positioning of thecathode is very important. So we need special bias
voltage between cathode and wehnelt to manipulate theelectric field around cathode surface. On the other hand,
we developed the 3 dimensional self-developed code 3-D
FDTD [6] and compared with 2 dimensional simulation
code. The trend of position dependence of the emittanceis good agreement between them, and both of them still
result in the small value of normalized emittance. The
result of electron beam extraction and normalized
emittance is shown in Fig.7, and the macro-particle

681

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Proceedings of FEL 2006, BESSY, Berlin, Germany

distribution and phase space distribution at the end point
are shown in Fig.8.

Figure 8: The macro-particle distribution and phase space
distribution at the end point according to a simulation
with 3D FDTD.

Figure 5: An electron beam extraction and normalized
emittance of 300 mA in a DC gun according to asimulation with KUAD2.

In another result of the 3D FDTD simulation, weapplied bias voltage between wehnelt and cathode to
manipulate the electric field around the cathode surface asshown in Fig.9. At the low bias voltage, a little focussing
action, therefore, the emittance is gradually grow andbecome smoothly when the bias voltage was increased
from 200 V to 400 V. The minimum point of emittance
was shifted backward to cathode side by increasing ofspecial bias voltage. At the high bias voltage, the negative
field from wehnelt predominates and deflects the electron
beam away from anode, so the 600 V case shows the overcorrection of emittance. This result shows that we canmanipulate the equipotential line near the cathode surface
by adjusting the special bias voltage to optimize theextracted beam emittance.

Figure 6: The macro-particle distribution and phase space
distribution at the position 200 mm from cathodeaccording to a simulation with KUAD2.

Figure 7: An electron beam extraction and normalized
emittance of 300 mA in a DC gun according to asimulation with 3D FDTD.

682

Figure 9: The bias voltage dependence of normalized
emittance.

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH042

SUMMARYREFERENCES

Presently the DC gun has been examined on a test
stand, and characteristics of the extracted beam from thegun are measured. Some numerical calculations have also
been performed using 2 dimensional code and 3
dimensional self-developped code. There are some good
agreement in calculated results between them. Moreover,both of them show the small value of normalized
emittance. So that, the beam transportation after the gun
should be carefully designed to keep such small emittanceand utilize the beam. We can also apply special bias
voltage to manipulate the electric field near the cathodesurface.

[1] K. Kim et al., Nucl. Instr. And Meth. A 475 (2001)
158.
[2] H. Kobayashi et al., Emittance Mearsurement for
High-Brightness Electron Guns, 1992 Linear
Accelerator Conf., Ottawa, Canada, August 1992.
[3] K. Togawa et al.,”CeB6 Electron Gun for the Soft Xray FEL Project at Spring-8”,FEL2003, Tsukuba,
Japan, September 2003.
[4] K. Masuda, private communication.
[5] K. Masuda, Development of Numerical Simulation
Codes and Application to Klystron Efficiency
Enhancement ,Ph.D thesis , Kyoto University(1997).
[6] H. Hama, et al., Nucl. Instr. And Meth. A 528 (2004)
371.

ACKNOWLEDGEMENT
This work was supported by the KEK grant for related
university accelerator science and the authors would liketo thanks Prof. Kai Masuda for his 2 dimensional code
calculation and the discussions.

FEL Technology

683

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Proceedings of FEL 2006, BESSY, Berlin, Germany

STABLE RF PHASE INSENSITIVE TO THE MODULATOR VOLTAGE
FLUCTUATION OF THE C-BAND MAIN LINAC FOR SCSS XFEL
Jong-Seok Oh1, 2, #, Takahiro Inagaki1, Katsutoshi Shirasawa1, Toru Hara1, Tsumoru Shintake1
1
RIKEN Harima Institute, 2PAL/POSTECH.
Abstract
The SCSS (SPring-8 Compact SASE Source) XFEL [1]requires extremely stable RF system in both amplitude
and phase. The pulse-to-pulse fluctuation of RF output ismainly caused by modulation of the klystron beamvoltage pulse, which is directly governed by the charging
stability of a klystron modulator. During R&D study on
beam stability, we found a special operation point, where
the beam energy gain is insensitive to the modulator
voltage fluctuation. This phase can cancel out the bothfluctuations and provide constant accelerating field. The
stable phase depends on the klystron parameters such as
the length of drift tube, operating voltage, efficiency. It is
about +9° in case of the C-band main linac for SCSS
XFEL. The bunch length after bunch compressor is so
short that additional longitudinal energy spread due to the
RF curvature is about 5% of the one caused by thelongitudinal wake field. The particle energy is highenough so that longitudinal defocusing is negligible. The
reduction of beam energy due to off-crest acceleration isless than 2%. This paper shows the analytical relation of
the stable phase. ELEGANT [2] simulation shows noappreciable degradation of the slice parameters.

RF SENSITIVITY
The klystron voltage is directly determined by the PFN
charging voltage in a modulator. The sensitivity of a
klystron voltage defined by⎛ dVK ⎞ ⎛ dVO ⎞ ⎛
⎞ ⎛
⎞
Z
Z
⎟ = ⎜1 + PFN ⎟ / ⎜1 + 1.5 PFN ⎟
⎟ /⎜
⎟
⎜
⎟
⎜
⎟
⎜
ZK ⎠ ⎝Z K ⎟⎠⎝ VK ⎠ ⎝ VO ⎠ ⎝sV = ⎜⎜

is obtained by using the Ohm’s law
VO = VK + Z PFN × I K ,(2)and the klystron beam current
I K = k V K1.5

(3)

where Vo is a PFN charging voltage, VK is a klystronvoltage, ZPFN is PFN impedance, k is a klystron perveance,
Zk is klystron impedance. At the nominal klystron voltage
where the impedance is matched, the typical sensitivity ofa klystron voltage becomes 0.8.
The RF phase φRF from a klystron [3]⎛INTRODUCTION
The stability of the beam acceleration is determined by
the fluctuation of both RF power and phase that are
mainly caused by the modulation of a klystron voltage
pulse, which is directly governed by the PFN (pulse
forming network) charging stability of a modulator.
Therefore, it is useful to define the sensitivities of the RFparameters such as klystron voltage, RF phase and RF
power by its relative stabilities to the one of a charging
voltage. This paper analyzes the sensitivities of RF
parameters and beam energy, and shows a special
operation point, where the beam energy gain is insensitive
to the modulator voltage fluctuation.
In general, off-crest acceleration makes the beamenergy more fluctuate. However, at certain phase, it ispossible for this fluctuation to be same as the one due topower fluctuation with opposite polarity in the fallingslope with respect to beam. This phase is preferable to get
the stable beam energy even under the voltage fluctuationof the klystron. This paper shows the analytical relation of
the stable phase and experimental verification.
The longitudinal profile of a bunch has to be managed
to fit the SASE requirements. Energy spread, slice
emittance and peak current are analytically evaluated andcompared with numerical results obtained by ELEGANT
simulation.

(1)

φ RF = φ o − 2π f t transit = φ o − 2π ⎜⎜c⎞⎛ L KLY ⎞
⎟⎜
⎟
⎠

(4)

⎟
⎝ λ RF ⎠⎝ v

is delayed from a driving input RF phase φo by the transit
time ttransit of a drift length LKLY between the input cavity
and the output cavity of the klystron with an electron
velocity v where λRF is a wavelength in a free-space, c isthe speed of light in vacuum. Therefore, the RF phasefluctuation of a klystron is−1.5⎛ dφ RF ⎞ ⎛ dV K ⎞ ⎛ L KLY ⎞ 2⎟=⎜⎟ γ −1γ −1⎜⎟ / ⎜⎜⎟⎜⎟⎝ 2π ⎠ ⎝ V K ⎠ ⎝ λ RF ⎠

(

) (

)

(5)

where γ is the Lorentz factor of the electron. And thesensitivity of the RF phase is−1.5⎛ dφ RF ⎞ ⎛ dVO ⎞ ⎛ LKLY ⎞ 2⎟≈⎜⎟ γ −1γ − 1 × sV
⎟ / ⎜⎜⎟⎜⎟⎝ 2π ⎠ ⎝ VO ⎠ ⎝ λ RF ⎠sφ = ⎜

(

) (

)

. (6)

The typical sensitivity of the RF phase at 350 kV is 1.26
for a C-band klystron.
The RF power PRF of a klystron is given by
PRF = η I K V K = η kV K2.5

(7)where η is the RF conversion efficiency of a klystron.
Therefore, the RF power fluctuation of a klystron is⎛ dPRF ⎞ ⎛ dV K ⎞ ⎛ dη ⎞ ⎛ dV K ⎞ ⎛ dk ⎞ ⎛ dV K ⎞⎜⎟ /⎜⎟ = ⎜⎜⎟+⎜⎟ + 2.5 . (8)⎟⎟ / ⎜⎜⎟ / ⎜⎜
⎜ P
⎟ ⎜
⎟
⎟
⎟
⎝ RF ⎠ ⎝ V K ⎠ ⎝ η ⎠ ⎝ V K ⎠ ⎝ k ⎠ ⎝ V K ⎠___________________________________________#

jsoh@postech.ac.kr

684

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany⎛ dP ⎞ ⎛ dV ⎞s P = ⎜⎜ RF ⎟⎟ / ⎜⎜ O ⎟⎟ ≈ sη + 2.5 sV⎝ PRF ⎠ ⎝ VO ⎠(9)where sη is the sensitivity of efficiency given bysη = (dη / η ) / (dVo / Vo )

1.01
0.50%
0.25%
0.00%
-0.25%-0.50%

1.00
Relative Energy Gain

Figure 1 shows the calculated relative variation of RF
power, efficiency and perveance due to the klystronvoltage fluctuation of the C-band klystron (Toshiba
E3746A). The perveance dependency is relatively sosmall that it is neglected in the sensitivity of the RF power

0.99

0.98

0.97

.

(10)

0.96
-30

The efficiency variation of a klystron at low voltage haslarge effect on the sensitivity of RF power. The typicalsensitivity of the RF power at 350 kV is 2.4 for the Cband klystron.
108(dη/η)/(dVk/Vk)
Relative Change

-20

-10

0

10

20

30

Phase (degree)

Figure 2: Relative energy gain vs. RF phase with charging
voltage variations at the klystron voltage of 350 with a Cband klystron. The stable phase is +7.2° at 350 kV level.
Figure 3 shows the sensitivity of energy gain for the
crest phase and the off-crest phase. The typical sensitivityof the energy gain at 350 kV is 1.2 for a C-band unit. Theenergy gain is insensitive over wide range of klystronvoltage at the off-crest phase of +9°. A little large angle
than +7.2° provides better sensitivity for wide operating
range below 350 kV. The loss of energy gain by the offcrest acceleration is 1.2%.

(dPrf/Prf)/(dVk/Vk)

6

THPPH043(dk/k)/(dVk/Vk)

4

2

0

5

-2
150

4

(dE/E)/(dVpfn/Vpfn) @ crest
250

300

350

(dE/E)/(dVpfn/Vpfn) @ off-crest

400

Klystron Voltage (kV)

Figure 1: Relative variation of RF power (Prf), efficiency(η), and perveance (k) of a C-band klystron.

ENERGY SENSITIVITY(dE/E)/(dVpfn/Vpfn)

200

3
2
1
0
-1

The energy gain of an accelerating unit is-2

E ∝ PRF cos φ RF

.

(11)

(12)

Using Egs. (6) and (9), the sensitivity of energy gain is⎛ dE ⎞ ⎛ dVO ⎞⎟ = 0.5 sη + 1.25 sV − 2π tan φ RF s φ . (13)sE = ⎜⎟ /⎜⎜⎟⎝ E ⎠ ⎝ VO ⎠Figure 2 shows the relative energy gain of C-band units
as a function of operating RF phase with charging voltage
variations at the klystron voltage of 350 kV. On a certain
RF phase of the falling slope with respect to beam, which
is marked by the circle in the figure, the amplitude issomewhat constant because the both fluctuations arecancelled out, which provides constant accelerating field.
The energy gain is insensitive to the modulator voltage
fluctuation around the stable phase satisfying following
condition⎛

1 ⎞⎟(0.5 sη + 1.25 sV ) .
⎜ 2π s ⎟φ⎝⎠

tan φ RF = ⎜FEL Technology

200

250

300

350

400

Klystron Voltage (kV)Thus, its relative fluctuation by a klystron is⎛ dP ⎞dE⎛ dφ ⎞= 0.5 × ⎜⎜ RF ⎟⎟ − (2π × tan φ RF )⎜ RF ⎟ .
E
P⎝ 2π ⎠⎝ RF ⎠

150(14)

Figure 3: Relative variations of energy gain due to thefluctuation of the PFN charging voltage for crest phaseand off-crest phase of +9°.
Including the effect of relative phase jitter σφ between
injected beams and C-band RF at an arbitrary phase, thesensitivity of energy gain becomess E2 = (0.5 sη + 1.25 sV − 2π tan φ RF sφ )2

σ φ ⎞ ⎛ dVo ⎞⎟⎟ /⎜+ (2π tan φ RF ) ⎜⎜⎟ ⎜⎟⎝ 2π ⎠ ⎝ Vo ⎠
2⎛

2

2

.

(15)

EXPERIMENTS
The SCSS prototype accelerator has a C-band main
linac after an S-band unit of an injector [4]. The main
linac has two RF sources and increases the beam energy
from 50 MeV to 250 MeV. The beam energy fluctuation ismeasured for different RF phases by the screen monitor
located at the middle of a chicane having a dispersion of685

THPPH043

Proceedings of FEL 2006, BESSY, Berlin, Germany

150 mm. Figure 4 shows the measured beam energy
fluctuation of the C-band main linac. The beam energy
stability at crest for two C-band units is 0.34% (6σ); thestability of energy gain per unit is 0.59% (6σ). The energy
fluctuation is sensitive to the operating phase and also isasymmetric with respect to the crest phase. The energy
fluctuation at the off-crest phase of +10° is reduced to
50% level of the one at crest acceleration.

4.0(dE/E)/(dE/E@crest)

3.5
3.0
2.5
2.0

0%
50%
100%
200%

1.5
1.0

C-band (060711)
C-band (060614)

0.5
0.0
-40

-30

-20

-10

0

10

20

30

40

Phase (degree)

Figure 5: Stability of energy gain per C-band unit
normalized by the one at crest phase for relative phasejitter of 0%, 50%, and 100%.

BEAM QUALITIESFigure 4: Beam energy fluctuation vs. RF phase of Cband main linac of SCSS prototype accelerator (0.01mm/pixel).
Figure 5 shows the stability trend of energy gain per Cband unit normalized by the one at crest phase:
22⎛
2π tan φ RF sφ ⎞⎛ dE ⎞ ⎛ dE ⎞⎟= ⎜1 −⎜⎟ /⎜⎟⎜0.5 sη + 1.25 sV ⎟⎠⎝ E ⎠ ⎝ E ⎠ crest ⎝

.

(16)

Each curve has different relative phase jitter normalized
by the energy stability at crest, (σφ/(2π))/(dE/E)crest. For
example, with 0.2% energy stability at crest, 50%
normalized phase jitter corresponds to 0.1% relative
phase jitter that is equivalent to 0.36°. Measured data (Cband 060614) in Figure 5 agree to the case of 50%
normalized relative phase jitter. It means that the phasejitter is about 1.1° that corresponds to the timing jitter of
0.52-ps at C-band frequency.
At the off-crest phase satisfying Eq. (14), the energy
stability becomes.

(17)

Then, it becomes ~ σφ/(2π) at 350 kV. Therefore, the totalenergy stability is directly determined by the phase jitter.
Measured data (C-band 060614) indicate that theminimum fluctuation of the beam energy is located atabout +8° from the crest as expected. The fluctuation at
this phase is limited by the phase jitter. The different setof measured data (C-band 060711) shows that thenormalized relative phase jitter is increased to 100%,
which is identified later to be caused by the instability ofa maser RF oscillator.

686

Zo c

π a2

(18)

exp(− s / s oo )

where
g
a
(
)2 ,
8 α ( g cell / Lcell ) Lcell(19)

α (γ ) = 1 − 0.4648 γ − 0.0704γ ,

(20)

soo =

and

2

0.5 sη + 1.25 sV ⎞⎛ σ φ ⎞⎛ dE ⎞ ⎛⎟⎜⎟⎜⎟=⎜⎟⎜ 2π ⎟⎜sφ
⎝ E ⎠ ⎝⎠⎠⎝

W (s) =2σ ⎞ ⎛ dE ⎞ 2+ (2π tan φ RF ) ⎜⎜ φ ⎟⎟ / ⎜⎟⎝ 2π ⎠ ⎝ E ⎠ crest
2⎛

The geometry of a C-band accelerating structure withiris radius a, cavity radius b, gap length g, and cavity
period Lcell is shown in Figure 6. The short-range
wakefield of the structure is evaluated by the K. Bane’s
formula [5]and Zo = 120π [Ω].
g
2a

2b

Lcell
C-L

Figure 6: The geometry of a C-band accelerating
structure: a = 7.6 mm, b = 21.2 mm, g = 15.2 mm, andLcell = 19.682 mm.
With structure parameters of a C-band unit, soo = 982
μm, and W(0) = 0.623 kV/pC/m. This paper uses thebeam parameters given in the “Optimization of
Parameters” of the 6-GeV SCSS CDR [1] where theaccelerating gradient is 34.0 MV/m after the second
bunch compressor BC2. The compressed bunch length s
after BC2 is 24 μm. It is so short that the wakefield overthe bunch is close to W(0), then the longitudinal energy
spread of a bunch due to the short-range wakefield with abunch charge Q over a total accelerator length L isapproximately

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany
ΔW ≈ −eQW (0) L .

(21)

There are 25 accelerator modules in the C-band main
linac of the SCSS 6-GeV machine. Each module has 4units of 1.8-m long structures. Therefore, total
accelerating length is 180 and the longitudinal energy
spread becomes -44.6 MeV. Considering the effect offinite bunch length, it is -40.1 MeV. The net change ofhead-tail energy spread through the C-band linac obtainedby ELEGANT code is – 41.3 MeV as shown in Figure 7.

Head
Δγ = -50

THPPH043

SUMMARY AND DISCUSSION

Δγ = +30.7
Head

800 MeV

6 GeV

Figure 7: Structural wake effect on the longitudinalenergy profile of a bunch (left: 800-MeV beam at the inletof C-band main linac, right: 6-GeV beam after C-band
main linac, bunch head at left side).
There is energy gain difference ΔWRF between the headelectron and the tail electron of a bunch, which is causedby the phase difference of RF fields along the bunch.
ΔWRF = Δ[eEL cos φ ] ≅ −eEL sin φo ΔφFigure 9: Horizontal slice emittance (top), vertical slice
emittance (middle), and peak current (bottom) profile of abunch (left: on-crest acceleration, right: +9° off-crest
acceleration).

(22)

where e is electronic charge, E is peak accelerating field.
In case of 6-GeV SCSS design, eEL = 5200 MeV, and Δφ= 0.164° for s = 24 μm. Therefore, the energy spread dueto the RF fields becomes -2.33 MeV for the off-crest
phase of φο = +9°. This energy spread is 5.81% of the one
caused by wakefield. The ELEGANT simulation shows
the difference of -1.53 MeV as shown in Figure 8.

The SCSS XFEL is a challenging machine that requires
extremely stable RF system. Therefore, it is critical issue
to realize stable RF system for both phase and amplitude
to provide stable XFEL. The phase-dependent stability
characteristics are in detail analyzed and examined. It is
confirmed that the off-crest phase of around +9° provides
better stability in case of the C-band main linac for SCSSXFEL if phase jitter is small. The low-level RF control
has to provide better stability than the one of a klystron
modulator for this scheme to be effective. The reductionof beam energy due to off-crest acceleration is about 1%.
The additional longitudinal energy spread due to the RF
curvature is about 5% of the one caused by thelongitudinal wake field and there is no appreciable
degradation of the slice parameters.
The RF unit for a velocity buncher or a bunch
compressor is more sensitive to the RF fluctuation
because of the off-crest operation to provide a necessaryenergy chirp. For example, the energy fluctuation is morethan 4 times higher than the crest one at the typical off
crest phase of -40° for SCSS accelerating units between
BC1 and BC2.

REFERENCES

Δγ = 30.7

Δγ = 33.7

On-crest+9º Off-crest

Figure 8: Comparison of longitudinal energy profile of abunch for the on-crest acceleration (left) and +9° off-crest
acceleration (right).

[1] http://www-xfel.spring8.or.jp[2] M. Borland, “ELEGANT” LS-287, ANL, Argonne,
IL 60439, USA.
[3] Linear Accelerators, P. M. Lapostolle and A. L.
Septier, editors, North Holland Publishing Company,
p322 (1970).
[4] T. Hara, “Electron Beam Simulations on the SCSS
Accelerator,” the 26th International Free Electron
Laser Conference, Italy, 2004.
[5] K. L. F. Bane, “Short-Range Dipole Wakefields inAccelerating Structures for the NLC,” SLAC-PUB9663, LCC-0116, 2003.

The slice parameters such as slice emittance and peakcurrent are dominant governing parameters of SASE
process. We have to keep the slice parameters as good as
possible. It is confirmed that there is no appreciable
degradation of slice parameters for off-crest acceleration
as shown in Figure 9.

FEL Technology

687

THPPH044

Proceedings of FEL 2006, BESSY, Berlin, Germany

ANALYSIS OF INVERTER CHARGING WAVEFORM FOR ULTRASTABLE SCSS MODULATOR
Jong-Seok Oh1, 2, #, Takahiro Inagaki1, Katsutoshi Shirasawa1, Tsumoru Shintake1
1
RIKEN Harima Institute, 2PAL/POSTECH.
Abstract
The SCSS (SPring-8 Compact SASE Source) XFEL [1]requires ultra stable RF sources. The SCSS smart
modulator driving a klystron RF source uses an inverter
charging system. Therefore, the stability of RF sources is
directly determined by the one of inverter power supplies.
The regulation and the stability of an inverter depend on
not only the structure of inverter topology but also thefidelity of a signal monitoring. For better stability, weneed stable and adequate monitoring of a charging voltage.
The charging waveform is composed of a net PFN (pulse
forming network) voltage and ripple components that is
related to the system-dependent circuit parameters. This
ripple is proportional to the ratio of the PFN capacitanceto the stray capacitance of a pulse transformer and a
klystron load. We can manipulate the feedback signal withsuitable filtering but it is shown that the charging stability
depends on the way of signal conditioning also. The longterm drift has to be minimized by the temperaturestabilization of the probe and feedback circuits.

INTRODUCTION
The SCSS XFEL uses normal conducting technology
for beam acceleration, in which pulse-to-pulse powerfluctuation in RF-system dominates beam stability. The
RF output is mainly fluctuating due to the pulse-to-pulse
variation of a klystron voltage that is determined by the
PFN charging voltage of a modulator. The inverter is
responsible to the RF stability because it charges the PFN
capacitor. In order to stabilize the charging level, we needa clean and stable signal for the PFN voltage. There are
not only pulse forming network capacitors but also
protective series resistors and distributed reactive
components of a pulse transformer and a klystron load in
the charging path. Therefore, the charging waveform
becomes somewhat complicated. The understanding of
the charging waveform and the proper conditioning of
feedback signal is necessary to realize an ultra stablecharging performance. This paper shows the detailanalysis of the charging waveform of SCSS modulatorsand the stability dependency on the signal conditioning.

SCSS MODULATOR
Figure 1 shows the circuit topology and its charging
waveform for inverter charging scheme using a constantcurrent source. This scheme is compared with the ones of
the traditional resonant charging scheme using a constantvoltage source. The inverter topology provides highreliability: a thyratron switch is safely turned off because___________________________________________#

jsoh@postech.ac.kr

688

next charging schedule is digitally controllable, it isinherently fail-safe system under short-circuit condition
due to the current limit feature of a constant current
power supply. In addition, it is naturally compact by using
a high frequency inverter. Also it has other attractive
features: expandability, easy maintenance, and flexible
control interface [2]. These features are well matched to
the next generation modulator for SCSS XFEL facility.

Figure 1: Basic circuits and charging waveforms of a
voltage source and a current source power supply.
Figure 2 shows the simplified circuit diagram of SCSS
modulator that consists of a PFN, a thyratron switch, apulse transformer, and an inverter power supply as a PFN
charging unit. The inverse voltage is limited by a tailcircuit absorbing the magnetic energy stored in the pulse
transformer. The main specifications are as follows; 114MW peak power, 30-kW average power, 60-pulse persecond, 3.8-μs pulse width, 1:16 step-up ratio, 350-kV
peak voltage (secondary side) [3].
Rcharging
HV
InverterPower
SupplyRINV

ZPFN, N Stage

REOLC
DINV

DTAIL
RSNUB

Thyratron

Pulse
Transformer
1:n

CSNUB
RTAIL

Figure 2: Simplified circuit diagram of SCSS modulator.
Figure 3 shows detailed charging waveforms of a Cband modulator (CPFN = 0.4 μF) around the charging levelof 38 kV. The average increment of charging step ΔVPFN
is about 100 V with a switching frequency f of 34.6 kHz;
therefore, the average charging current Idc is 1.38 A at thischarging level according to the following equation.
I dc = C PFN ΔVPFN f(1)

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany
The charging voltage is not rising smoothly andmonotonically but includes high-frequency spikes. The
magnitude of spikes is larger than the increment ofcharging level for each switching cycle. The voltage
waveform at the pulse transformer secondary shown in
the figure has similar oscillating pattern. Therefore, it isexpected that the spike is made by the circuit components
connected in parallel to the pulse transformer. The noisy
spikes seem to be harmful for the feedback circuit tocorrectly compare the charging level with a reference
level.

I ac
4 ∞cos nωt=− ∑π n = 2 ( n + 1)(n − 1)
I peak=−

THPPH044( n = even only )4 1
1[ cos 2ωt + cos 4ωt +15

π 3K] ≈ − 34π cos 2ωt(2)

The output current from an inverter power supply, I,
has to flow through the series impedances of R1, R2, ZPFN,and ZL in the equivalent charging circuit shown in Figure
5. The charging current flows through the complicatedload impedance network ZL. The spike voltage is
generated by oscillation caused by the total stray
capacitance and the magnetizing inductance of a pulse
transformer.
R1

ZPFN

R2

ZL
I

Figure 3: Waveforms of charging buckets (Upper box:
charging voltage waveform, Lower box: expanded viewof square box marked on the upper box for pulse
transformer secondary voltage (upper curve, 1.18 kV/div)
and PFN charging voltage (lower curve, 100 V/div),
Horizontal: 100 μs/div)

ANALYSIS OF CHARGING WAVEFORM
In order to analyze the circuit response of charging
current, it is useful to know the Fourier components ofcharging current. The inverter output is a full-wave
rectified current as shown in Figure 4.
1.2
Relative Magnitude

1.0
0.8
0.6
0.4
0.2
0.0
0

5

10
Angle (rad)15

20

Figure 4: Full-wave rectified current (thick blue line) andFourier series.
It has an average value of Idc and higher frequency
components Iac. The average current is 2/π of a peak value
Ipeak. The second harmonic current is dominant and it is4/(3π) of the peak value according to Eq. (2). Therefore,
the magnitude of second harmonic current is 66.7% of theaverage charging current; Iac = (2/3) Idc.

FEL Technology

DI

S

R3

Figure 5: Equivalent charging circuit.
To improve the present stability of SCSS modulators, itis planed to use an ultra stable inverter power supply thatis operating in parallel with a main inverter. The concept
and design example is described in Ref. [4]. This inverter
has small charge per switching with higher switchingfrequency. The frequency response of the charging
network of a SCSS modulator measured because of thepossibility of a resonance, which distorts the charging
waveform. Figure 6 shows the measured data and thecalculated frequency response by the circuit model. The
phase transition occurs at 40 kHz that is caused by theparallel resonance driven by the magnetizing inductance
Lmag of a pulse transformer and total stray capacitance
Cstray of a pulse transformer and a klystron load. Series
resonance at higher frequency of Figure 6-(b) is driven by
Cstay and a series inductance in the charging path.
The second harmonic current of a SCSS modulator iscapacitive-coupled because its frequency is higher that 40
kHz. There is no resonance till 250 kHz and the gain ismonotonically decreasing. Therefore, higher frequency isable to be applied without serious waveform distortion fora high precision inverter up to 100 kHz.
The ripple voltage, Vac introduced by the second
harmonic current through a stray capacitive impedance Xc(=2πfCstray) is given by
Vac = I ac X c = I dc /(6πfC stray ) .

(3)

The ripple factor defined by 2Vac / ΔVPFN is the relative
magnitude of the ripple voltage to the increment of acharging voltage per one cycle of an inverter switching.
By using Eq. (1) and (3), the ripple factor is689

THPPH044

Proceedings of FEL 2006, BESSY, Berlin, Germany
voltage (VPFN) has 100-V ripple with second harmonicfrequency. It shows that the DC component Idc is flowing
through the magnetizing inductance of a pulse
transformer (I_Lmag) and AC ripple current is mainly
flowing through the stray capacitance (I_Cstray). Figure7(b) is the charging waveform at the 38 kV level. The
former half of the full-wave rectified current is gradually
increasing to two-time large value than the initial one, andthe latter half is gradually decreasing to zero. Accordingly,
the diode in the tail circuit is turned on as the positive
primary peak is increasing. At last, it becomes half-wave
rectified waveform having a two times large peak current
but the net average charging current is still same.

(degree)

(dB)

(a)

Parallel
Resonance
SeriesResonance(a)(b)
Figure 6: Frequency response of a charging network of a
SCSS modulator: (a) measured data, (b) circuit simulation.
2 Vac / ΔVPFN = C PFN /(3πC stray ) .

(4)

Table 1 shows the summary of ripple voltage
parameters for the SCSS modulator. In order to verify thisevaluation, equivalent circuit analysis is performed.
Table 1: Ripple voltage parameters of charging waveform
PFN capacitance, CPFN
0.4 μF
Average charging current, Idc
1.58 A
Switching frequency, f
34.6 kHz114.2 V
Increment of charging, ΔVPFNStray capacitance, Cstray
25.9 nF
Ripple current, Iac
1.05 A
Charging impedance, Xc
Ripple voltage, Vac
Ripple factor, 2Vac /ΔVPFN

88.8 Ω
93.2 V
1.63

Figure 7 shows the simulated charging waveform withthe conditions given in the Table 1. Figure 7(a) is theinitial charging waveform. The net PFN voltage (VPFNV_primary) is monotonically increasing but the PFN

690

(b)
Figure 7: Simulated charging waveforms: “V_PFN” =PFN voltage from ground potential, “V_PFN V_primary” = net PFN voltage: (a) initial charging
waveform, (b) charging waveform around 36 kV.
The Fourier series of the higher harmonic for the halfwave rectified waveform depicted in Figure 8, is
described by
I ac
I peak==1
2 ∞cos nωtsin ωt − ∑π n= 2 (n + 1)(n − 1)2

(n even only )1
2 1
1
sin ωt − [ cos 2ωt + cos 4ωt +
2
π 3
15

K] .

(5)

The dominant term now has same frequency as theswitching one and its magnitude is 50% of the average

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH044

Voltage (V)charging current that is similar to the one of dominantterm for the full-wave rectified waveform. Therefore, its
ripple has same magnitude as the one of full-wave mode.
1.2
Relative Magnitude

1.0
0.8
0.6
0.4
0.2
0.0
-0.2

(a)

-0.4
5

10
Angle (rad)15

20

Figure 8: Half-wave rectified current (thick blue line) andFourier series.

EFFECT OF SIGNAL FILTERINGThe charging voltage is determined by the commandreference. The reference level is compared with afeedback signal coming from a high voltage probe.
Therefore, not only the reference level but also the
feedback signal has to have high fidelity and stability.
Figure 9 shows how improper conditioning of monitoringsignal affect the charging stability under the reference
level of 30 kV. The high frequency ripple on the risingslop of a feedback signal is well filtered out in the case(a); 1-kHz low pass filter. The charging voltage isregulated at the level higher than the reference one.
Therefore, it is not able to correct the time dependent
variation of the droop of top level. If the circuit has low
frequency cut below 0.5 Hz, then, the actual PFN voltage
is gradually rising even the comparator circuit is feelingthe same level of feedback signal as shown in the case (b).

SUMMARY AND DISCUSSIONThe SCSS modulator has many features fitting to the
XFEL application, which are provided by adopting theinverter power supply that is one of governing factors forthe stability of electron beams of SCSS linac. The ripple
voltage superimposed on the PFN charging waveform isanalyzed as a function of circuit parameters. It is foundthat the ripple factor is proportional to the ratio of the
PFN capacitance to the stray capacitance. The
conditioning of the feedback signal has large effect on theregulation of PFN voltage. The understanding of thecharging waveform and the proper conditioning of
feedback signal is essential to realize an ultra stablecharging performance.
It is possible to measure the net differential voltage byusing an additional probe that has equally calibrated andbalanced for high frequency response.
The high voltage components of a probing system suchas resistors and capacitors are temperature sensitiveelements. The devices on the low level feedback circuits

FEL Technology

Voltage (V)0(b)
Figure 9: Regulation characteristic for different filteringof a feedback signal with high voltage probe attenuationof 1/10,000: (a) 1 kHz low pass filter, (b) 0.5 Hz high passfilter.
also have thermal drift. Therefore, it is essential tostabilize the temperature of the probe and feedback
circuits to remove the long-term slow drift of beamenergy.

REFERENCES[1] http://www-xfel.spring8.or.jp[2] J. S. Oh, et. al., “Development and Application of an
Inverter Charging Supply to a Pulse Modulator,” theXXI International LINAC Conference, Korea, 2002.
[3] T. Inagaki, et. al., “High Power Test of the Compact,
Oil-Filled Modulator for C-band Klystron,” the third
Asian Particle Accelerator Conference, Korea, 2004.
[4] J. S. Oh, et. al., “Development of an Ultra Stable
Klystron-Modulator for PAL XFEL,” the 27th
International Free Electron Laser Conference, USA,
2005.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

ELECTRO-OPTIC SAMPLING METHOD USING HIGH DC VOLTAGE
APPLYING SETUP*
Yong-Woon Parc#, Changbum Kim, Jung Yun Huang, Jangho Park, Sung-Ju Park, In Soo Ko,
PAL, Pohang, Korea
Xiang Dao,
Department of Engineering Physics, Tsinghua University, Beijing, China.
Abstract
A RF photo-cathode (RF PC) gun with 1.6 cell cavity is
installed at GTS(Gun Test Stand) being built at the
Pohang Accelerator Laboratory (PAL). The short, intense,and low emittance electron beams are produced by the RF
PC gun. For the successful construction of PAL-XFEL,
the timing jitter and bunch length of the beam at the exitof the gun should be measured accurately. EOS (ElectroOptic Sampling) is a very promising method to measure
the jitter without any interference with the electron beam.
The spatially resolved method will be used in thisexperiment, which is a single shot measurement using
cooled CCD carmera due to very low energy. Before themeasurement with the beam at the exit of the gun, thecalibration experiment is done with DC high voltage
applying setup with 1mm thick ZnTe crystal. The
broadening of our laser pulse by the ZnTe crystal will bemeasured with auto-correlation method to know theresolution limit in this experiment and to do data analysis
properly. In this presentation, the result of calibration
experiment will be presented with a description of theexperiment in detail and simulation result for low energy
beam.

INTRODUCTION
EOS (Electro Optic Sampling) method to measure short,intense electron beam which is essential to construct
XFEL light source is developed greatly in last few year
[1,2,3,4]. For the successful construction of XFEL lightsource, the monitoring of timing jitter of electron beam is
crucial in online condition. The method can be used formonitoring the timing jitter of all section of the lightsource for example injector, bunch compressor, undulator
sections. We are now trying to measure the electron beamat the injector part of XFEL to be constructed in PAL. A 2
MeV electron beam with a tunable bunch length and
0.2nC bunch charge has recently been realized at
PAL[5,6].
* This work is supported by the KOSEF under the contract number
R01-2006-000-11309-0 and also by the Ministry of Science andTechnology.
#
young1@postech.ac.kr

692

THEORYThe theory for the signal detection scheme of EOS iswell described in ref[7], so we give only a short summaryof it here.

Balanced detection scheme
The vertical and horizontal polarized part intensities of
the incident laser to the ZnTe crystal is changed due to thebirefringence of the crystal induced from the electron
electric field. The analytic expression is in Eq.(1),(2)

Γ=

ω0 d
c

( nh − nv ) =

πd 3
nr E
λ0 0 41 0(1)

I h − I v = E h − E v = E02 sin ( Γ )
2

2

(2)

where the Γ is the relative phase shift between the twopolarized parts of the laser field, and d is the crystal
thickness.

LayoutIn order to understand the theory for the signal
detection scheme of EOS, the layout is described in detailin Fig. 1. The linearly polarzed laser experiences thebirefringence in EO crystal due to electric field from theelectron beam. The difference of the vertical andhorizontal part of the laser field can be measured withquarter wave plate and Wollaston prism with sine function
proportionality as mention in above section.
EO crystal 1

I0

4

wave plateΓ = 15D

Wollaston prismΓ = 105D

Ih
Iv

c
Figure 1: Layout of Electro-opti sampling

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

DC SETUP EXPERIMENT
To test the EO crystal response to the electric fieldstrength, we made a high DC voltage applying setup. The
result is shown in Fig. 2.

THPPH045

know the response of the electric field inside the crystal.
We know the speed of each Fourier component in the
crystal, which make us possible to reconstruct the field
profile passing through the crystal. The field profile isshown in Fig. 3 with time domain representation.

Ring approximation of electron beam
The exact field profile of the electron beam iscomplicated to expressed in an analytic form. Instead ofthe exact field profile, we can use the ring approximation
which has an exact solution which allowed the relativistic
expression. The result showed that we can make almost
exact field profile with only two terms, one is monopole
term and the other is quadrupole term. The quadrupoleterm amplitude is very small compared to the monopole
term. The Equation(3) showed the relativitic expression of
the ring approximation.
Figure 2: The response of the ZnTe crystal in DC electricfield. The circle(red line) is theory, the triangle(green line)
is balanced detected result and the square(black line) is
measured result from the vertical part of the laser using
single photodiodeThe result showed that the crystal which thickness is
3.2 mm used in this experiment followed the theory well.

SIMULATION

Simulation method for Thz propagation
The ZnTe crystal showed frequency dependent
refractive index which is propotional to the electric field
called Pockel effect. The electric field profile due to theelectron longitudinal profile is Fourier transformed tor⎡⎤⎢ 2 2 2 2 3/ 2⎥(γ v t + r )
⎥
qγ ⎢
⎢
⎥ (3)
Er =
2
2
2
2
⎛
4πε 0 ⎢
5r ( 2γ v t − r ) ⎞ ⎥
2r
a2 ⎜
⎟⎥
−
+
⎢
4 ⎜ ( γ 2 v 2 t 2 + r 2 )5 / 2 ( γ 2 v 2 t 2 + r 2 ) 7 / 2 ⎟ ⎥⎢⎣⎝⎠⎦In the above equation, q is the charge of the electron
beam and v is the velocity of the beam and r is the
distance between the laser passing point and the electron
beam. In Fig. 4, the green line shows the field profile in
the free space and the blue line sowes it in the crystal
which is smaller than free space case because of thereflection in the surface of the crystal due to the boundary
condition of electro-magnetic theory.

Figure 4: Electric field strength in free space (green) andin the crystal (blue).

Balanced signal
Figure 3: Electric field propagation in the crystal. The
blue line showed the electric field strength, the red line
showed the laser pulse. The r is the distance between thelaser and electron beam and d is the thickness of thecrystal.
FEL Technology

The laser pulse speed and the Thz radiation speed in the
crystal is not same which makes the slippage between two
pulse. In our simulation, we calculate the relative phaseshift from the integral with 50 sections of the crystal.

693

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Figure 5: The simulated balanced signal of low energy
beam which energy is 5MeV, beam charge is 0.2nC andthe pulse length is 10ps uniform beam. R the distance
between the laser and electron beam is 5mm.τ is thearrival time of the laser at the crystal compared to theelectron beam.
The result showed that the low energy beam of theinjector of XFEL can also be measured with EOS very
successfully. The signal level is almost 1/10 of initial laser
intensity incident in the crystal which is very easily
detected using phtodiode or balanced detector.

LOW ENERGY BEAM DIAGNOSITICS
At present, we completely installed the EOS
experiment setup in the GTS(Gun Test Stand) in PAL.
The coarse timing of the arrival time of electron beam694

and laser beam at the crystal is solved with measurementof all path of the UV and IR laser and the distance
between the gun cathode and electro optic crystal
chamber. Belanced detector signal is observed easily inthe oscillocope which is not saturated. We moved two
mirrors in the path of 800nm laser beam to make timedelay between electron beam and laser beam to find exact
synchronization to see the change of the signal. The
precision timing will be done very accurately withbalanced detector. Sampling method is not appropiate tomeasure the bunchlength due to the electron arrival time
jitter. Instead of the sampling method, the spatial method
which is using the CCD carmera to take a picture of thelaser gives a way to measure the bunch length and timing
jitter simultaneously.

REFERENCES[1] X. Yan et al., Phys. Rev. Lett. 85, p 3404 (2000).
[2] I. Wilke et al., Phys. Rev. Lett. 88, p 124801 (2002).
[3] G. Berden et al., phys. Rev.. Lett. 93, p 114802(2003).
[4] A. L. Cavalieri et al., phys. Rev.. Lett. 94, p 114801(2005).
[5] Jangho Park et al., to be appeared in FEL2006(2006).
[6] Tae-Yeon Lee et al., to be appeared in FEL2006(2006).
[7] M. Bruken et al., TESLS Report 2003-11, (2003).

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH046

PRELIMINARY MEASUREMENT OF EMITTANCE EVOLUTION USING
EMITTANCE METER AT THE PAL*
Jangho Park#, Sung-Ju Park, Changbum Kim, Yong-Woon Parc, Jung Yun Huang, and In Soo Ko,
Pohang Accelerator Laboratory, POSTECH, Pohang 790-784, Korea
Xiang Dao, Department of Engineering Physics, Tsinghua University, Beijing 100084, China
X.J. Wang, NSLS, Brookhaven National Laboratory, Upton, NY 11973, USA.
Abstract
A high-brightness electron beam is emitted from a RF
photocatoode gun with 1.6 cell cavity from October 2005
at the Pohang Accereator Laboratory (PAL). The projectof 4th Generation Light Source (4GLS) with the
Spontaneous Amplification Sponteneous Emission Freeelectron Laser (SASE FEL) in the PAL is called Pohang
Accereator Laboratory X-ray Free-electron Laser (PALXFEL). In order to success of the PAL-XFEL project, it isnecessary to research the high-brightness electron beam at
the injector. A emittance meter (E-Meter) is installed forthe high-brightness research in GTS (Gun Test Stand).
The measurement of transverse emittance and beam size
profile along the longitudinal direction was done by the
E-Meter. Precise measurement of the emittance profile
will be provided with a powerful tool for thecommissioning of the 4GLS injectors based on theemittance compensation principle. We are going toachieve this with the use of slit-based E-Meter that can be
moved along the longitudinal direction. In this article, we
present a preliminary measurement of the emittanceevolution with the E-Meter for the commissioning of thephotocathode RF gun.

INTRODUCTION
The Pohang Accelerator Laboratory X-ray Free
Electron Laser (PAL X-FEL) is proposed with self
amplifiered spontanous emision (SASE) lasging shemethat will use the final 3.7 GeV for the drive beam energy[1-2]. The performance of the PAL X-FEL in the 3.0
Angstrom regime is predicted on the capacity of 1 nC,
100 A beam at the end of the photoinjetor with transverse
normalized rms emittance of 1.2 π mm mrad. For the low
emittance beam, emittance compensation scheme isessential for the design and commitioning of thephotoinjector.
In this paper, we review and report the emittanceevolution in the beam drift region with emittance meter(E-Meter). This paper is composed of previous work on
the subject of the emittance evolution measurements
systems and the preliminary measuring of the beamemittance evolution of the photocathode rf gun. We thendescribe preliminary experimental result at the PAL
where the slit based emittance measurement technique isused to measure the emittance evolution of the PC RF gun.
________________________________________*Work supported by the CHEP and the KOSEF (Project No.: R012006-000-11309-0) of Korea.
#
wpjho@postech.ac.kr

FEL Technology

The results of the experiment, which show that apossibility of the emittance evolution measurement foundwith the E-Meter, are compared with simulation.

EMITTANCE COMPENSATIONThe emitance compensation is a technique used toreduce the normailzed rms emittance of the beam at thephotoinjector. The emittance compensation typicallyinvolves two complementary stages: the rotation of phasespace for each slice of the beam in the solenoid and therealignment of the slices and fast acceleration in the
booster. Essentially, the principle of the emittancecompensation by solenoid is the balance between therepulsive forces due to space-charge and external
focusing forces. After the beam goes through the solenoid
magnet region, the beam is blowed up by space-charge
force if there is no booster linac [3-4]. Thus a booster isneeded to fast accelrate the beam to a relatively highenergy region at which the phase space is frozen and thebeam is emittance dominated. To shift the second
emittance minimum to the enterance of the booster where
the beam is emittance dominated, Serafini and Ferrario
suggested a matching condition [3-4] for properly
matching the space-charge dominated beam from the gun
to the booster,σ ′ = 0,
γ′=

2

σ

IP
,
2 IA γ(1)where σ is the rms transverse spot size, I P is peakcurrent of the beam, I A = 17 kA is the Alfven current.
The booster matching point will be investigated by ourexperiments for optimizing the emittance compensation
process i.e., by the emittance characterizations for various
longitudinal position which will be performed with theEmittance-Meter using a slit based emittance measument
technique. We use the rms emitance and the normalized
rms emitance, defined by [5]ε rms =x2

x '2 − xx 'ε n ,rms = βγε rms ,

2

,

(2)

where β and γ = 1/ 1 − β are the relativistic factors,
the bracket denotes an average over the beam distribution
at each location, the primes refer to axial derivatives, and2695

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Proceedings of FEL 2006, BESSY, Berlin, Germany

located between the half cell and full cell is utilized tocouple rf power from the full cell to half cell. A home
distribution.
made klystron was proceeded to yield 80 MW at an rf
A BNL GUN-IV type rf photo-cathode gun for far pulse length of 1 μs of 2856 MHz. The klystron can be
infra-red radiation (FIR) project is installed in the PAL. A operated with maximum 60 Hz repetition rate at a 10MW
resonant frequency of the gun cavity is 2856.0 MHz with rf power. The field gradient in the cavity was built by the
3.4 MHz mode separation. The photoelectron beam is rf power with 2856 MHz of 2 μs pulse width. The
emitted from the PC RF gun at the PAL since October temperature of the cavity can be maintained by the2005. The beam parameters are achieved 2.5 MeV beam precision cooling system for tuning the rf resonant
energy with 2.5 % relative energy spread and 400 pC condition. In order to reduce the space-charge induced
beam cahrge at the 30º laser injection phase. The emittance growth should be quickly accelerated in the gun.
emittance, the beam size, and the beam energy are After the gun, a solenoid for the transverse emittancesimulated by the PARMELA code for the PAL XFEL compensation is directly mounted with four ceramic key
injector with fullfilled emittance matching condition and to prevent heat transmission. A steering magnet withthe emittance compensation as shown in Fig. 1.
maximum magnetic field of 80 Gauss is installed a space
between inside the solenoid bore and outside the vacuum
pipe. Immediately following the solenoid is an integrated
current transformer (ICT) to measure the beam charge
without beam dump.
After the ICT there was a screen to downstream formeasurement and monitoring of the beam profile. The
screen, which is about 15 μm layer of YAG:Ce doped onaluminium substrate of 100 μm thickness, is mounted on
an aluminium holder at the 45° with respect to the beamaxis. The position of the screen is 0.56 m from thecathode. A charged coupled device (CCD) camera toacquire of the electron beam image is synchronized to theelectron beam for a shot-to-shot measurement. The
spectrometer with a 60° sector dipole magnet for electron
beam energy and the energy spread is located downstream
Figure 1. The beam size (solid line), the normalized rms of the screen.
emittance (dot line), and the beam energy (dash line) are Laser Systems
simulated by PARMELA code for PAL-XFEL injector
The laser system consists of an active mode-lockedwith fulfilled emittance matching condition.
Ti:Sapphire oscillator, a regenerative amplifier, a second
harmonic generator (SHG), a third harmonic generator
EXPERIMENTAL SETUP(THG), and a custom designed UV stretcher system. The
Our electron beam parameters are shown in Table1. laser system for the rf PC gun is installed in a clean room
The beam parameters depend on the laser parameters and which temperature stability is dynamically controlled
rf power and phase.
within 0.5 °C for stable operation. The oscillator isoperated at a frequency of 79.33 MHz by using a
Photocathode RF Gun and Basic Instruments
frequency divider (/36) with the master oscillator of 2856
Figure. 2 shows the experimental setup with a 1.6 Cell MHz for the lock-to-clock between the master and laser
photocathode S-band (2856 MHz) rf gun with 8 pancake- oscillator. The oscillator output is phase-locked with alike solenoids. The PC rf gun was developed and reference 79.33 MHz divided rf frequency byconstructed by collaboration of the BNL, KAIST, and dynamically adjusting the cavity length of the oscillator
PAL. The laser driven copper cathode rf gun consisted of with piezo mirror by lock-to-clock module. The timing
1.6 cell cavity with a half cell and a full cell. The half cell jitter is measured to within an rms value of 130 fs using aof the 1.6-cell rf gun is symmetrized by two laser ports phase detection method. The measured energy stability ofwhich are rotated 45° from the waveguide, tuner, and the oscillator output using by infra-red (IR) power meterpumping port in the full cell. The laser incident port, there is 1 % peak to peak. From the oscillator, 105 fs width
is an angle of 67.5° between the laser propagation with a full width at half maximum (FWHM) value, 800
direction and the cathode normal vector, allows for ultra- nm wavelength pulse is generated with 79.33 MHz
violet (UV) laser to flash the cathode surface and to repetition rate. These laser pulses come into theminimize the transmission loss. The gun is operated in pi- regenerative amplifier to amplify the pulse energy up tomode at S-band with multi-pole suppression achieved about 2.5 mJ with 1 kHz repetition rate. After thethrough cavity symmetrization. The coupling between the regenerative amplifier, the amplified laser pulse comeswaveguide and the full cell is accomplished via the into the THG with a pair of frequency conversion noncoupling slot on the full cell cavity. An electric coupling linear crystals to obtain 266 nm UV light with maximum

x 2 , x '2

696

are the second monents of the beam

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Proceedings of FEL 2006, BESSY, Berlin, Germany

laser energy of 250 μJ. The UV laser pulse still has anultra short pulse width. An UV pulse stretcher with a pairof prisms is installed in order to stretch the pulse width of
the UV laser to 10 ps FWHM. In addition, the UV pulse
stretcher has a capability to change the pulse duration of
the UV laser from 1 ps (FWHM) to 10 ps (FWHM). A
cross correlator with a BBO crystal is installed in order to

THPPH046

short and the other case it should be large to make an
optimized image size at the screen. In the last part, we put
another bellows to make the vacuum force balance in thefront part bellows. We will check the position of the slit
plate chamber and the screen chamber with CCD cameras
and a long scale attached on the shelf. The slits arefabricated by high power Laser micro-drilling with 30

Figure 2: Schematic diagram of experimental setup of the gun test stand (GTS) for photo-injector developments of the PAL-XFEL.

measure the pulse width at the UV region using crosscorrelation method.

Emittance Meter
We have designed the Emittance-Meter which has themovable slits chamber and screen chamber along thebeam axis with bellows independently, which will be used
to demonstrate the emittance evolution predicted bytheory and simulation [3-4]. The transverse emittanceevolution after solenoid magnet to compensate of thebeam emittance along the beam axis can be measured bythis Emittance-Meter. Designed Emittance-Meter was
shown in Fig. 2, the left side part was the PC RF gun, andthe right side part was the Emittance-Meter. The
Emittance-Meter consisted of three long bellows, the slit
plate chamber with the YAG screen to make beamlet andto measure the main beam size, at the downstream of theslit chamber YAG screen chamber to measure of thebeamlet size. The long bellows is used for the transverse
emittance measurement from 0.9 m to 2.1 m position
measured from the cathode. The length of the bellows canbe changed from 0.54 m to 1.54 m without vacuum
breaking. The distance from pin-hole chamber to screen
chamber can be moved along to the beam divergence. If
the beam has a big divergence, the distance should be

FEL Technology

μ m , 40 μ m , and 50 μ m silt widths in tungsten platewith 0.5 mm thickness. The plates in the Emittance-Meter
are designed to be changeable at the specific experimental
position with stepping motor. We can compare theemittance value to each slit width along to a space-charge
dominance factor [6]. The sizes of the slit are determinedby considering the signal to noise ratio (SNR) and theacceptance angle when the beam goes through the plate[7]. Also, very small size hole should be aligned on the
beam axis for beam measurement, because if the hole is
not aligned, the beam is dumped on the tungsten plate.
We designed to realize an alignment technique withgoniometric motion, rotary motion, and linear motion
with high accuracy stepping motor. The single slit
scanning method will be used in usually with x and y
directional linear motion which method is needed
precision moving control, however the analysis of thedata files is easy [8].
.

THE PRELIMINARY MEASUREMENT OF
TRANSVERSE EMITTANCE EVOLUTION
The transverse emittance evolution was measured by apair of a singe slit with 30, 40, and 50 μm slit width and697

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Proceedings of FEL 2006, BESSY, Berlin, Germany

an YAG screen downstream of the slit. The beamlet.is
created by the slit plate, which is made by 0.5 mm
tungsten plate. The beamlet distribution is then imaged on
the screen downstream of the slit plate at a distance of 71
cm from the slit. The width of the beamlet has aconnection with a measure of the width of the transverse
momentum distribution at the slit. The beamlet yield thecorrelated beam divergence and the rms transverse
divergence,xc′ =< x − w > / L,

σ′ =

x2
2

L

− ( xc′ ) ,2

where L is the distance between the slit and the YAG
screen, x is the measured beamlet size on the screen, andw is the slit width. Here the average is performed overthe distribution in the measured beamlet. The beamlet size

performed with the condition of 2.0 MeV beam energy
and 350 pC beam charge with 30º laser injection phase.

SUMMARY
The experimental measurement by the E-Meter is tomeasure the emittance evolution in the drift region formany experimental conditions to find optimized operating
condition for our injector. We measure the firstmeasurement of the emittance evolution at the drift regionof the photo-injector. For better results of the emittanceevolution, we need to improve data analysis methodology,
and to automate data acquisition processes. For advanced
experiments, we need to improve high energy (more than
5 MeV at the gun) beam experiment or normal laser
incidence.

REFERENCEth[1] 4 Generation Light Source: Conceptual Design
Report, Pohang Accelerator Laboratory (Nov. 2004).
[2] T.-Y. Lee et al., J. Korea Phys. Soc. 48 pp. 791-795(2006).
[3] M. Ferrario et al., SLAC-PUB-8400, March 2000.
[4] L. Serafini, J.B. Rosenzweig, Nucl. Instrum. andMeth. A 311 (1992), 437.
[5] J. D. Lawson, The Physics of Charged-Particle
Beams, 2nd ed., Oxford University Press (1988).
[6] S. G. Anderson and J. B. Rosenzweig ed. al., PRSTAB Vol 5, 014201 (2002).
[7] K. Flottmann, TESLA-FEL 96-09, May 1996.
[8] A. Cianchi, et al., Proceedings of EPAC 2004,
Lucerne, Switzerland (2004).
Figure 3: Preliminary measurement of the emittanceevolution (solid circle) and the beam evolution (empty
circle).
is measured about 10 times larger than the slit width to
reduce the space-charge effect in the emittancemeasurement In generally, quad technique for beamemittance measurement was reported over-estimated dueto the purely space-charge dominated region [refer insert].
The position of the slit from the cathode can be changed
with stepping motor without vacuum break which of theleast position of the slit is 1.4 m from the cathode. The
distance between the slit and the YAG screen can bechanged for optimizing of the beamlet measuring on the
YAG screen.
The distance is 0.71 m between the slit chamber withthe screen and the screen chamber for measuring of abeamlet size. The main beam size on the #2 screen at theslit chamber and beamlet size on the #3 screen at thescreen chamber are measured by the synchronized CCD
camera. From measured the beam size and the beamlet
size the beam gradient is calculated which for the beamemitance calculation. The evolution of the beam emitanceand beam size is shown in Fig.3.This experiment is

698

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH050

BEAT-WAVE LASER-DRIVEN PHOTOINJECTOR FOR SUPERRADIANCE
FREE-ELECTRON LASER
Yen-Chieh Huang, Han-Lung Chang, and An-Chung Chiang, National Tsinghua University, Taiwan.
Abstract
A periodically bunched electron beam is useful for
generating electron superradiance. This paper studies thegeneration and acceleration of density-modulated electron
beams from a photocathode electron gun driven by a laser
beat wave. Computer simulation shows feasibility ofaccelerating and preserving the density-modulated
electron beam in an accelerator.

INTRODUCTION
Radiation from relativistic electrons is important for
generating THz and x-ray wavelengths at which solidstate laser sources are not readily available. The spectral
brightness of electron radiation is strongly influenced by
the electron bunch length relative to the radiation
wavelength. When the electron bunch length issignificantly shorter than the radiation wavelength, theradiation fields from all electrons are coherent and can besummed to a large value.
In a conventional free-electron laser (FEL) the opticalfeedbacks from resonator mirrors can help the electron
bunching process during laser buildup. At shortwavelengths a single-pass, mirrorless FEL generating
self-amplified spontaneous emission (SASE) is thepreferred mode of operation due to the scarce of mirror
materials at deep UV and x-ray wavelengths. However, it
usually takes a long undulator for a high-quality electron
beam to form micro-bunches and reach the onset of the
SASE mode. It is therefore desirable to invent anaccelerator that generates a periodically bunched electron
beam with an arbitrarily tunable bunch length and bunch
frequency. Perviously Neumann et al. [1] used a comb
filter to induce a few temporal ripples to the driver laserof a photocathode gun and observed coherently enhanced
radiation at THz. In the paper, a laser beat wave with atunable beat frequency is employed to induce a densitymodulated photocurrent from the photocathode cathode ofan electron gun. We study in this paper the acceleration of
the density-modulated electron beam and theimplementation of such a beat-wave laser system.

SUPERRADIANCE
Superradiance from relativistic electrons has beenstudied theoretically and experimentally in numerous
papers. To facilitate subsequent discussions, we briefly
review a few key concepts of superradiance based on
Gover’s work [2].
Regardless of the nature of the radiation device orscheme, let (dW/d ω)1 denote the spectral energy emitted
from a single electron, where W is the radiation energy, ωis the angular frequency of the radiation, and subscript 1

FEL Technology

denotes “a single electron”. When a long stream of N
electrons traverses a radiation device, the electrons radiatewith all possible phases between 0 and 2π and theradiation has a spectral energy expressed by(dW dω )inc = N (dW dω )1 ,

(1)

Eq. (1) is linearly proportional to the total number ofelectrons participating in the radiation process, because
not all the radiation fields from the electrons are added up
constructively. However, if Nb electrons are distributed in
an infinitesimal time period, all the radiation fields fromthe electrons are in phase and summed up constructively,
resulting in a total spectral energy equal to N b2 (dW d ω )1 .
This radiation process is dubbed as superradiant emission
or superradiance. To account for a finite electron bunch
length τb the total energy spectral density from an electron
bunch is expressed by(dW d ω )SR = N b2 (dW d ω )1 M b2 (ω ) ,(2)

where Mb( ω) is the Fourier transform of the electron
pulse-shape function with a unitary peak amplitude.
Usually M b2 (ω ) has a characteristic width ~1/τb in thefrequency domain. If there are Npb electron “microbunches” repeating at a rate ωpb/2π and there are Nbelectrons in each micro-bunch, the total spectral energy
from such an electron beam becomes(dW dω )SR , pb = N b2 N pb2 (dW dω )1 M b2 (ω )M pb2 (ω ) ,

(3)

where
2
M pb
(ω ) =

sin 2 ( N pbπω / ω pb )2
N pb
sin 2 (πω / ω pb )(4)

is the coherent sum of the radiation fields from all the
micro-bunches and has a unitary amplitude at theresonance frequencies (m = 1, 2, 3…). At ω = ωpb, thespectral energy, Eq. (3), is enhanced by a factor equal to
the number of electrons compared with that from an
unbunched beam. Superradiance power has a quadratic
dependence on a beam current, as can be seen from Eq.
(2, 3); whereas the incoherent radiation power from along-bunch beam is linearly proportional to a beam
current, according to Eq. (1).
In Eq. (1), the spectral linewidth of the radiation from along electron bunch is determined by the radiation
bandwidth of a radiation device or a radiation scheme.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

The superradiance linewidth from a short electron bunch,according to Eq. (2), is further modulated by M b2 (ω ) . Fora short electron bunch, M b2 (ω ) is usually a broadband
curve. The coherent sum Eq. (4), however, has narrowspectral peaks at the frequencies ω = m ωpb. Each resonantpeak has a linewidth of ωpb/Npb. The superradiancelinewidth from periodically bunched electrons can begreatly reduced for a large Npb.

where t is the time variable, I0 is the average intensity ofeach laser component, and ω+Δ ω/2 is the central
frequency of the laser beat wave. A laser beat wave canalso be generated from a superposition of several laser
fields with a constant frequency shift Δ ω. For example,
the coherent sum of the Nl equal-amplitude laser fields
gives a time-averaged intensity

N l Δω
t2.
I avg = N I
22 Δω
N l sint2
sin 2

GENERATION OF LASER BEAT-WAVE
BUNCHED BEAM
We illustrate in Fig. 1 the schematic of the proposedbeat-wave bunched beam technique for producing andaccelerating periodically bunched electrons with avariable bunch frequency. The idea is to use a laser beatwave to induce periodically density-modulated
photoemission from the photocathode of an electron gun.
The density-modulated photocurrent is then accelerated tosome energy for generating superradiance in adownstream radiation device. The beat-wave laser system
consists of wavelength-tunable lasers for generating laser
beat waves with a variable beat frequency. If the desired
electron bunch frequency is higher than the beatfrequency available from a laser beat wave, one could in
principle first generate an energy-chirped, densitymodulated beam and compress it in a magnetic
compressor to obtain a beam with a higher bunch
frequency.
alpha magnet
accelerator

Laserbeat wave

Radiation
devicePhotocathode gun
Figure 1: A laser beat wave excites a density-modulated
photocurrent from a photocathode, which is subsequently
accelerated to some energy for generating superradiancein a radiation device. An alpha magnetic could compress
a density-modulated, energy-chirped beam to obtain abeam with a higher bunch frequency.
A laser beat wave can be generated from asuperposition of two laser fields with a constantfrequency offset. Assume that a beat-wave field isgenerated from the sum of two equal-amplitude laser
fields with a frequency offset Δ ω. The instantaneous
intensity of the beat wave is given by
Δω
Δω ,
(5)
I ins = 4 I 0 cos 2 [(ω +)t ] ⋅ cos 2 (
t)
2
2

700

2
l 0

(6)

Eq. (6) shows laser beat pulses repeating at a frequency
Δω with a pulse width equal to (2π / Δω ) / N l . The beatpulses given in Eq. (6) are very useful for providing highcontrast density modulation to the photocurrent from a
photocathode. By adjusting the number of interferingwaves Nl one can adjust the beat-pulse width to optimize
the modulation depth of the photocurrent emitted from a
photocathode. In fact the locked-locked laser pulse
commonly used for exciting a photocathode gun is aconsequence of beating many longitudinal modes in alaser cavity with a beat frequency of ~100 MHz. To
obtain a narrow beat pulse repeating at THz, one could,
for example, use an intense laser to pump a Raman
material with a THz Stokes shift and generate multiple
Stokes waves beating at the Stoke shift. Of course, theshortest electron bunch that can be generated fromphotoemission depends on the temporal response of a
specific cathode material. In view of the mechanism of aphotoemission process, it is also preferred that all thebeat-wave photons have photon energy higher than thework function of a cathode material.

ACCELERATION OF PERIODICALLYBUNCHED ELECTRONS
A major concern for the proposed bunching technology
is whether particle acceleration following the densitymodulated photoemission would smear out the periodic
electron micro-bunches. In the following we conduct a
feasibility study for accelerating ps and fs micro-bunches
by using a space-charge tracking code ASTRA [3].
We first simulated the particle acceleration for the 1-1/2
cell SSRL electron gun [4] with twenty-five Gaussian
electron bunches with 1-fs rms bunch length periodicallyemitted over 250-fs duration from the photocathode. The
emitted charges have a uniform radial distribution on a 3mm diameter cathode. Each micro-electron bunchcontains 1 pC in a 10-fs time period. The total 25 pC
charge was evenly divided into 12500 negatively charged
macro-particles. The average current over the whole 250
fs duration is 100 A. With a peak acceleration field of 125
MV/m in the 2nd gun cell and an acceleration phase of
211.6°, Fig. 2 shows periodic density modulation of a 4MeV beam with a characteristic period of 6 μm along the

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

axial distance (ze) at the gun exit. The output pulse
duration is stretched to 500 fs and thus the average beam
current is reduced to 50 A. Since the 250-fs emission time
only occupies a very small RF acceleration phase, we
confirm in the ASTRA simulation that the space charge
field is responsible for the pulse-length increase.
Although the shortest possible electron bunch is limited
by a cathode material, the above computer stimulation isjust an illustration of preserving periodic fs electron
bunches during particle acceleration. Whether generationof fs electron bunches from a certain cathode mateiral ispractical or not, it is another subject of study in the future.

harmonics of the bunching frequencies. For example, with
6.25×103 electrons/bunch and 1000 bunches over a 1 ns
time, the spectral energy is coherently enhanced byalmost 7 orders of magnitude at 1 THz.
0

10

(a)

-1

10

-2

10

-3

10

-4

10

-5

180

Number of macro-particles

THPPH050

10

160

-6

10

140
120

-7

10

100

0

0.5

1

1.5

2

2.5

3

2.5

3

Frequency (THz)

80

0

10

60
40

-1

10

(b)

20
0
-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

ze (mm)Figure 2: Histogram of the 4-MeV charges versus z at theexit of the SSRL gun with an input beam of twenty-fiveGaussian bunches periodically emitted over 250 fs. The
output beam distribution shows a good contrast in thedensity modulation.
A Smith-Purcell emitter driven by a keV, mA electron
gun usually generates negligible radiation at THz. This
proposed technique could be very useful for producing
coherent radiation at THz frequencies from a miniature
Smith-Purcell free-electron laser. Previously Ref. [5]reported Smith-Purcell superradiance, which wasinterpreted by Ref. [6] as coherent radiation from surfacemode induced electron bunching at the sub-harmonic of
the Smith-Purcell radiation frequency. Up to date, no
independent experiment can verify the superradianceclaimed by Ref. [5]. A convenient approach is to produce
electron bunches repeating at the radiation frequency
directly from an electron source and generate wavelength
tunable superradiance from a Smith-Purcell radiator. In
our simulation, we emitted 50 Gaussian electron bunches
each having a 0.2-ps rms bunch length from thephotocathode of a 42 keV DC accelerator over a 50-ps
time period. Each electron bunch contains 1 fC charge or
6.25×103 electrons, resulting 1 mA average current overthe 50 ps macropulse. The electrons have a uniform radial
distribution on the cathode with an rms radius of 0.3 mm.
The electron gun has a length of 4.5 cm with 1-Tesla axial
magnetic field for beam confinement. Figures 3(a) and (b)2
are the M b2 (ω ) M pb
(ω ) for the emitted electrons and the
42-keV output electrons, respectively. The accelerated
electrons are slightly re-distributed due to the spacecharge force. Nonetheless the enhancement in the spectral
power due to the periodic bunching is apparent at the

FEL Technology

-2

10

-3

10

-4

10

-5

10

-6

10

-7

10

0

0.5

1

1.5

2

Frequency (THz)
Figure 3: The [Mb(ω)Mpb( ω)]2 of 50 electron bunches
repeating at 1 THz (a) before and (b) after acceleration in
a 40 keV DC electron gun. Spectral enhancement at theharmonics of 1 THz frequency is apparent.

FREQUENCY-TUNABLE BEAT-WAVE
LASER SYSTEM
Although the laser beat wave can simply be obtained byoverlapping two chirped pulses from the laser driver of aphotocathode gun, the intensity contrast in the beat wave
and the tunability in the beat frequency are not ideal [7].
We describe below one example of engineering a beatwave UV laser system capable of generating mJ-level, 10ps laser pulses near 260 nm with a tunable beat frequency
range over 200 THz. Figure 4 shows the block diagram ofthe proposed beat-wave laser system, which consists ofthree major stages with a beat-wave seed source, a firststage broadband pulsed amplifier and a second harmonic
generator, and finally a frequency-tripled Ti:sapphire laser
amplifier. The two seed lasers in the first stage are often
used in optical communications. The Ti:sapphire laser
amplifier and harmonic generators are commonly seen for
driving a Cu photocathode gun. Specifically, one canstarts with the beating of kHz-linewidth distributedfeedback (DFB) and frequency-tunable external-cavity

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Proceedings of FEL 2006, BESSY, Berlin, Germany

diode lasers (ECDL) near the optical-communication
wavelength 1.5 μm. An Erbium-doped fiber amplifier(EDFA) following the DFB diode laser and ECDL boosts
the beat-note power to ~100 mW. The CW beat signal canbe further amplified in a pulsed optical parametricamplifier (OPA) pumped by, say, a diode-pumped modelocked Nd:YVO4 laser to generate ~10-ps beat-wave
pulses with nJ pulse energy. After frequency doubling thebeat-wave pulses in a second harmonic generator (SHG),
the wavelengths of the beat wave will fall into the
bandwidth of a Ti:sapphire amplifier. Therefore, the restof the laser system can be a replication of the UV laser
amplifier for driving a Cu photocathode gun. The
proposed beat-wave laser system spares a mode-locked
Ti:sapphire laser oscillator from a typical photocathodegun laser driver. Instead, a user-friendly, directly diodepumped mode-locked Nd:YVO4 is proposed for pumping
the OPA to generate beat-wave pulses near the opticalcommunication wavelengths.
To produce the proposed Smith-Purcell superradiance,
the mode-locked Nd laser can be replaced by an economic
Q-switched Nd laser, and harmonic generators candirectly follow the OPA to generate long-pulse UV laser.

Computer simulations using the space-charge tracking
code, ASTRA, showed feasibility of accelerating andpreserving the density-modulated electron beam at bothnonrelativistic and relativistic energies.
We have also described the implementation of a beatwave laser system with a beat-frequency tuning range
over 200 THz. The laser system adopts the state-of-the-art
and yet economic photonics products often used in the
optical-communication and laser industries. Real-timetuning on the beat frequency provides unprecedented
flexibility to match the frequency of down-stream
radiation devices.
The shortest electron-bunch length from the proposedbeat-wave bunching technique could be limited by thebeat-wave frequency or the response time of a cathodematerial. We proposed chirped-pulse compression in analpha magnet to increase the bunch frequency. Knowing
the potential problem of microbunching instability in thecompression, we have planned a feasibility study in thenear future.
The author is in debt to Michael Borland and Klaus
Floettmann for advices on computer simulations. This
work is supported by National Science Council underContract 95-2112-M-007-027-MY2 and NTHU Frontier
Research Initiatives under Project Code 95N2509E1.

REFERENCES

Figure 4: One example of a beat-wave laser systemmodified from a typical UV laser system for a Cuphotocathode gun.
The beat frequency of the laser system can bearbitrarily tuned by adjusting the wavelength of the ECDLor by plugging in assorted narrow-line telecommunication
diode lasers with a wavelength range between 1.3 and 1.6
μm. Taking into account the successive harmonic
generations leading to the 260 nm photons, one would
expect a beat-frequency tuning range well over 240 THz.

SUMMARY
We have described a novel scheme for generating
tunable periodic electron bunches for superradiance FEL.
Specifically a laser beat wave is used to introduce density
modulation to the photocurrent of a photocathode electrongun. The periodic electron bunches are subsequently
accelerated to high energy in a particle accelerator.
702[1] J.G. Neumann, P.G. O’shea, D. Demske, W.S.
Graves, B. Sheehy, H. Loos, and G.L. Carr, “Electron
beam modulation by using a laser-driven photocathode” Nucl. Inst. Meth. Phys. Res. A 507, 498(2003).
[2] A. Gover, “Superradiance and stimulated-superradiant emission in prebunched electron-beam radiators.
I. Formulation”, Phys. Rev. ST AB, 8, 030701(2005).
[3] K.
Floettmann,
ASTRA
User
Manual,http://www.desy.de/mpyflo/Astra_dokumentation.
[4] Y.C. Huang, H.C. Wang, R.H. Pantell, J. Feinstein,
J.F. Schmerge, and J. Lewellen, “Electron BeamCharacterization for a Far Infrared Free-electron
Laser,” IEEE J. Quantum Electronics, 31, 1637-41(1995).
[5] J. Urata, M. Goldstein, M.F. Kimmitt, A. Naumov, C.
Platt, and J.E. Walsh, “Superradiant Smith-Purcell
Emission”, Phy. Rev. 80, 516 (1998).
[6] H.L. Andrews, C.H. Boulware, C.A. Brau, J.D.
Jarvis, “Gain and coherent radiation from a SmithPurcell free-electron laser,” Proceedings FEL04,
Trieste, Italy, p. 278 (http://www.JACoW.org).
[7] A.S. Weling, B.B. Hu, N.M. Froberg, D.H. Auston,“Generation of tunable narrow-band THz radiationfrom large aperture photoconducting antennas,”
Appl. Phys. Lett. 64, 137 (1994).

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH053

3-D LASER PULSE SHAPING FOR PHOTOINJECTOR DRIVE LASERS*
Yuelin Li#, ANL, Argonne, IL 60439, U.S.A.
Xiangyun Chang, BNL, Upton, NY 11973, U.S.A.
Abstract
In this paper we present a three-dimensional (3-D)
laser pulse shaping scheme that can be applied forgenerating ellipsoidal electron bunches from a
photoinjector. The 3-D shaping is realized through laser
phase tailoring in combination with chromatic aberration
in a focusing optics. Performance of an electron beam
generated from such shaped laser pulses is compared withthat of a uniforma ellipsoidal, a uniform cylindrical, and a
Gaussian electron beam. PARMELA simulation shows
the advantage of this shaped beam in both transverse andlongitudinal performances.

INTRODUCTION
The emittance of an electron beam is governed by theemittance at its birth and the growth during its
propagation. If the beam is only subjected to linear force,the latter can be fully recovered with proper beamcompensation. It is well known that an ellipsoidal beamwith uniform charge distribution has a linear space-charge
force [1-3] and hence the most expected distribution formodern high-brightness beams. Recently, several
researchers looked at practical ways of generating such
ellipsoidal beams, including self-evolving [4], cold
electron harvesting [5], and laser pulse manipulations
including spectral masking, pulse stacking, and dynamic
spatial filtering [6]. In-depth analysis shows that inpractical situations, the ellipsoidal beams do generatebeam with lower emittance than Gaussian and cylindricalbeams [1, 6-8]. Applications for such high-brightness
beams include next-generation light sources such as the
Linac Coherent Light Source (LCLS), high-energy
colliders such as the International Linear Collider, as wellas energy-recovery linacs (ERLs).

expressed as [11]
⎛ 1
1
1 ⎞
(1)
= [n (ω ) − 1] ⎜⎜ − ⎟⎟ ,f (ω )
RR
1 ⎠⎝ 1
where R1 and R2 are the radius of curvature of the firstand second surface of the lens, respectively, and n is thefrequency-dependent refractive index. Clearly, the timedependent frequency can then be mapped onto a timedependent focal length. For an observer at the focal planeat a nominal frequency ω0, this is equivalent to a timedependent defocusing of the beam off(2)
δf (t ) = − 0 βδω (t ) ,n0 − 1
where we assume the frequency range is small and β =dn/dω is constant. For a Gaussian beam this translates into
a time-dependence of the beam size at the nominal focal
plane,
2⎡⎛ λ 0 δf ( t ) ⎞ ⎤
⎟ ⎥
2
⎟
⎥
⎝ πw0 ⎠ ⎦w(t ) = w0 ⎢1 + ⎜⎜⎢⎣To generate an ellipsoidal beam directly from thephotocathode, the laser pulse has to be shaped in 3-D. It is
well known that the longitudinal laser pulse shape can be
manipulated by controlling the phase space using
techniques such as DAZZLER [9] or SLIM [10]. One
essence of this phase modulation is to control the phaseand amplitude at certain frequencies at the same time. In
the meantime, we notice that the instant frequency of alaser pulse is related to the phase by ω(t) = dφ(t)/dt. This
gives a way of actively controlling the focal size of thelaser as a function of time using the chromatic aberrationof a common lens, of which the focal length can be______________________________________________* Work supported by U.S. Department of Energy, Office of Science,
Office of Basic Energy Sciences under Contract No. W-31-109-ENG-38.
#
ylli@aps.anl.gov

FEL Technology.

(3)Here, w0 = Νλ0/π is the beam waist at the nominal
wavelength λ0, and N is the numerical aperture. For δf >>w0, we have asymptotically,δf ( t ).
(3a)w(t ) ≅
N
To generate an ellipsoidal outline, the transverse beam
size should be of the form:2⎡⎛ t ⎞ ⎤
⎟ ⎥⎝ T ⎠ ⎦⎥

1/ 2.

w(t ) = W ⎢1 − ⎜⎣⎢(4)Here, W is the maximum transverse beam size at t = 0 and
2T is the laser pulse duration.
From Eqs. (3-4), we have⎡

LASER PULSE SHAPING

1/ 2

2

⎛ t ⎞ ⎤
⎟ ⎥⎝ T ⎠ ⎥⎦1/ 2

δω (t ) = Δω ⎢1 − ⎜
⎢⎣

,

(5)

where Δω = (n0-1)NW/βf0 is the bandwidth of the pulse;
hence the phase of the pulse isφ (t ) = ∫ [ω (t ) − ω0 ]dt
.
(6)
2
⎤
Δω ⎡ ⎛⎜ ⎛ t ⎞ ⎞⎟−1 t
= −ω 0 t ±⎢t 1 − ⎜ ⎟ + T sin⎥
2 ⎢⎣ ⎜⎝ ⎝ T ⎠ ⎟⎠T ⎥⎦To make the pulse intensity constant over time, i.e.,|A(t)|2/w(t)2 = constant, the amplitude of the pulse is thus2⎡⎛ t ⎞ ⎤A(t ) = A0 ⎢1 − ⎜ ⎟ ⎥⎝ T ⎠ ⎦⎥
⎣⎢

1/ 2

.

(7)

With a transverse top-hat spatial profile, the field E(t) =A(t)exp[iφ(t)] represents a 3-D ellipsoidal pulse at thenominal focal plane at λ0. The time domain representationof the pulse and its spectrum are shown in Fig. 1.

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Proceedings of FEL 2006, BESSY, Berlin, Germany
100

1.0

0

0.5

-50

I (Arb. units)

0.0

φ (rad)

50

-100
-2

0

2

t (ps)
1.0

0.5

BEAM SIMULATION

0.0
-0.06

Clearly, this shaped pulse differs from an ideal
ellipsoid. It has substantial substructures. The deviationfrom an ideal ellipsoidal is not unexpected due to thegroup delay across the plate, which is the source for the
distortion at the beginning and the end of the pulse. Thishas been studied theoretically and experimentally by a
few authors and is an important effect in focusing shortduration, short-wavelength laser light [12].
The substructure is due to the fringes typical of theFourier transform of a square waveform. As is shown
below, those substructures seem to have minimum impact
on the performance of the beam.

-0.05

-0.04

-0.03

-0.02

Δω/ω0

Figure 1: Laser pulse calculated using Eqs. (6) and(7). The intensity and phase in the time domain (top)and its spectrum (bottom).
Note that the above model used Gaussian beamgeometrical optics, and the effects of group velocity delay(GVDE) and group velocity dispersion (GVDI) due to thevarying thickness across the aperture of the lens are notincluded [11]. It does not take into account the wave
property of the light. To evaluate the effects of GVDE andGVDI, we use the method elaborated by Kempe et al. [12]to calculate the temporal-spatial distribution of the pulse
near the focus of a lens. The calculation assumes acollimated beam with top-hat intensity distribution for the
input and was performed in the frequency domain. The
final result was Fourier transformed into the time domain
to give the laser intensity distribution at the focal plane asa function of time. Figure 2 shows one example of such ashaped pulse generate by sending a pulse in Fig. 1 thougha zone plate (a zone plate has similar chromatic aberration
as a lens).

To evaluate the performance of this shaped laser beam,
preliminary simulations using PARMELA were
performed and compared with other beam shapes for thefollowing setting.
The simulation followed a setup for the design of theelectron cooling ring injector for Relativistic Heavy Ion
Collider [13]. The gun is a 1.5-cell rf gun at 703.75 MHz
with maximum field on axis of 29.5 MV/m and maximum
field on surface at 49.3 MV/m. The rf initial phase is set
at 40 degrees. Beam distortion due to image charge isconsidered. The gun is followed with a drift space before
entering a linac.
A series of simulations were performed using
PARMELA. The simulations compared the performanceof the 3-D laser pulse against three standard cases (seeTable 1): c) a perfect ellipsoidal beam, d) a cylindricalbeam, and e) a transversely uniform but longitudinally
Gaussian beam. For the shaped beam, two cases were
tested: a) without considering the substructures and b)
with. The simulations use the parameters listed in Table 1.
Both the longitudinal and the transverse emittances arecompared at the exit of the gun. In total, 46,600 particles
are used in each simulation, representing 0.15 nC of
charge. The low charge is used due to the relatively low rf
field in this setup.
The emittances as a function of the propagation
distance are shown in Fig. 3. In general, the performances

Figure 2: An ellipsoidal laser pulse. The isosurface plots show the structure at different laser intensities of 0.05, 0.1,
0.15, and 0.2. The pulse is generated using a zone plate with 20-mm diameter and 150-mm focal length at 249 nm.
The pulse parameter is shown in Table 1, case b.

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1.5

(a)
a
b
c
d
e

1.0

0.5

0

20

40

60

80

100

120

Longitudinal emittance (deg keV)

Trnasverse emittance (mm mrad)

Proceedings of FEL 2006, BESSY, Berlin, Germany

Distance (cm)

THPPH053

8.0

(b)

6.0

4.0

2.0

0.0
0

20

40

60

80

100

120

Distance (cm)Figure 3: Transverse (a) and longitudinal (b) emittances as a function of propagation distance. The labels correspondto those in Table 1. Clearly, the shaped pulse has a better performance in comparison with those of the cylindricaland Gaussian form, even with the presence of the substructures shown in Fig. 2. The gun exit is located at 48 cm,
followed a drift space.
Table 1. Initial Beam Conditions
Length (ps)Radius (mm)a.Shaped, no17
1.28
substructureb.Shaped,
17
1.28
substructure
c. Ideal ellipsoid18
1.28
d. Ideal cylinder
18
1.13
1.13
e. Ideal Gaussianσ = 3.82,
truncated at 9of the shaped-pulse cases closely trail the performances of
the ideal ellipsoidal beam in both longitudinal andtransverse emittances. More remarkably, the substructure,
as shown in Fig. 2, has almost no impact on theperformance of the beam in this setup. It will beinteresting to perform simulations with bending magnets,
such as a chicane structure to evaluate the influence ofcoherence transition radiation, which is detrimental tocylindrical and Gaussian beams but has minimum impact
on an ideal ellipsoidal beam. One simulation indicates thatafter accelerated to high beam energy, the ellipsoidal
beam shape will be destroyed but the low emittance of thebeam is preserved [8], making it favorable for applicationin free-electron lasers such as LCLS and ERLs.

SUMMARY
We described a scheme for generating an ellipsoidal
laser pulse and performed preliminary simulations
comparing the electron beam generated from this laser
beam with an ideal ellipsoidal beam, a cylindrical beam,
and a Gaussian beam. It is shown that although the beam
generated still defers from an ideal ellipsoidal beam, it has
clearly better performance than a cylindrical beam and a
Gaussian beam in providing smaller transverse andlongitudinal emittance. Further beam simulations are

FEL Technology

needed to investigate the coherent synchrotron radiation
effect for setup relevant to LCLS and future ERLs.

REFERENCES[1]

F. Sacherer, IEEE Trans. Nucl. Sci. NS-18, 1105
(1971).
[2] I.M. Kapchinskij, V.V. Vladimirskij, Conference on
High Energy Accelerators and Instrumentation,
CERN, Geneva, 274 (1959).
[3] P.M. Lapostolle, IEEE Trans. Nucl. Sci. NS-18,
1101 (1971).
[4] O.J. Luiten, S.B. van der Geer, M.J. de Loos, F.B.
Kiewiet, and M.J. van der Wiel, Phys. Rev. Lett 93,
094802 (2004).
[5] B.J. Claessens, S.B. van der Geer, G.Taban, E.J.D.
Vredenbregt, and O.J. Luiten, Phys. Rev. Lett 95,
164801 (2005).
[6] C. Limborg-Deprey and P. Bolton, Nucl. Instrum.
Methods A557, 106 (2006).
[7] J.B. Rosenzweig et al., Nucl. Instrum. Methods
A557, 87 (2006).
[8] S.B. van der Geer, M.J. de Loos, T. van
Oudheusden, W.P.E.M. op’t Root, M.J. van derWiel, and O.J. Luiten, Phys Rev. ST-AB 9, 044203(2006).
[9] P. Tournois, Opt. Commun. 140, 245 (1997).
[10] A.M. Weiner, D.E. Leaird, J.S. Patel, and J.R.
Wullert, Opt. Lett. 15, 326 (1990).
[11] M. Born and E. Wolf, Principles of Optics,
University Press, Cambridge, UK, 2003.
[12] M. Kempe, U. Stamm, B. Wilhelmi, and W.
Rudolph, J. Opt. Soc. Am. B9, 1158 (1992).
[13] I. Ben-Zvi et al., Nucl. Instrum. Methods A557, 28(2006).

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LINAC COHERENT LIGHT SOURCE UNDULATOR RF BPM SYSTEM *R. Lill, G. Waldschmidt, D. Walters, L. Morrison
Advanced Photon Source, Argonne National Laboratory, Argonne IL
S. Smith, T. Straumann, Z. Li, R. Johnson
Stanford Linear Accelerator Center, Sand Hill Road
Menlo Park, CA 94025 USA
Abstract
The Linac Coherent Light Source (LCLS) willbe the world's first x-ray free-electron laser (FEL) when it
becomes operational in 2009. The LCLS is currently inthe construction phase. The beam position monitor (BPM)system planned for the LCLS undulator will incorporate ahigh-resolution X-band cavity BPM system described inthis paper. The BPM system will provide high-resolution
measurements of the electron beam trajectory on a pulseto-pulse basis and over many shots. The X-band cavity
BPM size, simple fabrication, and high resolution make it
an ideal choice for LCLS beam position detection. We
will discuss the system specifications, design, andprototype test results.

INTRODUCTION
The LCLS FEL will produce x-ray radiation over the
1.5-to 15-Angstrom wavelength range. To produce x-raysin this regime, the electron and photon beams within the
131-m-long undulator must be collinear to less than 10%of the transverse beam size ( | 37 Pm rms) over aminimum distance that is comparable to the FEL
amplitude gain length ( | 10 m) in order to achieve
saturation [1,2]. To establish and maintain the electron
beam trajectory, a high-resolution and stable BPM system
has been designed. The requirements for the system aredelineated in Table 1. The beam-position resolution andstability over 1-h and 24-h periods were the major design
challenges for the BPM system.
Other design
considerations were physical size, centering accuracy,radiation hardness, and reproducibility.
The LCLS undulator hall will house 33 undulators.
The BPMs will be located in the drift space between each
undulator and at the upstream end of the first undulator
for a total of 34 BPMs. There are also two BPMs placedin the Linac to Undulator (LTU) transport line. The BPM
system must provide stable and repeatable beam position
data for both planes on a pulse-to-pulse basis for up to a
120-Hz repetition rate. The BPMs are critical for beambased alignment and operations.

Table 1. General system specifications.
Parameter
Specification
Conditions
Resolution
0.2– 1.0 nC< 1 Pm rms
Offset Stability< +/- 1 Pm rms

1 hourOffset Stability< +/- 3 Pm rms

24 hours

Dynamic Range,
Position
Dynamic Range,
Intensity+/- 1mm0.2-1 nC

10mm diameterchamber
PC Gun(single bunch)

Gain Error< +/- 10 %+/- 1mm range

BPM SYSTEM OVERVEIW
The system proposed for the LCLS undulator
features a high-resolution X-band cavity BPMs. EachBPM detector has a reference cavity and position cavity
as shown in Fig. 1. The major sub-systems include thecavity BPM, receiver, and data acquisition components.
The cavity BPM and downconverter will reside in thetunnel and the analog-to-digital converter (ADC) will belocated in surface buildings.

*Work supported by U.S. Department of Energy, Officeof Basic Energy Sciences, under Contract No. W-31-109ENG-38.
Figure 1: System block diagram.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

X-BAND CAVITY DESIGN
The simplicity of fabrication and assembly of the
X-band cavity BPM due to its cylindrical geometry makeit our first choice for the LCLS undulator. The cavity
BPM offers the advantage of being a small, compact
detector that inherently reads zero when the beam iscentered. Cavity BPMs show extremely good resolution
and stability. The two-cavity BPM design shown in Fig. 2
illustrates the cross section of the detector. The beam
passes through the monopole reference cavity, shown on
the left, which excites the TM010 monopole mode signal at
11.384 GHz, proportional to the beam intensity or charge.
The second cavity, 37 mm downstream through the 10
mm diameter beam pipe, is the TM110 dipole cavity shownat the far right. The output of the dipole cavity produces asignal that is dependent on the relative beam displacement
r rfix shown in equation 1 [3]. Where Rs Q is thenormalized shunt impedance of the TM110 mode, Z is theoutput line impedance, Qext is the external quality factor
and q is the charge. The voltage is linearly dependent on
the offset and can be scaled.

V out

Z0
2

Z § Rs ·r¨¸q.
Q ext ¨© Q ¸¹ fix r fix(1)

THPPH054

The single-shot resolution will be limited by otherprocessing and data acquisition electronic noise.

Vn | k u T u Z u B(2)Horizontal and vertical position signals are
generated from the two polarizations of the TM110 dipole
mode. The polarized fields are coupled to four iris slots
equally spaced around the cavity. The magnetic field of
the dipole couples to the TM110 mode of the rectangular
waveguide shown in Fig. 2. The distinctive modal
patterns of the TM010 monopole and TM110 dipole modes
make it possible to couple only to the dipole mode andreject the monopole mode. This selective couplingtechnique, pioneered by SLAC, has been incorporated inthis design [4]. The iris couplers are precisely electricaldischarge machined (EDM) into the solid copper block toensured repeatable and accurate coupling. EDM provides
the exceptional accuracy and repeatability that is critical
for this device. This technique also ensures that the
waveguide braze has little or no affect on the cavity
performance from the migration of braze material. The
two cavities are designed to operate at the same frequency
and a small amount of tuning is provided for adjustment
after brazing.
The outputs of the cavity are fed into 76-mm-longlinear E-plane tapered waveguide transitions, whichtransform the cavity outputs (3 mm by 19.05 mm) to
standard WR-75 waveguide (9.53 mm by 19.05 mm). The
vacuum window shown in Fig. 3 is brazed into the WR75
waveguide flanges with a gold germanium filler alloy.
The rf windows are made from glass fused onto a kovar
base. The kovar is plated with nickel and then copper tofacilitate brazing. The overall electrical performance ofthe transitions and windows together have a -20-db returnloss with less than 0.2-dB insertion loss over a 200-MHz
bandwidth centered at 11.384 GHz.

Figure 2: X-Band Cavity BPM Cross-Section.
The X-band cavity BPM inherently has thecapability of resolving the beam position in the tens ofnanometers, far exceeding the 1-micron resolution
requirement indicated in Table 1. Equation 2 estimates the
BPM thermal noise voltage output. Given the Bolzmann
constant k, operating temperature T in Kelvin, impedance
Z is 50 Ohms, the signal bandwidth B is about 2 MHz,and considering a system noise figure of 3 dB theminimum resolution would typically be less than 10 nm.

FEL Technology

Figure 3: X-Band Cavity RF Window.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

The BPM is a brazed assembly made up of thebody, waveguide transitions, cavity end caps, rf windows,
and end EVAC-type vacuum flanges. The 11.738-mmradius monopole and 14.937-mm-radius dipole cavities
are machined within a +0.000/-0.015-mm tolerance, witha surface finish of 0.1 ȝm (4 ȝin Ra) or better into a single
piece of oxygen-free electronic copper. The machining
tolerance deviation of +0.000/-0.015 mm will equate to afrequency increase of 7.5 MHz, which is within thesystem tuning capability. The final assembly is brazed ina vacuum furnace back-filled with dry hydrogen.
To facilitate installation alignment, the outersurface of the BPM body shown in Fig. 2 is machined tobe concentric to the cavity to within 0.025 mm. Thissurface will be used as the fiducilization reference to alignthe BPM during installation.
There are two waveguide outputs for each plane on
the dipole cavity. The output flanges are connected
directly to the flexible WR75 waveguide shown in Fig. 4
to mechanically decouple any shock or vibration from therest of the components. The waveguide provides an idealtransmission line for the X-band signals exhibiting very
low loss and excellent radiation hardness. The original
design concept incorporated optional magic tee power
combiners at each pair of outputs on the dipole cavity.
This effectively reduces the common mode noise
generated by unwanted modes by about 20 db. It is
expected that full compliance to the specification can beaccomplished without the use of the combiner. This
would facilitate the potential for using the unused or
terminated ports for future diagnostics.
Each of the three inputs to the receiver is band
limited by bandpass filters. The filters provide a 20-MHz
bandwidth (-3 dB) centered at 11.384 GHz. The filters
also provide a broadband -10 dB return loss match to thecavities. Out-of-band filtering of -60 db reduces unwanted
modes from saturating the receiver input.

RECEIVER DESIGN
The receiver topology used is a single-stage threechannel heterodyne receiver shown in Fig. 1. The cavity
BPM X-band signals are downconvertered to a 25- to 50MHz intermediate frequency (IF) in the accelerator
tunnel. The signals are first amplified in a low noise
amplification (LNA) stage, then translated to a lower IF
by mixing with a local oscillator (LO). The LO is a phaselocked dielectric resonate oscillator (PDRO) featuring low
phase noise. One option is to lock the LO to the SLAC
119-MHz timing reference. This has the advantage ofsynchronizing the data with the beam. The other option
would have the LO operate in a free-run mode. A single
LO will drive all three channels and will be housed in thereceiver chassis. The LNA is protected against highpower surges by a limiter that is rated at 50 W peak. Afterthe X-band signals are down-converted, they are filteredand then amplified. The signals are then cabled out of thetunnel. The expected output of the receiver will be a bipolar +/- 1-volt full-scale exponentially decaying sine
wave between 175-260 ns (Q=2000-3000) in duration.
The receiver will be housed in an aluminum 3 in.
high × 12 in. wide × 12 in. deep shielded enclosure. The
unit will not dissipate more that 20 W and can be heatsunk. Special consideration is given to electro magnetic
interference (EMI) susceptibility and emissions by using
DC blocks on the inputs, EMI gaskets, feed through pins,
and proper grounding. The receiver will be mounted in
the tunnel below the undulator girder.
The data acquisition utilizes a commerciallyavailable ADC digitizer board. The ADC front end shouldhave a minimum of 14-bit resolution and a sampling rateof 119 MSPS. The ADC clock will be synchronized to thefrequency of the 119-MHz timing system of the SLAC
linac. This will be considered the minimum requirement
for the ADC and it is hoped that the performancerequirement can be exceeded when the system is required.
The original plan for acquiring data for the
prototype was to simply capture the exponentiallydecaying waveform and digitally peak detect the reference
and position signals. The position and reference cavity IF
signal data would then be fit to an exponential curve, withthe position data being normalized to the reference.
Another processing algorithm being investigated is
to digitally down-convert the IF signals. The raw digital
waveform is multiplied point-by-point by a complex LOe jZt where Z is the IF frequency. A digital low-passfilter removes the 2Z component leaving a complex

Figure 4: X-band cavity testing.

708

baseband signal. A quasi-Gaussian, symmetric, finite
impulse response (FIR) digital filter is chosen to remove
the 2Z product as well as out-of-band noise. The
complex amplitude of the position signal is normalized by
the reference cavity to remove bunch charge dependence(amplitude) and beam arrival time dependence (phase).
Normalized phase and amplitude are converted to position
via scaling and rotation by calibration data.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH054

PROTOTYE RESULTS
Two X-band cavity BPMs have been prototyped andcold tested using a test fixture that precisely moves an
O E probe driven by an Hp 8510 network analyzer that4
excites the cavity and then measures the response. Table
2 shows the predicted and measured results of a boltedtogether prototype and brazed prototype. The monopoleand dipole cavities were modeled using HFSS [5]. The
difference of predicted vs. the measured frequency for the
TM110 dipole mode was less than 0.2 % for bothprototypes.
Table 2: Prototype cold test results.
Parameter
Predicted Measured(500 ȝm
Prototype
offset)# 1 bolted
end caps
Frequency 8.262 GHz 8.271 GHz
TM010

MeasuredPrototype# 2 brazed
end caps
8.243 GHz

Coupling
TM010
Frequency
TM110-53 dB-69 dB-62 dB

11.364GHz

11.344GHz

11.357
GHz

Coupling
TM110
Q (loaded)
TM110
X/Y
Isolation
TM110
Dipole to
Monopole
cavityIsolation
Frequency
TM020-32 dB-28 dB-24 dB

2704

2086

2391

-26 dB-33 dB-23 dB

Coupling
TM020

Table 3. Prototype ITS test results.
Predicted
Cold Test
ITS Test
11.364 GHz 11.357 GHz 11.359 GHz
2704
2391
2500
-26 dB-23 dB-21 dB

CONCLUSIONS
X-band cavity BPM and receiver electronics havebeen designed and tested for micron-level resolution foreventual installation into the LCLS. Preliminary lowpower test and beam test using the ITS have produced
encouraging results in validating the design for achieving
the stated goals. ITS testing is scheduled to continue toobtain valuable operational experience.
The second phase of testing will involve building three
new BPMs and installing them at a fixed distance fromeach other in order to measure single-shot trajectories.
The new BPMs will incorporate changes that will
facilitate a small amount of cavity tuning. The BPMs will
be installed in the APS LEUTL tunnel in October 2006.
The testing objective is to provide a complete compliancetable for the given specification given in Table 1. Beamconditions will be similar to the expected LCLS photo
cathode beam. The prototype testing should be completeby early next year, followed by the production of 34
cavity BPMs.

ACKNOWLEDGMENTS<-80 dB<-85 dB<-89 dB

15.825GHz

15.767GHz

15.785GHz-78 dB-64 dB-50 dBThe brazed prototype cavity BPM is presently
installed in the Advanced Photon Source Injector Test
Stand (ITS) shown in Fig. 4. The BPM is mounted on a
precision 2-axis translation stage to test and calibrate theBPM. The ITS provides 1-nC single-bunch charge withbunch lengths 3-4 ps FWHM. The preliminary data shownin Table 3 indicates good correlation with the cold test andpredicted values. An estimated voltage output of thedipole cavity was calculated to be 2.3 mV/Pm/nC and themeasured value was 1.22 mV/Pm/nC. The current monitor
used for this measurement has been recently recalibrated
and the BPM output response will be re-measured.

FEL Technology

Parameter
Frequency
Loaded Q
Isolation
X/Y

The authors would like to acknowledge Stephen
Milton, John Carwardine, Glenn Decker, and Om Singhfor many helpful discussions. The authors would also liketo thank Randy Zabel for all his help with building andtesting the prototypes.

REFERENCES[1] R. Hettel, R. Carr, C. Field, and D. Martin,“Investigation of Beam Alignment Monitor
Technologies for the LCLS FEL Undulator,” BIW 98,
Stanford CA, May 1998, p. 413.
[2] P. Emma, J. Wu, “Trajectory Stability modeling andTolerances in the LCLS,” EPAC 2006, Edinburgh,
Scotland, June 2006.
[3] A.Liapine, www.hep.ucl.ac.uk/~liapine/part_one_
waveguides_and_cavities.doc[4] Z. Li, R. Johnson, S. Smith, T. Naito, J. Rifkin,“Cavity BPM with Dipole-Mode-Selective Coupler,”
PAC 03, Portland Oregon, May 2003.
>5@ Ansoft HFSS, version 10.0, Ansoft Corporation,
Pittsburgh, PA, USA, 2005.

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NONINTERCEPTING BEAM SIZE AND POSITION MONITOR USINGODR FOR X-RAY FELS*
A.H. Lumpkin**, N.S. Sereno, W.J. Berg, D.W. Rule†, B.X. Yang, and C.-Y. Yao
Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, U.S.A.
†
Carderock Division, NSWC, West Bethesda, MD 20817 USA.
Abstract
Interest in nonintercepting (NI) beam size and position
diagnostics between the undulators of x-ray free-electron
lasers (XFELs) is driven by the requirement of beamemittance matching and beam alignment, as well as by theneed to minimize radiation damage to the undulator
permanent magnets from scattered beam produced by theinsertion of converter screens. For these reasons ourinvestigations on optical diffraction radiation (ODR) as
relative beam size and position diagnostics are
particularly relevant to XFELs. We report the extensionsof our studies at 7-GeV beam energy to aspects of thevertical and horizontal polarization components of the
ODR near-field and far-field images. The near-field,
vertically polarized data are particularly interesting
because the vertical field lines at the metal more directlyreflect the actual horizontal beam sizes. Although ourexperiments to date are with mm-scale beams and impact
parameters of 1-2 mm, our analytical model indicates that
this technique scales with beam size and has sensitivity at
the 20- to 50-μm regime with an impact parameter, d = 5
times σy = 100 μm. This is the x-ray FEL intraundulator
beam size regime.

INTRODUCTION
The interest in nonintercepting (NI) diagnostics forbeam size and position in the undulators of x-ray freeelectron lasers (XFELs) for beam match reasons is driven
by the need to minimize the radiation damage to theundulator permanent magnets by scattering of beam byinserted converter screens. For such reasons ourinvestigations on optical diffraction radiation (ODR) as
NI relative beam size and position diagnostics [1-10] areparticularly relevant. We reported initial experiments at
FEL05 [11], and now we report the extensions of ourstudies at 7-GeV beam energy to aspects of the verticaland horizontal polarization components of the ODR nearfield and far-field images. It appears that the near-field,
vertically polarized data are particularly interesting. For
our measurements of the beam size along the horizontal
axis with a vertically displaced metal screen, the induced
currents from the vertical field lines at the metal more
directly reflect the actual beam size as revealed by scansof the upstream quadrupole fields. In addition, in our
experimental configuration the vertical polarizer also
rejects the strongest component of a weak background of_____________________________________________*Work supported by the U.S. Department of Energy, Office of Science,
Office of Basic Energy Sciences, under Contract No. W-31-109-ENG38.
**
lumpkin@aps.anl.gov

710

visible-light optical synchrotron radiation (OSR)
generated when the beam transits the horizontal bend
dipole magnet that is 5.84-m upstream of the ODR station[12]. This same concept would be applicable to blocking
the polarized visible undulator radiation co-propagatingwith the e-beam in an XFEL.
Although our experiments are with larger beams andimpact parameters of 1-2 mm, our analytical model
indicates that the technique scales with beam size and has
sensitivity at the 20- to 50-μm regime with the impact
parameter, d = 5 times σy = 100 μm. The beam size issimilar to the 30-μm beam size in the XFEL
intraundulator location. In addition, a direct comparisonof the horizontal position readings of the nearby rf beam
position monitor (BPM) and the ODR image centroid
values during the scan of the upstream dipole current
showed good agreement. The ODR data were also foundto be very similar to an OTR image value during a similar
dipole current scan. Our experimental results and somemodeling results will be presented.

EXPERIMENTAL BACKGROUND
The Advanced Photon Source (APS) facility includes
an injector complex with an rf thermionic cathode gun, an
S-band linear accelerator, a particle accumulator ring(PAR) that damps the linac beam at 325 MeV, a booster
injector synchrotron that ramps the energy from 0.325
GeV to 7 GeV in 220 ms, and the 7-GeV storage ring. At
the exit of the booster, a dipole magnet allows direction of
the beam to an alternate booster extraction beamline(BTX) that ends with a beam dump. This spur line has
been used to develop our optical transition radiation(OTR) and our ODR diagnostics. The setup includes the
upstream corrector magnets, two quadrupoles, and adipole; and then, 5.8-m downstream the rf BPM(horizontal), the OTR/ODR imaging station, a localized
beam-loss monitor based on a Cherenkov radiation
detector, a Chromox beam-profiling screen, and the beamdump, as schematically shown in Fig. 1. An additionalfeature of the remote control of one strategic lens changes
the optics from near-field to far-field imaging.
The ODR converter is a polished Al blade/mirror that is
1.5-mm thick, 30-mm wide, 30-mm tall, and it is mountedwith its surface normal at 45º to the beam direction on a
vertical stepper assembly. Its horizontal edge can bevertically positioned with an overall accuracy of ±10 μm
over a span of 27.5 mm. The alignment of the optics withconverter surface angle was done with an alignment laser
placed on the surveyed beamline axis during an access

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Proceedings of FEL 2006, BESSY, Berlin, Germany
period as described previously [12]. The near-fieldmagnification resulted in calibration factors of 60-μm per
pixel in x and 45-μm per pixel in y. Two 6-position filter
wheels were used to select neutral density (ND) filters,
bandpass filters, or two polarizers, which are oriented at
90 degrees to each other. The images are detected with astandard SONY charge-coupled device (CCD) camera,
and the video is digitized with a MaxVideo MV200
digitizer interfaced to the Experimental Physics andIndustrial Control Systems (EPICS) software architecture.
The online image processing allows the selection of aregion of interest, formation of the projected x and yprofiles, and both a Gaussian fit to the profile and anumerical evaluation of the FWHM of the profile. The
rms size is then the sigma of the Gaussian result or theestimated value found by dividing the numericallycalculated FWHM by 2.35.
Fluorescent Screen
Assembly Al2O3: Cr

ODR Assembly
Cherenkov Detector
BEAM

Beam
Dump
CCD
CameraGaussian when extracted from the 7-GeV booster
synchrotron. Next, in Fig. 3, we show the observed
vertically polarized ODR image profiles with an impact
parameter of 1.25 mm during a similar quadruople field
scan. The vertically polarized ODR horizontal image
profiles track the beam size changes as seen qualitatively
by the shape of the curve with AQ2 current. A directcomparison of the OTR and ODR is seen in the Fig. 4
combined plot of their fitted rms values. The ODR
profiles are about 10% to 25% larger than thecorresponding OTR profiles from the largest beam size tothe smallest, respectively. The ratio of ODR/OTR for thesize scan is next plotted in Fig. 5 to act as a lookup table
for the beam-size monitor. As can be seen, at theminimum size of 1300 μm for the OTR, the ODR fit value
is only 25% larger. This is much better than our factor of
two results with unpolarized ODR observed on the same
shift for this minimum beam focus and also reported at
BIW06 [12]. The vertical polarization component would
appear to be more reliable and direct in monitoring theactual beam size to better than 10% one has the ratio tableor plot for these conditions.

Dipole & Vertical
Corrector Magnets
Upstreamrf BPM(horizontal)
OpticalTransport
Turning
MirrorODR CCD
CameraFigure 1: A Pro-E drawing of the OTR/ODR imaging
station showing the rf BPM, the cube and stepper drive,the optical transport, the Cherenkov detector local loss
monitor, and the Chromox profile monitor.

EXPERIMENTAL AND ANALYTICALRESULTS
As mentioned in the previous section, the ODR profile
results are referenced to complementary OTR profile
results, and the image centroids are compared to the
nearby, upstream rf BPM. The SDDS tools are used forthe tracking of the process variables [13, 14].
The potential to monitor relative beam size has been
discussed in our earlier papers [11, 12, 15]. However, in
this case we now have the results of vertically polarized
data. The OTR image profiles were first obtained byinserting the Al metal screen during a scan of the
upstream AQ2 quadrupole field. This quadrupole strongly
affects the horizontal beam size at our OTR/ODR station.
Unfortunately, this is at a dispersive point in the lattice so
we do not get emittance data cleanly from the quadrupole
field scan. However, we do obtain a test of ODR as arelative beam size monitor. As seen in Fig. 2, theunpolarized, OTR-measured horizontal beam size varies
from 2300 μm down to about 1300 μm. Results of bothalgorithms are shown, and they are seen to be in very
good agreement because the beam shape is basically

FEL Technology

THPPH055

Figure 2: A plot of the OTR rms horizontal profile sizes
for the upstream AQ2 quadrupole field scan. Both aGaussian fit and a simple peak intensity to FWHM
algorithm were used, which are in good agreement.

Figure 3: A plot of the vertically polarized ODR rms
horizontal profile sizes for the upstream AQ2 quadrupole
field scan. Both a Gaussian fit and a simple peak intensity
to FWHM algorithm were used to measure image sizes,
which are in good agreement.

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calculated for the 50-μm beam size. Image processing
should easily detect this change and use of polarization
would improve the sensitivity. This should be a good
match to monitoring beams of 30-μm size in the XFELs,
subject to signal levels.
1.0

Relative Intensity

Figure 4: A direct comparison of the ODR (plus) andOTR (diamonds) Gaussian-fit horizontal profile size s
during the quadrupole field scan. The vertically polarizedODR tracks the beam-size changes.

σx = 1300 μm

σy=200 μm

0.9

σx = 1040 μm

0.8

σx = 1560 μm

0.7

e points

-1

0.6
0.5
0.4
0.3
0.2
0.1
0.0
0

1000

2000

3000

4000

5000

ux (μm)Figure 6: Analytical model results for the effects on theunpolarized ODR horizontal profiles for a variation of thebeam size by ±20% around the 1300-μm value with
d=1000 μm.
1.00.9

σx = 20 μm

Figure 5: The ratio of ODR/OTR horizontal image sizesfor different beam sizes during the AQ2 quadrupole scan.
This ratio is noticeably smaller than for unpolarized datareported earlier.

Relative Intensity

0.8

σx = 50 μm

0.7

Half-widths

0.6
0.5
0.4
0.3
0.2
0.1
0.0
0

In Fig. 6, we show the analytical results from our model
described previously [11] for a beam size change of ±20%around the nominal σx=1300-μm value and thecorresponding ODR image profile changes at the 1/epoints in intensity. First, it is clear there is sensitivity to
the beam-size changes that should be detectable in thecamera images. Second, the HWHM values indicate an
ODR profile of about 1.2 times the actual beam size as
seen in the polarized data comparisons. These were donewith a fixed σy = 200 μm. Initial vertical polarization
effects have also been calculated, but further work isneeded. The calculated ODR x width using the verticalpolarization component was 20 to 50% narrower than that
calculated using the horizontal component for d = 1000
and 2000 μm, respectively.
We also have calculated the sensitivity of ODR profiles
to smaller beam sizes. In this case, we held the y size
constant at 20 μm and varied the x-size from 20 to 50 μm
using an impact parameter of 100 μm and beam energy of
7 GeV. In Fig. 7 it is clear that approximately a 25%
increase in the ODR horizontal profile half width is

712

100

200

300

400

500

ux (μm)Figure 7: Analytical results for the change in unpolarized,
horizontal ODR profiles for a change in beam size from
20 to 50 μm while holding the y value constant at 20 μm.
The impact parameter is 100 μm for the 7-GeV beam.
This is relevant to XFEL beam-size monitoring.
In addition, we repeated our relative beam position
measurements first done with unpolarized ODR andcompared to the rf BPM and OTR values [11]. In thiscase, we again used vertically polarized ODR with an
impact parameter, d = 1.25 mm and a vertical size σy of
200 μm or less. The plot in Fig. 8 actually compares thecentroid values from both OTR and ODR to the horizontal
BPM readings. The OTR and ODR data overlap eachother almost completely. This was done with the beam
size σx = 1300 μm, the AQ2 quadrupole field set for the
beam size minimum. Again, we believe the verticallypolarized ODR component benefits the measurement
sensitivity in the horizontal axis. Sensitivity at the 50- to

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Proceedings of FEL 2006, BESSY, Berlin, Germany
100-μm relative position level is attained. As in the caseof beam size monitoring, for the much smaller beam andimpact parameter in the XFEL case, we would expect
much better position sensitivity (sub-10 μm) subject tosignal level. Correspondingly, a vertical, single edge of ametal screen or aperture can be employed to obtain
information on vertical position and beam size.

Figure 8: A plot of the OTR and ODR centroid valuechanges versus the nearby rf BPM values in mm during ascan of the upstream dipole current supply (and magnet
fields). Horizontal position information can be reliably
obtained from the vertically polarized ODR image
centroids.

SUMMARY
In summary, we have extended our NI diagnostics
techniques by evaluating the vertical and horizontal
polarization components of near-field ODR images. As
expected, the induced currents from the vertical field lines
more directly represent the horizontal beam size in ourconfiguration. Our results indicate that the tracking ofrelative beam size and position can be scaled down toaddress the potential needs of x-ray FELs.
Complementary information on beam trajectory angle andbeam divergence is being explored as well for higher
average current beams.

THPPH055

REFERENCES
1. A.P. Kazantsev and G.I. Surdutovich, Sov. Phys. Sokl.
7, 990 (1963).
2. M.L. Ter-Mikaelian, High Energy Electromagnetic
Processes in Condensed Media (Wiley/Interscience,
New York, 1972).
3. M. Castellano, Nucl. Instrum. Methods A 394, 275(1997).
4. Y. Shibata et al., Phys. Rev. E 52, 678 (1995).
5. A.P. Potylitsyn, Nucl. Instrum. Methods B 145, 169(1998).
6. R.B. Fiorito, D.W. Rule, and W.D. Kimura, AIP Conf.
Proc. 472, 725 (1999); W.D. Kimura, R.B. Fiorito,
and D.W. Rule, Proc. of the 1999 Particle Accelerator
Conference, 487 (1999).
7. D.W. Rule, R.B. Fiorito, and W.D. Kimura, AIP Conf.
Proc. 390, 510 (1997).
8. R.B. Fiorito and D.W. Rule, Nucl. Instrum. Methods
B 173, 67 (2001).
9. T. Muto et al., Phys. Rev. Lett. 90(10) 104801-1(2003).
10. P. Karataev et al., Phys. Rev. Lett. 93, 244802 (2004).
11. A.H. Lumpkin et al., “Nonintercepting Electron
Beam Diagnostics Based on Optical Diffraction
Radiation for X-ray FELs,” Proceedings of theInternational FEL05 Conference, Stanford, CA, Aug.
21-26, 2005, JACoW/eConfC0508213, p. 604.
12. A.H. Lumpkin et al., “Developments in OTR/ODR
Imaging Techniques for 7-GeV Electron Beams at
APS,” submitted to Proceedings of BIW06, Batavia,
Illinois, May 1-4, 2006.
13. L. Emery, M. Borland, H. Shang, R. Soliday, “User’s
Guide for SDDS-Compliant EPICS Toolkit Version
1.5,” Advanced Photon Source, March 9, 2005.
14. H. Shang, Proc. of PAC2003, 3470 (2003).
15. A.H. Lumpkin et al., “Near-Field Imaging of Optical
Diffraction Radiation Generated by a 7-GeV Electron
Beam,” submitted to Phys. Rev.

ACKNOWLEDGMENTS
The authors acknowledge the support of Brian
Rusthoven, Al Barcikowski, and Mike Bracken in the
Mechanical Engineering Group, Joe Gagliano and Wayne
Michalek in the Vacuum Group, Chuck Gold of the
Diagnostics Group, and Bill Jansma and Horst Friedsamin the Survey Group for installation and resurvey,
respectively, of the station in December 2005 and January
2006. The laser alignment proved to be a criticalcontribution to the new optics setup and the rotated BPM
addressed the horizontal plane request.

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INITIAL SEARCH FOR 9-keV XTR FROM A 28-GeV BEAM AT SPPS*
A.H. Lumpkin, J.B. Hastings,** and D.W. Rule***Advanced Photon Source, Argonne National Laboratory
Argonne, IL 60439 USA
Abstract
The potential to use x-ray transition radiation (XTR) asa beam diagnostic and coherent XTR (CXTR) as a gain
diagnostic in an x-ray FEL was proposed previously. At
that time we noted that the unique configuration of the
SLAC Sub-picosecond Photon Source (SPPS) with its
known x-ray wiggler source, a special three-element x-ray
monochromator, x-ray transport line, and experimental
end station with x-ray detectors made it an ideal location
for an XTR feasibility experiment. Estimates of the XTR
compared to the SPPS source strength were done, andinitial experiments were performed in September 2005.
Complementary measurements on optical transition
radiation (OTR) far-field images from a 7-GeV beam arealso discussed.

INTRODUCTION
The use of x-ray transition radiation (XTR) as a beamdiagnostic and coherent XTR (CXTR) as a gain
diagnostic in an x-ray free-electron laser (XFEL) was
proposed previously at FEL04 [1]. There have been anumber of experiments to develop XTR as a source of xrays in the past at several laboratories using moderatebeam energies of a few hundred MeV to GeV [2-6], butthere have been no applications in the FEL world to date.
Partly based on recent experiments with a 7-GeV beamwith optical transition radiation (OTR) and far-field or
focus-at-infinity imaging [7], we projected that there
should also be useful diagnostic information in the XTR
field. In addition, we wanted to evaluate how to measure
CXTR in an XFEL at 1.5 Angstroms. We identified theconfiguration of the SLAC Sub-picosecond Photon
Source (SPPS) [8] with its known x-ray wiggler source, aspecial three-element x-ray monochromator, x-raytransport line, and experimental end station with x-ray
detectors as a large-scale and ideal location for an XTR
feasibility experiment. It was also the closest setup towhat one might encounter in an x-ray FEL such as the
Linac Coherent Light Source (LCLS) with its capabilityof translating in the 3-m undulator segments one at a timein the 100-m string of magnetic structures [9].
A test of XTR intensity with respect to the x-rays
emitted by the SPPS wiggler when a 28-GeV beamtransited it was proposed. Estimates of the XTR weredone, the experiment proposal was approved, and initial
experiments were performed in September 2005.

EXPERIMENTAL BACKGROUNDThe OTR experiments were performed at the Advanced
Photon Source (APS) as described elsewhere [7], and the
XTR experiments were performed at the SPPS. The SPPS
has been a short-pulse x-ray facility since 2004 [8]. The
28-GeV electron beam with a charge of Q = 3 nC, anemittance of 35 π mm-mrad, and bunch length of 230 fs
was transported to the Final Focus Test Beam (FFTB)
facility from the main SLAC accelerator [10] and throughthe single, permanent magnet wiggler as shown
schematically in Fig. 1. The SPPS source was tuned to 9
keV by adjusting the wiggler gap, and a three-element xray monochromator is used to direct the x-rays down a
50-m long beamline to the end station. In addition, as
noted in the schematic, there are several OTR stations
with 1-μm-thick Ti foil installed in support of the series ofexperiments on beam driven plasma Wakefield
acceleration by M. Hogan and his collaborators [11].
These Ti foils were used to generate the forward XTR for
the trial experiments. A dipole at the end of the electron
beam beamline directed the electrons to a beam dump.

Figure 1: A schematic of the FFTB facility showing the beamline, SPPS wiggler, OTR stations, monochromator, andx-ray detectors.
___________________________________________*Work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. W-31-109-ENG-38.
**SPPS/SLAC, Menlo Park, CA USA***Carderock Division, NSCW, West Bethesda, MD USA

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Figure 2: A schematic of the generation of XTR from afoil or foil stack from a 14-GeV beam and with competing
wiggler x-rays or spontaneous emission in a SASE FEL.

EXPERIMENTAL RESULTS ANDDISCUSSIONOTR Results at 7 GeV
As a point of reference, the results of complementary
experiments on the 7-GeV beam at APS are included. In
this case a single Al screen was used to generate thebackward OTR. At this beam energy the expected OTR
opening angle would be 70 μrad. This is within a factor of
two of the angle in LCLS and of four in that for SPPS. In
Fig. 3 we see the unpolarized, vertically polarized, andhorizontally polarized images for the beam extracted fromthe booster synchrotron. For beam charges of 3 nC one
could image these far-field angular distributions. The
depth of the central minimum indicates the ensemble
beam divergence is much smaller than 70 μrad, probably
less than 10 μrad. An analytical model [12] was used toevaluate the expected profiles for different divergences.
An example is shown in Fig. 4 for 3-μrad divergence.

Y (1-mrad

range)

This dipole was the source of broadband x-ray
synchrotron radiation (XSR) that also would beinteracting with the three-element crystal monochromator.
The three-element monochromator was adjusted totransport 9-keV x-rays from the wiggler using a series of
x-ray detectors along the beamline.
At the end station an ANDOR x-ray CCD camera andPhotonic Science X-Ray Eye intensified camera wereused as the principle diagnostic components. The wiggler
x-rays were also aligned based on a series of x-ray APDs
along the beamline. The ANDOR camera is designed tobe cooled to reduce read noise and dark current.
Unfortunately on these particular experiments, a small
vacuum leak in the camera prevented the final cool down,
so we ran it at room temperature. The X-ray Eye waspositioned about 1 meter downstream of the CCD camera
and was used for initial wiggler beam and hencemonochromator alignments. The attenuation of the SPPS
source x-ray was done with various selections of Al foil
thicknesses that were calculated to attenuate 9-keV x-rays
by factors of up to 4000. At 10-keV x-ray energy thecounts per detected photon was about 391, resulting in a
dynamic range of 167. This assumed a 16-bit device and again of seven photoelectrons per count in the CCD.
Aspects of the possible eventual XTR application to
LCLS are shown in Fig. 2. In the schematic the beamenergy is 14 GeV and the OTR and XTR are generated bya thin foil (or foil stack). For OTR an off-axis mirror
might be used, but for XTR an annular crystal would be
used. The expected opening angle of the radiation conesin either case would be 1/γ = 35 μrad. For OTR an
imaging system would be used, and for XTR the YAG:Ceconverter plus lens and CCD camera might be employed.
A far-field imaging experiment with lenses appears
feasible for the OTR. This would be done in a manner
similar to our recent 7-GeV beam work at APS [7].

THPPH056θθX (1.2-mrad range)
Figure 3: Example of far-field OTR images generated by a 7-GeV beam at APS; a) unpolarized, b) vertically polarized,
and c) horizontally polarized.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Intensity (counts)

THPPH056

2000

0

0

Figure 4: An analytical calculation of the OTR single foil
angular distribution for a 7-GeV beam with 3-μrad
divergence. The opening angle is ~70 μrad.

500
1000
θy (pixel no.)Figure 6: A vertical angular distribution profile from
Fig. 5.

9-keV X-rays

θx

XSR
Nozzleθx

In the case of the SPPS experiments we accepted thestandard tuneup for 9-keV photons. The nominal intensity
was projected to be 107 photons per 3 nC of charge. We
had calculated the XTR yield from carbon foils as ~103
photons per 3 nC. The initial SPPS result is shown in
Fig. 5 using the Al foil attenuation of 1000. The observed
image corresponds to supported transport of 30×80 μrad2.
The three-element crystal monochromator is oriented in
the horizontal plane with a spatial acceptance of about 1
mm, but subtends larger vertical angles. An example
profile is shown in Fig. 6, indicating a vertical FWHM of
about 20 μrad. In Fig. 7 we show the 9-keV x-ray imageof the background XSR (attributed to the dipole upstreamof the monochromator) obtained with the wiggler gap
open and foils extracted. The gas nozzle from theexperimental chamber just upstream of the x-ray CCD is
actually inserted vertically from the top. It shadows the xrays, and was seen in the horizontal axis because the CCD
camera is rotated 90 degrees in the installation. The
uniform stripe of the XSR from the vertically deflecting
dipole is seen clearly. There is also a ghost image in the
10-shot average due to some camera trigger
inconsistency.

θyFigure 7: An x-ray CCD image of 9-keV XSRbackground coming down the beamline. The gas jet
nozzle in a chamber upstream of the camera is shadowed.
It is vertically insertable.
In Fig. 8 we show the observed x-ray image signal withall three foils inserted using a selected region of interest(ROI) with 4x4 pixel binning and with backgroundsubtraction of the signals with the wiggler gap open andall three foils out. This is a localized ROI pixel binning to
improve statistics and camera sync. In Fig. 9 the profile inθy is shown. There is a hint of an annular shape, and theopening angles are marked on the profile as might be forthe middle foil distance. Based on a calibration factor of
1.1 μrad per 4-pixel bin, the 18-μrad location is estimatedfor a foil at 80 m. In Fig. 10 a calculation for OTR from a28-GeV beam is shown as a point of comparison for adivergence value of 5 μrad. The central minimum isdeeper in the calculation than in the data profile.

θyFigure 5: An x-ray CCD image of the SPPS 9-keV x-rays
from the wiggler. The camera is rotated 90º so θy is along
the image horizontal axis. The signal is attenuated by
1000.

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THPPH056

SUMMARYθx (pixel no.)

1000
800
600
400
200
0

500
1000
θy (pixel no.)Figure 8: A background subtracted x-ray CCD ROI imageof the 9-keV x-rays with three Ti foils inserted.

ACKNOWLEDGMENTS
The authors acknowledge the assistance of Kelly
Gaffney on the x-ray CCD, Aaron Lindenberg forborrowing the X-ray Eye, and the team of SPPS graduate
students who rotated through the extended shifts at SLAC.
They also thank Mark Hogan for use of the OTR stationsin the FFTB.

8000

18 μradIntensity

6000

In summary, we have shown the possibilities of OTR
far-field imaging for a 7-GeV beam and report our initialattempts to extend such research to XTR from a 28-GeV
beam. Due to the unfortunate event that the x-ray CCD
camera could not be cooled during the XTR trials, theresults are inconclusive. Certainly, XTR was generated by
the Ti foils, but the unambiguous imaging of thatradiation was problematical. The concept of a foil stack toenhance the XTR signal and the ability to actually cool
the CCD were next on the agenda. The closing of the
SPPS facility occurred before these experiments could bedone, but the LCLS or SABER facilities at SLAC may
provide a future opportunity to test the concepts.

REFERENCES

4000

2000

0

500
θy (pixel no.)1000

Figure 9: An x-ray CCD region of interest for the three
XTR foils inserted case including background subtractionof the XSR source.

Figure 10: A calculation of the OTR angular distribution
for a 28-GeV beam and 5-μrad divergence.

FEL Technology[1] A.H. Lumpkin, W.M. Fawley, and D.W. Rule, “A
ConceptforZ-dependent
Microbunching
Measurements with Coherent X-ray Transition
Radiation in a SASE FEL,” Proceedings of the 2004
FEL Conference, Trieste, Italy, Editors: Bakker,
Giannessi, Marsi, and Walker, 515 (2005).
[2] A.N. Chu et al., J. Appl. Phys. 51 (3) 1290 (March1980).
[3] Michael J. Moran, Nucl. Instrum. Methods B24/25
335 (1987).
[4] Michael J. Moran, Nucl. Instrum. Methods B33, 18(1988).
[5] M.A. Piestrup et al., Phys. Rev. A 45 (2) 1183 (1992).
[6] H. Backe et al., Z. Phyz. A 349 87 (1994).
[7] A.H. Lumpkin et al., “Developments in OTR/ODR
Imaging Techniques for 7-GeV Electron Beams at
APS,” submitted to Proceedings of BIW06, Batavia,
Illinois, May 1-4, 2006, AIP (in press).
[8] J.B. Hastings, “Sub-Picosecond Pulse Source: Recent
Results,” presented at PAC2005, Knoxville,
Tennessee, TOPB002.
[9] R.M. Bionta, “Characterization of X-ray FEL
Radiation,” presented at FEL2005, Stanford, CA,
THOB003.
[10] P. Emma et al., Proceedings of the PAC2003, 3129
(2003).
[11] M.J. Hogan et al., “Review of Beam-Driven Plasma
Wakefield Experiments at SLAC,” presented at
PAC2005, Knoxville, Tennessee, TOPA002.
[12] D.W. Rule, code Singlef, transported to APS Unix
system 1992.

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MODELING AND MEASUREMENT OF μ-METAL SHIELDING EFFECT
ON THE MAGNETIC PERFORMANCE OF AN LCLS UNDULATOR*
Shigemi Sasaki, Isaac B. Vasserman, Emil Trakhtenberg
APS/ANL, Argonne, IL 60439, USA.
Abstract
In a previous paper [1], we presented results showing that
the Earth’s field might have a significant effect on the
Linac Coherent Light Source (LCLS) undulator
performance due to a large concentration of the field by
the undulator poles. Based on the result of model
calculation, we decided to shield the Earth’s field bysurrounding the undulator backing structure with a
1-mm-thick μ-metal sheet.
First, the effect of the shield was modeled using thecode RADIA. According to the calculation, the shielding
factor of a “C-shape” μ-metal shield was better than afactor of eight. Second, we measured the Earth’s fieldshielding effect without an undulator. In our measurementlaboratory, the vertical component of the Earth’s field wasabout 0.5 gauss. It was suppressed down to smaller than
0.1 gauss with the shield. After these backgroundmeasurements, we examined the effect of the shield withan undulator in place. The measurement results show very
good agreement with the model calculation.

in an undulator. The horizontal component of Earth’s
field was found to be well suppressed on the undulator
axis.
Because a dipole field above 0.7 gauss in an undulator
gives an electron trajectory excursion of more than 2 μm
from the undulator axis, this unwanted field needs to be
suppressed or corrected. Figure 1 shows the model used
for the calculation of shielding effect of μ-metal.
The
B-H curve of CO-NETIC sheet [4] was assumed for the
calculation.

INTRODUCTION

EARTH’S FIELD MODELINGAs shown in our previous paper [1], a seven-period
undulator model with a large surrounding solenoid wasused for simulating the Earth’s field effect. By using thissimple model, we found that the averaged field
concentration factor was about 2.4, i.e., a 0.5-gaussexternal vertical dipole field gave a 1.2-gauss dipole field___________________________________________* Work supported by the U.S. Dept. of Energy, Office of Science,
Office of Basic Energy Science, under Contract W-31-109-ENG-38.
#
sasaki@aps.anl.gov

718

Figure 1: A μ-metal shield model used for the calculation.
0.000252mmCONETIC
1mmCONETIC

0.00020

Field [T]For the commissioning of the Linac Coherent Light
Source (LCLS), beam-based alignment will be used tocorrect the offsets of quadrupoles and beam position
monitors. This strategy works only when the field
integrals in each undulator segment are small enough [2].
Undulator segments will be measured and tuned in themagnetic measurement facility (MMF) at the Stanford
Linear Accelerator Center and then installed on the irongirders and moved to the LCLS tunnel. Several sources oferrors are possible here. The first one is due to thedifference of the Earth’s field at the locations of MMF
and tunnel. This difference is exaggerated by aconcentration of the Earth’s field by vanadium-permendur
poles of the device. Another possible source of error is theexistence of the magnetic elements, such as iron, used in
the support system and other elements of the tunnel.
Based on the computer simulations using a simple modelin the RADIA code [3], we decided to use the μ-metal
sheet to shield unwanted external field effect.

No shield

0.000150.000100.00005

0.00000
-300

-200

-100

0

100

200

300

z [mm]

Figure 2: Summary of calculated results.
Figure 2 shows the summary of calculated results. The
green curve represents the field change due to the 0.5gauss external vertical field without a shield. In thecentral region, a field strength averaged over a half period
is about 1.2 gauss. The red and blue curves are for 1-mmand 2-mm-thick μ-metal shields, respectively.
The
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Proceedings of FEL 2006, BESSY, Berlin, Germany

MEASURED RESULTS
The first and second articles of LCLS undulators weretuned in the magnetic measurement facility (MM1) at theAdvanced Photon Source. Prior to the measurement, thebackground field along the measurement bench wasmeasured with a moving coil. Figure 2 shows the Earth’s
field distribution along the z-axis.

In Figure 5, the solid green curve is the second field
integral of the raw data measured without the shield, andthe blue broken curve is the prediction for after the shield
is installed.
300

2Second Field Integral [Tmm ]averaged field was 0.156 gauss for a 1-mm sheet and
0.147 gauss for a 2-mm sheet, respectively. Based onthese calculations, we decided to use a 1-mm thick sheet
for better cost performance. (A sheet with a double
thickness provides only 6 % better shielding.)
From these results, we find that the concentration(enhancement) factor by the poles in an undulator is 2.4,
and the suppression (damping) factor by the μ-metalshield is eight.

THPPH057

200
100
0
-100
-200
-300

w/o Shield Corrected-400

w/o Shield before Corr.

-500
-2000

-1500

-1000

-500

0

500

1000

1500

2000

z [mm]

Figure 5: Second field integrals of raw data and corrected
data.

-35

Field [T]-40

Figure 6 shows the predicted second field integral andthe integral measured after the shield was attached.

-45
-50

2

-55
-60x10

-6

-1500

-1000

-500

0

500

1000

1500

z [mm]

Figure 3: Earth’s field distribution measured in MM1.
From this result, we can estimate the shielding effect by
the μ-metal in an undulator based on the simulation result
described in the previous section. Without the shield, thefield, By, in an undulator due to the Earth’s field ismagnified by a factor of 2.4, i.e., By = BEF x 2.4. After
applying the shield, the remaining field, Byrem, is reduced
by a factor of eight, i.e., Byrem = By/8. Therefore, thesignature of shield, Bsig, is: Bsig = By-Byrem.
Figure 4 shows the signature of μ-metal shield. Aftermeasuring the undulator field without the shield, we canpredict the field distribution with the shield by adding theshield signature to the raw data.
1.6E-04

1.2E-04
1.0E-04
8.0E-05
6.0E-05
4.0E-05
2.0E-05
0.0E+00
-2000

200
150
100
50
0
w/o Shield Corrected-50with Real Shield

-100
-2000

-1500

-1000

-500

0

500

1000

1500

2000

z [mm]

Figure 6: Second field integrals predicted from data without
shield (blue broken line) and the data with the shield (redsolid line), respectively.

The actual measured field data with the μ-metal shield
is in good agreement with the corrected data based on
simulation with a simple model.

DISCUSSION AND SUMMARY

1.4E-04

Shield Signature [T]Second Field Integral [Tmm]

250

-1500

-1000

-500

0

500

1000

1500

z [mm]

Figure 4: Signature of the μ-metal shield.
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2000

In the example shown in this paper, we applied
additional trajectory shims and phase shims to straighten
the trajectory and to reduce the phase error after applying
the μ-metal shield. Also, we corrected the first andsecond field integrals by applying appropriate shims at theentrance and the exit ends of undulator. Figure 7 shows
the trajectory after the final tuning with the shield. The
net kick (corresponding to the first integral) and the net
displacement (corresponding to the second field integral)
are well below the tolerances as shown. Also, thetrajectory excursion in the undulator is well below thetolerances (2 μm).

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Proceedings of FEL 2006, BESSY, Berlin, Germany

1.0

Trajectory [ μ m]

0.5

0.0

-0.5

-1.0

-1.5
-2000

-1500

-1000

-500

0

500

1000

1500

2000

z [mm]

Figure 7: Trajectory of the first article undulator after
final tuning.
In the example in this paper, we used the estimation
procedures in a relatively early stage of the tuning process
in order to demonstrate the effectiveness of this method.
However, because the effectiveness of this method had
been proven, we used it at the very end of the tuning
process for the second article of LCLS undulators.
Here are the steps of the tuning procedures:• Mechanically align an undulator to the Hall-probe
measurement bench.

720• Magnetically align the undulator axis to theHall-probe.
• Set a proper gap by changing the thickness and/or thelocation of spacers (mechanical shims).
• Straighten the horizontal (x) trajectory by using
trajectory shims.
• Minimize the phase errors by using phase shims.
• Straighten the vertical (y) trajectory.
• Apply shims to compensate multipoles.
• Apply μ-metal shield and do final measurements andtuning of field integrals.
• Do final fine tuning, if necessary.

REFERENCES[1] S. Sasaki and I. B. Vasserman, Proceedings on 27th
International Free Electron Laser Conference(FEL2005), Stanford, CA, August 2005.
[2] “Conceptual Design Report (CDR) for the Linac
Coherent Light Source Project,” SLAC-R-593, April
2002, http://www-ssrl.slac.stanford.edu/lcls/cdr .
[3] O. Chubar, P. Elleaume, J. Chavanne, J. Synchrotron
Radiat. 5, 481 (1998).
[4] http://www.magnetic-shield.com/ .

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH058

BEAM SPREADING AND EMITTANCE OSCILLATION OF AN INTENSEMAGNETIZED BEAM IN FREE SPACE∗
Chun-xi Wang† , Kwang-Je Kim, ANL, Argonne, IL 60439, USA
Jack G. Zhang, IIT, Chicago, IL 60616,USA
Abstract
Intense beams with large angular momentum have important applications in electron cooling and in producing
flat beams suitable for ultrafast x-ray generation, SmithPurcell radiators, and possibly for a future linear collider.
To gain a basic understanding of the influence of beam angular momentum in an otherwise space-charge-dominatedbeam, the behavior of such a beam in free space will be
examined here, in particular, beam spreading due to spacecharge force, as well as emittance oscillation. Drift space
is an important part of a split photoinjector and plays a significant role in emitance compensation of a high-brightness
photoinjector.

INTRODUCTION
By immersing the cathode in a magnetic field, beamwith (large) angular momentum can be created and is referred to as “magnetized” beam. High-intensity magnetized beams have important applications in electron cooling and flat-beam generation. The emittance oscillation ofa non-magnetized beam in the drift space of a split photoinjector has some generic properties such as the “double
minimum” feature [1], which has been explained by spacecharge induced beam spreadings of individual slices [2].
Here, we generalize the technique used in [2] to examine
the influence of beam angular momentum on beam spreading and emittance oscillation in drift space.
For a round beam in an axisymmetric channel, the beamenvelope is governed by the reduced beam envelope equation [3, 4]σ̂  +

2


κ
κs 1
− 3 = 0.
σ̂ − 2 2β2γ2β γ σ̂
σ̂(1)√where σ̂ = βγ σ is the reduced envelope, κ represents
the external focusing, and perveance κ s = I/2IA gives
the space-charge defocusing. Here, we consider uniform
non-accelerating channels with constant κ and κ s . In adrift space, κ = 0 and κ s decreases somewhat due tolongitudinal debunching, which will be ignored here. The
emittance  is conserved and may contain two parts: thermal emittance and angular momentum. Although angular momentum is correlated motion and intrinsically different from random thermal emittance, from the beam envelope evolution point of view, these two types of emittances make no difference. In high-brightness photoinjectors, the thermal emittance is sufficiently small such that
∗ Work supported by U.S. Department of Energy, Office of Science,
Office of Basic Energy Sciences, under Contract No. W-31-109-ENG-38.
† wangcx@aps.anl.gov; http://www.aps.anl.gov/~wangcx

FEL Technology

a non-magnetized beam can be considered space-charge
dominated. However, the existence of beam angular momentum qualitatively changed the property of the envelope
equation by addding a significant emittance term. In thefollowing, we present preliminary exploration of the effects
of angular momentum. Because we will only consider nonaccelerating beams, βγ = 1 is set in the following sections
to simplify the notation. By the same token, we will use σinstead of σ̂ for the reduced envelope as well.

BEAM SPREADING IN A UNIFORMNON-ACCELERATING CHANNELIn a uniform non-accelerating channel, the coefficientsin the beam envelope equation are all constants. The corresponding envelope Hamiltonian (with the setting βγ = 1)
H=

p2
σ2
ε2
+κ
− κs ln(σ) + 2
2
2
2σ

(2)

is a constant of motion, whose value can be expressed with
the initial σ0 and σ0 . Thus, we have the first integral
ε2ε2= σ0 2 + κσ02 − κs ln σ02 + 2 .
2
σ
σ0
(3)
The beam envelope is bounded by the potential well [4].
The lower bound is due to space-charge defocusing andemittance pressure. If any, the upper bound is due to external focusing. It reaches an extreme size σ m at σ  = 0,
which can be determined byσ 2 + κσ 2 − κs ln σ 2 +σ0 2 +κσ02 −κs ln σ02 +

ε2
ε2
2
2
=
κσ
−κ
ln
σ
+
.
s
m
m
2
σ02
σm

(4)

Note that in drift space, i.e., without external focusing,σm> 0, there will be a beam waist for a converging beam.
With external focusing, σ m may be a minimum or maxi
. From these equations,
mum depending on the sign of σ mσ can be solved as




1
σ
κs
ε2

2
2
σ̃ =
= ± κ (1 − σ̃ ) + 2 ln σ̃ + 4 1 − 2 ,
σm
σm
σm
σ̃
(5)
where σ̃ ≡ σ/σm . The sign depends on whether the beam
is converging (−) or diverging (+). By integrating Eq. (5)we obtain the solution of the beam envelope as 1sign(σ0 ) dx

s=

2 
σ0
κ (1 − x2 ) + σκ2s ln (x2 ) + σε4 1 − x12
σm
m
m
 σσ
m
sign(σ  ) dx
+
 . (6)2 
1
κ (1 − x2 ) + σκ2s ln (x2 ) + σε4 1 − x12
m

m

721

THPPH058

Proceedings of FEL 2006, BESSY, Berlin, Germany

This integral cannot be expressed with elementary functions. In the case κ = κs = 0, this integral yields thewell-known hyperbola envelope for a bunch of free particles. For a space-charge dominated beam in free space(κ =  = 0), this integral yields the so-called universal√
beam-spreading curve for σ/ κs , which is independent ofslice perveances. However, for a magnetized beam, there isa non-zero emittance term. Thus, the beam perveance can
not be scaled away from the envelope equation. Therefore,
beam spreading of a magnetized beam will have nontrivial
dependence on beam perveance, and there is no universal
beam-spreading curve anymore.

ENVELOPE EVOLUTIONS NEARBY A
REFERENCE ENVELOPE
The relative motions of various beam slices are responsible for the variation of projected emittance in highbrightness photoinjectors. Thus, it is interesting to examine the evolution of envelopes nearby a reference envelope.
Assuming small deviations, we expand a slice envelope
around the reference envelope (σ̄, σ̄  ) as

 



σ
σ̄
∂qα σ̄
=+δq α ,(7)σ
∂qα σ̄ σ̄ αwhere δq α represents a small deviation in certain parameterq α . Here, we consider the deviations in the initial values
δσ0 and δσ0 , as well as the slice perveance δκ s , assuming
all slices have the same emittance and angular momentum.
To compute the partial derivatives with respect to σ 0 , wetake derivatives on both sides of Eq. (6) with respect to σ 0
and use Eq. (5) for simplification, which yields
0=

1
1
∂σ σm
σ
σ0
∂σ0
− 
∂σ0
+ 0
Fx ,

σ /σm
σm
σ0 /σmσmσm(8)where Fx denotes the integral,

Fx =

+

 1 sign(σ  )
0

κs
2 ln
σm


 2
2 
x + 2 σε4 1 − x12 dx

σ0
σm

m

1

m

2
k (1 − x2 ) + σκ2s ln (x2 ) + σε4mm



1 − x12

σ
σ
+
∂σ σm

σ0
σm 0




σ0
σ
,
−
−
F
x
σ
σ0

κσ0 − κs /σ0 − ε2 /σ03
σ0
=
,
3

κσm − κs /σm − ε2 /σmσmwhich is non-zero unless staying at equilibrium.

(11)∂σ0 σ =σ0 σ  − σ0 σ
σ0 σ 
+
Fx ,


σm σm
σm σm

(12)

∂σ0 σ  =


1  
σ − σ0 ∂σ0 σ  ,

σ0

(13)

∂σ0 σ  =
σ0 σ σ  (σσ  − σm σm) σ0 σ 
− 0 
+F . (14)


 x
σm σm
σm σm σσm σmThe last two expressions can be obtained by differentiating
the first two expressions with respect to s. Clearly, thesederivatives have the initial values ∂ σ0 σ(0) = ∂σ0 σ  (0) = 1
and ∂σ0 σ(0) = ∂σ0 σ  (0) = 0. In the special case κ = 0
and ε = 0, these expressions reduce to the simple resultsof Eqs. (16) and (18) in [2], and F x = s. It is important to note that, for a space-charge dominated beam where
the emittance term can be neglected, all these expressions
are independent of slice perveance, with or without external focusing. This property may play a significant role inemittance compensation of high-brightness photoinjectors.
However, for a magnetized beam, these expressions will
depend on the perveance of the (reference) slice.
To evaluate the effect of small perveance variations, we
compute ∂κs σ and ∂κs σ  similarly. Differentiating Eqs. (3)and (4) yield, respectively,


σ
1


+ σ ∂κs σ ,(15)∂κs σ =  ln
σ
σ0
1
σ0
∂κs σm =  ln
.
(16)
σm σm

where the function F s is defined the same as Fx except thatκs = 1 and  = 0 are set in the numerators. (Thus, fora space-charge dominated beam, F x = κs Fs .) The initialvalues of both ∂ κs σ and ∂κs σ  are zero.

(9)

EMITTANCE OSCILLATION

where ∂σ0 σm can be obtained by differentiating Eq. (4) as∂σ0 σm =1  σ − σ0 ∂σ0 σ ,
σ0

.

 3/2

Thus, ∂σ0 σ can be solved as∂σ0 σ =

∂σ0 σ =

Differentiating Eq. (6) with the help of function F x and theabove expression for ∂ κs σm gives


σ0
σ
σ0
σ
σ
Fs , (17)
ln
−
−
F
+
∂κs σ =
x


σm σm
σ
σ0
σm
2

m

 3/2
2 
k (1 − x2 ) + σκ2s ln (x2 ) + σε4 1 − x12mm
 σσ sign(σ  ) κ2s ln x2  + 2 ε42 1 − 12  dx
mσ
σx

Similarly, taking derivatives on both sides of Eq. (6) withrespect to σ0 yields the derivative ∂ σ0 σ. Combined with
Eq. (9), they give the first two expressions in the following
sets of four derivatives:(10)

From the envelope expressions in Eq. (7), assuming thevarious deviations from the reference envelope are uncorrelated, the emittance due to slice envelope variations canbe calculated as [2]env 

Wq2α (δq α )2

qα

2

,

(18)

α

722

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany
where

Wqα ≡ (σ̄∂qα σ̄  − σ̄  ∂qα σ̄) q α .

(19)Here, the bar over δq α and q α indicates averaging over theslices.
Inserting the above partial derivatives into Eq. (19), we
have
 



σ̄0
σ̄σ̄0
σ̄σ̄ − σ̄ 2Wσ = σ̄01 −  ∂σ0 σ̄ −  , (20)
σ̄ 
σ̄
σ̄
  0 2σ̄σ̄
σ̄σ̄ − σ̄(21)∂σ0 σ̄ + 0 .
Wσ = σ̄0σ̄ σ̄These expressions reduce to the special results of Eqs. (17)and (19) in [2]. Since ∂ σ0 σ̄ equals zero at the beginning,
we have the initial values
Wσ (0) = −Wσ (0) = −σ̄0 σ̄0 .

(22)

To examine the extreme values of W σ (s) and Wσ (s), we
take the s-derivative of these functions and have, after somealgebra,σ̄σ̄  − σ̄  σ̄   σ̄ − σ̄0 ∂σ0 σ̄ ,σ̄0 σ̄σ̄σ̄
− σ̄  σ̄ Wσ  = σ̄0
∂σ0 σ̄.
σ̄ Wσ = σ̄0

(23)
(24)

It is easy to see that the factorε2σ̄σ̄  − σ̄  σ̄ 
κs
+
2
= 0,
=
−2
σ
σ
σ3
thus Wσ reaches the extreme value of −σ̄ 0 σ̄0 σ̄/σ̄  whenσ̄  = σ̄0 ∂σ0 σ̄, and Wσ reaches the extreme value ofσ̄0 2 σ̄/σ̄  when ∂σ0 σ̄ = 0. Using Eq. (12) and the condition for the extreme, we can further express the extreme
values Wσm as
Wσm = −σ̄0 σ̄0
Wσm = σ̄0 2

σ̄0
σ̄

=  (σ̄m σ̄m− σ̄0 σ̄0 ) − σ̄0 σ̄0 Fx , (25)
σ̄ 
σ̄0

σ̄
= σ̄0 σ̄0 + σ̄0 2 Fx
σ̄ 

(26)

where Fx integrates up to the extreme point. However, it
is not obvious that the condition for the extremes can besatisfied (except the trivial case Wσ  = ∂σ0 σ̄ = 0 at the
beginning).
From these expressions, a few general properties can be
drawn about emittance oscillation. In particular, for a beam
focused into a drift, σ̄ 0 < 0, σ̄0 > 0, σ̄m σ̄m− σ̄0 σ̄0 > 0,mthus Wσ (0) > 0 and Wσ < 0, which leads to emittanceminimum when W σ crosses zero, as discussed in [2]. Furthermore, Wσm < 0 requires σ̄  > 0 at that location, thus
the emittance maximum due to W σ is always located after
the beam waist where σ̄  = 0.
Similarly, Wκs can be worked out asσ̄
σ̄σ̄  − σ̄ 2
σ̄
+
∂
σ̄
,
(27)
Wκs = κ̄s  ln
κs
σ̄
σ̄0
σ̄ 
where ∂κs σ̄ is given by Eq. (17). Clearly, W κs (0) = 0.

FEL Technology

THPPH058

EFFECTS OF BEAM ANGULAR
MOMENTUM
To see the influence of beam angular momentum on the
beam envelope spreading of an individual slice and on theemittance oscillation of a bunch of slices, we plot a set offive figures showing the quantities σ, σ  , Wσ , Wσ , andWκs , using the expressions given above. In each figure,the red curve shows the evolution of a space-charge dominated beam and the blue curve shows the same beam butwith an angular momentum term 10 times larger than thespace-charge term at the beam waist (2 mm). The otherparameters are σ0 = 9 mm, σ  = −9.5 mrad, βγ = 12,
κs = 0.05, which are adopted from an optimized SPARC
photoinjector design.
Through this example and the above analysis, we see
that, qualitatively speaking, the basic behavior of beam
spreading and emittance oscillation in drift space are notchanged by the large angular momentum, although there
are significant quantitative changes. For example, the beam
waist becomes much larger and is reached much quicker.
Also, the emittance oscillation amplitude gets larger, andso on. From this point of view, W κs may be an exception because there is no zero crossing anymore for the blue
curve.
However, emittance compensation for magnetized beam
[5] may be significantly different from conventional spacecharge dominated beam. For example, there is no invariant envelope solution for the envelope equation in abooster when there is a significant emittance term. Thus,
the matching condition for space-charge dominated beam
may not be appropriate any more. Furthermore, the ability to compensate emittance may be limited by the fact thatbeam perveance cannot be scaled away from the envelope
equation of a magnetized beam.

CONCLUDING REMARKWe developed a technique to examine the beam spreading and emittance oscillation of a magnetized beam in freespace. Clearly, the technique also applies to a beam withsignificant thermal emittance and/or in a uniform focusing
channel (we have kept both focusing κ and emittance 
in all the expressions). In a focusing channel, a beam
may reach both minimum and maximum size because it
is bounded by a potential well. For example, a diverging beam reaches a maximum beam size in the focusing
solenoid for emittance compensation. The emittance evolution in the solenoid can be described by the same expressions presented above. Much more work is needed to understand emittance compensation of a magnetized beam.

REFERENCES[1] M. Ferrario, J.E. Clendenin, D.T. Palmer, J.B. Rosenzweig,
L. Serafini, SLAC-PUB-8400 (2000).
[2] C.-x. Wang, “Emittance oscillation in the drift space of split
photoinjectors,” Proceedings of the 35nd Advanced ICFA

723

THPPH058

Proceedings of FEL 2006, BESSY, Berlin, Germany

Beam Dynamics Workshop on Physics and Application ofHigh-Brightness Electron Beam, October 2005.
[3] See, for example, J.D. Lawson, The Physics of Charged Particle Beams, 2nd ed. (Oxford University Press, New York,
1988).

Wσ [mm-mrad]
200

100

[4] C.-x. Wang, Nucl. Instrum. Methods A557, 94 (2006).
[5] X. Chang, I. Ben-Zvi, J. Kewisch, BNL-73192-2004-CP.

0.5

1

1.5

2

2.5

3

s [m]
-100

-200

Figure 3: Emittance oscillation in free space due to initial slice envelope variation for space-charge dominatedbeam (red) and beam with large emittance (blue). The solid
curves plot the absolute values.

σ [mm]Wσ' [mm-mrad]

50
75

40

50
25

30
0.5

20

1

1.5

2

2.5

3

s [m]

-25
-50

10

-75

0.5

1

1.5

2

2.5

3

s [m]

Figure 1: Reduced envelope in free space for spacecharge dominated beam (red) and beam with large emittance (blue).

Figure 4: Emittance oscillation in free space due to initial slice slope variation for space-charge dominated beam(red) and beam with large emittance (blue). The solid
curves plot the absolute values.

Wκs [mm-mrad]

σ ' [mrad]

150

20

125

15

100

10
75

5

50

0.5

1

1.5

2

2.5

3

25

s [m]
0.5

-5
-25

1

1.5

2

2.5

3

s [m]

-10

Figure 2: Reduced envelope slope in free space for spacecharge dominated beam (red) and beam with large emittance (blue).

724

Figure 5: Emittance oscillation in free space due to slice
perveance variation for space-charge dominated beam (red)and beam with large emittance (blue). The solid curves plot
the absolute values.

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH059

ENERGY MODULATION OF THE ELECTRONS BY THE LASER FIELD IN
THE WIGGLER MAGNET: ANALYSIS AND EXPERIMENT
A.A. Zholents #, LBNL, Berkeley, CA 94720, U.S.A.
K. Holldack, BESSY, 12489 Berlin, Germany.
Abstract
Energy modulation of the electron beam after theinteraction with the laser field in the wiggler magnet canbe calculated using interference of the laser field and thefield of spontaneous emission in the far field region of
wiggler radiation. Quite often this approach gives a
deeper insight on the process than traditional calculations
where the effect of the laser field on the electron energy is
integrated along the electron trajectory in the wiggler. We
demonstrate it by showing the agreement between theanalytical model and the experiment involving wiggler
scan measurements with large detuning from the FEL
resonance producing more than one order of magnitude
variations in the amplitude of the energy modulation. The
high sensitivity was achieved using the THz radiationfrom a sub-mm dip in the electron density that energy
modulated electrons leave behind while propagating along
the storage ring lattice. All measurements were performedat the BESSY-II electron storage ring.

K eB0 / k w mc , B0 is the peak magnetic field and E z is
the normalized velocity along the wiggler, i.e.:t³

c E z t c dt c # ct zt

0

In what follows we consider on-axis electrons only.
This assumption can be extended to all electrons in theelectron bunch if the electron beam size V x , y  a 0 .
Then, using (1) and (3) we write:
eE0 K
dJ^cos(k z  ct  k w z  \ )2
dz 2mc J 1  z / z 2

ExW 2 / 4V W2

 cos(k z  ct  k w z  \ )`e
It is further convenient to define the resonance electronenergy, also called an FEL resonance energy,k
J r2
1  K 2 / 2 and assume a small energy spread
2k w'J / J r such as to obtain:k ( z  ct )22

E0 / 1  z / z 0 2 sin[k z  ct  \ ]e W / 4VW ,(2)where k is the wave number of the laser field,z 0 ka02 / 2 is the Rayleigh length, a0 is the waist size
which is assumed to be in the center of the wiggler,\ \ 0  tan 1 z / z 0 , where \ 0 is the phase of the
wave at the beginning of the interaction with the electron
at the entrance of the wiggler and V W is the rms width ofthe laser pulse intensity.
For electron motion inside the wiggler one obtains:
Ex
Ez



K

J
1

sin k w z ,

(3)

1

1

J

2J 2

where k w

 E x2 | 1 2

2

1 K / 2 

K2
4J 2

cos 2k w z

2S / O w and O w is the wiggler period,# AAZholents@LBL.GOV

FEL Technology(5)0

ENERGY MODULATIONThe energy gain/loss obtained by the electron in theinteraction with the laser field E x polarized in thehorizontal plane and co-propagating the planar wiggler
magnet together with the electron in z direction can befound by solving the equation [1]:
 ,
(1)
dJ
e2
Ex E xdz mc
where J is the relativistic factor, E x v x / c , where v x
is the horizontal velocity of the electron and c is the
speed of light, e, m are the electron charge and mass, and1 §¨K 2 ·¸K2
1
ct 
sin 2k w z (4)
2 ¨
¸
2 ¹
2J ©
8k w J 2

k w zJ r2 [
 sin 2k w z
J2 2

(6)

with [ K 2 /( 2  K 2 ) . Using a generation function for
Bessel functions [2] we found:>@cos k w z 1  J r / J 2  [ / 2 sin 2k w z  \ >

2

cos k w z 1  J r / J@ [ / 2 sin 2k w z  \ |>J 0 [ / 2  J1 [ / 2 @cos>k w z 1  J r / J 2  \ @where in the last step we retain only slowly varying termswith 1  J r / J 2  1. Finally, using dimensionlessvariables in Eq. (6) [3]: zˆ z / Lw , Q N 2GJ / J r , andq Lw / z 0 , where Lw is the length of the wiggler with

N periods, V W V W / W 0 and W 0 2S N / kc , one obtains:
dJd zˆ

eE0 KLw
22mc J^JJ ` cos 2SQ z  tanˆ1

q zˆ  \ 0

1  q zˆ 22

2e  z / 4VW (7)where definition ^JJ ` J 0 [ / 2  J 1 [ / 2
is usedfollowing [4]. Introducing the laser pulse energy
AL

E 02 / 8S S a02 / 2 2S V W c , Eq.(7) can be written as:

dJ
d zˆ

2
mc 2
u

ALD !Z 0 s2q


2S 1 / 2 V W

K2
2 K2

^JJ `

cos 2SQ zˆ  tan 1 q zˆ  \ 0
1  q zˆ 2

(8)
e



 z 2 / 4V W2

where D is the fine structure constant, Z 0 s is central
frequencies of the field of spontaneous emission, and ...

725

THPPH059

Proceedings of FEL 2006, BESSY, Berlin, Germany

defines averaging over one wiggler period. By integrating
Eq.(8) one obtains for the amplitude of the energy
modulation:'J (q,Q , V W )

2
2

mc

ALD !Z 0 s

K2
2 K2

^JJ ` f (q,Q , VW ) (9)where:
f (q,Q , V W )

2q
2S



cos 2SQ z  tan 1 qz  z 2 / 4VW2 edz
V W 0.5
1  qz 2
0.5³

1/ 2 

Figure 1 shows plots of f (q,Q , V W ) for various q and Q

and
VW .
Using
the
maximumvalueoff (q 8,Q 0.7, V W 0.25) =2.2, one finds:'J max #2
mc 2

5 ALD !Z 0 s

K2
2 K2

^JJ `

(10)

where we used substitution
x ZW 0 / 2
andx0 s Z 0 sW 0 / 2
and
x0 L Z 0 LW 0 / 2 . The entire
expression inside the figure bracket shows theoverlapping of the spectra of the laser signal and thespectra of spontaneous emission signal. This expression isnormalized in such a way that it is approximately one
when Z 0 s Z 0 L and V W =0.25 corresponding to the
optimal condition of the maximum energy modulation
found previously. Finally we note that in the case of alarge detuning from the FEL resonance a contribution of
the second term with sin x  x0 s / x  x0 s could becomparable to a contribution of the main term withsin x  x0 s / x  x0 s and, thus, should be added to theoverlapping integral.

EXPERIMENT
Figure 1. Function f (q,Q , V W ) for VW =0.25 (left plot) and Q =0.7 (right plot) and for q = 4, 6, and 8 (curves 1, 2, and 3).

Alternatively, the energy gain/loss obtained by theelectron in the interaction with the laser field can becalculated considering the interference of the field of its
spontaneous emission in the wiggler and the laser field.
This technique takes it roots in a so-called acceleration
theorem [5,6] declaring that the very existence of
spontaneous emission is mandatory if the acceleration by
the external field is employed in a linear order to thisfield. Following this idea and using Parseval’s theorem,
we write for the amplitude of the energy modulation:
S a 2cmc 2 'J max 2 0
E s t E L* t dt
16S
(11)
S a02 c*E s Z E L Z dZ
216S

The energy modulation of electrons by the laser field
was measured as a function of the detuning of the central
frequency of the electron spontaneous emission in the
wiggler from the central frequency of the laser field. The
experiment was conducted at BESSY-II synchrotron lightsource [7]. The laser operated at a fixed wavelength of
800 nm while wiggler detuning covered large range of
frequencies with the wavelengths changing from 200 nm
to 1000 nm, i.e. in the range greatly exceeding the
bandwidth of the laser pulse. As an illustration, Figure 2
shows normalized spectra of the laser field and the fieldof the electron spontaneous emission in the wiggler for asingle set point during this scan.

³³

where E s Z
2 / S E 0 s sin Z  Z 0 s W 0 / 2 / Z  Z 0 s is
Fourier component of the field of spontaneous emission,
2

2

E L Z E 0 L 2V W  e  Z Z0 L VW is a Fourier componentof the laser field, and Z 0 L is the central frequency of thelaser field. Further defining the energy of spontaneousemission (see, also [3]):K2^JJ `2 (12}AS
E s2 / 8S S a02 / 2 W 0 c 5D !Z 0 s22 K
radiating in the mode with a rms divergence of the
2O s / SLw , where O s 2S c / Z 0 s , one
intensity V Rc

can obtain from (11):'J max #

726

2
mc

2

­ 
AL As ® V W¯³e 4 x  x0 L 2 V W2 sin x  x 0 s

x  x0s

½
dx ¾
¿

(13)

Figure 2. Spectra of the laser field (curve 1) and the field ofspontaneous emission of electrons in the wiggler (curve 2).

Measurements of the energy modulation were
performed indirectly using coherent THz radiation from abending magnet 11 m downstream of the wiggler magnet.
THz radiation was produced by the dip in the electron
density distribution that energy modulated electrons leavebehind after propagating the storage ring lattice with nonzero time-of-flight properties, a phenomena which is
described elsewhere [8]. Use of the THz signal allowed us
to obtain sufficient signal-to-noise ratio even with wiggler
settings leading to very small amplitudes of the energy
modulation. A typical example of THz spectra and the dip
in the electron density distribution is shown in Figure 3.
The width and the magnitude of the dip are defined by
the amplitude of the energy modulation of electrons andby time-of-flight parameters R51 , R52 , R56 of the lattice

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH059

amplitude of the energy modulation dropped below'E / V e <3. The other parameters used to obtain the fit
were N 9.75 (i.e. effective number of wiggler periods
instead of 10 real periods), V W = 45 fs and a floor level of
10-4 (defined in the units used in Figure 5) as given byincoherent synchrotron radiation from the regular bunch.

Figure 3. a) THz spectra for different wiggler gaps
corresponding to different detunings near the FEL resonance, b)
a dip in electron density determined from spectra measured at
the FEL resonance and corrected for beamline transmission.

between the wiggler magnet and a source of the THz
radiation. Figure 4 shows the magnitude of the dip
calculated as a function of the amplitude of the energy
modulation normalized on the relative energy spread ofelectrons V E . The following parameters were used:

V E 10 3 , R56 =-0.011 m, R51 = 5.5 10-5, R52 = 0.53 m[9] , the electron beam size and angle in the wiggler
magnet V x =320 Pm and V xc = 55 Prad.

Figure 4. A relative magnitude of the dip as a function of theamplitude of the energy modulation 'E mod . The magnitude of
one corresponds to 100% electron density modulation.

Variations in width and magnitude of the dip affect theTHz signal, which was measured using an InSbbolometer during the wiggler scan and plotted in Figure 5.
Analyzing this measurement, we assumed that the THz
signal is proportional to the square of the magnitude ofthe dip and that the magnitude of the dip itself is
proportional to the amplitude of the energy modulation ofelectrons. We calculated the amplitude of the energy
modulation using Eq. (13), which was, essentially, a
calculation of the function F x0 s , x0 L , V W , i.e. theoverlapping area between two spectra shown in Figure 2.
These calculations are more accurate than calculations
using Eq. (9) because of the assumption of a small
detuning used there does not work for a broad scan of the
wiggler wavelength as used in the experiment.
The width of the dip defines the spectra of the emitted
THz signal [8] and, therefore, indirectly impacts themeasurement because of the spectral dependence of thedetector and THz beamline transmission. We accounted
for this effect using empirically defined coefficient 0.75
for calculated intensity of THz radiation when the
FEL Technology

Figure 5. THz signal produced by the electron bunch with a
dip in the electron density. The black curve shows theexperimental result and the red curve the analytical fit.

CONCLUSION
Using a concept of the far field region we demonstrated
that the energy modulation of electrons in the wiggler
magnet by the laser light can be found by calculating theinterference of the laser field and the field of the electron
spontaneous emission in the far field region of theelectron radiation in the wiggler. This allowed us toobtain a correct explanation for the measurements, where
the wiggler detuning from the laser frequency covered alarge range of frequencies exceeding the bandwidth of thelaser field by many times.
Acknowledgement. A.Z. is grateful to M. Zolotorev
for reading the manuscript and critical comments. K.H. isindebted to T. Quast, R. Mitzner, S. Khan and D.Ponwitz.
This work was supported by U.S. DoE under Contract No:
DE-AC03-76SF00098 and by the Bundesministerium für
Bildung und Forschung and the Land Berlin.

REFERENCES[1] J.B. Morphy, C. Pellegrini in: Laser handbook, vol 6,
p.9, Elsvier Science Publisher, (1990).
[2] M. Abramovitz and I. Stegun, Handbook of Math.
Functions, DOVER, New York, 1972, p.360;[3] W.B. Colson, in: Phys. of Quantum Electronic, vol.5,
p.157, Addison Wesley, (1978).
[4] K.-J. Kim, in: AIP Conf. Proc., Am. Inst. Phys., New
York, p.565, (1989); LBNL/PUB-490, Rev.2, (2001).
[5] R. B. Palmer, in, AIP Conf. Proc. No. 335,edited by
P. Schoessow, , AIP, NewYork, (1995)90.
[6] Z. Huang, G. Stupakov, M. Zolotorev, Phys. Rev.
Spec. Topics Acc. and Beams, 7, (2004)011302.
[7] BESSY-II, http://www.bessy.de/[8] J. Byrd et.al., Phys. Rev. Lett., 96, (2006)164801;
K. Holldack et.al., Phys. Rev. Lett., 96 (2006)054601.
[9] courtesy G. Wüstefeld.

727

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Proceedings of FEL 2006, BESSY, Berlin, Germany

CALCULATION OF THE BEAM FIELD
IN THE LCLS BUNCH LENGTH MONITOR
G. Stupakov, Y. Ding and Z. Huang
Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309, USA.
Abstract

FORMULATION OF THE PROBLEM

Maintaining a stable bunch length and peak current is a
critical step for the reliable operation of a SASE based xray source. In the LCLS, relative bunch length monitors(BLM) right after both bunch compressors are proposed
based on the coherent radiation generated by the short electron bunch. Due to its diagnostic setup, the standard far
field synchrotron radiation formula and well-developed numerical codes do not apply for the analysis of the BLM
performance. In this paper, we develop a calculation procedure to take into account the near field effect, the effectof a short bending magnet, and the diffraction effect of theradiation transport optics. We find the frequency responseof the BLM after the first LCLS bunch compressor and discuss its expected performance.

A simplified layout of the problem is presented in Fig.
1. The beam passes through a short magnet (e.g., the last
dipole of the first LCLS bunch compressor or BC1) oflength lm with the bending radius ρ and propagates alonga straight line. A reflective mirror of diameter D with acircular hole of diameter d is located at a distance L fromthe exit edge of the magnet. The mirror is tilted at 45 ◦ andsends the beam field to the detector at the right angle to thebeam trajectory. To simplify the calculation we, however,assume that the mirror’s plane is perpendicular to the beam
orbit (that is, it reflects the radiation back toward the magnet) and calculate the fields incident on as well as reflectedfrom the mirror. Such modification of the geometry does
not loose any significant physical effects of the problem.

x

INTRODUCTION
Maintaining a stable bunch length and peak current is a
critical step for the reliable operation of a SASE based xray source. In the LCLS, relative bunch length monitors(BLM) right after both bunch compressors are proposed
based on the coherent radiation generated by the short electron bunch [1]. A similar diagnostic device is used in theoperation of the DESY VUV-FEL (FLASH) [2].
In the previous calculations of the beam radiation [1]standard formulae for the synchrotron radiation in the far
field were used. However, due to the close proximity of thereflecting mirror to the magnet, applicability of these formulae is not fully justifiable. An additional factor which
complicates the radiation pattern is the short length of themagnet comparable to the formation length of the radiation
with the wavelength of the order of the bunch length. To
the authors’ knowledge, the available computer codes forcalculation of the beam radiation (e.g., the Synchrotron Radiation Workshop [3]) cannot be used for our case because
the beam passes through the hole in the mirror.
It is a goal of this paper to calculate the electromagnetic
field of an electron bunch which takes into account the nearfield effect, the effect of a short bending magnet, and thediffraction of the radiation caused by reflection from themirror. We find the energy spectrum intercepted by the
mirror in the first LCLS bunch compressor (BC1). We
carry out these calculation assuming radiation in free spaceand neglecting the effect on the radiation of the conducting
walls of the vacuum chamber.
We use Gaussian units throughout this paper.

728

d

z

BX14

lm

D

L

Figure 1: Layout of the bunch length monitor. The coordinate z is measured in the direction of beam propagation
after the magnet with z = 0 at the exit edge of the magnet. The coordinate x is in the plane of the orbit, and thecoordinate y is perpendicular to the plane.
We carried out calculations in the frequency domain. To
calculate the Fourier component at frequency ω of the beam
field on the surface of the mirror we used two approaches.
In the first one, a standard expression for the electromagnetic field of an electron moving in free space was used
(see, e.g., [4])
 ∞
e
n−β
E(r, ω) = 2
dt 2
eiω(t+R/c)γ −∞ R (1 − n · β)2e ∞n × [(n − β) × β̇] iω(t+R/c)
+
dt
e
.
c −∞
R(1 − n · β)2(1)Here R, n, β and β̇ are functions of time t: R is the vector connecting the current position of the electron with theobservation point r, with R = |R|, n is the unit vector directed along R, β and β̇ are the velocity and acceleration

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany
normalized by the speed of light, and γ = (1 − β 2 )−1/2 .
The first term in Eq. (1) is usually referred to as the velocity field. Note that for a relativistic particle with γ  1 theintegrands in Eq. (1) have sharp narrow peaks in the direction for which n is parallel to β because in this direction
the denominators (1 − n · β) 2 ∼ 1/4γ 4 become extremely
small.
We remind the reader that the usual approximation for
the far zone (FZ) is to neglect the velocity field and to takethe limit R → ∞: ∞en × [(n − β) × β̇] iω(t+R/c)
E FZ (r, ω) ≈
dt
e
.
cR −∞
(1 − n · β)2
In this expression, the value of R in front of the integral
and the vector n are considered as constant but R in the
exponential (and of course β and β̇) are functions of time.
If one integrates this expression over a finite time intervalfrom t1 to t2 the result isieω t2dt n × (n × β)eiω(t+R/c)
E FZ (r, ω) = −cR t1
e n × (n × β) iω(t+R/c) e+
cR 1 − n · βt2e n × (n × β) iω(t+R/c) e− .
cR 1 − n · β
t1
The last two terms are responsible for the edge radiation in
the far zone [5].
We found advantageous for numerical calculations to use
another expression for the electromagnetic field of a moving point charge [6]:ieω ∞ dt
E(r, ω) =[β − n (1 + ic/ωR)] eiω(t+R/c) .
c −∞ R(2)
This is the underlying equation used in the Synchrotron Radiation Workshop code [3]. Although this equation looks
very different from Eq. (1), they give the same result forE(r, ω). The derivation of Eq. (2) using Lienard-Wiechert
potentials can be found in Ref. [7]. In passing, we notethat neglecting the velocity field in Eq. (1) is not justified
in our situations and yields very different numerical results
as compared to Eq. (2).
To integrate Eq. (2) over the particle’s orbit we split the
integration path into three pieces. The first one is a straightline before the entrance to the magnet, the second one isan arc of a circular orbit inside the magnet, and the third
one comprises the part of the trajectory after the exit fromthe magnet. The first two integrals were computed numerically using the Mathematica built in integration routine [8](in the first integral the lower limit of integration −∞ was
replaced by a large negative number). A direct numericalintegration of the third integral turns out be slow and poorly
convergent because of a fast variation of the phase in the
integrand. To improve the speed of calculation we used amethod described in Ref. [7], which is valid in the limitof large values of γ. Although formally the integration in

FEL Technology

THPPH062

Eq. (2) is extended beyond the position of the mirror, thedominant contribution to the integral comes from the partof the trajectory located in front of the mirror.

RESULTS OF THE CALCULATIONS
The quantity c|E(r, ω)| 2 /8π can be considered as an energy flow of the electromagnetic field. We calculated thisquantity at the location of the mirror for various frequencies
ω and integrated it over the mirror surface. The resulting
quantity is a measure of the energy reflected by the mirror
in a unit interval of frequencies.
To illustrate the distribution of the spectral energy in theplane of the mirror, we plot in Fig. 2 the quantity |E| 2 (inarbitrary units) in the mirror plane at the distance L = 22cm for ω/c = 50 cm−1 . We also assume that the γ factor
for the beam is equal to 500, the bending radius of the magnet is 2.5 m, and the magnet length l m = 22 cm. The plot

Figure 2: Square of the electric |E| 2 (in arbitrary units)
in the observation plane x, y. The picture is symmetricwith respect to the axis x. The color coding goes from redthrough yellow, green, and blue as the intensity increases.
is truncated at small distances close to the trajectory of thebeam after the magnet (x = y = 0) because the field hasa singularity at the trajectory. Since the reflecting mirror
has a hole for the passage of the beam, the field from thisregion is not reflected by the mirror.
Fig. 3 shows the same field as in Fig. 2 projected onto thesurface of the mirror. The mirror outer diameter D = 7.6
cm, and the diameter of the hole is d = 1.5 cm. Note acomplicated pattern of the field on the surface of the mirror.
We calculated the spectral energy S(k) intercepted by
the mirror
 as a function of the wavenumber k = ω/c,
S(k) ∝ mirror |E(r, k/c)|2 d2 r. It is normalized in such a
way that the total energy reflected by the mirror due to thepassage of a bunch with the longitudinal charge distribution
λ(z) ( λ(z)dz = 1) is given by ∞E=
dkS(k)F (k) ,(3)0where F (k) is the form factor related to the shape of the729

THPPH062

Proceedings of FEL 2006, BESSY, Berlin, Germany

Energy, ΜJ

150

100

50

0
0

100

200

300

Σz ΜmFigure 5: The reflected energy as a function of the compressed rms bunch length.
Figure 3: Distribution of the quantity |E| 2 on the surface ofa round mirror. Shown is a hole at the center of the mirror
for the beam passage.

electron bunch,
2
 ∞


ikz

λ(z)e dz  .
F (k) = (4)−∞

The plot of the function S(k) for the geometry of the mirror
shown above is shown in Fig. 4.

S, ΜJnC2 cm1

To calculate the field reflected from the mirror, we use
the vectorial diffraction theory as the wavelengths of interests (comparable to the bunch length) are much smaller
than the size of the mirror [4]. The detector is assumed to
be located far away from the mirror. Although there may
be additional optical elements between the mirror and thedetector, we neglect them here in order to illustrate the calculation method. According to the diffraction theory, thedetected field is given byieikR1k×(n1 × E s )e−ik·r d2 r , (5)
Er =
2πR1
mirrorwhere R1 is the distance between the detector and the mirror, E s is the induced field at the mirror, and n 1 is theunit vector perpendicular to the mirror surface dS. The induced field is defined as follows. The total electric field on
the surface of the mirror is the sum of the beam field E(calculated in the previous section) and the induced field
E s . Due to the boundary condition on the metal surface, the tangential component of this sum should vanish,
n1 × (E s + E)mirrror = 0, which gives

0.6

0.5

0.4

0.3

(n1 × E s )mirrror = −(n1 × E)mirrror .
0

100

200
k cm1 

300

(6)

400

Figure 4: The spectral energy of the beam field interceptedby the mirror as a function of wavenumber k = ω/c. The
dots show the calculated values of S.
Using the calculated spectrum we computed the amountof energy intercepted by the mirror for various values ofthe bunch lengths, taking a parabolic bunch profile that is
expected after BC1 [1]. This energy as a function of thecompressed rms bunch length is shown in Fig. 5.

730

FIELD REFLECTED FROM THE MIRROR

We will make the small angle approximation around thefield propagation direction (for the mirror perpendicular tothe beam orbit, the reflected field propagates in the direction opposite to the z axis). Using the cylindrical coordinate system r and φ in the mirror plane, we find the reflected field at the point with coordinates x and y in thedetector plane as follows: 2π
ikeikR1 D/2
rdr
dφE tang
2πR1 d/20kr
× exp −i (x cos φ + y sin φ) ,R1

E r (x, y) =(7)

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany
where the superscript “tang” indicates the component of
the electric field tangent to the surface. Given the beam
field E on the mirror as found in the previous section, we
integrated Eq. (7) numerically to compute the detected signal. As a numerical example, Fig. 6 shows the reflected
field intensity distribution at the distance R 1 = 81 cm fromthe mirror for ω/c = k = 50 cm −1 . Note that the maxi-

THPPH062[3] O. Chubar and P. Elleaume, in Proceedings of the 6th European Particle Accelerator Conference (1998), p. 1177.
[4] J. D. Jackson, Classical Electrodynamics (Wiley, New York,
1999), 3rd ed.
[5] R. A. Bosch, Il Nuovo Cimento 20 D, 483 (1998).
[6] O. V. Chubar, Rev. Sci. Instrum. 66 (2), 1872 (1995).
[7] G. Stupakov, Y. Ding, and Z. Huang, Calculation of the beam
field in the LCLS bunch length monitor, Preprint SLAC-PUB11890, SLAC (2006).
[8] S. Wolfram, The Mathematica Book (Wolfram Media/Cambridge University Press, 1999), 4th ed.

1
0.75
E2
0.5
0.25
0

3
2

2
4
6
x, cm

y, cm

1
8
10

0

Figure 6: Square of the electric |E| 2 (in arbitrary units) inthe detector plane x, y located 81 cm away from the mirror.
The plot is symmetric with respect to the x axis.
mum of the field in the detector plane is shifted along thex coordinate. Equation (7) can be generalized to include aparaboloid mirror that focuses the radiation.

CONCLUSION
We calculated the electromagnetic field intercepted andreflected by a metallic mirror for the geometry of the LCLS
bunch length monitor. Unlike the previous calculations, we
do not assume the far zone approximation for the radiation
field. Our calculation takes into account the near field effect, the short length of the bending magnet (the so called“edge radiation” effect), and the diffraction of the radiation
caused by reflection from the mirror.
Our calculations assume propagation of the beam in freespace and neglect the effect on the radiation of the conducting walls of the vacuum chamber. In reality, those effects
are not negligible, and our result should be considered as
an approximation to the real spectrum.

ACKNOWLEDGMENT
We wish to thank P. Emma, H. Loos, and J. Wu for useful
discussions. This work was supported by Department ofEnergy contract No. DE–AC02–76SF00515.

REFERENCES[1] J. Wu, P. Emma, and Z. Huang, in Proceedings of the 2005
Particle Accelerator Conference (2005), p. 428.
[2] S. Casalbuoni, L. Fröhlich, O. Grimm, O. Peters, and J. Rossbach, in Proceedings of the 2004 European Particle Accelerator Conference (2004), p. 2586.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

IN-SITU CLEANING OF METAL PHOTO-CATHODES IN RF GUNS
J.F. Schmerge, J.M. Castro, J.E. Clendenin, E.R. Colby, D.H. Dowell, S.M. Gierman, H. Loos,
M. Nalls, and W.E. White, SLAC, Menlo Park, CA, U.S.A.
Abstract
Metal cathodes installed in rf guns typically exhibit
much lower quantum efficiency than the theoretical limit.
Experimenters often use some sort of in situ technique to“clean” the cathode to improve the QE. The mostcommon technique is laser cleaning where the laser isfocused to a small spot and scanned across the cathodesurface. However, since the laser is operated near thedamage threshold, it can also damage the cathode andincrease the dark current. The QE also degrades overdays and must be cleaned regularly. We are searching fora more robust cleaning technique that cleans the entire
cathode surface simultaneously. In this paper we describe
initial results using multiple techniques such as keV ion
beams, glow discharge cleaning and back bombarding
electrons. Results are quantified in terms of the change in
QE and dark current.

INTRODUCTION
The LCLS RF gun requires fields up to 120 MV/m toachieve the desired emittance of 1 μm with 1 nC of charge
in a 10 ps bunch. The high field requires the use of a Cu
cathode to avoid breakdown at the cathode joint. The
LCLS laser can produce 250 μJ of energy at 255 nm
which will require a QE of 2 10-5 to generate 1 nC of
charge. In the case of the Gun Test Facility (GTF) drive
laser operating at 263 nm, the theoretical QE for a cleanCu surface using a 263 nm photon is 33 10-5 with a 100
MV/m rf field and 8.4 10-5 with no applied field [1].
However, experience with multiple cathodes at the GTF
indicate the QE of Cu can vary from as low as 10-6 tonearly 10-4 at 100 MV/m. In addition the QE is notconstant over the laser spot leading to increased emittancefrom the non-uniform space charge forces.
Our experience with laser cleaning [1] has convinced us
to search for a better technique that cleans the entire
surface simultaneously, does not increase the dark current
and is easily repeatable. Here we report QE and darkcurrent measurements before and after using multiple
techniques intended to clean the metal surface andincrease the QE.

Ion Beam Cleaning
Previously we reported QE measurements on Cu
samples before and after exposing the sample to a few
keV ion beam [3]. The measured QE as a function ofillumination wavelength with no applied field agreed very
well with the theoretical Cu QE [4] after dosing thesample with up to 10 mC of charge. X-ray photoelectron
spectroscopy (XPS) measurements showed the primarycontaminant was carbon.
This ion gun could not be installed on the GTF gun due
to interference with the gun solenoid. The SLAC
Accelerator Research Department B (ARDB) rf gun isnearly identical to the GTF gun but with more clearance
between the gun and solenoid. Thus the ion gun, model
number ZMB7C from Micro Photonics Inc., was installedon the ARDB rf gun.
The two rf guns haveinterchangeable cathode plates but the lasers operate atslightly different wavelength. The ARDB drive laser
wavelength is 266 nm and the GTF wavelength is 263 nm.
The ion gun was installed on one of the two laser ports
in the half cell as shown in Figure 1. The beam has adirect line of site to the cathode through an oval opening
in the cavity side wall measuring 0.433” X 0.25” withapproximately a 70° angle of incidence at the cathode.
The beam size at the cathode is approximately 1 cm indiameter.
H-ion gungun solenoid
2 ½” long spool

1 1/3 to 2 ¾zero length
adaptor
Laser port

0.433”
0.25”

3.49”

~5.2” , ~132 mm
working distancerf guncathodeIN-SITU TECHNIQUES AND RESULTS

Figure 1: Layout of the ion gun and rf gun. The gun isinstalled on a laser port with a direct line of site to thecathode.

One of the simplest proposed cleaning methods is toheat the entire gun and drive off any surface contaminantswith thermal energy. This was motivated by a test wherea small Cu sample was heated in a vacuum chamber to
230 C for 100 minutes which increased the QE over 2
orders of magnitude [2]. All four Cu cathodes installed at
the GTF have been baked after installation to 200 C for
several days, resulting in measured QEs that range from
10-6 to nearly 10-4 at 60 MV/m.

The QE was measured prior to the ion gun installation
and was only 0.4 10-5 at 60 MV/m. The rf gun was vented
using LN2 tank boil-off and the ion gun installed. Before
the ion gun was operated the QE was re-measured andfound to have increased nearly an order of magnitude to 3
10-5. The ion gun was then operated for 40 minutes at 2
keV and 2μA for a total integrated charge on the cathodeof nearly 5 mC. After pumping out the hydrogen the QE
was measured and found increased to 6 10-5 with no732

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Proceedings of FEL 2006, BESSY, Berlin, Germany
increase in the dark current. The ion gun was operated fora second time for 2 hours at 4 μA for a total dose of 29
mC but the QE decreased back to 3 10-5. An additional 7
mC dose (1 hour at 2 μA) did not change the QE. The
dark current was not affected by the hydrogen ion beam.
Although the QE increased initially after the firsthydrogen ion beam cleaning, the subsequent QE wasunchanged at 3 10-5 at MV/m. This is significantly lower
than the 10 10-5 measured on the Cu samples at the same
wavelength with no applied field [3].
The most
interesting result was the substantial increase in QE after
the gun was vented. This was also observed at the GTF
and will be discussed in the next section.
The hydrogen was replaced with Argon and the ion gun
operated for 30 minutes at 2-2.5 keV between 1.5-3 μA
for a total dose of 3 mC. The dark current was measured
but the rf system failed before the QE could be measured.
The total integrated dark current more than doubled from
1.6 nC prior to the Argon cleaning to 3.4 nC after cleaning
with a peak field of 105 MV/m. The peak dark current in
the macropulse went from 1.1 mA to 2.6 mA.
The poor results compared to the test samples may
partially be explained due to misalignment of the ion gun
and thus limited cleaning at the center of the cathode. The
70° angle of incidence of the ion beam relative to the rf
gun cathode is 33° larger than tested on the Cu samples
which may limit the effectiveness of the ion beam
cleaning. It is also theorized that contaminants removed
from other areas exposed to the ion beam migrate to thecathode instead of getting pumped out of the gun.

Glow Discharge Cleaning
Glow discharges are commonly used to clean vacuum
vessels [5-6] and optical components [7]. A possible
advantage of this technique over the ion beam is that it
cleans the entire surface of the gun which should reduce
migration of contaminants and improve the cathodelifetime. Glow discharges have also been used to clean
Cu accelerator structures such as the AFEL linac [8], an
eleven cell photo-injector/linac. There it was observedthat the glow was largely confined to a single cell, but
could be moved to different cells through small changes
in the rf drive frequency used to excite the glow
discharge.
This technique was implemented on the GTF gun using
both hydrogen and an oxygen-helium mixture (90% He
and 10% O2). Gas can flow into the gun through either
the half cell via the laser port or the full cell via the
waveguide and is pumped out the beam exit port of the
gun with a scroll pump. The discharge is started using an
rf source connected to the waveguide. We have used botha 26 W CW rf source and a pulsed 1 kW rf source with 30
μs pulse length, 200 Hz repetition rate and 5 W average
power. The rf frequency can be adjusted to control thelocation of the glow discharge as determined by a visualinspection. Exciting the glow at the π mode frequency of2856 MHz confines the glow to the full cell and exciting
the 0 mode at 2852.5 MHz confines the glow to the half

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cell. However, atoms can move between cells through thecell to cell coupling aperture.
The QE of the cathode was 0.5 10-5 at approximately 80
MV/m after the gun was vented with LN2 boil-off toinstall the leak valve used to introduce the gas. The firstdischarge was on for roughly 1 hour using hydrogenflowing into the full cell with an inlet pressure of
approximately 300 mTorr. The discharge was excitedwith the CW rf source at 2856 MHz. The QE increased
significantly to 6 10-5 and further increased to 8 10-5 after
a second hour with the glow discharge. Then we switchedto the 0 mode frequency of 2852.5 MHz with all otherparameters constant and the QE dropped over one order ofmagnitude to 0.3 10-5. Multiple glows at 2856 MHz atpressures ranging from 30-600 mTorr had no effect on the
QE. This was an attempt to control the mean free pathand thus the number of ions that reach the cathode fromthe glow discharge in the full cell.
We theorized that with the glow in the half cell we had
actually added carbon to the surface possibly by migrationof carbon from the stainless tubes attached to the laser
ports on the half cell to the cathode. We introduced
oxygen to the system which is expected to bond with thecarbon forming CO or CO2 and accelerate the removal
rate of surface carbon [5,7]. After a glow with the oxygenand helium gas at a pressure of 200 mTorr with the CW
rf source at 2856 MHz the QE dropped to 0.01 10-5 whichis the lowest value we have ever observed. An identicalglow discharge with hydrogen restored the QE to 0.3 10-5.
It appears the oxygen attached to the Cu surface instead of
the carbon and the hydrogen glow discharge removed theoxygen. Apparently the hydrogen ions are not energetic
enough to remove the carbon. We tried to increase thehydrogen ion’s energy by exciting the hydrogen with the
1 kW pulsed rf source for one hour and the QE increased
to 0.8 10-5. However later glows with the pulsed rf source
caused the QE to decrease.
In an attempt to flow more hydrogen through the halfcell we installed a leak valve on the laser port and thenflowed directly into the half cell instead of into the fullcell from the waveguide. However, the QE decreased
every time we glowed with the gas flowing into the halfcell possibly indicating some sort of contamination
introduced through this leak valve. We also repeated theglow at 2852.5 MHz with the hydrogen flowing into thehalf cell instead of the full cell. This time the QE had an
insignificant change compared to the previous glow at
2852.5 MHz when the QE decreased over an order ofmagnitude. This seems to indicate the flow rate is an
important parameter and may help remove contaminants
instead of relocating them.
One interesting result was an increase in the QE nearly
every time we vented the gun with LN2 boil-off. In one
case the QE increased from 0.08 10-5 to 1 10-5 after
venting and in another case it increased from 0.3 10-5 to 2
10-5. The QE would slowly decrease after every glow andthen increase once the gun was vented. We theorize that acontaminant in the LN2 boil-off attaches to the surface
and reduces the work function or modifies the surface733

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Proceedings of FEL 2006, BESSY, Berlin, Germany

states to increase the QE [9]. Subsequent hydrogen glow
discharges then remove this contaminant which reduces
the QE but leave the primary contaminant, Which isassumed to be carbon, untouched. This “doping” of thesurface was also observed on the ARDB cathode after
venting the gun.
The dark current emitted from this cathode actually
decreased during these tests. Prior to the glow discharge
the total integrated dark current at a field of 95 MV/m was
250 pC with a peak current of 0.3 mA. The final charge
was only 100 pC with a peak current of 0.1 mA. The
Fowler-Nordheim field enhancement factor decreased
from 120 to 90 but the emitting area increased nearly anorder of magnitude. The dark current decrease occurred
after the glow discharge at 2852.5 MHz.

Electron Bombardment of the Cathode Surface
The possibility of cleaning photo-cathodes withelectrons was also investigated. A very simple method
using electrons is possible by selecting a laser arrival timesuch that the electrons do not exit the gun but actually
reverse direction and strike the cathode. These backbombarding electrons have been extensively studied inthermionic rf guns [10-11].
By adjusting the laser arrival time, the energy of theback bombarding electrons can be controlled as shown in
Figure 2 where the energy of the electrons exiting the gun
and those returning to the cathode are plotted as afunction of laser phase for a peak field on axis of 95
MV/m. Electrons that reverse direction in the full cell are
emitted at a laser phase between 93 and 117°. Electrons
emitted at a phase greater than 119° reverse direction in
the half cell and thus typically have lower energy at thecathode. Interestingly there are two narrow phase regions
where the electrons actually reverse direction twice andfinally exit the gun. This phenomenon is observed
experimentally when the emitted charge versus laser
phase is carefully measured. The emitted charge falls tozero around 115° and then a small peak reappears around120°. Of course the exact phase where the charge turns
on and off depends on the rf field amplitude and the laser
pulse length.

Total Energy (MeV)

6
Energy at Gun Exit
Energy at Cathode

5
4
3
2
1
0
70

80

90 100 110 120 130 140 150 160 170

Experiments were conducted with a Mg cathode and3000 back-bombarding pulses with an estimated total
charge of approximately 1 μC. The initial experimentused a laser phase of 140°, which should produce anelectron with a kinetic energy of 0.85 MeV striking thecathode. No change in the QE was detected. The laser
phase was adjusted to 160° and later to 125°
corresponding to a kinetic energy of the bombarding
electrons at the cathode of 0.076 MeV and 1.4 MeV. In
all cases no measurable effect on the QE was observed.
Back bombarding electrons also had no effect on themeasured dark current.
The total dose of the electrons is over a factor of 1000
less than the ion beam dose and is possibly insufficient toproduce a measurable effect on the QE. Plus the electron
beam size may be larger when it returns to the cathodefurther limiting the total charge available for cleaning.
The electrons may also penetrate too deep to remove
surface contaminants.

CONCLUSIONSGlow discharge cleaning appears to remove somesurface contaminants without increasing the dark current.
However, at least one contaminant, which is assumed tobe carbon, was not removed but rather appears to haveincreased. Introduction of a small amount of water vapor
may significantly improve the removal rate of surface
carbon [7]. The hydrogen ion beam has the potential toremove all contaminants but the initial results showed no
improvement in QE possibly due to misalignment of theion beam or migration of contaminants. The electron
beam bombardment had no effect on the QE or darkcurrent possibly due to the low amount of charge per unit
area incident on the cathode.
It is clear that additional diagnostics are necessary tounderstand the surface chemistry. We hope to add an
RGA to the vacuum system to understand what species
are present. Plus the surface contaminant coverage of thecathode should be measured using a technique such as
XPS when the cathode is removed from the rf gun. It is
important to understand which contaminants are present
since this information can help determine what technique
is best suited to remove them. In addition it is desirable tomeasure the QE versus wavelength to understand thecontaminants effect on the emission process. The
wavelength dependent QE gives detailed information
regarding the work function and density of surface states.
Perhaps a combination of techniques such as heating,glow discharge, ion beams and doping will be required to
produce a clean metal cathode with high QE. We willcontinue to study various cleaning techniques and theeffect on the cathode QE, dark current and lifetime.

Laser Phase (°)

Figure 2: Simulation of the electron energy at the gun exit
as a function of laser phase is plotted as diamonds. The
squares show the energy of the electrons that return andstrike the cathode.

734

ACKNOWLEDGMENTS
We would like to acknowledge many helpful
discussions and suggestions with R. Kirby and P. Pianetta
at SLAC. Their surface science expertise has helped us

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THPPH063

better understand the cleaning process and guided us inchoosing experimental parameters. This work was
supported by Department of Energy contract DE-AC0276SF00515.

REFERENCES[1] J.F. Schmerge et al., proceeding of the SPIE Free
Electron Laser Challenges II at Photonics West, San
Jose, CA, 1999.
[2] D. Palmer et al., SLAC-PUB-11355, 2005.
[3] D.H. Dowell et al., Proceedings of the 27th Int. FEL
Conf., Stanford, CA, 2005.
[4] D.H. Dowell et al., PRST-AB 9,063502(2006);,
SLAC-PUB-11788, 2006.
[5] H.F. Dylla, J. Vac. Sci. Tech. A, 6, 1276, (1988).
[6] E.Hoyt et al, SLAC PUB-95-6990, 1995.
[7] E.D. Johnson et al, Rev. Sci. Instrum., 58, 1042,(1987).
[8] R.L. Sheffield et al., Nucl. Instrum. and Meth. A, 318,
282, (1992).
[9] Q. Yuan et al., J. Vac. Sci. Tech. B, 21, 2830, (2003).
[10] H. Liu, Nucl. Instrum. and Meth. A, 302, 535,
(1991).
[11] C.B. McKee and J.M.J. Madey, Nucl. Instrum. andMeth. A, 296, 716, (1990).

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BUNCH LENGTH MEASUREMENTS AT JLAB FEL
P. Evtushenko, J. Coleman, K. Jordan, J. Michael Klopf, G. Neil, G. P. Williams
Thomas Jefferson National Accelerator Facility 12000 Jefferson Avenue, Newport News, VA 23606,
U.S.A.
Abstract
The JLab FEL is routinely operated with subpicosecond bunches. The short bunch length is importantfor high gain of the FEL. Coherent transition radiation has
been used for the bunch length measurements for many
years [1]. This diagnostic can be used only in the pulsed
beam mode. It is our goal to run the FEL with CW beam
and a 74.85 MHz micropulse repetition rate, which, withthe 135 pC nominal bunch charge corresponds to thebeam average current of 10 mA. Hence it is very desirable
to have the possibility of making bunch length
measurements when running CW beam with any
micropulse frequency. We use a Fourier transform
infrared (FTIR) interferometer, which is essentially aMichelson interferometer, to measure the spectrum of thecoherent synchrotron radiation generated in the last dipoleof the magnetic bunch compressor upstream of the FEL
wiggler. This noninvasive diagnostic provides bunch
length measurements for CW beam operation at any
micropulse frequency. We also compare the measurements
made with the help of the FTIR interferometer with dataobtained using the Martin-Puplett interferometer [1].
Results of the two diagnostics agree within 15 %. Here we
present a description of the experimental setup, data
evaluation procedure and results of the beammeasurements.

INTRODUCTION AND MOTIVATIONThe Jefferson Lab Free Electron Laser (FEL) facility isa superconducting rf (SRF) energy recovery linac based
light source [2]. It is capable of running CW electron
beam with an average current of up to 10 mA. The
nominal bunch charge is 135 pC. The maximum possible
micro-pulse frequency is 74.85 MHz, which is the 20thsubharmonic of the fundamental (1497MHz) frequency ofthe linac. The micro-pulse frequency can be reduced by afactor of 2n, where n is an integer ranging from 1 to 8.
Thus the accelerator can be operated at the nominal bunchcharge but at the lower average beam current that isessential for the machine setup and tuning. Another set-up
used for tuning up the machine is pulsed beam mode,
where the beam consists of 250 μs long macro pulses
coming with a repetition rate of 2, 10 or 60 Hz. The
micro-pulse frequency within such a macro pulse is not
more than ~4.68 MHz. Thus the average beam current in
the pulse beam mode is kept very low and this beam modecan be used for invasive measurements of the beam
properties.
A modified Martin-Puplett interferometer built by U.
Happek [1] has been used for several years for the bunch
length measurements at JLab FEL. The interferometer is736

used with the coherent transition radiation (CTR). To
generate the CTR, a view screen made of 100 μm thingold plated silicon wafer is inserted in to the beam. Thisdiagnostic is invasive and can be used only in pulsed
beam mode. The challenge of the bunch length diagnostic
was to be able to measure the bunch length when running
CW beam with average beam currents from 0.5 mA to 10
mA.
The coherent synchrotron radiation (CSR) can be used
for the bunch length measurements the same way as theCTR. The longitudinal bunch compression is finalized by
the magnetic bunch compression placed upstream of the
wiggler. The bunch length at the wiggler is almost thesame as at the exit of the bunch compressor. In fact theamount of the CSR generated in the last dipole of thebunch compressor is very high. A beam line was built totransport the CSR to one of the FEL user labs where it
will be used for user experiments [3]. We use a rapid-scanMichelson interferometer with the CSR for thenoninvasive bunch length measurements when running
CW beam.

USING COHERENT RADIATION FOR
BUNCH LENGTH MEASUREMENTS
The underlining principals of using coherent radiation
produced by an electron bunch for the bunch length
measurements have been described in detail many times
in the literature [4]. Here is a short summary of theprincipals upon which the measurements with coherent
transition radiation, as well as for the ones with coherent
synchrotron radiation, are based. Consider an electron
bunch consisting of N e electrons generating transition
radiation (TR) or synchrotron radiation (SR). For awavelength shorter than the bunch length, the radiation
power is proportional to N e , since for every electron
there is on average another electron radiating in an
opposite phase, and so the coherence term is zero. BothTR and SR are very broadband. For a wavelength much
longer than the bunch length, all electrons radiate almostin one phase and, since the phase difference is constant,the radiation is coherent and therefore the power of theradiation is proportional to

N e2 . There is a transition

region where the spectral power density changes fromN e to N e2 . The position of this transition depends on thebunch length. Hence measurements of the radiation
spectrum, which would cover the transition region,
contain information about the bunch length. Rigorously it
is expressed as follows, spectral power density associatedwith the radiation of the entire bunch is

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Proceedings of FEL 2006, BESSY, Berlin, Germany
2~
Pb (ω ) = PS (ω ) ⎡ N e + N e ( N e − 1) f b (ω ) ⎤⎢⎣⎥⎦where PS (ω ) is the spectral density of a single electron
2~is the so-called longitudinalradiation and f b (ω )THPPH064

scan interferometer. The frequency resolution of themeasurements with a Michelson interferometer depends
on the scan range and in our measurements is typically
about 50 GHz.

bunch form factor.

INTERFEROMETERS
The first device we use is a modified Martin-Puplettinterferometer [1]. That is a step-scan device installed in
the accelerator vault right next to the beam line. A lensmade of polished Picarin is set in front of theinterferometer and is used to transform the divergent TR
into a nearly parallel beam going in to the interferometer.
Wire grids made of 20 μm tungsten wire are used as thepolarizing beam splitter and as the polarizer-analyzer. The
period of the grid is 50 μm. A linear stage with a step
motor is used to change the position of the movablemirror in the adjustable arm of the interferometer. An offaxis parabolic mirror is then used then to focus theradiation onto the input window of the Golay cell
detector. Figure 1 shows an example of an interferogrammeasured with the interferometer and the corresponding
spectrum, which, as will be explained later, is a Fouriertransform of the interferogram.
Another interferometer, which we use for themeasurements with the synchrotron light, is a rapid-scandevice. This interferometer is commercially available
from Thermo-Nicolet, and called a Nexus 670. The
optical beam line used to transport the synchrotron
radiation to the user lab is all reflective and is made ofoff-axis ellipsoidal and plane mirrors [3].
A synchrotron radiation opening angle of 150
milliradians is collected from the accelerator. The final
beam is collimated into the Michelson using a 6” focal
length off-axis paraboloid. For the measurements
presented here we used a beam splitter made of silicon.
For the measurements with the synchrotron radiation weused a PY55 detector in conjunction with a PAPY 1153
amplifier, both made by Goodrich [5]. One fundamental
difference between the two interferometers is thedetermination of the path length difference. In the rapidscan interferometer the path length is changed by a freerunning mirror, which moves with constant velocity
during a scan. To measure the path difference in theinterferometer there is one more interferometer built into
it. The additional interferometer utilizes a HeNe laser, thefixed and the movable mirrors of the main interferometerand a beam splitter which is nested inside the maininterferometer beam splitter. The detector for the HeNelaser light is placed at the output port of theinterferometer. During the interferometer scan, the signalof the HeNe detector is a sine function with one period of
the signal corresponding to a path length change of one
wavelength of the HeNe laser, which is 632.8 nm. Thus
the effective sampling frequency of the rapid-scaninterferometer is much higher than the one of our step-

FEL Technology

Figure 1: Interferogram measured with the modified
Martin-Puplett interferometer and the corresponding
spectrum.
In our measurements one scan of the rapid-scaninterferometer takes about 2 seconds. Since bothinterferometers we use are essentially Michelsoninterferometers, the same data evaluation procedure forthe bunch length reconstruction can be applied to the dataobtained from either interferometer.

BUNCH LENGTH RECONSTRUCTION
We use the following data evaluation procedure for thebunch length estimation. The procedure is similar to theone described in [6]. According to the Wiener-Khintchine
theorem [7], the autocorrelation function is the Fouriertransform of the power spectrum. We use a Fast Fourier
Transform (FFT) algorithm to calculate the powers
spectrum from the interferogram since the data arediscrete. The power spectrum defines uniquely the
amplitude of the components of the frequency domain
representation of the pulse. However, information about
the relative phases of the different Fourier components islost in the interferometric measurement. This is why a

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Proceedings of FEL 2006, BESSY, Berlin, Germany

direct pulse shape reconstruction from the power
spectrum is not possible.
We assume a Gaussian shape of the bunch, with the
RMS bunch length σ t . The Fourier transform of the
distribution function is also a Gaussian function. Thus we
can write the Gaussian bunch power spectrum as

2~
P (ω ) = C ⋅ e − (ωσ t ) , where C is a constant. In themeasured power spectrum, the intensity is strongly
reduced below a certain threshold frequency as shown in
Fig. 1. The reduction of the spectral density is due todiffraction losses. The general Huygens’ integral can beused to describe the diffraction losses [8]. Result of theintegration of the general Huygens’ integral is not ananalytical function and is not very convenient to use forfurther data evaluation. We approximate the low
frequency cut-off function with the following analytical

F filter = 1 − e − (ω ω0 ) , where ω 0 is the
4function

important that with the Michelson interferometer andsynchrotron radiation we can do bunch length
measurements as a function of the average beam current.
Figure 2 shows spectra of the CSR measured at 0.31 mA,
0.62 mA, 1.25 mA and 2.5 mA of beam average current
and the measured CTR spectrum measured with pulsed
beam, all the measurements were done with the samemachine setup. The figure also shows the corresponding
fit functions and the resulting RMS bunch length. The
measurements show that the bunch length is not changing
when the average beam current is increased. This is what
one would expect, since the average current is increased
by increasing the pulse repetition rate, keeping the bunchcharge constant. However, at present the FEL efficiency
has been decreasing with beam current and one
explanation would be that it is due to an increase in bunch
length. These measurements are therefore critical inruling this out.

characteristic cut-off frequency. The product of theGaussian power spectrum and the filter function is themodified power spectrum()

f fit (ω ) = 1 − e − (ω ω0 ) ⋅ C ⋅ e − (ωσ t ) .
4

2

Once the modified power spectrum is expressed as ananalytical function it can be used as a fit function with thenonlinear least square fit (NLSF) to approximate ameasured power spectrum. From such a fit we can obtainσ t , which we define as the RMS bunch length. There areseveral options regarding the characteristic cut-off
frequency ω 0 . The best would be to have it measured, butsuch a measurement in the frequency range of theinterests is very difficult. Another option, which we haveused so far, is to add in the effects of ω 0 to the fit
parameter and to make sure it stays consistent during themeasurements.

EXPERIMENTAL RESULTS
The accelerator setup is always done in diagnostic
mode with pulsed beam. In this mode the modified
Martin-Puplett interferometer is used for the bunch length
measurements. We routinely operate the machine with an
RMS bunch length of about 150 fs. However, dependent
on the machine setup we have been measuring RMS
bunch lengths in the range from about 100 fs up to 200 fs
RMS. That implies that we do indeed successfullyreconstruct the bunch lengths from the interferometermeasurements as was described in the previous section.
Figure 1 shows an example of an interferogram measured
with the step-scan interferometer, while the corresponding
spectrum also shows the fit function, which is the result of
the data evaluation. For this particular measurement the fit
gives the RMS bunch length of 153 fs.
When the accelerator is set up we can run CW beamand use the rapid-scan interferometer. Our experience isthat the results of the measurements with twointerferometers agree to within about 15 %. It is very

738

Figure 2: Spectra of the CSR measured at different
average beam current with the CTR spectrum and thecorresponding fit functions for bunch length
reconstruction.
Another significant finding we have made is that thebunch length at the wiggler depends very strongly on thebunch charge. The bunch compression is normally
optimized for the nominal bunch charge of 135 pC. When
operating with much smaller bunch charge and without
any changes in the machine setup, we have a much shorterbunch at the entrance to the linac. This results in a verysmall energy spread of the bunch at the exit of the linac.
As a result, the M56 of the 180° bend and the chicane do
not provide the same compression as for a bunch withnominal charge. As a result a bunch with a very small
charge will be much longer at the wiggler than a nominal
bunch. Figure 3.a shows measurements of the CSR
spectrum of the nominal bunch, with an RMS bunch
length of 129 fs, and that of a bunch with a very small
charge where the RMS bunch length was measured to be
384 fs.
The rapid-scan interferometer provides more
information than just a spectrum of CSR. Consider theinterferometer scanning with the mirror velocity of
5mm/sec. Then the optical path length difference changes

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Proceedings of FEL 2006, BESSY, Berlin, Germany
at a rate of 10 mm/sec. If the incoming radiation has, forexample, a wavelength of 1 mm it will result in amodulation of the signal at the detector at a frequency of
10 Hz.

THPPH064

All the measured CSR spectra shown in Fig. 2 show
local minima in the spectral power density, these are dueto the water vapor absorption. This data corruption
certainly reduces the accuracy of our bunch length
reconstruction. To improve the setup we will switch to anewer Michelson interferometer operating in vacuum. It
has been already demonstrated that such an interferometercan be operated in vacuum [10].

ACKNOWLEDGMENTS
We would like to thank S. Benson and D. Douglas for anumerous stimulating discussions and for operating themachine during measurements and systematic study of theinterferometers.
This work supported by The Office of Naval Research
the Joint Technology Office, NAVSEA PMS-405, the Air
Force Research Laboratory, U.S. Army Night Vision Lab,
the Commonwealth of Virginia, and by DOE Contract
DE-AC05-84ER40150.

REFERENCES

Figure 3: (a. top) spectra of the CSR measured at nominal
bunch charge and much smaller bunch charge.;(b. bottom)
the same data are shown on a logarithmic scale.
Thus different wavelengths measured by theinterferometer be modulated at the detector at different
frequencies. The frequency of the detector signal
modulation is f M = 2v / λ , where v is the velocity ofthe mirror during the scan and λ is the wavelength of themeasured radiation. If the intensity of the incoming
radiation is modulated, for instance due to a beam
instability at some frequency, that will also result inmodulation of the detector signal at that specificfrequency. Hence the interferometer measurements also
contain information about the beam stability. This
technique has been used at numerous synchrotrons todiagnose and improve the beam stability [9]. Figure 3.bshows the data shown in Fig. 3.a on a logarithmic scaleand over a bigger frequency span. The spectral power
density peak at 4.69 THz corresponds to the radiation
intensity modulation at 60 Hz; the next peak at 5.69 THz
corresponds to the intensity modulation at 72.8 Hz and soon. We have yet to study in detail, the origin of all theobserved beam modulations.

FEL Technology[1] G. A. Krafft, P. Piot, K. Jordan, and J. Song, U.
Happek and M. James, “Measuring andcharacterizing ultrashort bunches in the Jefferson Lab
Free Electron Laser”, Proceedings of the EPAC98[2] S. Benson, D. Douglas, M. Shinn, K. Beard, C.
Behre, G. Biallas, J. Boyce, H. F. Dylla, R. Evans, A.
Grippo, J. Gubeli, D. Hardy, C. Hernandez-Garcia, K.
Jordan, L. Merminga, G. R. Neil, J. Preble, T.
Siggins, R. Walker, G. P. Williams, B. Yunn, S.
Zhang, H. Toyokawa, “High Power Lasing in the IR
Upgrade FEL at Jefferson Lab”, Proceedings of the2004 FEL Conference, Trieste, Italy, 229 (2004)[3] S. Benson, D. R. Douglas, H. F. Dylla, J. Gubeli, K.
Jordan, G. R. Neil, M. Shinn, S. Zhang and G.P.
Williams, “High Power THz Generation from Sub-ps
Bunches of Relativistic Electrons”, Mater. Res. Soc.
Symp. Proc. 850, MM4.3.1 (2005)[4] U. Happek, A.J. Sievers and E.B. Blum, Phys. Rev.
Lett. 67, 2962 (1991)[5] http://www.oss.goodrich.com/datasheets/oss/
Goodrich_PAPY_DetectorPreamplifier.pdf[6] A. Murokh, J.B. Rosenzweig, M. Hogan, H. Suk, G.
Travish, and U. Happek, "Bunch Length
Measurement of Picosecond Electron Beams from a
Photoinjector using Coherent Transition Radiation",
Nucl. Instr. Meth. A 410, 452 (1998)[7] N. Wiener, Acta. Math. 55, 117, (1930)[8] A. Siegman, Lasers, University Science Books,(1986)[9] R. Biscardi, G. Ramirez and G.P. Williams, "Effectsof RF Side-Bands on Spectral Reproducibility for
Infrared Synchrotron Radiation", Rev. Sci. Instr. 66,
1856 (1995)[10] P. Brierley, B. Badeau, P. Dumas, M. Smith, G. P.
Williams, “Performance of a rapid-scan vacuum
Michelson interferometer at the NSLS”, Review of
Scientific Instruments 73, 1595-1598 (2002)

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LONGITUDINAL PHASE SPACE CHARACTERIZATION OF ELECTRONBUNCHES AT THE JLAB FEL FACILITY
S. Zhang, S. Benson, D. Douglas, D. Hardy, G. Neil, and M. Shinn
TJNAF, Newport News, VA23606, USA
Abstract
We report longitudinal phase space measurements ofshort electron bunches at the 10kW Free-Electron Laser
Facility at Jefferson Lab using broadband synchrotron
radiation and a remotely controlled fast streak camera.
Accurate measurements are possible because theoptical transport system uses only reflective
components that do not introduce dispersion. The
evolution of longitudinal phase space of the electron
beam can be observed in real time while phases ofaccelerator RF components are being adjusted. This
fast and efficient diagnostic enhances the suite ofmachine setup tools available to JLab FEL operators
and applies to other accelerators. The results forcertain beam setups will be presented.

Longitudinal phase space (LPS) measurements provide
extremely valuable correlated information between thetemporal position of the electrons and their longitudinal
momenta. Knowledge of LPS and perhaps more
importantly, its evolution with time, helps duringmachine setup. We report a convenient and noninvasive means to monitor LPS in real-time usingsynchrotron radiation and a fast streak camera. This
work builds upon work reported previously [1], and ispart of an ongoing effort to enhance the diagnostic
capabilities at the JLab 10KW FEL Facility. In thispaper, we describe the measurement technique anddiscuss the results obtained under different beam
setups.

SYSTEM DESCRIPTIONINTRODUCTION
High power Free-Electron Lasers (FELs) require very
short electron bunches. The picosecond electron
bunches produced by the DC high voltage GaAs
photoguns must be accelerated and compressed to
femto-second time scale using RF and magnetic
compressors (for example, RF buncher cavities, offcrest acceleration, drift spaces and magnet chicanes).
Setting and maintaining proper phase of the electron
bunches with respect to the RF fields in theaccelerating linac is critical for effective bunch
compression and high power FEL operation.

Figure 1 shows a schematic overview of the
Jefferson Lab 10kW energy-recovery FEL facility
which has been described in detail elsewhere [2].
Electron bunches from the gun are accelerated to
115MeV using a superconducting RF linac and turned
180 degree using a Bates-style arc magnet (ARC1)
toward the FEL wiggler magnet located midway
between the high-reflector and output-coupler mirrors.
The electron beam then passes through a second 180
degree arc magnet for energy recovery through thelinac.

Figure 1: Layout of 10kW FEL facility at Jefferson Lab. The 1KW UV line is under construction. The linac consists ofthree cryo-modules. The ARC bending magnets are located at each end with ARC1 in the lower-left corner.
Managing the beam energy spread is critical for highcurrent, high micro-bunch charge accelerator operation.
In addition, it is particularly important to see how
energy spread varies for the two states of accelerator
740

operation: FEL on and off. As described in this paper,
energy spread can be monitored non-invasively bymonitoring the SR light emitted from the 180 degree
bend magnets because electrons with lower energy
FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

The streak camera is a Hamamatsu Synchroscan
FESCA system, the measured resolution is about 700fs.
Having the streak camera outside the harmfulenvironment of the accelerator vault is beneficial
because sometimes local alignment of the camera mustbe performed, although data acquisition is completely
remotely controlled.

FE

SC

A

travel a shorter radial path compared to electrons withhigher energy. By monitoring the emission profile of
the SR light in the horizontal plane, one can measure
the size of the electron beam and therefore the beamenergy spread.

THPPH066

MEASUREMENT AND DISCUSSION
Energy Calibration and Resolution

M9
M7
M6

M8

Breadboard
CM3

M2 CM1

Beam Tube

M4

M5

M3

CM2

ARC1
open port
M1SR

e-bunchFigure 2: Schematic of the optical transport system(OTS). M, flat mirrors. CM, concave mirrors.
Detailed description is given in the text.
For the measurement described here, SR light fromthe first 180 degree bend magnet (ARC1) was reflected
upwards and out of the accelerator vault using an allreflective optical transport system (Figure 2). The
optical transport was designed to image-relay the bunch
beam profile from outermost location of the beam orbit
in ARC1 to the streak camera entrance slit. The SR
light from the electron bunch is extremely broadband
and it is important that transmission optics such as
lenses are not used. Each mirror was coated withmetallic coating to eliminate the dispersion effect. The
three concave mirrors have radii of curvature of 200,
500 and 1000mm. Mirror M1 directs the SR beam fromthe bunch upwards through an open port to M2. The
beam then reflects off several mirrors mounted on asmall breadboard. The magnification can be adjusted
by changing the distance between CM1 and CM2 inorder to match the beam size to the camera cathode.
The SR light propagates through a tube inserted into apenetration in the building floor. The final image at thestreak camera was formed by the concave mirror CM3.
A HeNe laser was available for rough pre-alignment of
the system, but final alignment with SR light was time
consuming, mostly because the distance between thebend magnet and the streak camera is long, more than
8m. Final optimization of the optical transport system
was done with SR light during accelerator operations
using several motorized mirrors.

FEL Technology

LPS measurements are presented on twodimensional plots, showing energy spread along the
temporal distribution of the electron bunch. Notehowever that what is actually measured is beam size
versus the temporal distribution of the bunch. To
convert beam size to energy requires calibration of thestreak camera pixel display. This was accomplishedusing different beam energies and setups that provide
minimum energy spread. Figure 3 shows five streak
camera images for five different beam energies. The
red curve is the initial energy set-point of 115MeV.
The green (yellow) curve corresponds to higher (lower)with energy difference of 1.5%. The two peaks are
separated by 391 pixels which yields a calibration
factor of 0.00385% energy difference per pixel. Next,
the pixel/energy resolution was studied using twoenergies separated by only 0.046%. The blue and pink
peaks are separated by only 12 pixels but are clearly
distinct. So the system resolution is definitely better
than 0.05%.

Figure 3. Streak camera images for five different beamenergies. The yellow and green curves provide acalibration ratio, beam energy to pixel location. The
pink and blue curves demonstrate the high degree ofenergy resolution of the system. The red curve is thenominal 115 MeV setpoint energy.

LPS vs. Linac Gang Phase
Production of high power FEL light requires offcrest operation of the accelerator. Deviations from thisdesired phase relationship may lead to reduced FEL
output power. The phase relationship of the electron
bunches relative to the linac gang phase can bequantified using LPS measurement and the SR light741

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Proceedings of FEL 2006, BESSY, Berlin, Germany

streak camera. This is dramatically evident in Figure 4
which shows streak camera data for different linac RF
gang phases relative to on-crest operation. Eachpicture represents a snap-shot of data presented live
within the FEL control room while the accelerator was
running.

Figure 4: The LPS for different linac gang phase. Beam energy, 115MeV. Micro-pulse repetition rate: 9MHz. Macro-pulse,
1ms at 60Hz. Charge, 110pC per bunch.

From Fig.4, it is clear that the LPS can be quite
different even if the bunches sit symmetrically on thetwo sides of the RF crest. This is the case when thephase angles are equal but have opposite signs.
Apparently, a linear chirp and longer bunch length isobtained at 6 degree off-crest. At -6 degree off-crest,
the bunch length becomes shorter but the shape is more
like a banana, indicating high non-linearity. For oncrest operation, the bunches experience very little
energy spread and the phase space is straight up withthe least tilt.

742

LPS vs. Buncher Gradient
The whole injector of the JLab FEL facility consistsof a high-voltage DC gun, a quarter cryo-unit followed
by a transverse match section and an RF bunch
compressor. The electron bunches from the photocathode initially have the same temporal length as thedrive laser pulses but expand due to space charge
effects. Passage through the quarter cryo-module also
affects the electron bunch length. Optimum FEL
operation requires the electron bunches be compressed
before entering linac. We have observed that the
FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

gradient of the buncher can affect the phase space ofthe electron bunches. To investigate this phenomenon,

THPPH066

we did LPS streak camera measurements whilechanging the buncher gradient (Figure 5).

Figure 5: Longitudinal phase space for different buncher gradient. The beam energy, 115MeV. Micro-pulse repetition rate,
9MHz. Macro-pulse, 1ms at 60Hz. Charge, 110pC/bunch. The graph in lower right corner is explained in the text.

As the buncher gradient increases from low to high,the LPS trace gradually stretches out to become a linear
chirp. The low energy head is basically preserved
through the process while the curled tail disappears at
2.5MeV/m. The last graph in the lower right represents
normal FEL operating condition. The excellent linear
chirp can be seen across the whole 2.3% energy spread
range.
A small part of the information at the two ends of thegraph is lost, especially at low energy side of the plot.
This is perhaps due to the limited energy window. Thiscan be solved in the future by changing the opticaldemagnification at the expense of reduced resolution.
We also used several band-pass filters with different
bandwidth to see if there were dispersion effects
induced in the optical transport. No difference wasfound with and without filters in the bean path,testament to the all-reflective nature of our design.

SUMMARY
We have established a diagnostic that provides realtime longitudinal phase space information without
interruption to the accelerator operation. The
longitudinal phase space was successfully measured
with different linac gang phase and injector bunch

FEL Technology

gradient. The system was well calibrated with anenergy resolution better than 0.05%. We are expecting
to get better understanding on some important beamphysics as we push toward high current beam and highpower FEL on our facility in near future.
Acknowledgement
The authors would like to thank the FEL team,
especially the I&C group. Thanks to M.Poelker for
reviewing and extensive editing. This work is
supported by the Office of Naval Research, Research,
the Joint Technology Office, the Commonwealth of
Virginia, the Air Force Research Laboratory, and by
DOE Contract DE-AC05-84ER40150.

REFERENCES[1] S. Zhang, et al., “Temporal Characterization ofElectron Beam Bunches with a Fast Streak Camera
at Jlab FEL Facility”, FEL2005, SLAC, August
2005, p.640.
[2] D.Douglas, et al., “Driver Accelerator Design for
the 10kW Upgrade for the JLAB IR FEL”,
LINAC2001, Monterey, CA 2001, p.867.

743

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THE DEVELOPMENT AND APPLICATION OF A PHOTOEMISSION
MODEL FOR CESIATED PHOTOCATHODE SURFACES
K. L. Jensen, J. E. Yater, J. L. Shaw, Naval Research Laboratory, Washington DC, 20375 USA
N. A. Moody, D. W. Feldman, P. G. O’Shea, University of Maryland, MD 20742, U.S.A.
Abstract
A theoretical photoemission model including thermal
and field effects is presented. Particular attention is given
to considering the impact of electron-electron andelectron-lattice scattering and the development of an
integrated absorption-transport-emission model developed
to evaluate the moments of the electron emission
distribution function. For the experimental conditions towhich the theory is compared, there are no adjustableparameters. The performance of the model for the QE ofbare metals and coated surfaces is discussed. A simple
asymptotic model of emittance and brightness is given.1

INTRODUCTION
A high quantum efficiency (QE) photoemitter capableof in situ rejuvenation would fill a critical need in thedevelopment of high power FELs and linear accelerators.
The demands placed on photocathode and drive-laser
combinations by high power FELs are often bothdemanding and conflicting. Nano-Coulomb bunches inO(10) ps time scales require high quantum efficiency
photocathodes, but such cathodes have traditionallydegraded prematurely in vacuums characteristic of rf
photoinjectors, whereas more rugged metal photocathodes
require short wavelengths and therefore demand much of
the drive lasers. The dispenser photocathode is intended
to provide a rugged, low work function, long lived
photocathode addressing these conflicting needs, and its
development necessitated a validated photocathode model
capable of analyzing data and predicting performance. A
program to develop a controlled porosity dispenser (CPD)
photocathode led to the creation and validation of atheoretical model that accounts for low work function
surfaces from submonolayer coverage of alkali (and alkali
earth) metals [i]. Efforts to extend and update that model
have been in response to two needs: first, to provide
theoretical support to an experimental CPD photocathodeprogram by systematically studying cesiated surfaces,
conventional sintered tungsten dispenser cathodes, andultimately, custom engineered dispenser cathode; andsecond, to render the validated photoemission model in aform amenable to particle-in-cell (PIC) beam simulation
codes [ii, iii] to predict performance of an rf injector gun
using such a photocathode. Here the latest modifications
to the model and its application are discussed.
Changes to the theoretical model are on two fronts.
First, the scattering model affecting photoelectron excitedtransport to the surface has been revised. Second, therevisions motivated a moments-based emission modelthat is able to address cathode emittance. The beams of1high power FEL’s will be space charge dominated at somestage in the accelerator but especially in the gun. Nonuniform, transverse and temporal distributions affectemittance, and while the problem is of significant
concern, predictive modeling efforts of device operation
are compromised by the lack of adequate emission
models in beam simulation codes. The photoemission
models developed attempt to rectify the deficiency.

THE PHOTOEMISSION MODEL
Background
The photoemission model described in Ref. [i]represented quantum efficiency QE byq
QE (T , F ) =Fλ (T ) (1 − R ) P (hω )hω[1]U ⎡ βT (hω − φ )⎤⎦P (hω ) = ⎣U [βT μ ]where R(ω) is the reflectivity of the surface, P is a
probability of emission factor, U is the Fowler-Dubridgefunction, βT = 1/kBT is the inverse temperature, φ is thebarrier height above the Fermi level (work function minus
Schottky barrier lowering factor, or Φ − 4QF , where Q= 0.36 eV-nm and F is the product of electric field andelectron charge). When coatings such as Cs are
introduced, the work function Φ is dependent upon the
degree of coverage θ in a manner predicted by
Gyftopoulos-Levine theory. The scattering factor Fλ (notto be confused with field F) governs the probability that
an electron will suffer a scattering event on its trajectory
towards the surface and therefore be prevented frombeing photoemitted. It can be approximated by
1 π /2cos(θ )Fλ ≈ ∫dθ[2]
π 0 cos(θ ) + (δ / l(E))
where δ is the laser penetration depth, and the length l(E)is the product of the electron velocity and relaxation time(the notation has changed from Ref. [i])Amending recent work in measuring the QE of cesiatedsurfaces and the prediction of the QE of bare metals, wehave revised components of the QE model by first,
utilizing models of the relaxation rates τ implicit in fλ atthe electron energy augmented by the photon energy, andsecond, using a moments-based approach that changes theprobability of emission term P. It is the moments-based
approach that allows for transverse energy and velocity
expectation values to be determined, from which
estimates of the emittance and brightness can be made.

Support by Joint Technology Office & Office of Naval Research744

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany
100

The relaxation time is taken to be the sum of threecomponents:−1τ −1 = τ ee−1 + τ ac−1 + τ imp[3]80

where “ee” refers to electron-electron, “ac” refers toacoustic phonon, and “imp” to residual low temperaturescattering due to impurities or defects. In the case ofelectron-electron scattering, the scattering rate is given by⎡⎛
E − μ ⎞ ⎛ 2k F ⎞ ⎤τ ee = 2
1+
γ
⎥
2
2 ⎢⎜
α π mc (k BT ) ⎢⎣⎝ π k BT ⎟⎠ ⎜⎝ qo ⎟⎠ ⎥⎦4hK s2⎛tanx3x
γ (x) = ⎜⎜ tan −1 x +−4⎜
1 + x2−1

20

2where Ks is the dielectric constant, α is the fine structure
constant, kF is the Fermi wave vector, and qo is theThomas-Fermi screening length [iv] (the form given here
corrects coefficient errors that exist in Ref. [iv]). To
leading order, the Thomas-Fermi factor is given by
4α mc
[5]
qo2 =
2mμ
π h2 K s
For acoustic scattering, the rate is given by [v]πρh3vs2 (TD / T ) ⎛5τ ac =⎜⎜⎝

mk BTk F Ξ2

∫

TD /T

s5 ds

⎞
⎟
⎟
⎠

−1

(e − 1)(1 − e )
−s

s

0

[6]

where Ξ is the magnitude of the deformation potential, TD
is the Debye temperture, vs is the velocity of sound, andρ is the density. The Debye Temperature is given by
1/3
hv
TD = s 6π 2 Nr
[7]
kB
where N [#/cm3] is the number density of the crystal, r isthe (# of atoms / unit cell), and vs is the sound velocity.

(

)

Cu

12
10
8
ln(Tau [fs])ln(Tac)ln(Tee)ln(TOTL)
Liq. Nitrogen
Room Temp

4
2
0
-2
0

1

2

3

4

5

6

7

ln(Temperature [Kelvin])
Figure 1: Determination of τimp and Ξ from thermal
conductivity data from the literature.

FEL Technology

0
0

0.5

1

1.5

2

2.5

3

3.5

4

E-Ef
Figure 2: Determination of Ks from Monte Carlosimulations (red line) compared to parameters consideredby Lugovskoy and Bray (green and blue)
Consequently, three parameters require an intricate
simultaneous determination: τimp, Ks and Ξ. The valuesof τimp and Ξ are determined by low temperature thermal
conductivity measurements after Ks is determined fromMonte Carlo simulations in the literature [vi].

Comparison to Experiment
An example for Cu is shown in Figure 1 and 2. The
procedure is reiterated for many metals, and in particular,
for tungsten (W) and silver (Ag) which are the twocesiated metals experimentally examined [vii].
Parameters extracted from the literature become part of alibrary of material terms implicit in code and are notadjusted further. Comparisons of predictions of theresulting model with experimental data have beenfavorable for the cases of photoemission from copper[viii] and lead [ix] for a range of photon frequencies, aswell as for other metals and particular frequencies
discussed in the literature.

Quantum Efficiencyln(Relaxation Time [fs])

14

6

40

−1

⎞
⎟
⎟
⎟
⎠

2

Cu
Tau
Lugovskoy Ks =1
Lugovskoy Ks=5.2
tau-ee [fs]tau-ac [fs]60

(x 2 + x ) [4]
2+ x

⎝

Tau

Scattering Rates and Their Determination

THPPH068

10

-1

10

-2

10

-3

10

-4

808 nm655 nm532 nm405 nm375 nmCs on W
0

20

40

60

80

100

Theta [%]
Figure 3: QE of Cs on W for low F and Iλ at 300 K
versus fractional surface coverage (Ar-cleaned W).
Symbols = experimental data; lines = theoretical model.

745

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Proceedings of FEL 2006, BESSY, Berlin, Germany

QE [%]

0.12
Theo
Theo x 0.85
ExpA
ExpB

0.08

Cs on Agλ = 405 nm
F = 0.0174 MV/m
Φ = 1.6 eV

0.04

min

α = 5.3 Angstroms
0.00
0

20

40

60

θ [%]

80

100

Figure 4: QE of Cs on Ag for conditions as in Fig. 3
Using the Gyftopoulos-Levine theory to relate thedegree of surface coverage of Cesium on a bulk metal to
the resulting work function [i], the prediction of QE for
Cs on W and Cs on Ag was made and compared toexperimental data. The results of that comparison are
shown in Figures 3 and 4, respectively. The low coverage
discrepancy shown in Fig. 4 is due to residual Cs on thesurface from one experiment to the other. Issues of
surface contamination led to investigations of cleaning
using Ar ions, resulting in the better results for Cs on W
shown in Fig. 3.

Origin Of Experimental-Theoretical Differences
The overall comparison between theory and experimentis shown to be remarkably good. Nevertheless, there aredifferences and an account of their probable origins isnecessary. Theoretically, a simple nearly-free electron
gas model is presumed, and so the significant
complexities introduced by the density of states near the
Fermi level are suppressed, and such complexities canmatter for transition metals. Experimentally, in contrast
to physical surfaces, the theoretical models are highly
idealized. Cleaning is required to remove contaminants,
and if due to sputtering, structure can be introduced. If
the cathode is heated for cleaning, not all metals endure
the necessary temperatures because of relatively low
melting points (W can be strongly heated, whereas Ag
cannot). Residual contamination can therefore remain in
addition to what collects from an imperfect vacuum.
Adsorbates often have higher work functions, e.g.,
carbon-based contamination can induce local work
functions of 5.5 eV. Assuming the surface is adequately
cleaned, different exposed crystal faces can show
markedly different work functions (e.g., faces of Cu canvary by almost 0.8 eV): moreover, in GyftopoulosLevine theory, the exposed crystal plane affects the ffactor (see Ref. [i]: affects the number of Cs atoms perunit area) and which changes the shape of the QE hump:observations of the tungsten face, as shown in Figure 5, as
well as considering other values of f suggest the generic(single) value chosen for f is not necessarily the optimalvalue when several faces are present.

746

Figure 5: Image of sintered tungsten surface showing
multiple crystal faces. Average grain size is O(10μm).

MOMENTS-BASED FORMULATION
The development of an energy-dependent relaxation
time coincides with efforts to develop a modified
emission probability model to replace Eq. [1], in which
the energy of an incident electron affects its transmission
probability T(E) over (or through for high fields) a barrier.
By using a distribution function approach, parallel andtransverse momentum expectation values are ascertained,
the former used to evaluate the photoemission current, thelatter to evaluated emittance (and both to evaluate
brightness). Define the nth moment
3/2

E dE ×( ) ⎜⎝ 2m
h ⎟⎠ ∫M n (x) = 2π

∫

π /2
0

⎛ 2m

sin θ dθ ⎜

⎞

−3 ⎛

2

∞

1/2

0

⎞

n/2

{

}

{

}

Ex 2 ⎟ T (E + hω ) cos 2 θ ×
2⎠⎝ hf λ (cos θ , E + hω ) f FD (E) 1 − f FD (E + hω )[8]where x = cos(θ) for parallel, and sin(θ) for transverse
components. T is the transmission probability; fλ is theintegrand of Fλ, and the factor fFD(1-fFD) represents theprobability that the initial state is occupied and the final
state is not based on the Fermi Dirac distribution. The
revised relaxation times are used in the determination of
the fλ factor.
The inclusion of the transmission
probability factor, and the impact on the integration limits
it entails, generally results in current density estimates on
the order of 30% less than the Modified Fowler-Dubridge
approach, all other factors being equal. Methods tocalculate Eq. [8] numerically rely on approximations to
the transmission probability and models for the relaxation
time in the scattering factor: below, however, an
asymptotic case is considered so as to provide a simple
model of emittance and brightness.
Under the Richardson approximation for thetransmission coefficient and the zero-temperatureapproximation for the FD functions, the asymptotic
expressions for the transverse (x = sinθ) moments are [x]FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

M0 ≈⎡ 2m ⎤
2 ⎢ 2 ⎥
2π ⎣ h ⎦

1

( )

3/2

μ1/2 (hω − φ )4 (μ + φ ) ⎡⎣ p (hω + μ ) + 1⎤⎦2[9]2m μ (hω − φ )M2 ≈M0
3h2 (hω + μ )From the definition of the emittance [xi] ash
2
ε n,rms (z) =x 2 kx2 − xkx[10]mc
and following a derivation and approximations (uniform
emission over a circular uniformly illuminated surfacearea) analogous to that leading to the widely-used thermal
emittance relation

ε n,rms (therm) = ρc / (4 βT mc 2 )[11]ρc ⎡ μ (hω − φ ) ⎤⎢⎥2 ⎣ 3mc 2 (hω + μ )⎦

[12]

1/2

where ρc is the cathode radius and βT is 1/kBT, it can beshown that εn,rms(photo) is proportional to the illumination
radius and the root of the 2nd and 0th moments, or
1/2

ε n,rms ( photo ) ≈3qmc 2 ⎛ (hω + μ )(hω − φ )⎞Bn≈
(1 − R ) I λ A 2π 2 μ 3hω ⎜⎝ 1 + p (μ + hω ) ⎟⎠200

λB /(1-R)I A [C/J]

where Bn is the brightness [xii], R is the reflectivity, Iλ isthe laser intensity per unit area, and A is the illuminatedarea. The brightness ratio in Eq. [12] is designed toforestall issues associated with reflectivity, laser
particulars, and illumination area. Two observations areimportant: first, the emittance does not depend on the
scattering factor to leading order (the brightness does
through the p factor); second, the asymptotic form of Bn
indicates that an optimal wavelength exits for which thebrightness is maximized. The behavior of εn,rms and Bn are
shown in Figure 6.

ε

n,rms

[μm]

n

100
0
0.8
0.4
Copper
0.0
0.05
0.1

0.15
0.2
0.25
Wavelength [µm]0.3Figure 6: emittance and brightness ratio as a function ofincident laser wavelength for copper parameters forconditions described in Ref. [viii].
Experimental values of emittance at 233 nm areapproximately 50% larger than the theoretical value
shown.
The emittance of thermionic sources are
generally within a factor of 2 larger than the theoretical

FEL Technology

THPPH068

estimate entailed by Eq. [11], and it is reasonable topresume similar explanations hold here: non-linear fieldcomponents in the cavity, wakefields, non-uniformity of
the illumination source (laser), thermal effects, quantum
efficiency non-uniformity due to contamination orcathode structure, and space-charge effects occur forsufficiently high charge in the bunch, and likely somecombination contribute to the theoretical-experimental
differences between the simple asymptotic limit herein
and experiment.

CONCLUSION
We have presented a revised photoemission model toaccount for theoretical-based scattering models and a
moments-based approach for the evaluation of quantum
efficiency. The revised scattering model enabled good
agreement with experimental data of cesiated surfaces.
The moments-based approach allowed for simple
asymptotic expressions of emittance and brightness.

Acknowledgements
We gratefully acknowledge funding provided by the
Joint Technology Office and the Office of Naval Research.
In addition, we have benefited from interaction withmany colleagues: in particular we thank (alph) C. Bohn,
C. Brau, D. Dimitrov, D. Dowell, Y.Y. Lau, J. Lewellen,
E. Nelson, J. Petillo, and J. Smedley.

REFERENCES
i

K. L. Jensen, Donald W. Feldman, Nathan A.
Moody, and Patrick G. O'Shea, Journal of Applied
Physics 99, 124905 (2006).
ii J. J. Petillo, E. M. Nelson, J. F. DeFord, N. J. Dionne,
B. Levush, IEEE Trans. El. Dev. 52, 742 (2005).
iii D. A. Dimitrov, D. L. Bruhwiler, J. R. Cary, P.
Messmer, P. Stoltz, K. L. Jensen, D. W. Feldman, P.
G. O’Shea, Conference Proceedings of the 27th Intl.
Free Electron Laser Conference (Stanford, CA, Aug.
21-25, 2005), paper TUPPE039.
iv A. V Lugovskoy, Igor Bray, J. Phys. D: Appl. Phys.
31 L78 (1998).
v Harald Ibach, Hans Lüth, Sold State Physics 2nd Ed.,
(Springer-Verlag, Berlin, 1995).
vi F. Ladstädter, U. Hohenester, P. Puschnig, C.
Ambrosch-Draxl, Phys. Rev. B70, 235125 (2004)
vii N. A. Moody, D. W. Feldman, P. G. O'Shea, K. L.
Jensen, J. L. Shaw, J. E. Yater, (Free Electron Laser
Conference, Berlin, Aug 27-Sep 1, 2006)
viii D. H. Dowell, F. K. King, R. E. Kirby, J. F.
Schmerge, J. M. Smedley, Phys. Rev. Spec. Top.-AB
9, 063502 (2006)
ix Data from J. M. Smedley (private communication).
x K. L. Jensen, P. G. O’Shea, D. W. Feldman, N. A.
Moody (submitted to Appl. Phys. Letters)
xi Patrick G. O'Shea, Phys. Rev. E57, 1801 (1998).
xii C. Brau, Nucl. Inst. Meth. Phys. Res. A407, 1 (1998).

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Proceedings of FEL 2006, BESSY, Berlin, Germany

EXPERIMENTAL PROGRESS TOWARD LOW WORKFUNCTIONCONTROLLED POROSITY DISPENSER PHOTOCATHODES*
N. A. Moody#, D. W. Feldman, E. J. Montgomery, A. E. Balter, P. G. O’Shea,
U. of Maryland, College Park, MD, USA
K. L. Jensen, J. E. Yater, J. L. Shaw, Naval Research Laboratory, Washington DC, USA.
Abstract
Photoinjectors for accelerator applications require longlived photoemitters with high quantum yield in the visible
range. Multi-alkali cesium-based photocathodes are
frequently used but suffer from short lifetime, due to lossof cesium. A novel dispenser cathode is proposed anddemonstrated that provides controlled delivery of cesium
to the cathode surface at <200°C. This method allows forin situ rejuvenation of the photoemitting surface andcould dramatically extend the effective lifetime of many
alkali-based high-efficiency photocathodes.

INTRODUCTION
Laser-switched photoemitters are a source of electrons
for high current applications such as free electron lasers[1],[2][3]. Photoinjector systems consist of a drive laser
producing short bunches of photons and an efficientphotocathode, which converts photon bunches into
electron beam pulses [4]. Development of bothtechnologies is required, but the scope of this project isrestricted to improvement of the photocathode. Most
high-efficiency photocathodes employ cesium-based
surface coatings to reduce work function and enableefficient electron emission in the visible range. Lifetime isseverely limited by the loss of this delicate coating, which
degrades rapidly in practical vacuum environments. Morerobust photocathodes exist, but have much lower
efficiency, and place unrealistic demands on drive laser
power and stability. A common figure of merit forphotocathodes is quantum efficiency: the ratio of thenumber of photoemitted electrons to incident photons. It
is related to photocurrent J e and optical intensity

Overall performance suggests that this cesium-delivery
mechanism can significantly enhance the efficiency andoperational lifetime of a wide variety of present and future
cesium-based photocathodes.

Dispenser Concept
A dominant degradation mechanism for high QE
cesium-based cathodes is the loss of cesium either from asurface monolayer or a stoichiometric compound.
Replenishing this layer with cesium continuously or
periodically could restore cathode performance. Ourconcept of a cesium based dispenser photocathodeinvolves three essential elements: a cesium reservoir, aphotoemitting surface, and an interface between the twothat controls the rate of cesium arrival. In this design,
shown schematically in Figure 1, a small stainless steel
cylinder contains a pellet of cesium chromate andtitanium powders. A disk of made from 70% dense
sintered tungsten (top) serves as both the photoemitting
surface and the interface boundary [5]. During an initialheating process, the pellet breaks apart and releases
elemental cesium, which diffuses through and across thesintered tungsten substrate to create a low workfunction
photoemitting surface. This simple cesium-on-tungsten
photocathode was used to characterize the behavior of thedispenser, but more complex cathodes such as cesium
antimonide could also be built on the substrate.

I λ according to:J e ⎡⎣ A/cm 2 ⎤⎦hω ⎛ J e ⎞
QE =
(1)
⎜
⎟ = 1.2398
q ⎝ Iλ ⎠I λ [W/cm 2 ]λ [ μ m ]This research proposes a novel dispenser concept that
dramatically extends the lifetime of high QE cesiumbased cathodes by continuously or periodically restoring
the cesium surface monolayer during an in situ
rejuvenation process. A prototype dispenser cathode wasfabricated and tested for two modes of operation:
continuous and periodic near-room temperature
rejuvenation. The data are compared with aphotoemission model of partially covered surfaces underdesign for integration with existing beam simulations.
___________________________________________*Work supported by Office of Naval Research, Joint Technology
Office, and Directed Energy Professional Society#
nmoody@ieee.org

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Figure 1: Schematic of Dispenser Cathode

Experimental Overview
In order to characterize the performance of thedispenser cathode, a detailed study of the photoemissive
properties of cesium on tungsten was undertaken using
the fabrication chamber shown in Figure 2.

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Proceedings of FEL 2006, BESSY, Berlin, Germany
40 L/s Ion Pump

RGA

Deposition Monitor
CathodeFeedthroughs

Ion
Gun
Alkali
SourcesGas Lines

Laser
Viewport
200 L/s
Ion
Pump

Figure 2: Vacuum Fabrication Chamber
Cesium was deposited externally using commercial
sources onto a sintered tungsten disk identical to the oneused to fabricate the dispenser cathode. QE was measured
during deposition at several wavelengths as a function ofcesium coverage, which was observed using a quartz
crystal balance. Because cesium deposition occurred
externally from an isotropic source, the resulting layer
was assumed to be uniform. A characteristic curve wasobtained whose shape and peak value depended upon thesurface conditions of the cathode. Recall that for adispenser cathode, cesium arrives at the surface throughdiffusion from within, so direct measurement of cesium
coverage is not possible. Studying the effect of external,
uniform deposition of cesium on tungsten, however,allows comparison of the dispenser’s QE to that of aknown system. This work is therefore divided in two
parts: 1.) photoemission measurements of cesium ontungsten and 2.) characterization of the dispenser cathode.

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Because a DC potential is used to extract charge fromthe cathode, ion back-bombardment occurs, where
positively charged contaminants within the chamber
accelerate toward and collide into the cathode, damaging
and/or removing the surface layer of cesium [6].
Minimizing contaminants during evaporation is difficult
because both the dispenser cathode and the cesium
sources (having been exposed to atmosphere) containtrapped gases and traces of impurities that are emitted
along with cesium. This effect is minimized by firstoutgassing the dispenser in a controlled manner attemperatures beneath that required to emit cesium.

EXPERIMENTAL RESULTS
Surface Metrology
The surface characteristics of sintered tungsten werestudied in detail using optical, scanning electron, andfocused ion beam microscopy. The porosity and thicknessof the sintered disks used in the dispenser cathode werechosen such that extremes in either case were avoided.
Figure 3 shows a side view of the sintered tungsten disk at
1000x magnification. Characteristic length scales of its
polished surface were determined, including average pore
diameter of 350nm, nearest-neighbor separation distanceof 3.1μm, and average grain size of 4.8μm. The surface
area each pore must coat with cesium was found on
average to be 33.3μm2 for uniform monolayer coverage.
These lengths are significant because they estimate thesurface diffusion length of cesium required to achievecomplete coverage. Coverage uniformity is crucial
because variation in the cesium surface coating causes
similar variation in work function and electron emission.

Experimental Setup
Cesium is deposited onto the surface of a clean metal
disk using SAES sources, while coverage is measured
using an Inficon quartz crystal deposition monitor situateddirectly above the cathode. A circular anode biased at+186 volts is separated from the cathode by a distance of
one centimeter. Photocurrent is measured across theanode-cathode gap using a Keithley 486 picoammeter.
The entire circuit is isolated from the chamber and allconnections are made using Triax to minimize noise andinterference.
Five semiconductor CW lasers are sequentially shown
onto the cathode while photocurrent, cesium coverage,
laser intensity, background pressure, and cathodetemperature are recorded using Labview. The lasers have
output powers of 5mW with 2% stability at 355nm,
405nm, 532nm, 655, and 808nm. A Labview-controlled,
motorized translation stage selectively positions a desiredlaser at the UHV chamber viewport, enabling QE
measurement at multiple wavelengths during a single
evaporation run. The laser spot is circular and expanded toa FWHM size of 1 cm.

FEL Technology

Figure 3: Side View of Dispenser CathodeCleaning Techniques
A standardized cleaning procedure using a 6.4keV ion
argon beam was developed and shown to be remarkably
effective in cleaning sintered tungsten. When cesium wasdeposited following the procedure, the effects of thetreatment became apparent: a two-fold increase in QE
with a peak QE of 0.11% in the UV, as shown in Figure
4.
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experiment (e.g., laser heating, damage to cathodesurface, etc.).
Coverage (Angstrom)

0.12

0.1

0.08

QE (%)

Higher Curves:
Ion Beam Treated

UV QE (%)
Blue QE (%)
Red QE (%)
IR QE (%)
Green QE (%)

Lower Curves:
Heat Annealed

0

1

2

3

4

5

6

7

8

0.12

TheoryExperiment

UV QE (%)
Blue QE (%)
Green QE (%)
Red QE (%)
IR QE (%)

0.1
0.06
0.08

QE (%)

0.04

0.02

0.06

0.04
0

0.2

0.4

0.6

0.8

1

1.2

Coverage (Theta)

0.02

Figure 4: Effects of Ion Beam Cleaning
Coverage θ is reported in the above graph as a fractionof a monolayer, where θ = 0 corresponds to baretungsten and θ = 1 is a full cesium monolayer. A single
45 minute treatment provided a 40mC dose of 6keV argon
ions which was sufficient to produce apparent atomic
cleanliness. This claim is justified because increasing thenumber of consecutive ion treatments and/or the energy of
the ion beam did not produce further improvement in QE.
Because cesium was deposited uniformly on an
atomically clean surface, the QE of 0.11% can be said tobe characteristic of a uniform, optimal cesium coating.
This cleaning technique dramatically reduces the amountof time required to prepare a cathode for cesium
deposition because it eliminates the need for a lengthy
high temperature anneal.

Theory Comparison
The model used in this work is based upon the FowlerDuBridge treatment of photoemission [6],[7] and follows
the Gyftopolous-Levine approach of accounting for theeffects of cesium coverage [9]. A distinguishing factor
about the modified model is that an effort has been madeto systematically reduce or eliminate unknowns, either bymeans of models or approximations, which werearbitrarily assigned or used as fit parameters in othertreatments. The components of the model relevant to theexperiments in this program are described in detailelsewhere [10]. Data describing the effect of surface
cesium coverage on the work function and QE of metal
photocathodes was compared to the model’s predictions
and found on average to be within 22% agreement, asshown in Figure 5. Similar agreement was found for
cesium-on-silver and suggests that the theory is capable ofpredicting performance of metallic-based photocathodes.
This experiment enables theory comparison for an
important set of operation parameters: low drive laser
intensity and low accelerating electric field. These
parameters are typically much higher and are usually citedas reasons for drastic discrepancies between theory and

750

0

20

40

60

80

100

Coverage Theta (%)

Figure 5: Comparison of Theory and Experiment
The inputs to the theory were simply generalizedmaterial parameters that could be widely applied to any
number of different photocathodes.

Dispenser CathodeThe two basic procedures for operating the dispenser
cathode are activation and rejuvenation. Activation occurs
at higher temperatures and initiates a chemical reaction
between the powders inside the cell, while rejuvenation
occurs at much lower temperature and involves bringing
atomic cesium to the surface in a controlled manner.
Initial activation prepared the dispenser for use, as seenby the onset of photoemission at 425°C, followed bycomplete activation at 477°C, which produced a reduction
in work function such that a large thermionic current wasmeasured. Because of the elevated temperature, asignificant amount of cesium was released throughout thechamber, producing up to a 50Å coating on an adjacentdeposition monitor. This release is expected, however,and is not considered problematic because 1.) a large
quantity of cesium remained within the dispenser
following activation, and 2.) the activation procedure for aworking dispenser cathode would most likely occur in achamber separate from the actual electron gun (whose
contamination with cesium would lead to field
breakdown).
Following activation, the dispenser was allowed to cooland its 1/e lifetime was measured to be 5.2 days. After 65
hours of continuous operation, its QE decayed from its
peak of 0.11% in UV to 0.06%. Complete rejuvenation
was demonstrated when QE returned to its previous peakvalue of 0.11% upon heating to 140°C, as shown in
Figure 6. Less than 3Å of cesium was deposited during
this process, suggesting that in situ rehabilitation of thecathode is possible. Coverage at peak QE was indirectly
measured to be about 64% using the relationship between
cesium coverage and QE.
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Proceedings of FEL 2006, BESSY, Berlin, Germany
Dispenser Cathode:Rejuvenation Process QE vs. Time
0.14

160
UV QE (%)
Blue QE (%)
Red QE (%)
IR QE (%)
Green QE (%)

140

0.1

120

0.08

100

0.06

80

0.04

60

0.02

40

0

20

40

60

80

100

120

Temp (Celsius)

QE (%)

0.12

Temp (Celsius)

20
140Time (min)Figure 6: Rejuvenation of Cathode Surface
Two modes of cathode operation were demonstrated:periodic and continuous rejuvenation. For the continuous
mode, temperature is held between 160-180°C, resulting
in constant replenishment of the cesium layer. The 1/eeffective (continuous duty cycle) lifetime in this mode
was an astounding 47 days.

CONCLUSIONS
A prototype design for a near-room temperature
dispenser cathode was proposed and demonstrated for thecase of cesium-on-tungsten using commonly available
components: thin-walled stainless steel and porous
sintered tungsten. It is distinguished from other dispensertype cathodes [11] by its low operating temperature,
which makes it a good candidate technology where
cathode thermal management is a concern. A method forconveniently integrating cesium chromate into thedispenser cell was demonstrated by forming the powder
into a solid pellet under high pressure. The peak QE of the

FEL Technology

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activated dispenser cathode, following an ion beam
cleaning treatment, was 0.11%. This QE value was shownto correspond to that of a uniform, optimal cesium coating
and suggests that the sintered tungsten interface facilitates
uniform cesium coverage. This result suggests that thesurface diffusion length of cesium across tungsten at
temperatures ranging from 200-400°C is at least 5μm. The
overall performance of the dispenser cathode suggests thatits design could serve as a temperature-controlled cesium
dispensing platform onto which a variety of high QE
cesium-based photocathodes could be built.

REFERENCES[1] P. G. O’Shea, H. P. Freund, Science 292, 1853
(2001).
[2] D. H. Dowell, S. Z. Bethel, K. D. Friddell, Nucl.
Instr. & Meth. in Phys. Res., A356 167 (1995).
[3] C. Travier, Nucl. Instr. & Meth. in Phys. Res. A304,
285 (1991).
[4] P. G. O’Shea, et. al., Proc. Particle Accel. Conf., vol.
5, San Fran., May 6–9, 1991, pp. 2754–2756.
[5] Fabrication performed by B. Vancil, E-Beam Inc,
Beaverton, OR.
[6] C. H. Garcia, C. A. Brau, Nucl. Instr. And Meth. in
Phys. Res., A 475 (2001) 559-563.
[7] R. H. Fowler, Phys. Rev. 38, 45 (1931); L. A.
DuBridge, Phys. Rev. 43, 727 (1933).
[8] J. H. Bechtel, W. L. Smith, and N. Bloembergen,
Phys. Rev. B15, 4557 (1977).
[9] E. P. Gyftopolous and J. D. Levine, Jour. of App.
Phys. 33, 67 (1962).
[10] K. L. Jensen, D. W. Feldman, N. A. Moody, P. G.
O’Shea, Jour. App. Phys., 99, 1 (2006).
[11] R. E. Thomas, J. W. Gibson, G. A. Haas, and R. H.
Abrams, IEEE Transactions on Electron Devices
37, 850 (1990).

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OPTIMUM BEAM CREATION IN PHOTOINJECTORS USINGSPACE-CHARGE EXPANSION∗
J.B. Rosenzweig, A.M. Cook, M. Dunning, R.J. EnglandParticle Beam Physics Laboratory, Department of Physics and Astronomy
University of California Los Angeles, Los Angeles, CA 90095, USA
M. Bellaveglia, M. Boscolo, L. Catani, A. Cianchi, G. Di Pirro,
M. Ferrario, D. Filippetto, G. Gatti, P. Musumeci, L. Palumbo, C. Vicario
Istituto Nazionale di Fisica Nucleare, Laboratori Nazionale di Frascati
00044 Frascati (Roma), Italy
S. Jones
Jet Propulsion Laboratory, California Institue of Technology
4800 Oak Grove Drive, Pasadena, CA 91101, USA.

Abstract
It has recently been shown that by illuminating a photocathode with an ultra-short laser pulse of appropriate transverse profile, a uniform density, ellipsoidally shaped bunchis dynamically formed, which then has linear space-charge
fields in all dimensions inside of the bunch. We study here
this process, and its marriage to the standard emittancecompensation scenario that is implemented in most modern
photoinjectors. It is seen that the two processes are compatible, with simulations indicating that a very high brightness
beam can be obtained. The scheme has produced stimulus
for a series of experiments at the SPARC injector at Frascati in 2006-2007. An initial time-resolved experiment has
been performed involving Cerenkov radiation produced at
an aerogel. We discuss the results of this preliminary experiment, as well as plans for future experiments to resolve
the ellipsoidal bunch shape at low energy. Future measurements at high energy based on fs resolution RF sweepers
are discussed.

INTRODUCTION
In order to obtain the highest brightness electron beams
from photoinjectors, it is most common to rely on the emittance compensation process [1]. Optimization of this process demands that the transverse fields be as uniform, andlinear (in radius r) as possible. The existing studies of emittance compensation have, to that end, assumed use of a
uniform density electron beam, having a cylindrical shape.
However, this shape produces space-charge fields near the
beam head and tail that have pronounced nonlinear dependencies on the spatial coordinates. These nonlinearities result in both transverse and longitudinal emittance growth.
It has been known for some time, however, that a uniform ellipsoidal density distribution yields space-charge∗ Work supported by the US Dept. of Energy under grant DE-FG0392ER40693, and the Italian Ministry.

752

fields that are linear in all dimensions [2]. Under such conditions, it is conceivable that one may obtain essentiallyemittance growth-free dynamics. How to produce such a
distribution has, until recently, remained an unansweredquestion.
In 1997, Serafini proposed the dynamic creation of an ellipsoidal bunch by launching an ultra-short, radially shaped
beam, which then evolves to achieve the desired longitudinal shape [3]. On the other had, it has recently been shown
by Luiten, et al., that in obtaining the correct final ellipsoidal distribution, there is essentially no requirement on
the shape of the initial laser pulse other than it be ultrashort (length τl much shorter than eventual beam length
after space charge expansion) [4]. Thus such laser pulses
are a natural, and technically achievable way of producing
an ellipsoidally shaped, nearly uniform density beam.
As the beam dynamics just after photoemission are qualitatively different in the traditional emittance compensation scenario and in the Luiten-Serafini scheme, it is not
immediately apparent that one may successfully combine
the two. The UCLA-SPARC collaboration has recently
shown [5] that this marriage is indeed possible; further, thecombination of emittance compensation and dynamic creation of the ellipsoidal shaped beam produces results thatin many ways are superior to those obtained in state-of-theart designs. As the bunches that are produced are shorter
than in standard cases, very high brightness beam creationis possible.
The basic idea behind the Luiten-Serafini scheme is simple: the beam profile expands and deforms longitudinallyto produce, in the final state, a uniformly filled ellipsoid of
charge. In the process, phase space rearrangements occur
which degrade the emittances– especially in the longitudinal dimension. In order to understand this process, tospecify experimental requirements, and to identify experimental signatures associated with the process, we have analyzed the dynamics of space-charge-dominated beam ex-

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Proceedings of FEL 2006, BESSY, Berlin, Germany
pansion [5].
This analysis may be summarized in a few points:
First, the injected bunch surface charge density
σb = dQb /dA must not be too high, or image charge effects at the cathode distort the final pulse profile so that
it is not ellipsoidal. This is quantified by the conditionα ≡ 4πσb /E0 << 1.
Second, the beam must be much shorter than its eventual
size in order to be able to ignore the details of the initial
pulse profile. In practice, 300 fs laser pulses (typical of
the limitations of the SPARC photocathode drive laser after conversion to UV) excite roughly the same length electron bunch, which expands to around 4 psec in our example cases. The pulse length after expansion is estimated as
Lb ≈ 2πσb me c2 /E02 .
The current density that is achieved after expansion
is Jz = eE02 /4πme c, a constant dependent only on theapplied electric field E0 .
All beams become uniform in density. To achieve the desired ellipsoidal
beam shape, one must choose the initial surface current density distribution
 correctly, which implies thatσb (r) = (3Qb /2πa2 ) 1 − (r/a)2 .
While the analysis of the beam dynamics is useful, thecentral issue of joining this regime with emittance compensation must be explored with simulations. The initial simulations begun in Ref. [5] that we have performed are in thecontext of the SPARC scenario, so that we may proceed
directly to discussing the experimental tests of this new
regime– now commonly known as the “blowout regime”–
of the photoinjector there.

BLOWOUT REGIME WITH EMITTANCECOMPENSATION: GENERAL STUDY
We have performed initial UCLA PARMELA [6] simulations to explore joining the Serafini-Luiten scheme withthe optimized emittance compensation working point of the
SPARC injector at LNF. We assume that the gun (1.6 cell,2856 MHz) and solenoid are the same, and run near to thestandard conditions. Through trials, we have optimized thelaunch conditions of the beam. In order to have values of
α which do not give excessive image charge effects, thebeam charge is lowered and the beam radius is slightly
enlarged. In the preliminary optimization, we launch a0.33 nC beam with an initial longitudinal Gaussian distribution having σ t = 33 fs beam, and a radial Gaussian with
σx = 0.77 mm (cutoff at 1.8σ). The gun is run with a peakon-axis gradient of 120 MV/m; the beam is launched at
33 degrees forward of crest. This is a bit advanced in comparison to the nominal launch phase for a standard bunch,and serves to control the excessive beam energy spread after the gun. The emittance compensation solenoid is run
with peak field Bz = 2700 G, which is slightly below thestandard scenario, as the beam has slightly lower energy
exiting the gun. We note that the peak value of α in ourcase is 0.11, as opposed to 0.42 in the LCLS design.
The formation of the quasi-ellipsoidal bunch is clearly

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Figure 1: (left) PARMELA simulation results of electron
bunch (x, z) distribution 133 cm from cathode (6.3 MeV
energy), showing ellipsoidal beam boundary. (right) Evolution of σδp/p in z for emittance compensation case, fromPARMELA simulation.
shown in Fig. 1, which displays the bunch (x, z) distribution at a point 133 cm from the cathode, in the drift space
after the gun and just preceding initial traveling wave linac
section. Here the beam has 6.3 MeV mean energy, and its
transverse dynamics are space charge-dominated. Thus one
sees clearly the “inflated” ellipsoidal beam shape. The final
bunch length is 1.3 mm full width, corresponding to a peakcurrent of 105 A. Thus even with one-third of the charge,
this scheme should produce a higher current than obtainedin simulations of the standard design.
Two notable defects are seen in the beam shape in Fig. 1.
The first is the extension of the half-ellipsoid in the trailing part of the bunch as compared with the initial half– anasymmetry caused by image charge effects. This non-ideal
behavior in fact gives the limit on σ; when one attempts
to launch a higher surface charge density, the bunch deformation from the desired symmetric ellipsoid produces poor
emittance performance. The second notable feature is theexistence of an anomalous ring at the outer radial edge ofthe beam. This part of the beam has low surface charge
density and experiences radially fringing fields due to itsedge location. Because of these effects, it does not experience enough longitudinal expansion to keep pace with therest of the bunch, but instead has a moderate amount ofradial expansion.
As the longitudinal space-charge during much of theacceleration is also linear, and total pulse length T isshort, the longitudinal phase space is very compact. The
evolution of the relative momentum spread σ δp/p in z
is shown in Fig. 1. The final achieved RMS valueis σδp/p = 1.6 · 10−4 , which is an order of magnitude
smaller than that obtained in the standard LCLS type (orSPARC type) design.
The evolution of the RMS transverse beam size σ x , andthe RMS normalized emittance  n,x are shown in Fig. 2.
While the behavior of σ x is similar in most respects to thestandard design, with the beam approximately matched atlinac entrance to the invariant envelope, the emittance behavior is not as familiar. In the standard LCLS design,  n,xachieves a minimum value in the post-gun drift, rising to a
local maximum at injection into the linac. The focusing andadiabatic damping of the motion in the linac then produce a753

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Proceedings of FEL 2006, BESSY, Berlin, Germany
pulse does not affect the final electron beam configuration
at this level.
The laser intensity needed for this scenario is a factorof 30-100 higher than in the LCLS case. The issue oflaser damage at the cathode surface has been examined,
and found based on previous experience at UCLA and at
the BNL ATF to not be worrisome [7].

Figure 2: (left) The evolution of RMS transverse beam size
σx for emittance compensation case, from PARMELA simulation. (right) Evolution of RMS normalized emittancen,x for emittance compensation case.
monotonic decrease of  n,x in z. In our case, the transverse
space-charge and thus the plasma/emittance oscillations do
not “turn on” until after the longitudinal expansion is wellunderway, thus delaying the emittance minimum in Fig. 2
to occur inside of the linac. In order to produce faster emittance oscillations in the linac to strongly diminish  n,x before acceleration removes the plasma-dominated beam behavior, the solenoid field in the first linac section has beenraised by 40% relative to the standard scenario. This ployworks well, as the final value (still slightly decreasing) of
n,x at the end of the second linac (84.5 MeV energy) is
0.68 mm-mrad. The thermal emittance at the cathode is
0.4 mm-mrad, and so the space-charge induced emittanceis well compensated.
After acceleration to higher energy (84.5 MeV), thebeam is not spacecharge dominated, and the (x, z) profile
no longer ellipsoidal. Nonetheless, the beam has excellent emittance,and maintains a current profile with shapeI(t) ∝ 1 − (2t/T )2 . With a high initial current, and low
intrinsic energy spread, this beam may be compressed further, with very high final peak current achievable [7].

Experimental signatures and measurements
In the SPARC experiment, we plan first to image thebeam (time-integrated) at low energy (5-7 MeV) in the region after the gun, using a YAG detector. For time resolved
measurements we will first convert the beam spatial information to photons with a Cerenkov convertor. In order tohave a manageably small angle of emission we use aerogel,
which has a small index of refraction (n = 1.005-1.02).
At 5 MeV the Cerenkov emission threshold is reached forn = 1.005; we may choose angles of emission from nearzero at this threshold to up to 9 degrees with the aerogels
that are presently in hand. The aerogels have been custom
fabricated at the Jet Propulsion Laboratory.
Simulations consist of providing electrons (typically
40,000) from PARMELA to GEANT [8], which simulates
the scattering of the electrons in the entrance foil and generates a collection of Cerenkov photons in the aerogel. The
photon distributions that result are then passed to a Mathematica based, optical ray-tracing program, Rayica.
The streak camera at SPARC has 2 ps FWHM time resolution, which is on the border of resolution for the bunch
length of interest. This will be handled in initial measurements by use of higher charges (above 1 nC), and thus
longer beams, to test the longitudinal expansion dynamics
of the beam. We thus must consider alternative schemes
based on ultra-fast gating [7].

FIRST RESULTSCONSIDERATIONS FOR SPARC
EXPERIMENT
Laser and photocathode issues
Before discussing the planned electron beam measurements, we first review some experimental considerations
specific to the use of such short lasers. First, we note thatthe laser pulse should be tailored, either by collimating
and relay imaging, and that it must be quite short. In firstmeasurements at SPARC, we have found, through crosscorrelation measurements, that the UV pulse is difficult tomake shorter than 300 fs using 3rd harmonic generation
with noncollinear mixing in the conversion crystals. In order to obtain even this result, we must give up UV energy,
going from 1.5 mJ to 0.2 mJ. While this energy is still adequate for obtaining 0.33 nC of charge using a metal cathode (Cu or Mg), to go shorter may be difficult. In order tocheck the effect of this extra pulse length on the scheme, wehave performed simulations analogous to the original exploratory, indications are that the added length in the laser

754

The first stage of experimentation on the blowout regime
took place at INFN-LNF beginning at the end of March
2006. During commissioning of the SPARC RF photocathode gun, the UCLA-produced gun was conditioned quickly
up to 11 MW, which produces 110 MV/m peak electricfield, and a 5.7 MeV electron beam.
The laser was reconfigured for short pulses (less than
0.5 psec FWHM) and up to 1.6 nC of charge. The conditions for observing the dynamic creation of nearly uniformly filled ellipsoidal charge distributions were not quite
present; in fact, the emittance was not of equivalent quality
to that obtained in standard operation. Nevertheless, impressive first data was obtained.
Initial measurements of the longitudinal-transverse profile of the beam were made with aerogel with index
n = 1.008, with the Cerenkov radiator placed 2.4 m awayfrom the cathode, downstream of the slit-based emittancemeasurement system. Streak camera images were obtainedusing the transport system described in the previous section. Such a streak, after correction, is shown in Fig. 3.

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Figure 3: Streak image from SPARC experiment, after correction.
This image displays the profile obtained from a bunchwith charge of 700 pC. A large charge is preferred in thiscase in order to discern information at a time scale longer
over the streak camera resolution; the 700 pC case is expected to have expansion of approximately 7 psec FWHM,
well in excess of this 2 psec FHWM resolution.
Streak images obtained in the highest temporal resolution mode are inherently noisy; this condition is requiredin order to avoid space-charge induced pulse distortion inside of the streak tube. Thus in order to extract information from single shots concerning the streak image– whichshould represent the beam density distribution in an (x, z)
slice in the midplane of the bunch– we have adopted a maximum likelihood analysis to test for different assumed typesof beam distributions.
The (x, z) slice distributions we have tested for consistency with the data include: (1) a bi-Gaussian (thermaltype) distribution; (2) a uniformly filled ellipse (assumed
arising from a parent uniformly filled ellipsoid); and (3) anearly uniformly filled ellipse with a tail, which we choose
to represent as a Fermi-Dirac distribution.
As all of the distributions assumed have contours of constant density that are elliptical, a systematic statistical approach is possible, in which we look at the total integrated
intensity inside of ellipses of size varying from zero area
to an area covering the entire streak image. These ellipses
are all required to have the same aspect ratio, which is givenby the intensity profile itself, R = σ x /vs σt , where vs is thestreak velocity, and σ t =3.45 psec for the streak in Fig. 3.
With these functions in hand, we can fit to the data givenin the streak images to determine the likelihood that oneof the assumed three profiles is more likely than the others.
Such an exercise has been performed for the streak given in
Fig. 3, with the results shown in Fig. 4. It can be seen thebi-Gaussian hypothesis can be rejected as the least likely
model. While the uniformly filled ellipsoid gives a good
fit near the distribution center, it is not very accurate at theedge, where one expects strong deviations in any case fromthis model. Finally, we note that the best fit obtained fromthe Fermi-Dirac model gives an excellent match to the data.

CONCLUSIONS
While the first measurements have established thesoundness of the basic experimental approach, much moreremains to be done. As of now, the SPARC injector
is being modified to allow for near-axis (as opposed to

FEL Technology

Figure 4: Analysis of streak data, with fraction of integrated intensity of data inside of elliptical contour shown.
Best fit of data points to three models are shown: bigaussian distribution, uniform elliptical distribution, andFermi-Dirac (uniform with tails) distribution.
70 degree) injection. Additional improvements should also
result from use of laser cleaning of the cathode. The
SPARC injector will soon be completed with the additionof post-acceleration linacs and beam diagnostics (e.g. RF
sweeper). In this fully mature experimental scheme, a complete test of the consistency of the Luiten-Serafini schemewith emittance compensation should be possible, using thelarge array of techniques described here. Further experiments will also emphasize the demonstration of high quality longitudinal phase space and concomitant low energy
spread, as well as high compressibility.

ACKNOWLEDGEMENTS
The authors acknowledge useful interactions with Scott
Anderson, Luca Giannessi, Marcello Quattromini, andDirk Lipka.

REFERENCES[1] L. Serafini and J.B. Rosenzweig, Physical Review E 55, 7565
(1997).
[2] I.M. Kapchinskii and V.V. Vladimirskii, in Proc. Int. Conf.
High En. Accs., CERN, Geneva, 274, 1959.
[3] L. Serafini, AIP Conf. Proc. 413, 321 (1997).
[4] O. J. Luiten, et al., Phys. Rev. Lett., 93, 094802-1 (2004).
[5] J. B. Rosenzweig, et al., Nucl. Inst. and Meth. A, 57 87(2006).
[6] E. Colby, UCLA PhD Thesis, FERMILAB-THESIS-1997-03(FNAL, 1997).
[7] J.B. Rosenzweig, et al., Proc. 2005 Phys. App. High Br.
Beams, Erice, 2006.
[8] S. Agostinelli, et al., Nuc. Inst. and Meth. A 506, 250 (2003).

755

THPPH071

Proceedings of FEL 2006, BESSY, Berlin, Germany

FREE ELECTRON LASERS IN 2006
W. B. Colson*, J. Blau, and A. Kampouridis
Physics Department, Naval Postgraduate School, Monterey CA 93943 USA

Abstract
Twenty-nine years after the first operation of the freeelectron laser (FEL) at Stanford University, there
continue to be many important experiments, proposed
experiments, and user facilities around the world.
Properties of FELs operating in the infrared, visible, UV,
and x-ray wavelength regimes are listed and discussed.

The following tables list existing (Table 1) andproposed (Table 2) relativistic free electron lasers (FELs)
in 2006. A location or institution, followed by the FEL’sname in parentheses, identifies each FEL; references arelisted in Tables 3 and 4. Another good site for FEL
references is http://sbfel3.ucsb.edu/www/vl_fel.html.
The first column of the table lists the operating
wavelength , or wavelength range.
The longer
wavelengths are listed at the top with short x-ray
wavelength FEL at the bottom of the table. The large
range of operating wavelengths, seven orders ofmagnitude, indicates the flexible design characteristics ofthe FEL mechanism. In the second column, z is theelectron pulse length divided by the speed of light c, andranges from almost CW to short sub-picosecond pulse
time scales. The expected optical pulse length can be 3 to
5 times shorter or longer than the electron pulse
depending on the optical cavity Q, the FEL
desynchronism, and the FEL gain. The optical pulse canbe up to 10 times shorter in the high-gain FEL amplifier.
Also, if the FEL is in an electron storage-ring, the opticalpulse is typically much shorter than the electron pulse.
Most FEL oscillators produce an optical spectrum that is
Fourier transform limited by the optical pulse length.
The electron beam energy E in MeV and peak current I
in Amperes provided by the accelerator are listed in thethird and fourth columns, respectively. The next threecolumns list the number of undulator periods N, theundulator wavelength 0, and the rms undulator
parameter K = eB0/2mc2 in cgs units, where e is theelectron charge magnitude, B is the rms undulator fieldstrength, and m is the electron mass. For an FEL klystronundulator, there are multiple undulator sections as listed
in the N-column. Note that the range of values for N, 0,
and K are much smaller than for the other parameters,
indicating that most undulators are similar. Some
exceptions are the long undulators containing many
periods N that are being developed for the x-ray FEL
amplifiers. Only a few of the FELs use the klystron———undulator at present, and the rest use the conventional
periodic undulator.
Most of the undulators are
configured to have linear polarization. The FEL
resonance condition,  = 0(1+K2)/2.2 where  is therelativistic Lorentz factor, provides a relationship that canbe used to relate K to , E, and 0. The middle entry of
the last column lists the accelerator type (RF for Radio
Frequency Linear Accelerator, MA for Microtron
Accelerator, SR for Storage Ring, EA for Electrostatic
Accelerator), and the FEL type (A for FEL Amplifier, O
for FEL Oscillator, S for SASE FEL, H for a high-gainhigh harmonic HGHG FEL). Most of the FELs are
oscillators, but recent progress has resulted in shortwavelength FELs using SASE (Stimulated Amplificationof Spontaneous Emission) and high-gain harmonic
generation (HGHG).
For the conventional undulator oscillator, the peak
optical power can be estimated by the fraction of theelectron beam peak power that spans the undulator
spectral bandwidth, 1/(2N), or P  EI/(8eN). For the FEL
using a storage ring, the optical power causing saturation
is substantially less than this estimate and depends onring properties. For the high-gain FEL amplifier, theoptical power at saturation can be substantially greater.
The average FEL power is determined by the duty cycle,
or spacing between the electron micropulses, and istypically many orders of magnitude lower than the peak
power. The Jlab infrared FEL has now reached anaverage power of 10 kW with the recovery of the electron
beam energy in superconducting accelerator cavities.
In the FEL oscillator, the optical mode that best
couples to the electron beam in an undulator of length
L = N0 has Rayleigh length z0  L/121/2 and has a mode
waist radius of w0  N1/2/. The FEL optical mode
typically has more than 90% of the power in thefundamental mode described by these parameters.
This year the DESY FLASH FEL has reached theshortest wavelength ever for an FEL,   0.013 μm.
There are several other new lasings: Rossendorf (U-100)
at   20-150 μm, RIKEN (SCSS Prototype) at   0.049
μm, and BNL (SDL FEL) at   0.198 μm. New FEL
lasings are highlighted in bold in Table 1.

ACKNOWLEDGMENTS
The authors are grateful for support from ONR,NAVSEA, and the JTO.

* Corresponding Author: 831-656-2765, Colson@nps.edu

756

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH071

Table 1: Free Electron Lasers (2006)
EXISTING FELs
Italy (FEL-CAT)
UCSB (mm FEL)
Novosibirsk (RTM)
Korea (KAERI-FEL)
Osaka (ISIR,SASE)
Himeji (LEENA)UCSB (FIR FEL)
Osaka (ILE/ILT)Osaka (ISIR)
Tokai (JAEA-FEL)
Bruyeres (ELSA)
Osaka (FELI4)
UCLA-Kurchatov
LANL (RAFEL)
Stanford (FIREFLY)
Rossendorf (U-100)
UCLA-Kurchatov-LANL
Beijing (BFEL)
Dresden (ELBE)
Korea (KAERI HP FEL)
Jlab (IR upgrade)
Darmstadt (FEL)
BNL (HGHG)
Osaka (iFEL1)Tokyo (KHI-FEL)
Nieuwegein (FELIX)
Duke (MARKIII)
Stanford (SCAFEL)
Orsay (CLIO)
Vanderbilt (FELI)Osaka (iFEL2)
Nihon (LEBRA)
UCLA-BNL (VISA)BNL (ATF)
Duke (OK-5)
Dortmund (FELICITAI)BNL (SDL FEL)
Orsay (Super-ACO)
Osaka (iFEL3)
Okazaki (UVSOR)
Tsukuba (NIJI-IV)
Italy (ELETTRA)
Duke (OK-4)
ANL (APSFEL)
RIKEN(SCSS Prototype)
DESY (FLASH)FEL Technology

(μm)
760
340
120-230
97-1200
70-22065-75
604732-150
22
20
18-40
16
15.5
15-80
15-150
12
5-20
3-22
3-20
0.7-10
6-8
5.3
5.5
4-16
3-250
2.7-6.5
3-13
3-53
2.0-9.8
1.88
0.9-6.5
0.8
0.6
0.45
0.42
0.2-1.0
0.3-0.6
0.3-0.7
0.2-0.6
0.2-0.6
0.2-0.4
0.193-2.1
0.13
0.05
0.013

 z(ps)
15-20
25000
70
25
20-30
10
25000
3
20-30
2.5-5
30
10
3
15
1-5
0.3-10
5
4
1-10
10-20
0.1
2
6
10
2
1
3
0.5-12
0.1-3
0.7
10
<1
0.5
6
0.1-10
50
0.5-1
15
5
6
14
28
0.1-100.3
10.025

E(MeV)
1.8
6
12
4.3-6.5
11
5.4
6
8
13-19
17
18
33
13.5
17
15-32
15
18
30
34
20-40
120
25-50
40
33.2
32-40
50
31-41.5
22-45
21-50
43
68
58-10070.9
50270-800450
100-250
800
155
607
310
1000
1200
399
250
700

I(A)
5
2
10
0.5
1000
10
2
50
50
200
100
40
80
300
14
240
170
15-20
30
30
400
2.7
120
42
30
50
20
10
80
50
42
10-20
250
100
35
90
300-400
0.1
60
10
10
150
35
400
800
2000

N
16
42
2x33
80
32
50
150
50
32
52
30
30
40
200
25
38
100
50
2x34
30x2
29
80
60
58
43
38
47
72
38
52
78
50
220
70
2x32
17
256
2x10
67
2x9
2x42
2x19
2x33
648
600
984

 0(cm)
2.5
7.1
12
2.5
6
1.6
2
2
6
3.3
3
8
1.5
2
6
10
2
3
2.73
3.5
5.5
3.2
3.3
3.4
3.2
6.5
2.3
3.1
5
2.3
3.8
4.8
1.8
0.88
12
25
3.9
13
4
11
7.2
10
10
3.3
1.5
2.73

K(rms)
0.75
0.7
0.71
1.0-1.6
1.5
0.5
0.1
0.5
1.5
0.7
0.8
1.3-1.7
1
0.9
1
2.7
0.7
1
0.3-0.7
0.5-0.831
1.44
1
0.7-1.8
1.8
1
0.8
1.4
1.3
1
0.7-1.4
1.2
0.4
0-4.75
2
0.8
4.5
1.4
2
2
4.2
0-4.75
2.2
1.3
0.81

RF,O
EA,O
RF,O
MA,O
RF,S
RF,O
EA,O
RF,O
RF,O
RF,O
RF,O
RF,O
RF,A
RF,O
RF,O
RF,O
RF,A
RF,O
RF,O
RF,O
RF,O
RF,O
RF,A
RF,O
RF,O
RF,O
RF,O
RF,O
RF,O
RF,O
RF,O
RF,O
RF,S
RF,O
SR,O
SR,O
RF,A,S,H
SR,O
RF,O
SR,O
SR,O
SR,O
SR,O
RF,S
RF,S
RF,S

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Table 2: Proposed Free Electron Lasers (2006)
PROPOSED FELs

(μm)

 z(ps)Tokyo (FIR-FEL)
Netherlands (TEUFEL)
Romania (NILPRP)
Dresden (ELBE)
Novosibirsk (RTM1)
Daresbury (4GLS-IRFEL)
Novosibirsk (RTM)
Frascati (SPARC)
Hawaii (FEL)
Jlab (UV FEL)
Harima (SUBARU)
Shanghai (SDUV-FEL)
Daresbury (4GLS-VUV)
Daresbury (4GLS-XUV)Frascati (COSA)DESY (FLASH)
Italy (SPARX)BESSY (Soft X-ray)
Trieste (FERMI)
Pohang (PAL X-FEL)
MIT (Bates X-Ray FEL)SLAC (LCLS)DESY (XFEL)RIKEN (SPring8 SCSS)

300-100018060
20-150
5-100
3-75
2-11
0.533
0.3-3
0.25-1
0.2-100.5-0.088
0.4-0.1
0.1-0.01
0.08
0.006
0.00150.00120.001-0.1
0.00030.00030.000150.00010.0001

5
20
10
1-10
10
0.5-1
20
0.1
2
0.2
26
1
0.1-1
0.1-1
10
0.17
0.1
0.08
0.1
0.1
0.05
0.07
0.08
0.5

758

E(MeV I(A)
N
)
10
30
25
6
350
50
7
2
100
20-40
30
38
50
20-100
3x33
18-50
70
27
98
100
4x36
142
500
6x71
100
500
84
160
270
60
1500
50
33,65
300
400
400
600
300
150
750-950 1500
1000
215
200
400
1000
2500
981
2500
2500
1000
2300
3500
1450
1200
500-2500 1140
3000
4000
6000
4000
1000
1500
14350
3400
3328
17500
5000
4700
8000
2000
1500

 0(cm)K(rms)

7
2.5
2
10
6
2.7
9
3
2.4
3.3
16,32
2.5
5
4.5
1.4
2.73
3
2.75
3.5
1.5
1.8
3
3.6
1.5

1.5-3.41
0.4
0.3-2.7
2
2
1.6
1.3
1.2
1.3
8
1.025
2
1-3.5
1
0.9
1.2
0.9
1.2
1.1
2
3.7
3.2
1.3

RF,O
RF,O
RF,O
RF,O
RF,O
RF,O
RF,O
RF,S
RF,O
RF,O
SR,O
RF,O
RF,O
RF,S
RF,O
RF,S
RF,S
RF,S
RF,S
RF,S
RF,S
RF,S
RF,S
RF,S

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THPPH071

Table 3: References and Websites for Existing FELs
EXISTING FELs
ANL (APSFEL)
Beijing (BFEL)BNL (SDL FEL)BNL (ATF)
BNL (HGHG)
BNL (VISA)
Bruyeres (ELSA)
Darmstadt (FEL)DESY( FLASH)
Dortmund (FELICITAI)
Dresden (ELBE)
Duke (MARKIII)
Duke (OK-4, OK-5)
Himeji (LEENA)
Italy (ELETTRA)
Italy (FEL-CAT)
Jlab (IR upgrade)
Korea (KAERI HP FEL)
Korea (KAERI-FEL)
LANL (RAFEL)
Nieuwegein (FELIX)
Nihon (LEBRA)
Novosibirsk (RTM)
Okazaki (UVSOR)
Orsay (CLIO)
Orsay (Super-ACO)
Osaka (FELI4)
Osaka (iFEL1)Osaka (iFEL2)
Osaka (iFEL3)
Osaka (ILE/ILT)Osaka (ISIR)RIKEN(SCSS Prototype)
Rossendorf (U-100)
Stanford (FIREFLY)
Stanford (SCAFEL)
Tokai (JAEA-FEL)
Tokyo (KHI-FEL)
Tsukuba (NIJI-IV)
UCLA-Kurchatov
UCLA-Kurchatov-LANLUCSB (FIR FEL)UCSB (mm FEL)
Vanderbilt (FELI)FEL Technology

Internet Site or Reference
J. W. Lewellen et. al., NIM A483, 40 (2002).
http://bfel.ihepa.ac.cn
http://www.nsls.bnl.gov/facility/Accelerator/DUVFEL
K. Batchelor et. al., NIM A318, 159 (1992).
A. Doyuran et. al., NIM A475, 260 (2001).
A. Tremaine et. al., NIM A483, 24 (2002).
P. Guimbal et. al., NIM A341, 43 (1994).
http://linaxa.ikp.physik.tu-darmstadt.de/richter/fel
http://flash.desy.de
http://www.delta.uni-dortmund.de/pub/fel/FEL.html
http://www.fz-rossendorf.de
http://www.fel.duke.edu/lightsources/mk3.html
http://www.fel.duke.edu
http://www.lasti.himeji-tech.ac.jp/NS/LEENA/LEENA_HP.html
http://www.elettra.trieste.it/projects/euprog/fel
A. Doria et. al, Phys. Rev. Lett. 80, 2841 (1998).
http://www.jlab.org/FEL
http://www.kaeri.re.kr/fel/index.php
http://www.kaeri.re.kr/fel/index.php
http://www.lanl.gov/orgs/ibdnew/usrfac/userfac03.html
http://www.rijnh.nl/n4/n3/f1234.htm
http://www.lebra.nihon-u.ac.jp
http://www.inp.nsk.su
http://uvsor-ntserver.ims.ac.jp
http://www.lure.u-psud.fr/CLIO.HTM
M. E. Couprie et. al., NIM A407, 215-220 (1998).
T. Takii et. al., NIM A407, 21-25 (1998).
http://www.fel.eng.osaka-u.ac.jp/english/index_e.html
http://www.fel.eng.osaka-u.ac.jp/english/index_e.html
http://www.fel.eng.osaka-u.ac.jp/english/index_e.html
N. Ohigashi et. al., NIM A375, 469 (1996).
http://www.ei.sanken.osaka-u.ac.jp
http://www-xfel.spring8.or.jp
http://www.fz-rossendorf.de
K. W. Berryman and T. I. Smith, NIM A375, 6 (1996).
H. A. Schwettman et. al., NIM A375, 662 (1996).
R. Hajima et. al., NIM A507, 115 (2003).
M. Yokoyama et. al., NIM A475, 38 (2001).
K.Yamada et. al., NIM A475, 205 (2001).
http://pbpl.physics.ucla.edu
http://pbpl.physics.ucla.edu
http://sbfel3.ucsb.edu
http://sbfel3.ucsb.edu
http://www.vanderbilt.edu/fel

759

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Proceedings of FEL 2006, BESSY, Berlin, Germany

Table 4: References for Proposed FELs
PROPOSED FELs
BESSY (Soft X-ray)
Daresbury (4GLS)DESY (XFEL)DESY (FLASH)
Dresden (ELBE)
Dresden (ELBE)
Frascati (COSA)
Frascati (SPARC)
Harima (SUBARU)

Italy (SPARX)
Jlab (UV FEL)
MIT (Bates X-Ray FEL)Netherlands (TEUFEL)
Novosibirsk (RTM)

Novosibirsk (RTM1)
Pohang (PAL X-FEL)
RIKEN (SPring8 SCSS)
Rocketdyne/Hawaii (FEL)
Romania (NILPRP)
Shanghai (SDUV-FEL)
SLAC (LCLS)Tokyo (FIR-FEL)
Trieste (FERMI)

760

References for Proposed FELs
M. Abo-Bakr et. al., Nucl. Inst. and Meth. A483, 470 (2002);
Tsukuba Mo-P-07,Mo-P-08,We-P-51 (Sept 2003).
M. W. Poole and B. W. J. McNeil, Nucl. Inst. and Meth. A507,
489 (2003).
http://xfel.desy.de
http://flash.desy.de
http://www.fz-rossendorf.de
P. Michel et. al., FEL2004 (2004) p. 8, http://www.JACoW.org.
F. Ciocci et. al., A. Torre, IEEE J.Q.E. 31, 1242 (1995).
A. Renieri et. al., Nucl. Inst. and Meth. A507, 507 (2003).
S. Miyamoto et. al., Report of the Spring-8 International
Workshop on 30 m Long Straight Sections, Kobe, Japan(August 9, 1997).
A. Renieri et. al., Nucl. Inst. and Meth. A507, 507 (2003).
S. Benson et. al., Nucl. Inst. and Meth. A429, 27-32 (1999).
http://filburt.lns.mit.edu/xfel
J. I. M. Botman et. al., Nucl. Inst. and Meth. A341, 402 (1994).
N. G. Gavrilov et. al., Status of Novosibirsk High Power FEL
Project, SPIE Proceedings, vol. 2988, 23 (1997); N. A.
Vinokurov et. al., Nucl. Inst. and Meth. A331, 3 (1993).
V. P. Bolotin et. al., Nucl. Inst. and Meth. A475, II-37 (2001).
pal.postech.ac.kr/kor
T. Shintake et. al., Nucl. Inst. and Meth. A507, 382 (2003);
http://www-xfel.spring8.or.jp
R. J. Burke et al, Proc. SPIE: Laser Power Beaming, Los
Angeles, Jan. 27-28, 1994, Vol 2121.
Proceedings of FEL 2006; www.jacow.org
Z. T. Zhao et. al, Nucl. Inst. and Meth. A528, 591 (2004).
M. Cornacchia, Proc. SPIE 2998, 2-14 (1997); LCLS Design
Study Report, SLAC R-521 (1998).
H. Koike et. al., Nucl. Inst. and Meth. A483, II-15 (2002).
C. J. Bocchetta et. al., Nucl. Inst. and Meth. A507, 484 (2003);
Tsukuba We-P-53 (Sept 2003).

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THCAU01

OVERVIEW ON DIAGNOSTICS FOR X- AND XUV-FEL
Bernhard Schmidt∗ , DESY, Germany.
Abstract
Controlling and optimizing the SASE process of X-FEL
and XUV-FEL requires detailed knowledge and information about the parameters of the driving electron beam
which are of critical influence on the laser performance.
Due to the very high peak current, collective phenomena
have to be carefully measured and controlled while integral(projected) parameters are of limited use. This necessitates
the development of a variety of diagnostics tools to monitor
the electron bunch parameters in detailedness beyond thecapabilities of conventional systems. Longitudinal bunch
structures can be derived from time domain methods likeelectro optic techniques or using transverse deflecting RFstructures, and from frequency domain methods using coherent radiation. The paper will report on recent developments with special emphasis on single shot and online
monitoring capabilities in this field. Other topics will be
new concepts and experience in measuring the projected
and time-sliced emittance of the beam, high precision beam
position monitors and sub-picosecond beam phase and arrival time monitor systems.

INTRODUCTION
Diagnostics for X- and XUV-FEL is a very wide subject and can not, even rudimentary, be covered in a shortconference contribution. This paper therefore concentrates
on certain areas which are especially demanding and where
new developments can be reported. Photon diagnostics is aseparate important issue but is completely omitted here.
Single pass FEL, as they are used for the production of Xand XUV radiation, are challenging machines in terms ofbeam quality and parameter control. On one side, the lasing process depends more or less exponentially on beam
parameters like emittance and peak current, on the otherside are these parameters subject to a delicate balance between concurrent externally steered and uncontrolled collective effects. Diagnostics has to measure and to control
these beam parameters such that optimum FEL operation isachieved. The feedback between the diagnostic tools measuring the parameters and the steering of the machine spans
all time scales from the very slow experienced human advice to ultra fast intra-bunch feedback on the microsecond
scale. A region of special importance is the longitudinal
phase space, since the FEL operation requires high peakcurrents with good transverse emittance. All the compression mechanisms used and proposed so far will achievethese conditions only for a fraction of the entire bunch∗ bernhard.schmidt@desy.de

FEL Technology

Figure 1: Simulated longitudinal bunch profile and emittance for a non-linear compressor scheme as used in
FLASH. The influence of space charge effects and coherent
synchrotron radiation on the bunch are included [1].
charge and the longitudinal diagnostic has to be sensitive
to the parameters of this specific fraction.
As an example, Fig. 1 shows the result of a comprehensive simulation of the longitudinal bunch profile andemittance for a non-linear compression scheme as used in
FLASH [1]. Collective effects like space charge and coherent synchrotron radiation strongly influence the beam
parameters and it becomes obvious, that projected values
are of very limited use. Diagnostics has to reveal detailsof the bunch structure and to do so on a single bunch basis since the collective phenomena are of partially ’chaotic’
behavior.

BEAM POSITION MONITORSSASE FEL are single pass machines and thus the trajectory of the electrons is not stabilized due to periodic
boundary conditions. It is subject to shot to shot fluctuations and requires meticulous monitoring along the fulllengths of the linac. The requirements on accuracy in theinjector and main linac sections are of the order a few tensof micrometer which can be achieved by conventional button or resonant strip-line BPMs which are numerously used
as workhorses in existing storage rings. Much higher demands on accuracy have to be faced in the undulators. Ac-

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Proceedings of FEL 2006, BESSY, Berlin, Germany

cording to simulations[2][10] , stable SASE operation at
X-ray wavelengths (1 Å) requires a well defined trajectory
which is reproduced with an accuracy of a few micron.
This means that undulator BPMs have to work with submicrometer resolution and an overall mechanical stability
at the same level. The requirements can be met by cavity BMPs which have demonstrated nanometer resolution
during prototype studies for the ILC[13] . For LCLS, Xband BPMs are under development at ANL and SLAC[6]while for the European XFEL, C-band structures working
at 4.38 GHz are foreseen[7]. These BPMs will be used ina fast intra-bunchtrain feedback system to correct the beam
trajectory actively [8]. Besides the monitors itself, maintaining the required mechanical accuracy requires sophisticated alignment tools and procedures for the undulator section; an overview on the status of the plans for LCLS has
been given during this conference[3].
Two specialties in the field of beam position monitors
should be mentioned here since they comprise new concepts. One idea is to use the beam induced higher ordermodes (HOM) in super-conducting cavities to derive information on the beam trajectory. The complex amplitudeof the various HO modes depends on the transverse location of the trajectory inside the cavities as well as on its
inclination with respect to the cavity axis. Accurate measurement of the HOM amplitude pattern therefor allows toderive these values with an accuracy of a few micrometerand μrad. Test measurements at FLASH[9] have shown
the feasibility of the method and impressive first results.
The second field to be mentioned are large aperture BPMs
to measure the beam position and size inside the dispersive
section of the bunch compressors. The aim is to derive accurate information on the mean energy and energy spreadof the beam with single bunch resolution. The accuracy
required on the transverse beam center is of the order 5 micron for an energy resolution of 10 −4 while the width of thebeam is of the order 50 - 100 mm. An interesting techniquewhich has been studied recently proposes to measure thearrival time of the signals on both ends of a transverse stripline across the compressor beam pipe with an accuracy on
the 10 fs scale[4]. The sum of left and right timing provides
the information on the transverse center of the charge andthus the mean energy while the timing difference contains
information about the width of the distribution and thus theenergy spread. The method to derive timing signals frombeam pick-ups with fs accuracy will be described in thenext section. An alternative method to measure the transverse distribution in the bunch compressors has been successfully investigated at FLASH; it is based on high resolution imaging of the synchrotron radiation in the UV range
produced in the bunch compressor dipoles [5].

ARRIVAL TIME (BEAM PHASE)
MONITORS
Monitoring the performance of the machine and providing high precision ’time stamps’ for the FEL users requires

762

Figure 2: Time difference between two bunches of thesame bunch train at FLASH, measured with a phase monitor using electro-optic detection of the zero crossing of apick-up signal. The combined time jitter and monitor resolution is of the order 50 fs[12].
to measure the arrival time of the electron bunches in frontof the undulators with fs accuracy. This is well above
the capabilities of conventional RF methods and requires
either specialized longitudinal diagnostics (see section
on electro-optic methods) or a new type of beam phase
monitors as proposed in ref.[11]. These monitors use
the rather large beam induced signals from conventional
button or ring pick-up electrodes to modulate the intensityof a probe laser pulse with electro-optic modulators (basedon ’Periodically Poled Lithium Niobate’ structures). These
modulators combine a bandwidth of several GHz withhigh sensitivity and allow to detect the zero crossing of
the signal with an accuracy of a few femtoseconds. A test
set-up at FLASH has demonstrated very promising resolutions recently. Fig. 2 shows the measured time difference
between two bunches of the same bunch train at FLASH.
The combined effect of real time jitter and resolutionof the phase monitor is of the order 50 fs. A potential
drawback of the method is, that it measures strictly the’center of charge’ of the bunch and not the actually lasing
part. Ideally, the probing laser of the phase monitor is partof an optical timing system of the machine which avoids
any additional timing jitter due to RF synchronization.

TRANSVERSE DEFLECTINGSTRUCTURES
Transverse deflection structures (TDS) are amongst themost powerful and developed tools to measure the phasespace distribution of particle bunches. They have been developed at SLAC during the 60th[15] of the last century
and used for both, beam separation and diagnostic purposes(e.g. [16]. Operating the deflecting structure close to thezero crossing of the RF, the bunches experience no net deflection but are streaked transversely. Adding a fast transverse kicker allows to send the streaked bunch to an off-

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THCAU01axis screen independent of the streak power. If the transverse deflecting structure is combined with a FODO section, quadrupol scans allows to investigate the slice emittance of the bunches. In combination with a dispersive section, the streaked bunch images the slice energy spread of
the beam. All future XFEL projects foresee transverse deflecting structures for diagnostic purposes. In the case of
the European XFEL, multiple pairs of TDS are foreseen to
allow measurements in both transverse planes at different
locations along the injector section. An overview can befound in ref. [17].
For operation at zero crossing, the transverse deflection at
the screen Δy depends on the longitudinal position Δz
with respect to the center as
Δy = ΔzeV 2π βc βs sin(Δψ)
E0 λHF(1)with V the total deflection Voltage of the cavity, E 0 the
beam energy and Δψ the phase advance between cavity
center and screen. It depends on both β-functions at thecavity and the screen and since the temporal resolution of
the method is determined by the ratio of Δy/Δz to theunstreaked transverse size of the beam, the optimal optics
for the TDS operation demands large β c and small βs .
This has to be foreseen during the design of the machine
and is not necessarily coincident with the optimal optics
for FEL operation.
An S-band TDS operating at 2,856 GHz from SLAC
(LOLA IV cavity) has been installed at the FLASH linac
and is routinely used for beam diagnostic measurements
and to develop the TDS method further. At optimized
conditions, a streak power of more than 1mm per 100f s
can be achieved which for a nominal beam diameter of
200μm would lead to a resolution of about 20f s (RMS).
Under normal FEL operation conditions, the resolution
observed is slightly less. The image of a typical, wellcompressed bunch is shown in Fig. 3, the width of thecharge spike at the bunch head is of the order 150f s(FWHM). Fig. 4 shows a bunch fragmented by spacecharge and CSR due to too high compression (notice thedifference in time scale compared to Fig. 3).
Scanning quadrupols in front and after the TDS, the slice
emittance of the bunches can be measured; a detailed report on recent results has been given at this conference[18].
If the streaked bunch passes a dispersive section in frontof the observation screen, the slice energy spread of thebunch can be derived with high accuracy. The example
shown in Fig. 5 demonstrates the complex structure of thelongitudinal distribution and the strong coupling between
ΔE and z. The bunch head clearly has two well separated
peaks in phase-space which almost coincide longitudinally.
Such observations are in good agreement with start-to-end
simulations and emphasise the necessity of powerful
diagnostics for a detailed understanding of the machine.
The TDS method can be called semi-parasitic since theobserved bunches are lost from the FEL process. The
read-out speed is limited by the complex imaging required,

FEL Technology

Figure 3: Image of a TDS streaked bunch at FLASH. The
phase of the first accelerating module is set such to produce
a well formed current peak[14].
the information can not be used for fast feed-back systems.

ELECTRO OPTIC (EO) METHODS
The longitudinal charge profile of the bunches can beprobed by detecting their relativistic Coulomb field bymeans of electro-optic crystals close to the beam trajectory.
The optical properties (namely the birefringence) of thecrystals is changed proportional to the electric field strengthand the cumulative effect on a co-propagating short laser
pulse can be detected. In this way, the temporal (longitudinal) structure of the bunch charge is impressed in a polarization modulation of the optical pulse. An overview on
the different methods to decode this information is shownin Fig. 6. The scanning delay method is not single shotand can not be used if the temporal jitter of the mean timeof the bunch is comparable or even larger than the lengthof the bunch. Single-shot EO bunch length measurements
were pioneered at FELIX [20] with the spectral decoding
method (EOSD), the more recently developed spatial decoding [22] and temporal decoding [23] techniques offer
higher resolution at the price of enhanced complexity.
The spectral decoding method is of striking simplicity:
the probing pulse is stretched to several ps by applying
a linear chirp, that is a correlation between time and ’local’ wavelength. The polarization modulation due to theEO effect is translated into an intensity modulation by a763

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Proceedings of FEL 2006, BESSY, Berlin, Germany
GaP orZnTe
fs laser

photo
diode

variable
delay
P

P

Scanning Delay Samplinggrating

GaP orZnTe
fs laseropticalstretcher

P

CCD

P

Spectral Decoding
GaP orZnTe
fs lasercylindical
telescope

CCD
P

P

Spatial Decoding

fixed
delay

GaP orZnTe

fs laseropticalstretcher

CCD
BBO

P

P

Temporal Decoding

Figure 6: Overview on different methods to decode thetemporal information form the laser pulse probing the EO
crystal [19].

Figure 4: Image of a TDS streaked bunch at FLASH. The
phase of the first accelerating module is set too much offcrest, the bunch is strongly distorted by space charge andCSR effects [14].

0.25
0.4
0.2
0.2
0.15
δ [%]

0
0.1
−0.2
0.05

−0.4

0

−0.6

−0.8

−0.05
0

0.5

1
Δ t [ps]

1.5

2

Figure 5: TDS streaked bunch with energy dispersion. The
bunch head is contains two separated peaks, less than 100
fs apart and with an energy difference of 0.5 % [18].

set of crossed polarizers, the intensity as function of wavelength, measured with a conventional grating spectrometer,
images the longitudinal charge profile. Unfortunately, themethod has an intrinsic limitation: the amplitude modulation of the probe pulse creates unavoidably a spectral modulation which mixes with the linear chirp and thus spoils
the ’decoding gauge’. For the very fast modulations (thatis short pulses), this creates an apparent broadening of the764

Figure 7: Single shot bunch profiles measured with electrooptic spatial decoding at the SLAC-FFTB using a ZnTe
crystal [22].

pulse and even artificial temporal structures. For the typical
optical wavelengths of 800 nm and a length of the chirped
pulse of a few ps, structures shorter than about 200-300 fs(FWHM) can not be decoded correctly. Nevertheless, thecentroid of the bunch can be detected with much higher
accuracy (<50 fs) and coarse deterioration (double spikesetc.) can be easily detected. The method has the potential for further developments in the direction to become aroutine on-line monitoring system. For that, the expensive
and delicate Ti:Sa laser systems used so far have to be replaced by more robust devices (potentially fiber lasers). If
the spectroscopy can be done by using a line camera with
fast readout, multi-bunch capability can be envisaged foreven the 200 ns bunch distance at the European XFEL.
Spatial decoding has been mainly developed at SLAC [22].

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany
The spatially extended short probing laser pulse hits theEO crystal with non-perpendicular incidence, thus a spatial
image of the crystal decodes the electric field a different
points in time. The method has the great advantage to be
free of the intrinsic limits of EOSD but relies on the spatial
uniformity of the EO crystal which can be, especially for
ZnTe, quite poor. It requires a quite complex optics andimaging system inside the accelerator tunnel but can operate with rather modest laser energy. Fig. 7 shows a result
obtained at SLAC using a ZnTe crystal, the resolution of
270f s achieved is close to the limit for this material. At
FLASH, a similar set up using GaP is installed and resolutions of the order 120f s have been demonstrated[21].
Temporal decoding is the most powerful and most complex
EO method developed so far. The short laser pulse is split
in two halves, one is chirped to a length covering the lengthof the electron bunch and passes the EO crystal in the beamline. The other one is kept short. The polarization modulation is transferred to an intensity modulation in the usual
way, after that the probing pulse hits a non-linear crystal(SHG). There it is merged under a certain angle of inclination with the short ’gate’ pulse from the same origin. In the
SHG crystal, a second harmonic component is created proportional to the product of both laser intensities, leaving the
crystal in a direction well separated from the two incoming
components. The temporal information thus is decoded by
optical cross correlation as shown in Fig. 8 schematically.
Since a non-linear optical process is involved, the method
requires much higher laser power ( mJ) and thus a complex
and expensive laser amplifier system. On the other hand,
the method has demonstrated the best resolution so far. At
an installation at FLASH, spike widths of the order 100
fs (FWHM) have been measured in good agreement with
TDS data recorded simultaneously (Fig. 9).
Single-shot electro-optic diagnostic techniques are rather
mature as experiments meanwhile but still in an infant
state as routine operation tools. Since they are totally nondestructive and can be applied to any bunch, it is worthwhile to spend considerable efforts to overcome the technical problems to make them more robust an usable ascontinuously running monitoring tools. The developmentof optical synchronization systems makes them even more
attractive, since they can be directly coupled to them bymeans of optical synchronization, avoiding any additional
jitter introduced by RF components. They are ideal candidates to provide not only detailed information about thebunch structure online but as well to act as extremely precise bunch arrival time monitors and time stamp generators
for pump-probe experiments.

COHERENT RADIATION DIAGNOSTICS
The relativistic electrons of the bunches radiate electromagnetic waves whenever their Coulomb field is subjected to changes: synchrotron radiation due to directionalchanges in the bending sections or transition and diffraction
radiation if the field enters regions of changing dielectric

FEL Technology

THCAU01

Figure 8: Temporal decoding of the intensity modulationof the probe pulse by spatial cross correlation in a second
harmonic (SHG) crystal.

Figure 9: Longitudinal bunch profile measured at FLASH
with the electro-optic temporal decoding technique using a
100μm thick GaP crystal [24].
properties. For wavelengths of the radiation longer than the
distance of two electrons, these electrons radiate ’in phase’or coherently, the intensity of this coherent radiation scaleswith the square of the number of contributing electrons andcan be a massive effect. More precisely, the radiated power
per frequency interval can be written asdU∝ N 2 |Flong (ω)|2 T (ω, γ, rb , Θ, source)dω
withFlong (ω) =

(2)

 ∞
−∞

ρ(t)exp(−iωt)dt(3)

Flong is the longitudinal form factor of the bunch, theFourier transform of the longitudinal charge distribution
and T summarizes all other, potentially complex, properties of the radiation source.
The most popular application of coherent radiation diagnostics is to measure a global intensity of the radiation
integrating over a certain (normally large) range of frequencies and use the signal strength as an index for the
shortness (the ’compression’) of the bunch. It should be
kept in mind that the information on the bunch length
obtained that way is restricted to the wavelength range765

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Proceedings of FEL 2006, BESSY, Berlin, Germany
non-linear compression+ collective effects

linearized compression

Figure 10: Simulated wavelength spectra of coherent
transition radiation for two compression schemes without
space charge and CSR effects and for an example of nonlinear compression including space charge and CSR effect(data courtesy M. Dohlus).
covered by the radiation detector. If the coherent radiation
intensity is observed spectrally resolved, information
about the longitudinal form factor and thus the charge
distribution can be obtained. For the typical bunch lengths
between 10 fs and 100 fs contributing to the FEL process,the corresponding range of wavelengths is in the far
infrared from 10 μm to 300 μm. As shown in Fig. 10, thewavelength spectra of coherent transition radiation from
ideally compressed electron bunches strongly peak in theregion below 200 μm, the position of the intensity maximum directly reflects the length of the current spike 1 . If
the bunch is distorted by collective effects, the wavelength
spectrum exhibits characteristic substructures which could
be used to get information on the strength and nature of
the collective phenomena. Despite the fact that a directreconstruction of the bunch shape from radiation spectra
is impossible due to the missing phase information, thewavelength spectra reveal sufficient information to act as’fingerprints’ of the longitudinal bunch structure.
The wavelength range of interest puts a few stringent
boundary conditions to the experimental set up: conventional crystalline quartz windows are not transparent
for wavelength shorter than about 80 μm and humid air
absorbs below 300 μm even over short distances substantially. In consequence, the radiation has to be coupled outof the beam pipe by using a CVD diamond window andthe entire coherent radiation set up has to be evacuatedor flushed with a dry gas. Conventional IR spectrometers
used so far in bunch length diagnostics are Michelson typeinterferometers measuring the autocorrelation functionof the radiation. This method is intrinsically not single
shot capable and the information has to be derived in acomplex de-convolution process. Recently, a new type ofspectrograph has been proposed[25] and assembled which
is able to measure wavelength spectra over a sufficiently
large range on a single shot basis. The central elements are
gratings as dispersive elements and a multichannel detector
with fast read out. In a first step, a set of reflective blazed
1 For a Gaussian bunch, the position of the intensity maximum in wavelength space depends linearly on the temporal width of the bunch

766

Figure 11: A set of successively recorded single shot spectra in the wavelength range 16-26 μm from coherent transition radiation at FLASH. While recording from right toleft, the off-crest phase of the first accelerating module wasscanned from zero to about -8 degrees.
gratings has been used to separate different wave length
bands and to detect them with single element pyro-electric
sensors. Such a device can be used as ’advanced bunch
compression monitor’ which is much more sensitive tothe actually lasing part of the bunch than conventional
integrating devices. It has been tested at the THz beamline[28] of FLASH using coherent transition radiation andproven capabilities. More details can be found in ref. [?].
The development of a 30 channel fast read out pyro-electric
sensor at DESY[29] made it possible to record coherent
radiation spectra for single shots online. The device hasa sensitivity of about 300 pJ per channel (5σ noise-level)
and is almost free of disturbing ’etalon’ resonances in thesensitivity in the interesting wavelength range from 1 μm
to 1mm. For this, newly designed pyro-electric sensors
have been developed together with industry. The device
has been used together with transmission gratings andreflective gratings for fist online single-shot spectroscopy
at the FLASH THz beamline 2 . As an example, Fig. 11
shows a set of successively recorded spectra in the rangeof 16-26 μm while the phase of the first accelerating
module was scanned over 8 degrees[27]. Radiation inthis wavelength range is produced in two (probably three)narrow regimes of the off-crest phase. One of them isusually used for FEL operation. In contrast to this, fig. 12shows the equivalent scan for very short wavelengths
between 5 μm and 8 μm. No such pronounced bands areseen, the intensity pattern fluctuates from shot to shot andthe overall intensity increases with larger off-crest phaseangles. This is a very clear indication for micro-bunching
on a few femtosecond scale.
Single shot coherent spectroscopy has made a step
forward but still to prove its benefits for bunch profile
diagnostics and online monitoring. Transmission gratings
2 The evacuated beamline images transition or diffraction radiationfrom an off-axis screen over a distance of 20m to outside the linac tunnel. A fast kicker is used to kick individual bunches to the screen, thus themeasurements can run in parallel to normal FEL operation.

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

THCAU01[5] C.Gerth, ”On-line Energy Spread Measurements Using Synchrotron Radiation in the Bunch Compressors at FLASH”,
Proceedings FEL06, THPPH011.
[6] R.M.Lill et al., ”Linac Coherent Light Source (LCLS) Undulator BPM System”, FEL06, THPPH054.
[7] D. Noelle et al., ”First Ideas for the XFEL BPM System”,
FEL06, THPPH014.
[8] B. Keil et al., ”An Intra Bunch Train Feedback System for
the European XFEL”, Proceedings FLS06, WG521.
[9] J. Frisch et al.,”High Precision SC Cavity Alignment Diagnostics with HOM Measurements”, Proceedings EPAC06,
TUYPA02.

Figure 12: A set of successively recorded single shot spectra in the wavelength range 5-8 μm from coherent transition radiation at FLASH. While recording from right toleft, the off-crest phase of the first accelerating module wasscanned from zero to about -8 degrees.
offer a wider spectral range but can not reach the shortest
wavelengths, reflective gratings span only about one octave
in wavelength but have higher efficiency and are available
down to the UV region. The natural next step is to ’stage’several reflective gratings with a final transmission gratingto span the full range of interest simultaneously. Equippedwith fast read-out, these devices can be used even for fast
feedback systems.

SUMMARY
Diagnostics for XUV and XFEL requires a variety of
new developments on various fields to cope with the very
demanding challenges of these machines. Considerable
progress has been made during the past years for beam
position monitors and especially on the field of longitudinal phase space diagnostics and arrival time monitors. But
most of the new methods are still not mature and more orless far from being applicable as routine online tool to control and steer the machine. This is a reach and challenging
field for the next years. On top of this, even more sophisticated techniques like the ”optical replica synthesizer” areon their way to be explored [30][31].

[10] J. Wu and P. Emma, ”Trajectory Stability Modeling and Tolerances in the LCLS”,Proceedings EPAC06, MOPCH049.
[11] F. Loehl et al. , ”A Sub 100 fs Electron Bunch Arrival-time
Monitor System for the VUV-FEL”, Proceedings EPAC06,
THOBFI01.
[12] F. Loehl , private communication.
[13] S. Walston et al., ”Performance of a Nanometer Resolution
BPM System”, Proceedings EPAC06, TUPCH105.
[14] courtesy Holger Schlarb, DESY.
[15] O.H. Altenmueller, R.R. Larsen and G.A. Loew, ”Investigation of Traveling-Wave Separators for the Stanford TwoMile Linear Accelerator”, The Review of Scientific Instruments, Vol. 35, Number 3, April 1964.
[16] R. Akre, L. Bentson, P. Emma and P. Krejcik, ”Transverse
RF Deflecting Structure or Bunch Length and Phase Space
Diagnostics”, Proceedings PAC 2001, p. 2353.
[17] C. Gerth, M.Roehrs and H. Schlarb, ”Layout of the Diagnostic Sections for Emittance and Energy Spread Measurements at teh European XFEL”, Proceedings FEL06, THPPH010.
[18] C. Gerth, M.Roehrs and H. Schlarb, ”Investigations of theLongitudinal Electron Bunch Structure at the FLASH Linac
with a transverse deflecting RF-Waveguide.”, Proceedings
FEL06, TUBAU06.
[19] S.P. Jamison et al., ”Femtosecond bunch length measurements”, Proceedings EPAC2006, TUYPA01.
[20] I. Willke et al., ”Single-shot electron-beam bunch length
measurements”, Phys. Rev. Lett. 88, 124801, 2002.
[21] H. Schlarb et al., ”Comparative Study of Bunch lengthand Arrival Time Measurements at FLASH”, Proceedings
EPAC2006, TUPCH024.

REFERENCES[22] A.L. Cavalieri et al., ”Clocking Femtosecond X Rays”,
Phys. Rev. Lett. 94, 114801 (2005).

[1] M. Dohlus, ”Modeling of Space Charge and CSR Effects
in Bunch Compressor Systems”, Proceedings EPAC2006,
MOPCH015.

[23] G. Berden et al., ”Electro-optic techniques with improved
time resolution for realtime, nondestructive single-shot measurements of femtosecond electron bunch profiles”, Phys.
Rev. Lett. 93, 114802, 2004.

[2] W. Decking, X-FEL Project Team at DESY, private communication.

[24] B. Steffen at al. , ”Single Shot Longitudinal Bunch Profile
Measurements at FLASH using Electro-Optic Techniques”,
Proceedings EPAC2006, TUPCH026.

[3] H.D. Nuhn, ”Electron Beam Alignment Strategy in the
LCLS Undulators”, Proceedings FEL06, THBAU02.
[4] K.E.Hacker et al., ”Large Aperture BPM for use in Dispersive Regions of Magnetic Chicanes”, Proceedings FEL06,
TUPPH054.

FEL Technology[25] H. Delsim-Hashemi et al., ”Broadband Single Shot Spectrometer”, Proceedings FEL2005, THPP029.
[26] H. Delsim-Hashemi et al., ”Bunch Compression Monitor”,
Proceedings EPAC2006, MOPTH016.

767

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Proceedings of FEL 2006, BESSY, Berlin, Germany[27] H. Delsim-Hashemi et al., ”Single-Shot Longitudinal Diagnostics with THz radiation at the Free-Electron Laser
FLASH”, Proceedings FEL2006, THPPH018.
[28] S. Casalbuoni et al., ”Far-infrared transition and diffraction
radiation Part II: the Thz beamline at the VUV-FEL linac”,
TESLA FEL 2006-04.
[29] B. Schmidt et al. , ”A 30 channel pyro-electric line detector
with MHz read out for mid and far infrared detection”, inpreparation.
[30] E. Saldin et al. , ”A simple method for the determinationof the structure of ultrashort relativistic electron bunches”,
Nucl. Instr. Methods A 539, 499 (2005).
[31] P. van der Meulen et al. , ”Technical aspects of the Integration of the Optical Replica Synthesizer for the Diagnostics
of Ultra-short Bunches into FLASH at DESY”, Proceedings
FEL2006, TUBAU05.

768

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THCAU02

LOW EMITTANCE INJECTOR AT SCSS
Hitoshi Tanaka*,A,B), Kazuaki TogawaA), Hitoshi BabaA), Toru HaraA,B), Atsushi HigashiyaA),
Takahiro InagakiA), Hirokazu MaesakaA), Hiroshi MatsumotoB,C), Kazuyuki OnoeA), Yuji OtakeA),
Katsutoshi ShirasawaA), Takashi TanakaA,B), Takanori TanikawaA),
Makina YabashiA,B), Tsumoru ShintakeA),A) RIKEN/SPring-8, 1-1-1, Kouto, Sayo, Hyogo, 679-5148, JapanB) JASRI/SPring-8, 1-1-1, Kouto, Sayo, Hyogo, 679-5198, JapanC) KEK, 1-1, Oho, Tsukuba, Ibaraki, 305-0801, Japan.
Abstract
The SPring-8 compact SASE source (SCSS) project
aims at SASE-based FEL at wavelength region of 1
angstrom. To generate a high quality electron beam, a low
emittance injector comprising of a 500 kV pulsed electron
gun, beam deflector and three-stage velocity bunchingprocess has been investigated [1, 2]. To confirm beam
performance of the injector, the SCSS prototype
accelerator with the identical injector system wasconstructed [3]. Via beam tuning of the prototype
accelerator over half a year, the first stage beamcommissioning was completed successfully and SASE at
wavelength of about 50 nm was observed in June 20th,
2006 [3]. The analysis of experimental SASE data
predicts that essential beam quality, i.e., "effective
electron beam brilliance" reaches to the target value, 200
A/π2mm2⋅mrad2. In this paper, we describe the injector
design of the SCSS prototype accelerator and show theachieved beam performance.

INTRODUCTION
In order to achieve SASE-based x-ray FEL, normalized
slice emittance of ~1 πmm.mrad is required with a highpeak current of a few kA. For this purpose, it has been
believed that a photo-cathode RF electron gun (RF-gun)based system is the most promising. The RF-gun based
system has been thus adopted as the injector for the LCLS
[4] and XFEL [5] projects.
In the SCSS project, we however took a different
approach to this problem. A conventional technologybased injector, which comprises of a pulsed electron gun
with a thermionic-cathode, a beam deflector and threestage velocity bunching process was chosen [1, 2]. This
choice is due to potentiality achieving simultaneously
high stability and tunability, which are criticallyimportant for realization of "stable" x-ray FEL. This
injector system is free from the dark current from thecathode, which could be a serious problem in the RF-gun
based system.
In the SCSS injector system, basic functions on beamhandling such as emission of electrons, beam pulse
processing, beam acceleration and bunch compression are
separated. Machine parameters in each function are thus*E-mail: tanaka@spring8.or.jp

FEL Technology

adjustable independently, which assures wide tunability inoperation. This is an advantage when compared to the
RF-gun based system, where these functions are tightly
coupled. Furthermore, the RF-gun based system has touse a state of the art laser system to extract electrons fromthe cathode, which may cause instability in the initial
beam condition.
Although the SCSS injector system has an advantage
on the electron beam stability and operation tunability,
there remains the question whether "emittanceconservation" through the injector is a sufficient level or
not under the practical error condition. To reply this, inother words, to confirm beam performance of the injector
and investigate hidden problems in operation, the SCSS
prototype accelerator was constructed and has been tested.

OUTLINE OF INJECTOR SYETEM
Figure 1 shows the schematic view of the injector
system of the SCSS prototype accelerator. Since the
SCSS injector is basically the same as that of the
prototype accelerator, we explain beam handling over the
injector by using Fig. 1.
Electron beams are extracted from the single crystal
CeB6 cathode by a 500 kV pulse voltage (1 in Fig. 1) [6].
The repetition rate is 60 Hz at most and the electron pulse
width is about 2 µsec. The theoretical thermal emittanceis 0.4 πmm.mrad. The initial beam energy is 500 keV andpeak current is 1 A.
The developed beam deflector (2 in Fig. 1) cuts out
about 1 nsec short pulse from the extracted beam. Due tothe fast rising and falling time of the deflector electricfield, 1 nsec beam pulse has a beam tail of about 100 psec,in front of and behind the beam. The deflector has acollimator with a hole of which diameter is 5 mm and thebeam is collimated into a cylindrical shape with atransversally hard edge.
Owing to the high beam energy of 500 keV, aconventional solenoid coil, which covers a wide beampath, is unnecessary. Instead of the solenoid, a special
magnetic lens, where the solenoid coil is covered by aniron york, has been developed (3 in Fig. 1). This magnetic
lens has two significant advantages: (1) Due to the
localized focusing field, three functions, beam focusing,beam acceleration and bunch compression can beseparated. (2) Due to the properly large aperture,
nonlinear fringe fields are suppressed enough to avoid the769

THCAU02

Proceedings of FEL 2006, BESSY, Berlin, Germany

Fig. 1: Schematic drawing of SCSS injector system.
emittance growth. The former advantage is quite
important for precise beam tuning.
The cylindrical beam with the pulse width of 1 nsec
receives energy modulation, about 400 keV in a peak-topeak value, in the 238 MHz pre-buncher (4 in Fig. 1). Theenergy modulated beam develops the density modulation
when passing through a 1.6 m drift section. The energy
filter (5 in Fig. 1) is now not used. In front of the booster,
the average beam energy is ~0.43 MeV and the peakcurrent reaches to 5 A (~200 ps). Then, in the 476 MHz
booster cavity (6 in Fig. 1), the beam energy is boosted up
to ~1 MeV to suppress the space charge effect and to
linearlize the velocity gradient. In the velocity bunchingprocess, both the voltage and phase of the two cavities are
crucial for the bunching performance. Structures of bothcavities were therefore carefully designed so that thefrequency and gap-voltage are not sensitive against avibration and temperature change. The peak current
increases up to 50 A (~10 ps) while the 1 MeV electron
beam flights over 1.3 m from the booster to the first Sband acceleration tube (7 in Fig. 1).
The energy of the electron beam is boosted by the two
S-band accelerating tubes (7 and 8 in Fig. 1) up to ~41
MeV with the design bunching phase and up to~50 MeV
with the crest phase. To suppress the emittance growth
due to the symmetry-break of the first acceleration tube,
APS structure was adopted. The velocity bunchingprocess completes by the end of the first tube, where thepeak current reaches to ~80 A (~6 ps).
Downstream of the first S-band accelerator tube, thebeam energy is higher than 10 MeV and a quadrupole
magnet (10 in Fig. 1) is used to focus the beam instead ofthe magnetic lens.
In the SCSS prototype accelerator, the beam is further
compressed for SASE experiments by the bunch
compressor, which comprises of four identical rectangularmagnets (10 in Fig. 1). The deflecting angle is 0.1 rad andthe maximum linear dispersion is about 110 mm. Afterthe bunch compression, the peak current reaches to ~800
A (~0.7 ps).

770

The injector system is divided into three main parts, theelectron gun, the beam deflector and three-stage velocity
bunching process. Details of each part are described in thefollowing three sections.

500 KV PULSED ELECTRON GUN
To constantly obtain low emittance electron beam withhigh beam current of 1~3 A, the electron gun was
significantly improved from conventional electron guns.
Table 1 lists the main electron gun parameters and Fig. 2
shows the CeB6 cathode assembly (left) and the cathodebeing heated in the test chamber. The major
improvements are:
•
•

•

•

A small sized single crystal CeB6, of whichdiameter is 3mm, was used as a cathode.
The control grid was removed from the cathode,because the grid increases beam emittance bydistorting the electric field.
The gun voltage was raised up to 500 kV to
suppress a space charge effect and remove
troublesome solenoid coils.
The cathode was stably heated up to hightemperature as 1400~1600 deg.C by use of graphite
heater.
Table 1: Gun Parameters
Beam Energy
Peak Current
Pulse Width (FWHM)
Repetition Rate
Cathode Temperature
Cathode Diameter
Theoretical Thermal
Emittance (rms)Measured Normalized
Emittance (rms, 90%particles)

500 keV
1~3A
2 µsec60 Hz
1400~1600 deg.C
3mm
0.4 πmm.mrad
0.6 πmm.mrad [7]

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany••

The graphite sleeve surrounding the cathode wasadopted to reduce beam halo.
The flat Wehnelt was used as the anode to reduce
emittance growth and to enlarge dynamic range ofthe peak current.

THCAU02

length by a several hundredth as the energy increases up
to a few tens MeV. In the design of the SCSS injector, itis thus important to suppress emittance growth caused bya space charge force. On the other hand, the highcompression ratio, higher than hundred, is required.
Hence, handling of nonlinearity in the compression
process is important.

Suppression of Emittance Growth
Assuming that the beam transverse shape is round andhard-edged and all electro-magnetic potentials are axialsymmetric, equation of motion under a space charge force
is described in a cylindrical coordinate by [8]r"" +Fig. 2: Cathode assembly (left) and heated cathode (right).

BEAM DEFLECTOR
Since the control grid was removed from the developed
electron gun to suppress beam emittance growth, beam
deflector, which cuts out a 1nsec short pulse from !thelong one, is indispensable for the SCSS injector system.
Figure 3 shows the principle of the beam deflector. The
deflector comprises of two parallel electrode plates andone steering coil. The coil generates a DC magnetic fieldin the horizontal plane, which deflects the beam verticallyand dumps it by using the narrow physical aperture asshown in the figure. The short pulsed electric field in thevertical plane, which cancels out the vertical kick by theDC magnetic field, achieves gating of ~1 nsec. The
driving pulse has a fast rising and falling time, ~200 psec,
which can generate a well-edged electron beam with ashort tail. The flatness of the pulsed electric fields at theflat top determines the emittance degradation in thedeflector. Hence, to achieve the sufficient field quality,
impedance matching was fully considered in the design ofthe electric circuit and the parallel electrode plates
including the casing chamber.

THREE-STAGE VELOCITY BUNCHINGThe SCSS injector starts beam compression from thelow beam energy of a 500 keV and reduces the bunch

Fig. 3: Schematic drawing of beam deflector.

FEL Technology% qB (2
#"
# ""
"
r
+
r
+
'
*r
$ 2#
2$ 2#
& 2m0c$# )(1)% p (2 1
2Ir+' , * 3 += 0,
32& m0c$# ) r ($# ) IA rm

where r, β, γ, B, pθ, I, IA and rm are the electron radius,
relative velocity, relative energy, longitudinal magnetic
field, azimuthal momentum, peak current and Alfven
current, respectively. The last term in L.H.S. shows thespace charge force acting on the electron beam,suggesting that the guideline on the bunch compression is
the ratio of γ 3. For example, when γ increases from 1 to 2,
criterion on the compression ratio is (2/1)3=8. This idea
was first proposed by T. Shintake [1].
The bunch compression in the SCSS prototype
accelerator however, apparently exceeds the above
guideline and the simulation code, PARMELA predicts
that the emittance growth is larger than that in 8-GeV
SCSS. Because the injector parameters of the prototype
accelerator were optimized not for SASE in wavelength
region of 1 angstrom, but for in VUV region under thelimited boundary condition, the peak current rather than
the slice emittance was pursued. In the 8-GeV SCSS
design, RF parameters, especially the RF voltage of 238
MHz pre-buncher will be re-optimized and the use of Lband accelerators instead of the S-band (7 and 8 in Fig. 1)
is under investigation.

Nonlinearity HandlingTo achieve the high compression ratio, suppression of
nonlinearity in the bunch compression process, which
originates from a RF voltage and velocity dependence on
relative energy of the beam, is the key. For the simple
system comprising of a RF potential, drift space andinitially mono-energetic beam, the condition achieving
the linear velocity distribution against time can be easily
solved by neglecting a space charge force and expressedusing only three parameters: an initial beam energy, peak
RF voltage and RF phase. By using 500 keV and 209 kV
as the initial beam energy and peak RF voltage of the prebuncher, respectively, the linear distribution is obtained atabout -125 deg. from the crest phase. Since the injector of
the prototype accelerator has the 476 MHz booster cavity
downstream of the pre-buncher, the condition for the771

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Proceedings of FEL 2006, BESSY, Berlin, Germany

linear distribution becomes more complicated at the exitof the booster, i.e., it also depends on the booster
parameters. Figure 4 shows the velocity distribution
dependence on RF phase of the pre-buncher behind thebooster, which was calculated with the injector
parameters of the prototype accelerator. In this case thephase between -100 and -120 deg. is found to be optimum.
In consideration of the experimental results obtained at
the prototype accelerator, all the parameters relating to thethree-stage velocity bunching process have been reinvestigated.

Fig. 4: Velocity distribution dependence on RF phase of
the pre-buncher behind the booster calculated with theinjector parameters of the prototype accelerator.

units, respectively, to compare the performance of the twocompressors. The nominal accelerating field gradient isabout 30 MV/m when the beam is accelerated at the crest
phase and in this operating condition RF power fed toeach acceleration tube is 46 MW on average of 300 nsec
filling time.
The undulator part is divided into two identical invacuum undulators of 4.5 m. The permanent magnet
material is NdFeB and magnet structure is a 45-deg. tilted
Halbach type [12]. Minimum, nominal and fully opened
gaps are 2, 3 and 25 mm, respectively. At the minimum(nominal) gap K-value reaches to about 1.8 (1.3) and thewavelength of the first harmonic is about 80 (60) nm withthe beam energy of 250 MeV. The period length is 15 mm
and the number of periods is 300 per undulator. To keep asmall beam size in the horizontal plane, one focusing
quadrupole locates between two undulators. In front of
the first undulator, a magnet chicane is installed to protect
the undulator permanent magnets from accidental electron
bombardments and dark currents from the C-band
accelerators.
The symbol “M” in Fig. 5 shows a chamber port for ausual beam profile measurement with fluorescence andoptical transition radiation. In the beam tuning, these
ports are also used to measure a longitudinal beam density
distribution by using coherent transition radiation because
evolution of the longitudinal distribution is quite
important for setting RF parameters in the velocity
bunching process. The symbol “S” shows a transverse
beam slit to collimate the beam in energy and transverse
space.

SCSS PROTOTYPE ACCELERATORTUNING STRATEGY OF SCSSPROTOTYPE ACCELERATORThe SCSS prototype accelerator comprises of the low
emittance injector, bunch compressor with a magnetic
chicane, C-band acceleration system, and two in-vacuum
undulators as shown in Fig. 5. To verify the injector
capability providing the high quality electron beam, thedesign target of the normalized slice emittance and peakcurrent was set at 2 πmm.mrad and 800 A, respectively.
Attainment of the target confirms that the beam
performance for x-ray FEL is reachable by smooth
extension of the prototype accelerator. And also, thetarget performance is enough for SASE lasing at
wavelength of 40 ~ 60 nm.
Since both the injector and bunch compressor werealready described in the previous sections (see Fig. 1), we
start a brief explanation of the prototype accelerator fromthe C-band acceleration system. The system is divided
into two acceleration units. Each unit has two 1.8 m-longchoke-mode type traveling wave acceleration (TWA)
tubes [9] driven by a 3/4π mode. Each unit has one
50MW C-band klystron. The RF power from the klystronis boosted up by a factor of 3.4 by the RF pulse
compressor and equally fed to the two acceleration tubes.
In the prototype accelerator, different compressors, SKIP
[10] and SLED [11] were adopted for the first and second

In the beam tuning, the following points were wellconsidered, because there is no diagnostics to measure theslice emittance directly.
(1) Suppression of slice emittance growth by a spacecharge force: Over-focusing of the beam causes theemittance growth by a space charge force and hence, it isimportant to tune the real beam envelope same as thecalculation. To this end, initial condition of the real beamfrom the electron gun should be fixed. We made series ofsystematic measurements on the beam profiles bychanging strengths of the plural magnetic lenses one by
one without RF power of both the 238 MHz pre-buncher
and 476 MHz booster. By analyzing the data, the virtual
beam source was thus determined for the prototype
accelerator.
(2) Suppression of slice emittance growth by overbunching: RF voltage and phase were calibrated and set
based on the real beam response for the pre-buncher,booster and S-band accelerators. As the beam response,
dependences of the bunch compression on these twoparameters were measured. The measurements were
performed with the developed microwave spectrometerand the detection system combining the wide frequency
band diode detector [13] with a high-pass mesh filter. For

772

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THCAU02

Fig. 5: Schematic drawing of SCSS prototype accelerator.
the crest phase detection, we used the following threemethods depending on the condition; beam induced field
method [14], the method based on the maximum beamtransmission and the method based on the maximum
displacement at the dispersive section.
(3) Suppression of slice emittance growth by nonlinear
fields: Nonlinear fields at both fringes of the magnetic
lenses and RF cavities increase the slice emittance. To
suppress this growth, electron beam centering to eachdevice is important. We centered the beam on each device
by dithering, i.e., by observing the beam responses
against the current and acceleration phase modulation.
(4) Confirmation of slice emittance: Condition of thetransverse phase space was indirectly confirmed bycomparing the measured data with the simulated ones. For
the comparison, five beam profiles upstream of the Cband acceleration system and three kinds of projected
emittance were used.

EXPERIMENTAL RESULTS OBTAINEDAT SCSS PROTOTYPE ACCELERATORIn this section, we summarize the obtained results, i.e.,
the projected emittance, bunch length, dark current,
stability and electron beam brilliance.

Projected emittance
The projected emittance values were measured under
the following three conditions: (1) 500 keV beam with thepulse-width of 1nsec after the beam deflector (M2 in Fig.
5), (2) 50 MeV beam accelerated at the crest phase of the
S-band TWA tube (M6 in Fig. 5), and (3) 250 MeV beam
accelerated at the bunching phase (crest -30 deg.) of the
S-band TWA tube and at the crest phase of the C-band
TWA tubes (M9 in Fig. 5). The emittance of condition (1)was estimated from the beam size and angular divergencemeasured by the horizontal slit scan. On the other hand,the emittance of the conditions (2) and (3) were estimatedby a conventional Q-scan method. Table 2 lists the

FEL Technology

estimated emittance values together with the calculated
ones. The measured emittance of the long pulse beamemitted from the electron gun is also shown. Comparing
the emittance values with and without the deflector, we
see that the emittance growth by the deflector is not
significant. We also see that the estimated values havegood agreement with the calculation at the beam energyof 50 and 250 MeV.
Fig. 6 shows the beam size dependences obtained by
the Q-scan method at the beam energy of 50 MeV. Eachpoint represents the average of 10 data. The solid anddashed lines represent the fitting curves of which form isdetermined by linear beam theory. Since scattering of 10
data is smaller than the radius of the plotted circles, it wasneglected in the figure. The error bar represents 1σ of a
fitting error. We see that the all data points over the wide
range of the focusing strength are well fitted by theparabolic curve. These facts show that the electron beamis stable enough for this kind of measurement.

Bunch length
Bunch length was measured with a femto-second streak
camera (Hamamatsu Photonics FESCA-200, temporal
resolution of 200 fs). Cherenkov radiation from conicallyshaped BK7 glass was observed for the 41MeV electron
beam and optical transition radiation (OTR) from an Au

Table 2: Estimation of normalized emittanceBeam Energy[MeV]
0.5(bef.deflector)

Norm.Emittance(εx, εy)[πmm.mrad](0.6, -)

Calculation(εx, εy)[πmm.mrad]-0.5(aft.deflector)
50
250(1, -)(3, 3)(4, 2)(2.8, 2.6)
(2.3, 2.3)773

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Proceedings of FEL 2006, BESSY, Berlin, Germany
projected to the horizontal plane is then observed withOTR from the Au thin film located in the middle of thechicane (M8 in Fig. 5). The linear dispersion at the OTR
screen is about 150 mm. Figure 7 shows the measured
density profiles under three different operating conditionsof the second C-band unit, i.e., RF turned off and at the
crest ± 90 deg. accelerating phase. By using the RFparameters and dispersion value, the full pulse width isestimated to be about 1.1 ps, which agrees well with thesimulation.

Dark current
When the deflector is switched on, dark current
downstream of the pre-buncher is invisible on a
fluorescence screen of M1 in Fig. 5. It is true that the darkcurrent from the electron gun is negligible for any beamtuning. Quantitative measurements are planned in next
operation period after the summer shutdown.
Fig. 6: Measured data by the Q-scan method at thebeam energy of 50 MeV.
thin film was observed for the 250 MeV electron beam.
The results are 5 psec (41 MeV) and 2 psec (250 MeV) in
1σ, which are much larger than the simulated bunch
length of 1 psec. As causes of this discrepancy, we
presently predict that the transverse beam size enlarges
the pulse length of Cherenkov radiation. And also, in
respect to measurement with OTR, we doubt that the
optics including streak camera system enlarges the pulse
length.
We measured bunch length with another method, where
the pulse length of beam is converted to a systematicenergy chirp by using a RF field gradient [15]. In our case,the second C-band acceleration unit (C-TWA#2 in Fig. 5)
is operated at a zero-crossing phase to generate asystematic energy chirp. Beam density distribution

Fig. 7: Measured beam density profile projected on thehorizontal plane with three different operating conditions.

774

Stability
Long-term stability of the electron beam or the
prototype accelerator is the following. The standard
SASE lasing is basically reproduced by reloading thenominal parameter set of the magnets and RF systems. At
present, the SCSS prototype accelerator has not been
operated continuously over a long period, but operated
day by day. In 2 to 3 hr after the operation starts in themorning, we suffer the slow drifts of some parameterssuch as the high voltage of the electron gun, etc, which isso far adjusted manually. Introduction of slow feedback
controls is thus under investigation.
With respect to short-term stability of the electron beam,
the stability of the beam energy is 0.37 % in full-width
downstream of the second C-band acceleration unit. Thiswas estimated by using the shot-by-shot fluctuation of thehorizontal position at M8 in Fig. 5. The beam orbit
stability was measured by using the beam position
monitor (BPM) [16] at the entrance of the first undulator,
where no linear dispersion exists in the design. The
horizontal and vertical orbit stabilities at this position are
13 and 21 µm in 1σ, respectively. These values are
smaller than a fifth of the beam size.
With respect to lasing stability, the peak performance
has not been achieved routinely. In order to maximize thelaser amplification, slight tuning is needed for the prebuncher phase, S-band TWA phase, position and width of
the slits, S4 and S6 in Fig. 5. Figure 8 shows the shot-byshot lasing stability measured by the photodiode(International Radiation Detectors Inc. SXUV100) in the
VUV beamline [17]. The energy per pulse was measured
by integrating the photogenerated charge of thephotodiode. The lasing wavelength is about 60 nm andthe repetition rate was 5 Hz. The data however were taken
asynchronously at 3 Hz due to the reading speed of thetemporary data acquisition system. We see that relatively
strong lasing occurred in all shots over the period of
measurement without any feedback correction.

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

Fig. 8: Shot-by-shot stability of lasing. The beam energy is 250 MeV and the undulator gap is 3 mm.

Electron beam brilliance
Effective electron beam brilliance, the ratio of a peakcurrent to 4-dimensional transverse phase space volume,is estimated by the following two approaches. One is toreproduce the measured dependence of the laser
amplification on the peak current by using the 1-D model[18]. The other is to reproduce the measured dependenceof the laser amplification on the K-value by using the 3-D
simulation code, SIMPLEX [19].
(1) Estimation with 1-D model: The bunch current wascontrolled with the slit S4 in Fig. 5. Through the bunch
length measurement with a systematic energy chirp, we
confirmed that the local density peak in the bunch
depends on the slit width of S4. Figure 9 shows thedependence measured by the photodiode in the VUVbeamline. The filled circles and error bars represent the
average and 1σ of 100 data, respectively. In thismeasurement, the gaps of both undulators were closed to
4 mm and the beam energy was accelerated up to thenominal energy, 250 MeV. Hence, the lasing wavelengthis 49nm.
In the 1-D model, the total radiation intensity I iswritten by the sum of the spontaneous radiation intensity
IN and coherent radiation intensity IL as

I = I L + I N = I L 0 exp( z / L1G ) + I N ,!

Here, εns and Ip represent the normalized slice emittanceand peak current, respectively. βx and βy are thehorizontal and vertical betatron functions, respectively.
The bracket < > represents the average of the insideparameter over the undulator length. First we determined
the betatron functions experimentally. Then, we fitted theexperimental data by using H as only a parameter inconsideration with the dependence of Eq. (2) and (3) on
the beam charge. The solid line in Fig. 9 shows the result,which agrees well with the experimental data. The ratio of
Ip to εns, namely H is estimated to be 480 A/πmm⋅mrad.
Assuming that εns is the design value, 2 πmm⋅mrad, theelectron beam brilliance becomes 240 A/π2mm2⋅mrad2.
(2) Estimation with 3-D model: Fixing the electron
beam condition, we measured the dependence of theangular photon flux density on the K-value by changing
the gap of the first undulator only. To extract the core
photon beam, the horizontal acceptance was limited
within ±100µm from the beam center by using thehorizontal slit in the VUV beamline. Then, thehorizontally narrow beam was monochromatized anddetected by the CCD camera [17]. We further set a small
window on the CCD image for limiting the bandwidth
and the vertical acceptance. The angular photon flux
density was finally obtained by integrating the intensities
in the window. Figure 10 shows the measured dependenceof the angular flux density on the K-value with the filled
circles. Each data was taken by the integration time of
10sec, i.e., the integration of 50 data. The vertical axis
represents the ratio of the flux density to that of the
spontaneous radiation. The spontaneous radiation data
were measured for each K-value by operating S-band
TWA at the de-bunching phase.
Assuming that the normalized slice emittance andmomentum spread are the design values, 2 πmm.mrad
and 0.1 % (1σ), respectively, we simulated the(2)where z and L1G represent the total length of theundulators and the 1-D gain length, respectively.
Assuming that the horizontal normalized slice emittanceis the same as the vertical one, L1G is expressed by using
the beam parameters as

L1G =

150.2
1/ 3

&
#
H
(
%
% " 1/ 2 " 1/ 2 (y'$ x

FEL Technology!

THCAU02

,H=

Ip

) ns

.

(3)
Fig. 9: Dependence of laser amplification on the beam
charge.

775

THCAU02

Proceedings of FEL 2006, BESSY, Berlin, Germany

REFERENCES

Fig. 10: Dependence of laser amplification on the
K-value.
dependence on the K-value with SIMPLEX. Here, thepeak current was used as a parameter. The solid lines inFig. 10 show the results. By comparing the simulation andexperimental data, we see that the experimental data
locate between the two lines obtained with 1070A and
1250A. The electron beam brilliance is estimated to be
270 ~ 310 A/π2mm2⋅mrad2.

SUMMARY
The SCSS injector system was designed to achieve thestable and flexible beam operation satisfying the highbeam quality required for SASE-based x-ray FEL. On theother hand, our design needs the bunch compression ofrelatively long electron beam in a low energy regime
ranging from 500 keV to a few MeV, with suppressing
the emittance growth due to a space charge force and nonlinearity. This is quite challenging and there remains thequestion whether "emittance conservation" through theinjector is a sufficient level or not under the practicalerror condition. To confirm beam performance of theinjector, the SCSS prototype accelerator was constructed.
Owing to careful beam tuning based on the emittanceconservation, SASE lasing in the wavelength ranging
from 40 to 60nm has been stably obtained at the SCSS
prototype accelerator. We analysed the reproducible
SASE lasing data by the 1-D model and 3-D simulator.
As a result, we found that electron beam brilliance isestimated to satisfy the design target, 200A/π2mm2⋅mrad2.
This experimental result shows that PARMELA gives agood design guideline in our case and concludes that thebeam performance for x-ray FEL is reachable by thesmooth extension of the prototype accelerator.

776[1] T. Shintake et al., “SPring-8 Compact SASE Source(SCSS)”, SPIE, Optics for Fourth-Generation X-Ray
Sources, Bellingham, August 2001, p. 12.
[2] ”SCSS X-FEL Conceptual Design Report”,
RIKEN/SPring-8, May 2005, Mikazuki, Japan,
http://wwwxfel.spring8.or.jp/.
[3] T. Shintake, “Status of the SCSS Test Accelerator
and XFEL Project in Japan”, EPAC’06, Edinburgh,
June
2006,
p.
2741;
http://wwwxfel.spring8.or.jp/fist_lasing/FirstLasingofSCSS.html.
[4] “Linac Coherent Light Source (LCLS) Conceptual
Design Report”, SLAC-R-593, April 2002.
[5] “TESLA Technical Design Report, PART V, The Xray Free Electron Laser”, ed. G. Materlik and Th.
Tschentscher, March 2001.
[6] K. Togawa et al., “CeB6 Electron Gun for the Soft Xray FEL Project at SPring-8”, NIMA, 528 (2004) 312.
[7] K. Togawa et al., “Emittance Measurement on the
CeB6 Electron Gun for the SPring-8 Compact SASE
Source”, FEL’04, Trieste, August 2004, p.351.
[8] M. Reiser, “Theory and Design of Charged Particle
Beams”, John Wiley & Sons, Inc., New York, 1994,
p. 210.
[9] T. Shintake et al., "HOM-Free Linear Accelerating
Structure for e+e- Linear Collider at C-band",
PAC’95, Dallas, May 1995, p. 649.
[10] T. Sugimura et. al, “SKIP–A Pulse Compressor for
SuperKEKB”, LINAC’04, Lübeck, August 2004,
p.754 (2004).
[11] T. Shintake et al., “A New RF Pulse-Compressor
Using Multi-Cell Coupled-Cavity System”, EPAC’96,
Sitges, June 1996, p. 2146.
[12] T. Tanaka et al., “Development of the short-period
undulator for the X-ray FEL project at SPring-8”,
SRI’03, San Francisco, August 2003, p. 227.
[13] International Radiation Detector Inc., http://www.irdinc.com/.
[14] R. B. Neal, “The Stanford Two-Mile Accelerator-I”,
W. A. Benjamin, Inc., New York, 1968, p.383.
[15] L. Rivkin et al., “Bunch Lengthening in the SLC
Damping Ring”, EPAC’88, Rome, June 1988, p.634.
[16] T. Shintake, “Development of Nanometer Resolution
RF-BPMs”, HEACC’98, Dubna, October 1998,
http://lcdev.kek.jp/Conf/HEACC98/133.PDF .
[17] M. Yabashi et al., in these proceedings.
[18]R. Bonifacio et al., “Collective Instabilities and HighGain Regime in a Free Electron Laser”, Opt.
Commun., 50 (1984) 373.
[19] SIMPLEX was developed by Takashi Tanaka(RIKEN/SPring-8),
http://radiant.harima.riken.
jp/simplex/.

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THCAU03

Operational Experience with the Emittance-Meter at SPARC∗
L. Catani† , A. Cianchi, INFN-Roma Tor Vergata, Roma, Italy
C. Ronsivalle, ENEA C.R. Frascati, Roma, Italy
P. Musumeci, M. Petrarca, INFN-Roma, Roma, Italy
M. Bellaveglia, R. Boni, M. Boscolo, M. Castellano, E. Chiadroni, L. Cultrera,
G. Di Pirro, A. Drago, M. Ferrario, D. Filippetto, V. Fusco, A. Gallo, G. Gatti,
F. Tazzioli, C. Vaccarezza, M. Vescovi, C. Vicario, INFN-LNF, Frascati, Roma, Italy
M. Migliorati, L. Palumbo, University La Sapienza, Roma, Italy.
Abstract
We report the operational experience of the movable
emittance meter at SPARC. It is based on the well-known
technique of pepper pot measurements (1-D slits in ourcase) but, in addition, it allows moving the measuring device along the beam line from about 840 mm to 2200
mm from the cathode, following the emittance oscillations. More than a simple improvement over conventional,
though non-trivial, beam diagnostic tools this device defines a new strategy for the characterization of high performance photo-injectors, providing a tool for detailed analysis of the beam dynamics, over a section of the accelerator
where emittance compensation take place. With this device
we planned to perform detailed and systematic studies on
beam dynamics with particular attention to the transverse
parameters as well as longitudinal.

INTRODUCTION
The aim of the SPARC [1] project is to promote R&D
towards high brightness photo-injectors to drive a SASEFEL experiment. The 150 MeV SPARC photo-injector
consists of a 1.6 cell RF gun operated at S-band (2.856
GHz, of the BNL/UCLA/SLAC type) and high-peak fieldon the cathode incorporated metallic photo-cathode of 120
MV/m, generating a 5.6 MeV, 100 A (1 nC, 10 ps) beam.
The beam is then focused and matched into 3 SLAC-type
accelerating sections, which boost its energy to 150-200
MeV. The first phase of the SPARC Project was dedicatedto the beam RMS emittance measurement along the drift
space following the RF gun, where the emittance compensation process occurs.
The complete characterization of the beam parameters
at different distances from the cathode is important to define the injector settings optimizing emittance compensation and for code validation. For this measurement, a dedicated moveable (in z, z being the distance from the cathode, measured along the accelerator axis) emittance measurement device [3] (emittance-meter) is used allowing tomeasure the RMS emittance in the range from about z=86
cm to z=210 cm.
∗ This work has been partially supported by the EU Commission in thesixth framework program, contract no. 011935 EUROFEL-DS1.
† luciano.catani@roma2.infn.it

FEL Technology

1 - upstream long bellow
2 - vertical and horizontal multi-slit masks actuators
3 - intermediate bellow
4 - CCD camera
2
5 - Ce:YAG screen actuator
4
6 - downstream long bellow
5
7 - alignment tool2
8 - steering coil holder
9 - leg extender
8

7

6

1

beam
3

9

Figure 1: 3D mechanical drawing of the SPARC emittancemeter
The technique to measure the beam emittance and thephase space, in both the horizontal and vertical planes,
makes use of a double system of horizontal and verticalslit masks [2]. Each mask consists of a slits array (7 slits,
50 µm width spaced of 500 µm, 2 mm thick) and two single slits, 50 and 100 µm width. The slits are realized byphoto-chemical etching providing, compared to mechanical machining, higher precision and improved smoothnessof slits edges. The multislits are used for single shot measurements, provided the beam size is large enough for anadequate beam sampling by the slit array. Alternatively,a single slit can be moved across the beam spot. In thiscase the accuracy of transverse sampling can be freely chosen adjusting the step between the different positions of theslit. This measurement is an integration over many pulses.
Linear actuators with stepper motors are used to control
the insertion of the slits masks into the beamline. A differential encoder and a reference end switch guarantee reproducibility and accuracy of the movement to better than 2µm, required for single-slit multi-shots measurements.
The projected cross-section of beamlets emerging fromthe slit-mask are measured by means of a downstream

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Ce:YAG radiator. Because beam size and divergence depend on the longitudinal position, the slit to screen distancemust be properly adjusted in order to optimize the accuracyof the beamlets profile measurement as the movable deviceis placed at different z. A bellow is therefore interposed
between the slit mask and the screen, allowing their relative distance to be changed while keeping the masks at a
fixed position with respect to the gun. This solution allows
to set the length of drift between slit mask and the screenthat best fits the different scenarios: converging beam, diverging beam, single or multi-slits. Refer to Fig.1 for aschematic drawing of the emittance meter.
Radiation emitted in the forward direction from theCe:YAG crystal is collected by a 45 degrees mirror downstream from the radiator. The back face of the transparent
crystal radiator is observed, thus minimizing degradation of
the spatial resolution due to the depth of field of the optics.
Beam images are acquired using digital CCD cameras
equipped with a 105mm ”macro” type objective. The magnification of 0.66 gives a resolution of 15.4 µm per pixel.
Beam charge is measured by means of a Faraday cup,
placed in a cross together with a chrome-oxide screen to
image the beam at 60 cm from the cathode. This screen
is also used to monitor the position of the laser spot on
the cathode. The emittance-meter is followed by a magnetic spectrometer measuring the beam energy and energy
spreadDETAILS ON MEASUREMENTS WITH
THE MOVABLE EMITTANCE-METER
The movable emittance-meter was built to perform a detailed characterization of the SPARC photo-injector studying the beam dynamics as function of relevant parameterssuch as the solenoid field, the beam charge and size, thelaser pulse length and its shape. Refer to [4] for more details.

Beam Envelope
Evolution of the bunch transverse size along the photoinjector is a important, though simple, measurement weregularly perform with the emittance-meter. It takes lessthan 5 minutes to complete the measurement consisting ofcontinuously changing the z-position of the movable system between the upper and lower ends to grabb beam images at various position. These images are on-line processed to filter out the background noise and to calculate
the RMS value of the beam size. In Fig.2 are shown resultsof measurements of the RMS beam size vs z for different
values of the solenoid field at the gun. The measurement
procedure is a completely automatic one-click operation of
the control system.
At a glance we can guess the solenoid current that gives
the waist in the required z position or, by comparing x andy envelopes curves, check for the causes that might produce beam envelope irregularities, laser or solenoid mis-

778

1800

185 A
188 A
191 A

1600

X-envelope RMS (µm)

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1400
1200
1000
800
600
400
200
0
1000

1200

1400

1600

1800

2000

2200

Figure 2: Envelope of the beam (x-plane) along z for different solenoid currentsalignment for instance. The different curves in Fig.2 show
how the beam waist and its position in z are changed asconsequence of the different solenoid currents.

Emittance
The emittance can be measured, in both x and y planes,at different positions along the emittance-meter. The beam
size and its divergence are expected to change as the distance from the cathode changes: the beam is converging
at the beginning of the emittance-meter and diverging inthe second half. Different measurement strategies are thenimplemented to achieve the best accuracy of the emittancecalculation algorithm.
When the beam is close to the waist, its size is small
and the multi-slits mask is not suited because it produces
a limited number of beamlets. The single-slits multi-shotmeasurement is also preferable in the region close to theend of the emittance-meter where the beam size is typicallylarger than the part of the mask covered by the slit-array
and when the beam is strongly converging because profilesof beamlets produced by the multi-slits mask might overlap. Typical values of the sampling distance between theslit positions ranges from 110 µm to 380 µm. At least nine
beamlets are always collected with the single slit. In allof the other conditions the multi-slits mask provides fast
single-shot measurements, while the single-slit is preferred
for accurate analysis.
It’s worth mentioning that, for given beam conditions,
results produced by both single-slit and multi-slit measurement have always been fully consistent. A simple
check of results produced by the emittance calculation algorithm consists in comparing the RMS beam size at theslit-mask (measured by moving the screen at the longitudinal position of the slit-mask during emittance measurement) against the value of beam size estimated by the emittance calculation algorithm. We always obtained an excellent agreement between the two results.

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Proceedings of FEL 2006, BESSY, Berlin, Germany
Fig.3 shows an example of emittance measurements at
different positions along the emittance-meter. In this casethe beam charge was 700 pC and the energy 5.14 MeV witha longitudinal profile σ= 4.35 psec.
A typical emittance measurement with the single-slit
mask consists of collecting 15 beam images for each slit
position. The center of mass and RMS size of beamlets arecalculated for each image and averaged. We verified thatlarger statistic doesn’t significantly improve the accuracyof results. In details, from each beamlets image we calculate the projection on the axis, subtract the baseline, try agaussian fit to find the best position for the center of intensity distribution, reduce the number of the relevant points
skipping these that are outside the 3 standard deviations
from the centre and only on the remaining points we calculate the RMS parameters.

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ferences from that in a linear optics crossover. In a ”standard” drift the particles being on the left (negative x) moveto the right crossing the origin thus following the lines of
motion of constant x. Here the particles that are on left at
the beginning of the beamline stay on the left. They getclose to the origin (both in x and x’) without crossing it andafter the laminar space charge dominated waist they moveback (still negative x) changing the sign of their divergence.

6(mm-mrad)5

4

3

Figure 4: Phase space measure along the e-meter
EmittXn - computed
EmittYn - computed
EmittXn - measured
EmittYn - measured

2

1

40

60

80

100

subsectionBeam energy and energy spread
The e-meter gives also the possibility to investigate thelongitudinal dynamics and correlation between transverseand longitudinal planes.
120
140
Z(cm)

160

180

200

5,50
Average beamlet Energy vs. X
Average beamlet Energy vs. Y

Figure 3: Emittance measurements along the e-meterTransverse phase space
The measurement of RMS Twiss parameters and emittance with the single-slit mask allow, as a side-product, thereconstruction of the beam transverse phase space [5]. For
each slit position, the beamlet profile on the screen yelds
the divergence distribution of particles at the given x position, i.e. those emerging from the slit-mask. Interpolationof the different profiles produces the two dimensional x x’ distribution.
In Fig.4 we show the phase-space measured at different
positions along the emittance-meter for a low charge (100pC) beam. Clearly the beam is going through a focus evolving from convergent to divergent. On the other hand, as thephotoinjector theory predicts, the evolution has many dif-

FEL Technology

5,45Energy (MeV)

The high magnification optical system, the high efficiency YAG screen and a CCD with a remotely controlled
gain always provide a good signal to noise ratio and large
number of sampling point for every beamlet in all the conditions.

5,40

5,35

5,30

5,25
-35

-25

-15

-5

5

15

slit position (ksteps)

25

35

Figure 5: Beamlet energy vs transverse position
Moving the x or y single-slit across the beam and measuring the energy at the spectrometer gives evidence of a
possible correlation between particles transverse position
and their energy. The measurements in Fig.5 show a varia-

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tion of beamlets mean energy when the position of the vertical single-slit is changed moving it across the beam in thehorizontal direction. The correlation, clearly stronger in thex-direction, suggest as possible cause the non-normal incidence of the laser beam on the cathode in the y=0 plane.
As a final example of the extended diagnostic capabilities of the emittance-meter we report in Fig.6 the evolutionof the energy spread measured for the central beamlet (i.e.
with the vertical single-slit centered on the beam center ofmass) as function of the position along z of the slit mask.
Note that all the points in the graph, except the last one
representing the energy spread of the whole beam obtained
removing the slit-mask from the beam path, correspondto positions within the high impedance bellows. Inside
the long bellows the wakefields contribution to the energy
spread adds to the longitudinal space charge effect and theenergy spread grows faster. These effects significantly contribute to the energy spread up to the slit-mask while for the
low charge beamlet the wakefields and space charge effectare practically negligible. As consequence an increasingenergy spread is expected as the distance of the slit-mask
from the cathode became larger. It is clearly confirmed by
the measurements.

that can be checked against those predicted by simulation
codes. Unfortunately, the changing of a set-point is often
hindering a cross-talk between different simulation parameters which so far has been taken into account somewhat
externally (for example varying the gun phase affects theextracted charge, and varying the solenoid strength changes
the quadrupole component effect).
The clear advantage in characterizing a photo-injector with
the SPARC movable emittance-meter is that once the working point is set, a single simulation run generates results
which reproduce the evolution of the experimental data
(beamsize, emittance, energy spread) taken with the movable measurement device at the different positions along
the beamline. In other words a single simulation run can bechecked against a number of experimental points, not justa single one, all representing, or measured with, the same
identical photo-injector working point.
Further work, more detailed and accurate measurements,
is foreseen in order to approach such ambitious goal, fully
understand the system, and validate the prediction capabilities of the modeling codes.

REFERENCES[1] D. Alesini et al., Nucl. Instr. & Meth. In Phys. Res. A 507(2003) 345-349C.
[2] M. Zhang, FERMILAB-TM-1988, Oct 1996.
[3] L.Catani et.al., Rev. Sci. Instrum. 77, 093301 (2006).
[4] M. Bellaveglia ”Commissioning of SPARC Photoinjector”,
these Proceedings.
[5] S. G. Anderson et al. ”Space-charge effects in high brightness electron beam emittance measurements”, Phys. Rev. ST
Accel. Beams 5, 014201 (2002).

Figure 6: Contribution of bellows to energy spread is evidenced selecting a small portion of the beam with the singlslit mask and moving it at different Z.

CONCLUSION
The final task of the SPARC photo-injector commissioning is to provide a complete sets of measurements (including transverse and longitudinal profiles of the laser) allowing a complete characterization of the beam dynamics byfollowing the evolution of all the beam parameters.
As it appears from the previous paragraphs, beam dynamics in a photo-injector is a non trivial problem that criticallydepends on many variables. In systems equipped with asingle (at a given longitudinal position) emittance diagnostic station, beamline parameters like solenoid strength orlaser launching phase are varied to obtain emittance values

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HIGH CURRENT ELECTRON EMISSION FROM MICROSCOPIC TIPS
R. Ganter, R.J. Bakker, M. Dehler, J. Gobrecht, C. Gough, E. Kirk, S.C. Leemann, K. Li, M.
Paraliev, M. Pedrozzi, F. Le Pimpec, J.-Y. Raguin, L. Rivkin, V. Schlott, H. Sehr, S. Tsujino,
A. Wrulich, Paul Scherrer Institut, Villigen CH 5232, Switzerland.
Abstract
In order to find electron sources with low intrinsic
emittance (< 5.10-8 m.rad) and high brigthness (B >5.1013A.m-2.rad-2), single tip field emitter as well as Field
Emitter Arrays (FEAs) are investigated. By field emission
very high current densities can be obtained (up to
1012A.m-2) from extremely small source sizes.
Illumination of such field emitting sources by laser pulses(photo-field emission) gives in addition the possibility to
pre-bunch the emission to very short pulse lengths.
Maximum peak currents, measured from single tips ofZrC with a typical apex radius around one micrometer arepresented. Voltage pulses of two nanoseconds duration
and up to 50 kilovolts amplitude lead to field emission
currents of several hundreds of milliamperes. By
combining these electrical pulses with laser pulses, peakcurrents of several amperes were extracted from the tip
apex. This high current emission mode is different fromfield emission or photo-field emission and has many
similarities with the so-called explosive electron
emission.

INTRODUCTION
Reducing the beam emittance while keeping highbrightness is the most direct way to reduce cost and sizeof Free Electron Lasers (FELs). In linear accelerators, theparameters of the accelerated beam depend strongly on
the performances of the electron gun. The beam emittancein the electron gun is ultimately limited by the intrinsic
emittance at the electron source which can be expressed
as follow [1,2]:R 2 E kin
ε n ,rms =2 3mc 2(1)
where R is the beam radius in the case of a uniform radial
distribution and Ekin is the mean transverse kinetic energyof emitted electrons (Maxwell energy distribution), m isthe electron mass and c the speed of light. In order toreduce the thermal emittance one can either reduce thebeam size (R) and/or the mean transverse kinetic energies(Ekin) of produced electrons. Field emitter arrays should
be capable of producing electron beams with extremely
low transverse kinetic energy due to a focusing electrodepositioned just one micrometer after the emitting point [35]. A single tip electron source should also produce low
emittance beam because of the extremely small emittingarea (<1μm2) [6]. Indeed, current densities as high as 1012
A.m-2 can be achieved by field emission [7]. In practice,
the strong dependence of the field emitted current on thelocal field enhancement factor (down to nanometric scale)and on the local work function (which depends on

FEL Technology

contaminants, crystal orientation) makes this emission
very difficult to control (breakdowns) and to stabilize(fluctuations). Laser illumination of field emission
electron sources gave encouraging results in stabilisingand increasing the total current emission [8]. If the regimeof emission is dominated by photo-field emission, it
should become possible to pre-bunch the emission down
to 10-30ps with picosecond lasers while keeping highcurrent densities.

LOW EMITTANCE GUN PROJECT
The goal of the Low Emittance Gun (LEG) Project [9]at Paul Scherrer Institute (PSI) is to produce electron
bunches of 15ps rms duration with a normalized
transverse emittance of 5.10-8m.rad and a minimum peakcurrent of 5.5A at an energy of 4 MeV (see also
companion paper [10]). The requirement in peak current
is already quite challenging for both FEAs and single tip
cathodes. Furthermore, if the electron source is capable ofreaching the targeted emittance then the acceleration ofsuch a beam into the relativistic regime without emittanceblow up remains very difficult. The LEG concept will
combine diode and RF acceleration. A few millimeters
gap will separate the electron source from the first radio
frequency (RF) cavity. Voltage pulses of 0.5MV and
250ns duration will be applied across this diode gap at arepetition rate of 10Hz. The resulting high accelerating
gradient should minimize the emittance growth caused by
space charge forces. Comissioning of this high voltage
pulser is under way at PSI [9]. After the diode gap theelectron beam will enter the RF cavities. A twofrequencies RF cavity (1.5GHz and 4.5GHz) has been
designed in order to obtain flat top acceleration waves
which minimize the emittance dilution due to RF
acceleration [11].

Figure 1: Field Emitter Array produced at PSI andsingle tip of ZrC from AP Tech Inc. .

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The maximum peak current reached with commercial
FEAs [12] was around 120 mA [8] for a one millimeter
diameter array with 50000 tips. The main limitation
comes from the non uniformity of the emission from tip
to tip. The intrisic emittance of the same commercial
single gated FEAs (no focusing grid) has recently beenmeasured to be around 2.10-6m.rad [13] for a one
millimeter diameter cathode. Performances achieved withcommercially available FEAs enabled us to better define
the ideal FEA for LEG. PSI is currently developping an
own production of FEAs based on a self aligned moulding
technique. With this technology, pyramid shaped tips canbe produced (see Fig. 1) which should better dissipate theheat and thus be able to carry more current. Since FEAs
are still under development at PSI the rest of the paper
will focus on single tip electron sources.
Single tips are produced by etching a wire which isthen inserted in a so called Vogel mounting (see Fig. 1).
This mounting allows current circulation and thus tip
flash heating as well as field forming [14] of the apex.
Metal carbides, like ZrC, are conductors with lower work
functions (~ 3.5 eV) than commonly used W or Mo
surfaces [15]. ZrC surfaces are also known to be moreresistant against sputter damage and the threshold
temperature for surface migration (~ 1500 K) is higher
than for W or Mo surfaces [16]. We used commerciallyavailable ZrC tips from APTech Inc. [17] (McMinnville,
USA). Field emission is always localised to small surface
imperfections which have a smaller work function and /or a more favorable geometry for field enhancement sothat current density goes rapidly to values as high as 1012
A/m2 [7]. The consequence is a fast local heat up with anincreased risk for a vacuum arc. The best way to limit theheat up is to emit during very short pulses and at low
repetition rates. Nanosecond voltage pulses were applied
to a ZrC tip in order to increase the emission current.

EXPERIMENTAL SETUP
Fig. 2 represents the experimental setup used tomeasure the emitted current from single tips of ZrC [17].
A fast pulser from the company FID GmbH delivering
pulses up to 100 kV in amplitude and with 2ns duration(FWHM) at 10 Hz was connected to the tip. A special
broad bandwidth (up to 1 GHz) coaxial vacuum
feedthrough has been designed to feed the ZrC tip. The tip
has a fairly large apex radius (r ~ 1 μm) and is positioned
1 mm behind an aluminium gate electrode (see inset in
Fig. 2). The gate has a 2 mm diameter hole and isgrounded. The faraday cup is also grounded and about 5
mm away from the tip apex on the same axis.

Figure 2: Experimental setup for pulsed field emission
and photo-field emission tests.
Field emitted current starts to be detected at voltages
around 20 kV (Fig. 3); peak currents as high as 460 mA
were measured for applied voltages around 50kV. At thislevel of current, amplitude fluctuations became relevant(as illustrated by the two pulses at 51kV on Fig.3, left
graph) and a monotonic decay of the amplitude wasobserved. Fluctuations usually indicate that the surface
temperature became high enough to activate surface
migration of contaminants which in turn change the fieldemission properties. At lower currents (Fig. 3, rightgraph), the emission was more stable and the current voltage characteristics could be measured. These
measurements are also represented in a Fowler-Nordheim(F-N) plot (Fig. 4, right graph). From the F-N plots, one
can estimate the field enhancement factor β as well as theemitting area [18,19]. The local electric field Floc at the tip
apex is then defined as Floc= β.VTip. A linear fit (see Fig.
4) of measured values gives β ~2.105 m-1 and an emittingarea around S ~104 nm2 (assuming a work function of
3.5eV for ZrC). This is consistent with a tip radius of 1
μm. With such a small emitting area and if we assume adivergence of sixty degrees [20] a rough estimate gives anormalized emittance less than 5.10-8m.rad and a beam
brightness around: B ~1013 A.m-2.rad-2.

FIELD EMISSION FROM SINGLE TIPS
Fig. 3 represents the current pulses collected by the
faraday cup when voltage pulses of amplitude VTip wereapplied to the tip.

782

Figure 3: Current pulses collected on the faraday cup
for different voltage pulse amplitudes VTip.

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Figure 4: Current voltage characteristics acquired at 5
min interval (left) and Fowler-Nordheim representation of
the same curves (right).
With the use of short (2ns) high voltage pulses at low
repetition rate, it has been possible to limit the heat up of
the tip and to increase the current that can be extracted
from a ZrC tip up to 470 mA. For comparison, with a DC
electric field, only currents below 10 μA could be safely
extracted. However, these high current field emitted
pulses revealed strong fluctuations in amplitude. The
illumination of the tip with picosecond laser pulses should
help to increase the stability and to reach higher peakcurrents.

LASER ASSISTED ELECTRON EMISSION
Laser assisted field emission [21] [22] is an interesting
approach to combine the advantage of field emission(high brigthness) and laser photo-emission (stability, shorttime modulation). In the photo-field emission regime, thehigh electric field around the apex lowers the potential
barrier of the crystal so that photoemission with large
wavelength (λ>532nm) becomes possible and efficient. In
previous experiments, similar ZrC tips were illuminatedby laser pulses while a DC electric field was applied [8].
Peak currents as high as 580 mA were reached with 10ns
long laser pulses of 532nm wavelength. Shorter laser
pulses of 1ns (FWHM) at 1064nm produced photo-fieldcurrent pulses of similar duration [23] suggesting thepossibilty to pre-bunch the emission to even shorter
levels. In consequence, we recently combined the voltage
pulser presented in the first part of the paper with apicosecond laser from the company Time Bandwith
Products (see Fig. 2).
The laser system provides 30 ps long laser pulses at
532 nm with a maximum energy per pulse of 40 μJ. The
laser was focused on the tip apex with a lens positioned at
the focal distance (200 mm) from the tip outside thevacuum chamber. Nanosecond voltage pulses wereapplied to a ZrC tip while laser pulses were illuminating
the tip apex at a repetition rate of 10Hz. If emission isdominated by photo-field emission then the expectedcurrent pulse should be as short as 30 ps (FWHM).
Unfortunately the bandwidth of our faraday cup (< 1GHz)
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limits the detection of such short current pulses. The
incident laser energy per pulse can be varied between 1
and 40μJ. At low laser energy (<5 μJ/pulse) no change
from the pure field emission mode was observed. Above
5 μJ, the current increased suddenly by one order ofmagnitude leading to the current pulses shown on Fig. 5.
Figure 5 represents the current pulses measured by the
faraday cup when laser pulses (532 nm, 20 μJ, 108-109
W.cm-2) were synchronised with the high voltage pulses
for different voltage amplitude VTip. The collected peakcurrent was as high as 5.5 A at a repetition rate of 10 Hz.
The shape of the current pulse follows the applied voltage
pulse (the satellite peak at t=3ns corresponds to a similarreflexion in the applied voltage). No significant jitter oramplitude variations were observed as it would be thecase for vacuum breakdowns. No decay of the amplitude
was observed after several hours of 10 Hz operation andpressure was stable around 10-8 mbar. This electron
emission was probably not resulting from photo-fieldemission since it was lasting several nanoseconds. The
dependence of the extracted current on laser energy (steplike dependence) indicates that there is a threshold above
which this large current emission is detected. This has
much in common with the so called explosive electron
emission (EEE) which is a kind of stable vacuum arc
regime. EEE has been largely described by Mesyats [24]and Fursey [7,25]. EEE takes place when a large amountof energy is concentrated into a small volume (by joule
effect or laser heating) which eventually explodes andgenerates a large flow of electrons together with otherparticles. The difference between this regime of EEE andnormal vacuum arcs is the very good reproducibility andstability of the process. The quasi-stationary behaviour isbased on the fact that at each explosion the surounding
surface melts and some new micro protrusions (andnearly identical) arise which serve as new emitting
centers.

Figure 5: Current collected on the faraday cup whenpicosecond laser pulses were synchronised (at t ~ -4ns)
with high voltage electrical pulses. One example of thevoltage applied to the tip is also represented.

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The current density during EEE can be extremely highusually above 1012 A.m-2 so that the size of the emitting
center is small (around 1 μm). Further tests are required tobetter understand and estimate the interest of these large
current pulses for a low emittance gun application.

CONCLUSION
Field emission naturally produces very large current
density beam so that good performances in terms of beamemittance and beam brightness can be expected from asingle tip. The consequence of large current density
emission is a high risk of overheating with generation of
vacuum arcs. For accelerator application field emission
sources must provide a minimum peak current of several
amperes. Pulsed field emission at low repetition rate
showed that larger peak currents (from 10 μA in DC toalmost 500 mA in pulsed mode) can be extracted from asingle tip of ZrC. In order to reach LEG goals, photo-fieldemission is an attractive mechanism which allows time
modulation with fast lasers. Preliminary tests ofillumination of a tip with picosecond laser pulses whilenanosecond voltage pulses are applied have been made.
An interesting regime of electron emission (similar to
explosive electron emission) delivering stable current
pulses of several amperes has been observed. Further tests
are still required to see if it has some relevance for a low
emittance gun application.

[14] B. Grishanov et al., Radiotekhnika i Elektronika
23, 575 (1978).
[15] W. A. Mackie et al., J. Vac. Sci. Technol. B 12,
722-726 (1994).
[16] F. M. Charbonnier et al., J. Vac. Sci. Technol. B
19, 1064-1072 (2001).
[17] http://www.a-p-tech.com/.
[18] W. Zhu, Vacuum Microelectronics (John Wiley& Sons, 2001).
[19] A. Brenac et al., Revue Phys. Appl. 22, 18191834 (1987).
[20] F. Charbonnier, Appl. Surf. Sci. 94/95, 26-43(1996).
[21] M. Boussoukaya et al., Nucl. Instr. and Meth. A
279, 405-409 (1989).
[22] C. H. Garcia et al., Nucl. Instr. and Meth. A 483,
273-276 (2002).
[23] R. Ganter et al., Nuclear Instruments andMethod in Physics Research A In Press (2006).
[24] G. A. Mesyats, Plasma Phys. Control. Fusion 47,
A109-a151 (2005).
[25] G. N. Fursey et al., Applied Surface Science
215, 286-290 (2003).

REFERENCES[1] S. Humphries, Charged Particle Beams (John
Wiley & Sons, 1990).
[2] J. E. Clendenin et al., NIM A 455, 198-201(2000).
[3] A. E. Candel, Ph. D. Thesis, ETHZ, 2005.
[4] A. E. Candel et al., Nuclear Instruments andMethod in Physics Research A 558, 154-158(2006).
[5] M. Dehler et al., J. Vac. Sci. Technol. B 24, 892897 (2006).
[6] V. M. Zhukov et al., Radioteckhnika ielektronika 10, 2153-2162 (1988).
[7] G. Fursey, Field Emission in Vacuum
Microelectronics (Plenum Publishers, New
York, 2005).
[8] R. Ganter et al., J. Vac. Sci. Technol. B 24, 974979 (2006).
[9] http://leg.web.psi.ch.
[10] R. J. Bakker, this Conference, 2006.
[11] J.-Y. Raguin et al., in Progress in the design of a
two-frequency RF cavity for an ultra-low
emittance pre-accelerated beam, Proceedings ofthe EPAC06 Conference, Edinburgh, Scotland,
2006.
[12] http://www.sri.com/psd/microsys/.
[13] S. C. Leemann et al., in First measurement
results at the LEG Project's 100 keV DC gun test
stand Proceedings of the EPAC06 Conference,
Edinburgh, Scotland, 2006.

784

FEL Technology

Proceedings of FEL 2006, BESSY, Berlin, Germany

FRAAU01

PHOTON OPTICS AT SCSS
M. Yabashi½ ¾ , T. Hirono½ ¾ , H. Kimura½ ¾ , H. Ohashi½ , S. Goto½ , S. Takahashi½ ¾ ,K. Tamasaku¾ , and T. Ishikawa½ ¾½
SPring-8/JASRI, Kouto 1-1-1, Sayo, Hyogo 671-5198, Japan¾
SPring-8/RIKEN, Kouto 1-1-1, Sayo, Hyogo 671-5148, Japan.
Abstract
Vacuum ultraviolet (VUV) optics for the SCSS Prototype Accelerator (electron beam energy ofMeV) and X-ray optics for SCSS ( GeV) are summarized. The VUV optics have been designed for the diagnostics of the photon-beam properties in order to optimize
the operation parameters of the accelerator. The systemcovers a radiation energy in the pulse from pJ to  Jin the visible to VUV range. The first results were obtained
during the commissioning period in the spring of 2006. In
the latter part, R&D for x-ray free-electron laser (XFEL)
optics at SPring-8 are introduced. Qualities of crystals,
mirrors, and windows have been improved for coherent xray applications.

VUV OPTICS FOR SCSS PROTOTYPEACCELERATORIntroduction
The SCSS Prototype Accelerator [1] has been constructed for investigating fundamental performance of theaccelerator system, which has been originally designed for
the Japanese XFEL project, SCSS [2]. The Prototype machine is composed of a thermionic electron gun [3], an
injector system, a main accelerator system with C-band
linacs, and a couple of undulators. The undulators (with aperiod of 15 mm, a total period number of 600, and a minimum gap of 3 mm) produce VUV radiation with a wavelength range shorter than 60 nm at an electron beam energyof 250 MeV. Strong SASE radiation is emitted with the optimized operation conditions.
The photon diagnostics system has been constructed forthe single-shot measurement of photon-beam properties
such as spectrum, radiation energy, spatial profile. These
parameters are crucial for studying accelerator conditions
and for tuning SASE amplification. The system covers awavelength range from visible (including a wavelength of
633 nm for the alignment with a He-Ne laser) to VUV light(  nm), and a radiation energy in the pulse from pJ(spontaneous radiation) to 10 J (SASE saturated radiation).
The system has been designed in the beginning of 2005,
and installed during the summer construction period. The
first beam of the visible light was observed in the end of
November. After the replacement of some optical components, the system has been dedicated for the VUV diagnostics in the commissioning period from May to July of
2006. In particular, the first lasing was observed in June,

X-ray Optics and Detectors

15th. After the first lasing, the beam tuning has been proceeded for optimizing SASE condition.

Design and Evaluation
General The schematic of the system is shown in
Fig. 1. The components are placed on two granite tables,
which are common designs to those used in the accelerator section. The beam pipes and components are evacuatedwith turbo-molecular pumps to a vacuum level of  
Pa. Since the average power of the incident radiation issmaller than 1 mW at a maximum, cooling for optical components is unnecessary. A plane mirror (Au coating on a
SiO substrate for VUV; Al coating on a SiO  substrate
for visible light) with a deflection angle of 170 Æ is placedat the downstream of the first table for eliminating highenergy bremsstrahlung. A dispersive spectrometer, whichis composed of an incident slit, a concave grating, and acharge-coupled device (CCD), is located in the second table. Several pneumatic actuators (indicated as monitors in
Fig. 1) are prepared for inserting detectors, screens, andoptical components in the beam path. At the upstream of
the first table, a CCD camera and a movable plane mirror
are installed for monitoring the He-Ne laser, which is usedboth for the alignment of the upstream components in theaccelerator section and for this optical system.
Spectrometer The spectrometer is designed in anormal-incidence, constant-deviation geometry. The radiusof the concave grating, the deflection angle, and the distance between the incident slit and the grating are  mm,  Æ , and    mm, respectively. The wavelength  focused in the center of the CCD is controlled bychanging the incident angle of the grating, , and the distance between the grating and the CCD,   , so as to satisfy
the following equations simultaneously,



and





            

(1)



(2)

where and are the diffraction order and the line density of the grating, respectively. Two laminar gratings (Shimadzu Corp., Al coating with 600 lines/mm; Au coating with 2400 lines/mm) are prepared for covering longer(  nm) and shorter (  nm) wavelength region,
respectively.
In the dispersed beam from the grating, different wavelengths are focused at different horizontal positions on the

785

SR

CCD

Distance from the 2nd undulator exit (m)56Concave grating

Monitor 3 (PD2)

Incident slit

Monitor 2

Plane Mirror

Pumping system

Monitor 1 (PD1)

Proceedings of FEL 2006, BESSY, Berlin, Germany

Alignment
mirror & CCD

FRAAU01

7

8

10

9

Figure 1: Layout of the optical system.

Intensity monitor Single-shot radiation intensities aremeasured with photodiodes, which are installed in the frontof the mirror (PD1) and in the downstream of the slit (PD2).
They are inserted to the beam axis by the remote control.
The devices are designed for high-dose measurement (IRD
Inc., SXUV100; SXUV100RPD [4]) with sensor sizes of

786

(a)
Vertical position

Wavelength(b)

Wavelength (nm)
500

58.2

58.3

58.4

58.5

58.6

400

Intensity

CCD. (Princeton Instruments Inc., PI-SX 400-1340B). The
device, which has a back-illuminated sensor with electriccooling, covers from visible to the x-ray range. A pixel
number and a pixel size are 1340 (h)400 (v) and   m , respectively. In the vertical direction, the concave
grating simply works as a concave mirror. Thus, the vertical intensity distribution corresponds to a real image in thevicinity of the incident slit. An example of the spectrum
image measured with the He lamp is shown in Fig. 2 (a).
The spectrum resolution is determined mainly from thefollowing conditions: i) the line number in the illuminatedarea of the grating; ii) the spatial resolution of CCD; and iii)
the aberration. Note that the incident beam to the slit is thequasi-plane wave, not focused as usual, because the plane
mirror is used as a pre-optic. Thus the illuminated area on
the grating is determined mainly by the beam divergence ofthe plane-wave diffraction at the slit.
Figure 3 shows calculated resolutions at a slit width of
100 m and a detector resolution of 60 m (3 pixels). The
measured values using a helium lamp (He I,  nm) and a mercury lamp (Hg I,   and 253.65nm) at the same slit width are also indicated in the figure.
The measured results are mostly agreed with that calculated with the detector limitation. The resolution   isgrater than 1000 even at    nm [see Fig. 2 (b)]. We
note that a ray-trace calculation shows that the effect of theaberration is smaller than the other two factors. This result
is supported by the experiment.
The spectrometer can be used for measuring a spatial
profile at the slit position by switching the diffraction condition to the 0th order.

300
200
100
0
650

660

670

680

690

Pixel number

Figure 2: (a) Spectrum image measured with He lamp. The
horizontal axis is the dispersive direction, where the right
direction corresponds to longer wavelength. The verticalaxis corresponds to the real image in the vicinity of theincident slit. (b) Intensity distribution along horizontal pixels, after the average over vertical pixels of (a). The upperaxis shows the corresponding wavelength.

10x10 mm  . The sensors are combined with a charge amplifier (PA-100) or with an oscilloscope. The gain of amplifier can be changed by a factor of 10  . The signal isconnected into the accelerator control system using an A/D

X-ray Optics and Detectors

Proceedings of FEL 2006, BESSY, Berlin, Germany

(a)

10000

Vertical position

1000
100
10
1
0

100
200
Wavelength (nm)300

Figure 3: Resolution of spectrometer with a line densityof grating of 2400 lines/mm. The dashed and solid lines
are calculated results from the line number and the detector resolution, respectively. The solid circles are measured
values.
converter.

Commissioning results
Spectrum Spectrum measurements for spontaneousand SASE radiations have been dedicated for tuning andevaluating the following conditions: i) optimization ofelectron-beam conditions including orbit, focusing, bunching condition, etc.; ii) tuning of undulators; iii) evaluationof the electron-beam density from SASE spectrum. In particular, the last [1].
The spectrum data are obtained typically with 100-shots
accumulation for spontaneous light, and with single shot
for SASE radiation. Figure 4 (a) shows a single-shot spectrum for SASE radiation at an electron charge of 0.24 nC,
an undulator gap of 3 mm, and a slit width of 100 m.
The arc shape of the spectrum indicates that the wavelength
tends to longer in the peripheral area, which is a similar
phenomenon to the spontaneous radiation. The split into
several lines are due to the fact that the beam is multimode.
Figure 4 (b) shows a central, on-axis spectrum. The central wavelength is determined to be   nm with a
FWHM of    nm.
The pulse length can be estimated from the spectrum.
For example, if one assume that the pulse has a rectangularshape, the energy bandwidth  and the pulse width  isrepresented as,     
(3)
  eVin the Fourier-limited pulse. In our case, is simply deduced from the relationship  .
Then the pulse width is estimated to be  fs.
Radiation intensity The radiation intensities measured with photodiodes are particularly used for quick optimization of the operation parameters such as electron-beamorbit, bunching condition, timing, beam collimation, alignment of undulators, etc.

X-ray Optics and Detectors

Wavelength(b)4[×10 ] 6

Intensity (arb. unit)λ/ΔλFRAAU015
40.234 nm

3
2
1
0
57

58

59
60
Wavelength (nm)61

Figure 4: (a) Single-shot image of SASE radiation. (b) Onaxis spectrum of (a) along the dased line.

The conversion from the output charge to the absoluteintensity is necessary for evaluating SASE energy. At
present, we use a catalog table [4] for refering the efficiency(  , output charge of the detector per incident energy of
the radiation pulse). However, it is desirable to determine
the efficiency experimentally. For the purpose, we havetested a calibration method using the spontaneous radiation. First, the accelerator parameter is set to be debunchingcondition for producing only spontaneous radiation. Thenthe output charge per pulse is measured. The theoreticalradiation energy to the detector is calculated using the sensor size and the distance to the detector. This partial energy
has small dependences of machine parameters except theelectron-beam energy and the charge. Thus the efficiency
can be accurately obtained from the normalization of themeasured charge by the calculated partial energy. The important point of the method is to choose moderate  parameter; the contamination of higher-order radiation is increased at a large  , while the dependence of the energy
on  is too large at a small value. The optimized value isconsidered to be 0.2 to 0.7.
Figure 5 shows efficiencies of PD1 and PD2, measured
with changing  parameter of the first undulator from 0.2
to 0.73. The catalog values are also indicated. The efficiency of PD1 is agreed with the catalog value within a
30 % deviation. Smaller values in PD2 are explained by
the fact that PD2 is located in the downstream of the Au
mirror, which has a reflectivity of   %. Thus, it is plausible that the method can be applied to the quick check of787

FRAAU01

Proceedings of FEL 2006, BESSY, Berlin, Germany(a)Vertical position

Efficiency (C/J)

0.2

0.1

0

20

30
40
50
Wavelength (nm)60

Horizontal position(b)5

the efficiency. We are planing to install thin-metal attenuators, because the present maximum energy, around 2 J, isnearly the saturation level of the detector. The above calibration method is effective even in this case. We note thatthe efficiencies in a wavelength range longer than 35 nm
will be measured with low-energy operation of the accelerator.
Spatial profile and coherence The spatial profile atthe slit position is measured using the 0th-order diffraction of the grating, where the grating simply works as aspherical mirror. Figure 6 (a) shows a single-shot image
at a lasing condition only using the first undulator. The
horizontal (vertical) width and divergence (in FWHMs) aredetermined to be 3.4 (3.9) mm and 240 (280) rad, respectively, using a distance of 13.9 m from the undulator exit to
the slit, as seen in Fig. 6 (b).
The spatial coherence is evaluated with a Young’s
double-slit experiment. The double slit with each width of
100 m (height of 500 m) and a central spacing of 400 mwere installed at the incident slit position. The grating was
replaced with a plane mirror, and the diffraction image wasrecorded with the CCD, as shown in Fig. 7. The image with
SASE radiation (single-shot detection) is compared to thatat spontaneous radiation (100 shots). The former image hasa higher visibility [Fig. 7 (c)], which indicate higher spatial
coherence. We are planing to make more quantitative measurement using double slits with different spacings.

Extension for user experiment
In 2007, we are planning to start the operation dedicated for user experiments. A present plan for the extension is as follows: The experimental hall (about 12 m  )is constructed at the outside of the accelerator tunnel. The
beam transport channel is branched from the middle of thepresent diagnostic system. The beam is two-dimensionallycollimated with double mirrors. A gas chamber with adifferential pumping system is installed for a transparent,
shot-by-shot monitor for the radiation intensity.

788[×10 ]

Intensity

Figure 5: Detector efficiencies for PD1 (red open circles)
and for PD2 (black closed circles). The blue open triangles
show the catalog values.

1.5
1
0.5
0

-4

-2

0
2
Position (mm)4Figure 6: Spatial profile of SASE radiation (a), and its projections for horizontal (solid line) and the vertical (dashedline) axes (b).

X-RAY OPTICS FOR SCSS
Introduction
The principal missions of the optics in XFEL are i) tocondition photon beam for user experiments, and ii) to diagnose radiation properties for the feedback to the accelerator. In this section, we will introduce R&D activities
proceeded at SPring-8.
There are two technological challenges in XFEL optics.
One is to suppress speckles possibly originating from imperfections of optical components under the coherent illumination. Both surface and bulk qualities should be strictly
controlled.
The other is to keep the radiation dose below the melting
limit [5, 6]. A simple solution is to extend the x-ray transport line for decreasing the energy density. However, in
the SCSS case, the magnification of the beam area, whencompared to that at the entrance of the beamline, is notlarger than 10 because of small beam divergence (0.4 rad
at =12.4 keV, for example) and the limited distance of  m. An alternative method is to use components
made from light elements such as Be, B, C, etc. Figure 8 shows calculated doses for several materials that areplaced normal to the incidence. The following beam parameters [2] are used for the calculation: the photon flux of   photons/pls, the STD beam size at the source of
50 m, and the distance from the undulator exit of 100 m.
The STD beam divergence is calculated from the diffrac-

X-ray Optics and Detectors

Proceedings of FEL 2006, BESSY, Berlin, Germany

Vertical position(a)

Dose (eV/atom)

Horizontal position

Vertical position

10-1
10-2
10-3
5000
10000
Photon energy (eV)

15000

600
400
200
-1

0
Position (mm)12Figure 7: Young’s double-slit experiment for SASE radiation with single shot (a), and for spontaneous radiation
with 100 shots (b). The cross sections of the cental region
at these conditions are shown in (c) as the red dot-dashedand black dashed line, respectively. A calculated result under the coherent illumination is also represented as a blue
solid line.
tion limited condition for each photon energy. It is foundthat i) the doses of light materials (Be and C) have a margin
to the threshold levels more than two-order of the magnitude, and ii) the dose of Si is still below the threshold, butiii) the dose of Cu is above threshold in the energy range
higher than the K-absorption edge.

Crystals and windows
Crystal monochromator is used to set specific spectral
window at SASE and spontaneous radiation. We have twocandidates for crystal materials: Si and diamond. The en) are     and    forergy resolutions (Si (111) and Diamond (111) reflections, respectively.
Si is the most popular materials for monochromator crystal at the present synchrotron facilities, because of theavailability of high-quality, large-volume ingots. Since theBragg angle for (111) reflection at keV is 11 degree, the dose per atom around this photon energy is decreased by a factor of 5, compared to the normal incidencecase shown in Fig. 8. The ratio is further increased forhigher photon energy (  , lower Bragg angle). Thus, Siwould be useful as XFEL monochromator above 10 keV.
Crystal cooling is not a serious problem for SCSS. Because

X-ray Optics and Detectors

Photon flux (photons/s)

Figure 8: Energy dependence of dose for several materials.
Solid lines are calculated values with SCSS beam parameters, while dashed lines are the threshold levels of melting
limit.

800

0
-2

100

10-4
0

Horizontal position

(c)
1000
Intensity (arb. unit)

Be
Diamond
SiC
Si
Cu

101

(b)

FRAAU01

1014

1013

0

10
20
30
Photon energy (keV)

40

Figure 9: Photon flux of the monochromatic beam at
SPring-8 undulator beamlines. The open circles and solidlines are measured and calculated values for diamondmonochromator, respectively, and the dashed lines aremeasured values for cryogenically-cooled Si monochromator.
the average power is smaller than 100 mW, water coolingwould be sufficient.
Diamond monochromator is the most promising whenutilized under a higher dose. We have collaborated with
Sumitomo Electric Industries Ltd. (SEI) to develop highquality synthetic diamond in type IIa [7]. Recently, (111)crystal plates with relatively large sizes (    mm  ) arecommercially available. We have tested performance of diamond double-crystal monochromator (DCM) at a SPring8 undulator beamline. Two (111) diamonds crystals, which
are attached to copper crystal holders using indium sheets,are cooled by water. Figure 9 shows the measured photon
flux. Experimental results are well agreed with the theory in the energy range below 20 keV. Topographic studies
showed a relationship between the surface condition andthe image quality. It is necessary to develop surface polishing technique.
For windows, Be foils have been widely used at syn-

789

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1

x-position(d)x-position

0y-position(b)

x-position(c)x-position

y-position

y-position(c)y-position(a)y-position(b)
Normalized intensity(a)y-position

Proceedings of FEL 2006, BESSY, Berlin, Germany

y-position

FRAAU01x-position

x-position

Figure 10: Transmission images of Be windows: PolishedPF-60 (a), polished IF-1 (b), polished PVD (c), and Kapton
  keV. The beam
foil (d). The photon energy isareas are  m . The distance between the sample
to the camera is 1400 mm. The round spots commonly seenat the bottom-right corners of (c) and (d) are caused from a
Kapton foil in the upstream of the system.
chrotron facilities owing to their low absorptions for xrays. They are also promising candidates for XFEL windows from the viewpoint of the dose issue (see Fig. 8).
However, it has been found that they produced speckles
under coherent illumination. From the experiment at the
1 km beamline of SPring-8, it was found that the speckles
in the conventional Be windows shown in Fig. 10 (a,b) are
originated mainly from voids in the bulk [9]. To remove
the voids, the physical vapor deposition (PVD) method has
been tested. The surface of the PVD Be foil has been polished to decrease the surface roughness to be 0.05 m. Finally, the image of a polished PVD Be shown in Fig. 10 (c)was found to be superior to that of a Kapton foil in (d) [10].
We note that Be will be useful for attenuators. Higher attenuation will be achieved using Si or SiC.

MirrorTotal-reflection mirrors are used for deflecting SASE radiation in order to eliminate high-energy bremsstrahlung.
Focusing is another important function of the mirror. The
surface quality is crucial for suppressing speckles under coherent illumination. From 2000, we have collaborated with
Osaka University to realize high-quality mirrors. Special
techniques of surface polishing have been developed: EEM(Elastic Emission Machining) and PCVM (Plasma Chemical Vaporization Machining) [11]. Figure 11 shows reflected images of Si mirrors measured at the 1 km beamline with a photon energy of keV. The incident
angles and the distance between the mirrors to the camera
are set at 1.2 mrad and 966 mm, respectively. The intensity fluctuations observed with the pre-machined surface in

790

x-position

Figure 11: Reflection images of Si mirrors: Pre-machined
surface (a), PCVM polished surface (b), and PCVM+EEM
polished surface (c).
Fig. 11 (a) are mostly suppressed with the PCVM+EEM
polished mirror in (c). Thus, we can conclude that the mirror is available for conditioning coherent x-rays.
These machining techniques with combination of a new
metrological method called the microstitching interferometry (MSI) [12] were applied to fabrication of asphericalmirrors for nano-focusing. A couple of Pt-coated mirrors are fabricated with figure accuracies of 2 nm (p-v).
Two dimensional focusing down to    nm  has been keV with the Kirkpatrick-Baez arachieved at
rangement [13].
Another critical issue for the XFEL mirror is to choose
appropriate surface material to suppress the dose under themelting limit [5]. Figure 12 shows the calculated doses andreflectivities for several materials. The beam parameters
are as same as those used in Fig. 8 with a photon energyof  keV. It is found that C or SiC seems to be
useful, while Si and Au are questionable. From the figure,the incident angles should be smaller than 2 mrad (0.14 degree). If we set an acceptance width to be 1 mm, the total
length of the mirror should be larger than 500 mm. Thus,
the next R&D issues for XFEL mirror fabrication are i) tostudy coating and polishing method for the light materials,
and ii) to product large mirror with a sufficient figure accuracy. It is also important to establish technologies to protect
the surface from contaminations or dusts, because small decrease of reflectivity can cause serious damage of the surface under the high-dose irradiation. Great care should be
required in the design of the driving mechanism in order tokeep an ultraclean environment.

Single-shot spectrometerAs shown in the previous section, the VUV single-shot
spectrometer has played a central role for the radiation diagnostics. Development of similar instrument that works

X-ray Optics and Detectors

Proceedings of FEL 2006, BESSY, Berlin, Germany

Incident angle (mrad)

Dose (eV/atom)

101

0

2

4

6

8

10

100
10-1
10-2
10-3

C
SiC
Si
Au

10-4

Reflectivity

10-5
1
0.8

FRAAU01

SUMMARY
The VUV diagnostic system for the SCSS prototype accelerator has been constructed and successfully operated.
At a lasing condition, a radiation energy in the pulse has
been evaluated to be   J. The pulse width is estimatedto be shorter than 100 fs from the measurement of the energy spectrum. The double-slit experiment showed thathigher spatial coherence is achieved at a lasing condition.
As XFEL optical components, we have developed highquality diamonds, mirrors, and Be windows. A single-shot
spectrometer for XFEL diagnostics has been tested andconfirmed to have a high resolution of   at

keV.

0.6

ACKNOWLEDGEMENT

0.4
0.2
0

0.1

0.2

0.3

0.4

0.5

Incident angle (degree)

0.6

Figure 12: (above) Angular dependences of doses for the
total reflection mirrors. Several materials are compared.
Solid lines are calculated values with SCSS beam parameters, while dashed lines are the threshold levels of the melting limit. (below) Dependences of reflectivities.

We thank all SCSS members for fruitful discussions andsuggestions. We acknowledge Dr. Y. Takata (RIKEN), Dr.
Y. Harada (RIKEN), and Dr. T. Tokushima (RIKEN) for
their suggestions on designing the spectrometer, Dr. A.
Higashiya (RIKEN), Dr. T. Matsushita (JASRI), Dr. Y.
Tamenori (JASRI), and Dr. A. Sekiyama (Osaka Univ.) for
their help in the calibration of the spectrometer, Mr. T. Kirimura (RIKEN) for the calibration of the photodiodes, Mr.
M. Tanaka (JASRI), Mr. T. Irie (JASRI), and Mr. K. Onoe
(ULVAC) for their activities in the installation of the VUVdiagnostic system.

REFERENCES
Detector
Mirror[1] H. Tanaka et al., in these proceedings.
[2] ”SCSS X-FEL Conceptual Design Report”, RIKEN/SPring8,
May 2005,
Mikazuki,Japan,
http://wwwxfel.spring8.or.jp/[3] K. Togawa et al., ”Emittance Measurement on the CeB Electron Gun for the SPring-8 Compact SASE Source”, FEL 2004
conf. proc. (2004) THBOC03.

Incident x-rays

Analyzer crystal

Figure 13: Setup for single-shot x-ray spectrometer.

[4] International Radiation Detector Inc.,
inc.com/

http://www.ird-[5] R. Tatchyn, ”LCLS Optics: Technological Issues and Scientific Opportunities”, SLAC-PUB-6064, SLAC, Stanford(1993).
[6] ”Linac Coherent Light Source (LCLS) Conceptual Design
Report”, SLAC-R-593, SLAC, Stanford (2002).

in the x-ray region is crucial. Recently, we have developed such a spectrometer that combines a high-quality mirror and a Si flat crystal. The former is used to diverge theincident parallel beam, while the latter is to select specificenergy according to the Bragg’s law. As a result, the exit
beam has an energy dispersion. The key point is again the
figure accuracy of the mirror to suppress speckles. Using(555) reflection for the analyzer crystal, the energy resolution of the instrument has been measured to be     
meV at keV with a full energy range of  
eV. Wider energy range can be easily obtained by changing diffraction plane to lower index [14].

X-ray Optics and Detectors[7] K. Tamasaku, T. Ueda, D. Miwa, and T. Ishikawa, ”Goniometric and topographic characterization of synthetic IIa diamonds”, J. Phys. D: Appl. Phys. 38 (2005) A61.
[8] M. Yabashi et al., ”Diamond double-crystal monochromatorfor SPring-8 undulator beamlines”, Proc. for SRI 2006 (inpress).
[9] S. Goto, M. Yabashi, K. Tamasaku, S. Takahashi, and T.
Ishikawa, ”Characterization of Beryllium Windows using
Coherent X-rays at 1-km Beamline”, AIP conf. proc. 705(2004) 405.
[10] S. Goto, M. Yabashi, K. Tamasaku, and T. Ishikawa, ”Characterization of Beryllium Windows for Coherent X-ray Optics”, Proc. for SRI 2006 (in press).

791

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Proceedings of FEL 2006, BESSY, Berlin, Germany[11] Y. Mori et al., ”Development of plasma chemical vaporization machining and elastic emission machining systems forcoherent X-ray optics”, Proc. SPIE, Vol. 4501 (2001) 30.
[12] K. Yamauchi et al., ”Microstitching interferometry for x-rayreflective optics”, Rev. Sci. Instrum. 74 (2003) 2894.
[13] H. Mimura et al., ”Hard X-ray Diffraction-Limited Nanofocusing with Kirkpatrick-Baes Mirrors”, Jpn. J. Appl. Phys.,
44 (2005) L539.
[14] M. Yabashi et al., ”Single-shot spectrometry for x-ray freeelectron laser”, Phys. Rev. Lett. 97 (2006) 084802.

792

X-ray Optics and Detectors

Proceedings of FEL 2006, BESSY, Berlin, Germany

FRAAU02

X-RAY DETECTORS AT DESY
H. Graafsma, DESY, Hamburg

Abstract
The European X-ray Free Electron Laser to be constructedin Hamburg, presents interesting challenges for the X-ray
detectors. Every pulse of the XFEL represents an entire experiment of its own, partly because of sample degradation
or destruction, and partly because of pulse to pulse fluctuations. Therefore, a maximum amount of data has to becollected in a single shot. This means first of all that photon counting detectors cannot be used, instead one has toconstruct integrating detectors, still with single photon sensitivity. Secondly, since the strength of the European XFEL
is a very flexible pulse structure with high repetition rates,
fast framing times down to 200 ns (5 MHz) are required. I
will present some of the requirements imposed by the science cases foreseen at the European XFEL, and some of thepossible solutions under consideration, both at DESY andat other places in the world.

PAPER NOTAVAILABLE

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WAVE-FRONT OBSERVATIONS AT FLASH
M. Kuhlmann, E. Plönjes, K. Tiedtke, S. Toleikis, HASYLAB at DESY, 22607 Hamburg, Germany
P. Zeitoun, J. Gautier, T. Lefrou, D. Douillet, ENSTA, 91761 Palaiseau cedex, France
P. Mercère, Synchrotron SOLEIL, 91192 Gif-sur-Yvette Cedex, France
G. Dovillaire, X. Levecq, S. Bucourt, Imagine Optic, 91400 Orsay, France
M. Fajardo, Centro de Física dos Plasmas, Instituto Superior Técnico,1049-001 Lisboa, Portugal.
Abstract
During the first year of user operation at the FreeElectron Laser in Hamburg (FLASH) wave-front
measurements were recorded in the vacuum-ultraviolet
region using a Hartmann sensor (by Imagine Optic). The
Hartmann principle is based on a hole array, which
divides the incoming beam into a large number of subrays monitored in intensity and position of individual
spots. The identification of the local slope of the incident
wave front makes the aberrations from a perfect sphericalwave front visible. Ray tracing in upstream directionaccesses the beam path especially the focal spot in sizeand position.
The intense and coherent vacuum-ultraviolet FEL beamleads to unique requirements for the wave-front sensor
setup. We report an optimized setup to observe themetrology of flat and curved mirrors at FLASH beamlines. The use of wave-front measurements to provide
reliable machine parameter is discussed.
The wave-front sensor proved to be a valuable tool toobserve the FEL beam quality and the performance of
optical elements, filters and diagnostic tools.

ultra-violet or soft x-ray domain. For the first time Le
Pape et al. used a wave-front sensor in the EUV regime.
The experiment took place at a tabletop saturated soft-xray laser [1]. Here, the wave-front sensor shall be
evaluated for• FLASH beam line commissioning• FEL characterisation• Online diagnostics as part of user experiments

SETUP
Setup of the beam lines
Five beam lines are in operation mode for user
experiments. At each an additional optical laser for pumpprobe experiments is available. Figure 1 shows a schemeof the FLASH experimental hall. The beam lines
discussed in the following are identified by the full-widthhalf-maximum (fwhm) beam size of their focal spot,
considering the theoretical design parameters of the FEL.
More than 10 switching or focusing mirrors are in use.
Only one beam line can make use of the FEL beam at atime.

GENERAL
FEL beam characteristics
The here-introduced wave-front sensor is used as toolin the photon diagnostics at FLASH. A free electron laser
beam shows specific characteristics which demand certain
requirements for any diagnostic tool.
Based on the SASE principle all FEL features differ
from shot to shot depending on the degree of saturation.
At a high level of some μJ per pulse the FEL operates in
an intensity regime of two orders of magnitude. The
required adaptations in the wave-front sensor setup andthe needed data statistics which can document the shot toshot changes are discussed in the following sections.
The wavelength regime of 13 nm to 60 nm is of noconsequence for the achromatically wave-front sensor.
The short pulse length of 10 – 50 fs and the variable rates
of repetition will be a challenge if the wave-front sensor
becomes an online diagnostic tool in the future.

Wave-front measurements
In the regime of visible light sensors based on the
Hartmann respectively the Shack-Hartmann principle areof common use. Astigmatism, spherical aberration andcoma are quantitatively determined. Aberrations of suchkind are generally of lower amplitude in the extreme-

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Figure 1: Scheme of the FLASH experimental hall and its
beam lines. Some photon diagnostics tools are outlined
along the FEL beam.

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FRAAU03was sufficient to illuminate the full field of view of thesensor. A pinhole 5 μm in diameter was used.

BEAM LINE COMMISSIONING

Figure 2: Setup for wave-front measurements at beam line
BL2. The sensor is positioned 3.5 m behind the focal spot.
Up to now, the wave-front sensor was used at the beamlines BL1, 2, and 3. All are high intensity beam lines
without a monochromator. Whereas at BL3 the unfocused
FEL beam can be measured, BL1 and BL2 are designed
to a focal spot size of approximately 100 μm and 20 μm,
respectively. All switching and focusing mirrors working
with an incident angle of 2 or 3 degree and have a carbon
coating.

Setup of the wave-front sensor
A perfect spherical wave is compared with the actual
beam to analyze its wave front. Therefore, both beams
have to pass through a two dimensional array of holes(Hartmann plate) and are recorded under similar
conditions on a CCD. Here, the Hartmann plate is madeof nickel. It consists of 51 x 51 square holes each 110 μm
in size and with a pitch of 387 μm. Therefore, themaximal field of view is 19.5 mm x 19.5 mm. The
quadratic holes are tilted by 25° to prevent the long-range
diffracted signal coming from one hole to interfere withthe spot of the adjacent hole, generating an unpredictableerror on data treatment. The sensor includes a direct CCD
camera, PI-SX1300, with 1340 x 1300 pixels, each 20 μm
in size. It is operated at –40° to minimize the noise level.
In general, a zonal reconstruction is used to take as muchpixels as possible into account [2]. To distinguish thecontributions of higher order aberrations a modal
reconstruction algorithm can be used, too. Imagine Optic
provides the complete sensor.
Figure 2 is the sketch of a typical setup. The plotted
example was build up at beam line BL2. The sensor ispositioned in 3.5 m distance from the focal spot, morethan the 2 m focal distance of the focusing ellipsoidal
mirror. This allows for a full illumination of the sensor. A
flat gold mirror placed in 45 degree absorbs 97% of thebeam intensity at a wavelength of 32 nm. Currently,
mirrors with gold, silver, and aluminium surfaces areused. The different mirrors are required to operate thesensor at different wavelengths and levels of intensity.
Otherwise the camera pixels are generally saturated.
Pinholes, generating a perfect spherical wave, can be
moved in the beam to allow relative measurements. The
sensor was calibrated using this setup in the direct beam
without the additional mirror. Only than the FEL intensity

X-ray Optics and Detectors

The spatial characterization of the wave front has
important applications in discovering localized defects inbeam line optics. The proposed intensities of FLASH
forced the beam line design to work with grazing
incidences of 2° to 4° for both switching and focusing
mirrors. The FEL wavelength of 60 nm to 13.1 nm in thefundamental demands full vacuum and particle freeequipment towards the experiment. The task is to prove
the feasibility of the sensor for the use as commissioning
tool at FLASH.

Documentation of the focal spot size
Beam line BL2 consists of two flat switching mirrors andone focusing ellipsoidal mirror. The design proposed a
spot size of 20 μm at a focal distance of 2 m. Figure 3
shows the depth of focus reconstructed from wave-front
measurements in October 05. Displayed are the fullwidth-half-maximum (fwhm) values of the beam size atdistinguished positions relative to the calculated focal
point. The focal spot is reconstructed to a fwhm-size of
31 μm x 31 μm, an error of ± 2 μm is given by theGaussian fit of the reconstructed beam spot. A minor
astigmatism can be seen in Figure 3 according thedifference in horizontal and vertical minimal focal spot
position. With further investigations this problem was
imputed to a switching mirror and was eliminated byremounting the mirror.

Figure 3: The depth of focus at beam line BL2 at awavelength of 32 nm. Shown are fwhm values atdistinguished distances from the measured focal positionin vertical and horizontal direction. The minimal beam
size is 31 μm x 31 μm (± 2 μm).
Nevertheless, the overall wave front here displayed in
Figure 4 is of high quality. Displayed are absolute valuesof the difference to a perfect wave for each pixel. So thecomparison of variable wavelengths of the FEL is
possible. For wave-front analysis the generally usedscaling in parts of lambda complicates the comparisonand documentation of different measurements. The wave
front can be characterized by the root-mean-square error
rms=3nm and the peak-valley difference PV=19nm. The

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wave front used for the calibration of the sensor wasmeasured with rms=0.64nm and PV=4nm. Additional the
position of the focal spot is recorded to allow for the shot
to shot characteristic of the FEL. In the here shown earlyphase of the FEL operation an unstable beam correspondto a standard deviation of 4.5 μm in spot size.
The design values for the beam line parameters are notachieved up to now. The wave-front measurements verify
that the situation is not origin in a misalignment or in
manufacturing errors of the optics. Further measurements
at the unfocused beam line BL3 explain the discrepancy
by the observation of a large source size, see section FEL
Characterization.

astigmatism caused by a wrong position in the yaw angle
direction, and 12% as coma, due to a minor misalignment
in the roll angle orientation. Further alignments are planedin the future after improvements, concerning the field ofview and some mirror mechanics, took place. The wavefront measurements proved the need of such upgrades atbeam line BL1.

0.03
0
-0.03
μm

rms
= 3nm
PV
= 19nmFigure 4: Full field of view (51 x 51 pixels) of a wave
front. Displayed are the absolute discrepancies from aperfect wave front. The achieved result is close to theactual resolution limit of the used wave-front sensor.

Mirror alignment
A toroidal mirror with a focal length of 10 m is used at
the beam line BL1. The critical alignment of the yaw
angle is demonstrated in Figure 5. First the small field ofview is obvious. Far from optimal for this kind of
measurements it is due to the long focal distance of 10 mthat we were forced to position the sensor only 2.55 mbehind the focal spot, which leaves the here displayed
beam size of ~3 mm. Image (a) shows a strong
astigmatism. The overall ellipsoidal beam profile isnarrow and tilted. The rms of 395 nm only documented
the obvious misalignment. From image (a) to image (b) in
Figure 5 the toroidal mirror was moved by 5 mrad in the
direction of the yaw angle. A strong change in beamprofile and shape took place. The beam profile is more of
the true circle of the FEL itself but still tilted. The rms ofthe distortions is 70 nm, only. The centre of the beam
stays at the same pixel position than before. From image(b) to image (c) the mirror was further moved by 5 mradaround the yaw angle. Closer to an optimal alignment the
improvement is not as drastic as it had been before. The
shape of the beam stays the same and only its diagonal
becomes a perfect horizontal line. Therefore the centre of
the beam moved by 5 pixels in x and in y direction. The
wave front is of rms=50 nm. The detailed analysis of thebest image (c) evaluated 73% of the distortions as

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Figure 5: Wave front changes during the optimisation of
the toroidal mirror in the direction of the yaw angle atbeam line BL1. The scales are different for the images to
identify the shape of each wave front. To document theposition of the spot the illuminated pixels of the CCD are
displayed, bottom and left. Between the images the mirror
was tilted in the yaw direction by total 10 mrad.

Long-term documentation
In the last year the FLASH beam performance shown
an incredible improvement. Especially the mean beam
intensity increases by more than one order of magnitude.
The long-term effects to the optical elements need to beobserved. The highly sensitive wave-front measurements
are excellent to show even slight damages to the carbon
coating of the mirrors. No other diagnostic tool can
provide us with such information during an operation
mode of the FEL.

Filter performance
A FEL beam consists of higher harmonic parts. Less
than 1% intensity of the fundamental can contribute in thethird harmonic, the most intense higher harmonic.
Nevertheless, orders up to the seventh harmonic were
measured. The application of filters and filter systems isrequired to make detailed use of these lower wavelengths
or to eliminate any ill effects for some experiments.
The standard used nitrogen gas absorber not influences
the FEL wave front. This was checked during a FEL
operation with a wavelength of 32 nm. The use of theabsorber to a transmission of only 0.1% leaves the FEL
wave front unchanged.

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Proceedings of FEL 2006, BESSY, Berlin, Germany
More critical is the use of solid filters, metal foils or
crystalline membranes. A generally used thickness ofsuch a filter is 200 nm. Up to now, no effect in thisregime is recorded. To get a change in wave front analuminium foil of > 2 μm had to be put in the beam. Eventhen, the wave front distortions are homogenous and of
only 13 nm rms. Therefore, the effect to the opticalgeometry by creating a second source component is of
more consequent for an experiment.
This result eased the wave front measurements itself inthe future, as the still complicated reactions on changes inintensity can be countered with additional filters without
questioning the achieved results.

FEL CHARACTERIZATIONFLASH is the first working FEL in the EUV and soft xray regime [3, 4]. Source size, shape, and position canvary on a shot to shot characteristic. The importance formost beam line optics has been pointed out in the section
above. Here the characteristic of the FEL itself and any
conclusions considering the machine operation is
discussed. The task is to evaluate the resolution of thesensor for the requirements at FLASH.
A good wave front of 4 nm rms was recorded at the endof beam line BL3 with four flat mirrors along the regularbeam path. Relative measurements to a beam origin in a
50 μm pinhole in front of these mirrors lead to a portionof 2 nm rms caused by the optics and of 2 nm rms origins
in the incident FEL beam. In this regime themeasurements are close to the limit of the sensor
calibration. Further, the shot to shot variations of the FEL
pulses were observed with the same magnitude. To allow
an analysis of such a beam we are in need of a better
calibration of the sensor.
Similar limits are recorded concerning the source sizeand distance. In general the realistic value of 82 m
distance to the source is reproduced. Nevertheless, thecurrent setup and software can produce errors of somemeters for a focal spot in a distance of more than 80 m.
This is unacceptable by at least one order of magnitude.
The beam size at the experimental station of BL3 in
February 06 was 10 mm fwhm. In a situation of not fully
reached the saturation level such a large beam size is not
surprising. The standard deviation of the x- and y-positionof the beam centre was 1.3 mm and 2.3 mm respectively,translated in an angle of ~24 μrad. These results matchthe theoretical parameters of a FEL just close to saturation[3].
A qualitative measurement of relevant machineparameter is not resolved with the current wave-front
sensor setup. Improvements are foreseen: First an
automatic alignment of some equipment parts is planed tominimize the sensor alignment time in respect to thelimited beam time available. In this context the diffraction
limit of the sensor design λ/120 at 13 nm [5] shall bereached at the FEL, too. Therefore a new and perfectcalibration is required. Thinkable is the use of a different
Hartmann plate or the development of a new sensor

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specialized for the different and progressed circumstances
at a FEL facility like FLASH.

ONLINE IMPLEMENTATION
In contrast to other diagnostic tools the here-introduced
sensor measured the wave front in a distance of somemeters behind the focal spot. A use as online diagnostic is
possible when the direct beam path is not blocked by theexperiment itself, e.g. most experiments operating in thegas phase. Even if a target block the beam a verificationof the FEL performance in between some measurements
is useful.
Main problems are the intensity and geometriccircumstances, which will be dictated by the experiment
itself and not by the wave-front measurements anymore.
As critical as these adaptations have been so far it is achallenge to provide a setup with even more flexibility.

CONCLUSION
The here reported measurements proved the feasibilityof wave front observations under FEL conditions. The
high sensitivity of the wave-front sensor is required forthe high beam quality at FLASH. First order aberrations
were recorded during first beam line commissioning. The
ongoing improvement of the FLASH beam quality instability, source size, and intensity as well as optimized
optics alignment was documented during the last year.
The non-invasive and remote sensor can be used as online
tool to document the shot to shot characteristics of the
FEL.

ACKNOWLEDGMENT
These measurements based upon the work of U. Hahn
and the HASYLAB optics and vacuum groups. The
commissioning is part of the FLASH team [3].
This work was supported by the European Community
Research Infrastructure Action under the FP6“Structuring the European Research Area” Programmethrough the Integrated Infrastructure Initiative“Integrating Activity on Synchrotron and Free Electron
Laser Science”, contract number RII3-CT-2004-506008.

REFERENCES
[1]

[2]
[3]
[4]
[5]

S. Le Pape, P. Zeitoun, M. Idir, P. Dhez,
J. J. Rocca, M. Francois, Phys. Rev. Lett. vol. 88(2002), p. 183901.
W. H. Southwell et al., JOSA, vol. 70 (1980) p. 8
V. Ayvazyan et al., Eur. Phys. J. D, vol. 37(2006), p. 297.
E. L. Saldin, E. A. Schneidmiller, M. V. Yurkov,
DESY Print TESLA-FEL, 2004-06 (2004).
P. Mercere, P. Zeitoun, M. Idir, S. Le Pape,
D. Douillet, X. Levecq, g. Dovillaire, S. Bucourt,
K. A. Goldberg, P. P. Naulleau, S. Rekawa,
Optics Lett., vol. 28 (2003), p. 135.

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A NEW GENERATION OF X-RAY OPTICS BASED ONPYROLYTIC GRAPHITE ∗H. Legall, H. Stiel, Max-Born-Institute, Berlin, Germany
A. Antonov, I. Grigorieva, Optigraph GmbH, Berlin, Germany
V. Arkadiev, IAP e.V., Berlin, Germany
A. Bjeoumikhov, IfG GmbH, Berlin, Germany and A. Erko, BESSY GmbH, Berlin, Germany
Abstract
Highly Oriented Pyrolytic Graphite (HOPG) is a mosaic
crystal, which consists of a large number of small nearly
perfect crystallites. The unique structure of HOPG crystals enables them to be highly efficient in diffraction in anenergy range between 2 keV up to several 10 keV. The mosaicity of the crystal is responsible for the dramatic increaseof integral reflectivity in comparison to perfect crystals.
Furthermore thin HOPG crystal films can be easily bent
and exhibit a very high thermal conductivity making theminteresting for application in experiments with high average
power x-ray sources. For application in x-ray spectroscopy
the achievable spectral resolution of the crystal optics is ofparticular interest. Recently performed measurements withvery low foil thickness have revealed a spectral resolutionof E/ΔE = 2900 in (004)-reflection. This is by far the highest spectral resolution reported for Pyrolytic Graphite (PG)
crystals. The integral reflectivity of these films is still comparable to that of ideal Ge crystals. In this work we present
new results concerning the energy resolution, integral reflectivity and application of thin bent Graphite films.

INTRODUCTION
Highly oriented pyrolytic graphite (HOPG) is an artificial graphite produced by thermal cracking of a hydrocarbon gas and deposition under low pressure and afterwards
annealing the deposit under pressure [1]. In this way andafter some further fabrication steps thin films of HOPG canbe made with thickness of less than 10 μm. These films canbe easily bent by mounting them adhesively on a mould of
any shape [2].
Sectional topographical diffraction measurements haveshown an arrangement of the small crystallites with some
μm in size to larger mosaic blocks with some 100 μm in
diameter and some 10 μm in thickness [3]. The angular distribution of the crystallites, with plane orientations
off to the normal axis to the crystal surface, is called mosaic spread. The mosaic spread between the crystallites ismuch smaller than that between the mosaic blocks. The
mosaic blocks again show a correlation in orientation andform larger crystal domains with some mm in size.
Because of its high thermal conductivity κ and low linear
thermal expansion coefficient α in basal plane (cp. Ta∗ Work supported by the German national program of supporting development, innovation and technology (ProFIT Programm zur Förderung vonForschung, Innovationen und Technologien, Land Berlin, #10126367) andthe European found for regional development (EFRE).

798

ble 1), which both are similar to those of diamond crystals, PG crystals could be interesting for many applications
with regard to x-ray sources delivering high average x-ray
power. Also the absorption thickness tabs of HOPG is similar to that of diamond. Consequently less heat is absorbed
in comparison to other crystals.
The diffraction properties influencing the energy resoluTable 1: Thermal properties and absorption thickness at 8
keV for different crystals.
Material
κ
α
tabs
(hkl)
[W/cm K] [/K x 10−6 ] [μm]Diamond(111)
Si(111)
Ge(111)
HOPG(002)(parallel (002))(perpendicular)
HOPG(004)

21
1.25
0.58

0.8
2.33
5.9

17
8

1
20

250
8.7
2.94
239

477

tion of PG films are determined by the mosaicity and the
intrinsic width of Bragg reflection. Latter refers to the diffraction properties of the small crystallites and is called theDarwin width for nearly perfect crystals. It results fromparticle size and/or strain broadening. Mosaicity makes
it possible that even for a fixed angle of incidence to the
crystal surface, an energetic distribution of photons can bereflected, because each photon of this energetic distribution can find a crystallite plane at the right Bragg angle.
The width of this energetic distribution depends on the mosaic spread. The mosaicity is also responsible for the dramatic increase of integrated reflectivity in comparison toperfect crystals in an energy range between 2 keV and several 10 keV [4]. The so-called mosaic-focusing, as shownin Fig. 1, which occurs in a 1:1 magnification geometry enhances further the intensity in the image plane.
In contrast to ideal crystals, in mosaic crystals the photon has to penetrate deeper into the crystal, before it finds
a crystallite aligned well, from which it can be reflected.
That means that the effective depth, from which diffraction
in mosaic crystals occurs, is much larger compared to ideal
crystals. Therefore the energy resolution can be strongly
affected by the thickness of the Graphite films. Recently
we have shown that very thin Graphite films can reveal
energy resolutions and integral reflectivity comparable toGe(111) [5].

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The x-ray source, which was used for the measurements,
is a low power microfocus x-ray tube (IfG) with a source
diameter of about 50 μm. Measurements were performed
with the Cu Kα emission of a Cu anode at 8 keV. The spec-

Figure 1: Diffraction properties of HOPG.
Figure 2: Experimental setup.
Because PG can be treated as an agglomeration of verysmall crystallites less strain is induced by bending the films
and therefore no drastically changes of the diffraction properties determining the spectral energy resolution are expected and were measured up to now.

EXPERIMENTAL AND RESULTS
Samples
Two kind of HOPG crystals manufactured by OptigraphGmbH were investigated. Firstly, the well known ”Highly
Oriented Pyrolytic Graphite” (HOPG) crystal and secondly a new kind of HOPG crystal. This new material
was already presented in [5]. Because the diffraction
properties of the new material differ considerably fromthe well known HOPG it will be named by Optigraphhenceforth ”Highly Annealed Pyrolytic Graphite” (HAPG)
to distinguish it from the commonly HOPG. This new
kind of PG crystal is optimized for the application in x-ray
spectroscopy by a modifed fabrication process. To get acomprehensive overview over the relationship between
energy resolution and thickness in flat and bent geometry,
crystals with different thickness were measured in (004)reflection in both geometries. To realize precise variationsin thickness the PG films were fabricated by stacking thin
10 - 15 μm thick PG films. The influence of the stacking
on the energy resolution was investigated by measuring
also thicker PG films consisting of only one sheet. The
flat crystals were mounted on polished glass plates andthe bent crystals were mounted on a cylindrical polishedlens with radius 150 mm. The thickness of the investigatedfilms was determined with an accuracy of ± 5 μm using a
micrometer screw before mounting them on the moulds. It
must be noted, that the measured thickness is an averaged
value. That means, that the thickness can vary slightly for
different sites of the crystal.

Experimental setup
The experimental setup is shown in Fig. 2. It consistsof the HOPG crystals, an x-ray tube and a CCD camera.

X-ray Optics and Detectors

tra were collected with a 16-bit deep depletion CCD camera (Roper Scientific model PI-LCX 1300) with a quantum
efficiency of about 50% at 8 keV. A thin (250 μm) Be window in front of the deep depletion CCD was used for vacuum sealing of the camera, so that a deep cooling (downto -50 ◦ C) of the CCD was possible. The distance between
source and crystal and between crystal and detector was
F = 400 mm in each measurement. All measurements werecarried out with the detector plane oriented perpendicularly
to the reflected x-ray beam.

Results
In Fig. 3 selected images of the reflected Cu Kα emission are presented for both investigated PG crystals. In
the upper image a 15 μm HAPG and in the lower image
a 10 μm thick HOPG crystal in flat geometry is shown.
As can be seen from the cross sections of the images in

Figure 3: Recorded images of the reflected Cu Kα emission
from a 15 μm thick HAPG and a 10 μm thick HOPG.
Fig. 4 the measured energy resolution of the flat HAPG
crystal is better than that of the HOPG crystal with nearlysame thickness. The energy resolution was determined bya convolution procedure as described in [5]. From the convolution procedure an energy resolution E/ΔE of 4100 was

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found for the 15 μm flat HAPG and 3500 for the 10 μm
flat HOPG. The reflection broadening due to crystal thickness, which is in the range of a single mosaic block, cannot
explain the difference in energy resolution between both
crystals. Therefore, the differences in energy resolution are
more likely a broadening due to the flat geometry of thecrystals. Latter gives rise to a focusing error in the image plane, because the alignment of the mosaic blocks inthe basal plane deviates from a Rowland circle. These socalled flat focusing error increases with mosaicity (cp. [6]).
Hence for the HAPG lower mosaic spread can be expected.
As mentioned above the 15 μm HAPG crystals are compa-

Figure 5: Measured rocking curves of a 15 μm thick HAPG
crystal in (002)-reflection. The measurements of the rocking curves where performed using a triple-crystal diffractometer (BESSY).
HAPG films can be determined by rocking curve measurements. The measurements of the rocking curves were
performed in (002)-reflection using a triple-crystal diffractometer at BESSY. In Fig. 5 the mosaic reflection and the
intrinsic width of reflection of HAPG(002) are shown. The
rocking curve width (FWHM) is 0,056 ◦ for the mosaic
reflection and 27 arcsec for the intrinsic reflection. Fromthe mosaic reflection the mosaic spread can be determined.
To determine the mosaic spread from the measured rocking curves a reflectivity formula [7] derived from Zachariasen’s treatment was used [8]. The best fit was obtainedwith a Lorentzian distribution and a mosaicity of 0.042 ◦ .
From the measured mosaic spread the energetic bandwidth
can be calculated in both reflection orders.
To enhance the reflectivity the thickness of the HAPG

Figure 4: Cross sections of the recorded images in Fig. 3.
The circles are measured points and the lines represents thefit curves of the convolution procedure.
rable to the 15 μm thick crystal which was presented in [5].
The energy resolution in Fig. 4 is higher because the distance F is larger. Taking the values for the energy resolution
from [5] and comparing these values with the measured energy resolution at 400 mm distance a nearly linear increaseof energy resolution over distance is observed.
As already reported in [5] the integral reflectivity of the
15 μm thick HAPG in (004)-reflection is similar to that ofGe(111) crystals. For the 10 μm HOPG the integral countrate on the CCD over the Cu Kα emission is by factor twohigher than that of the 15 μm HAPG.
The energetic reflection bandwidth of these thin 15 μm

800

Figure 6: Recorded images of the reflected Cu Kα emission
from a stacked 45 μm thick flat HAPG (upper left image),a 40 μm bent stacked HAPG (upper right image) and a
40 μm single sheet HAPG in flat (left lower image) andbent (right lower image) geometry.
films was increased. In Fig. 6 the images of a 40 μm thick

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Proceedings of FEL 2006, BESSY, Berlin, Germany
HAPG single sheet and a stacked HAPG of same thickness
are shown. Due to thickness broadening the energy resolution drops down to 3300 for both sheets. In contrast the
integral count rate increases by a factor 4 for both 40 μm
PG films in comparison to the 15 μm thick film. Also
shown in Fig. 6 are bent HAPG crystals of same thickness.
Bending these 40 μm thick HAPG crystals revealed fully
different energy resolutions . While bending increases theenergy resolution for the single sheet of HAPG as shownin Fig. 7, for the stacked bent HAPG the energy resolution
drops down to 2300 (not shown). This result was surprisingly and indicates maybe changes in the mosaic structure
by bending. In the case of the stacked HAPG an interaction
between different layer has to be taken into account.
Finally, to enhance further the integral reflectivity accom-

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CONCLUSIONHigh energy resolution can be obtained in (004)reflection using very thin PG crystals. These high energy
resolutions are accompanied with high integral reflectivity.
As shown, bending single sheets of these very thin crystals
seems not to decrease the energy resolutions.
Because of its good thermal properties PG could be interesting for many different applications based on high averaged x-ray sources, as e.g. the Free Electron Laser. A very
promising application for PG crystals could be the single
shot x-ray spectroscopy in an energy range between several keV up to several 10 keV. This can be done with PG
because the mosaic spread enables to record a broad energy
range with high energy resolution in a single shot.

REFERENCES[1] A.W. Moore, ”Chemistry and Physics of Carbon”, Vol. 11,
New York:Marcel Dekker (1973) 69-187.
[2] I.G. Grigorieva, A.A. Antonov, X-Ray Spectrometry 32(1)(2003) 64-68.
[3] M. Ohler, M. Sanchez del Rio, A. Tuffanelli, M. Gambaccini, A. Taibi, A. Fantini and G. Pareschiet, J. Appl. Cryst. 33(2000) 1023-1030.
[4] A. K. Freund, A. Munkholm and S. Brennan, Proc. SPIE
2856 68–81.
[5] H. Legall, H. Stiel, V. Arkadiev, and A. A. Bjeoumikhov, Opt.
Expr. 14 (2006) 4570-4576.
[6] G. E. Ice and C. Sparks , J.Nucl. Instrum. Methods A 291(1990) 110-116.
[7] G.E. Bacon and Lowde R.D., Acta Cryst. 1 (1948) 303-314.
[8] W.H. Zachariasen, ”Theory of X-Ray Diffraction in Crystals”, New York:Dover (1945).

Figure 7: Cross sections of the recorded images in Fig. 6.
The circles are measured points and the lines represents thefit curves of the convolution procedure.

panied with high energy resolution a 100 μm thick single
HAPG sheet was investigated. The integral count rate increases further by a factor 2 and the energy resolution drops
down to 2500 as can be seen in Fig. 7.

X-ray Optics and Detectors

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QUANTITATIVE DETECTION OF FEMTOSECOND X-RAY PULSES
Mathias Richter, Levent Cibik, Udo Kroth, Michael Krumrey, Hendrik Schoeppe,
Gerhard Ulm, PTB, Berlin;
Christian Blome, Ulf Jastrow, Jochen Schneider, Kai I. Tiedtke, Thomas Tschentscher, DESY, Hamburg;
Sergey Bobashev, IOFFE, St. Petersburg; Andrei Sorokin, PTB, Berlin, IOFFE, St. Petersburg;
Jerome Hastings, Rasmus Ischebeck, Stefan Moeller, SLAC, Menlo Park, California

Abstract
A detection system for femtosecond X-ray pulses has beendeveloped within close cooperation between the Deutsche
Elektronen-Synchrotron in Hamburg and the PhysikalischTechnische Bundeanstalt in Berlin. It is based on photoionization of Xenon gas and, hence, radiation hard. Photoions
generated are extracted by an electric field and, in contrast to former devices developed for the vacuum-ultraviolet
spectral range 1 , detected by an amplifying open electron
multiplier. Operation is performed at low gas pressure in
the range between 0.1 and 0.01 Pa. Thus, the detector isalmost transparent and may be used as a fast online monitor
for quantitative and pulse-resolved determination of photon
numbers and pulse energies of X-ray free electron lasers.
After design and construction, a prototype has been successfully characterized and calibrated for photon energies
from 4 to 10 keV in the PTB laboratory at the electron
storage ring BESSY II in Berlin. First application has recently been realized in collaboration with the Linear Coherent Light Source at the Sub-Picosecond Pulse Source in
Stanford with up to 1·106 photons per pulse detected at a
photon energy of 9.4 keV.

PAPER NOTAVAILABLE

1 M. Richter et al., Appl. Phys. Lett. 83, 2970-2972 (2003)

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FRBAU01SCIENCE AT SINGLE PASS X-RAY FREE ELECTRON LASERS
J.R. Schneider, DESY, Hamburg

Abstract
Based on recent experience gained at the Free Electron Laser
in Hamburg (FLASH) operating in the spectral range ofthe VUV, the first free electron laser user facility world
wide, the requirements for successful experiments will be
discussed. This includes the interplay between experimentalists on one and accelerator physicists and operators on
the other hand, the need for various diagnostic tools, samples and sample environment, as well as the need for new
approaches for data analysis

PAPER NOTAVAILABLE

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ONE- AND TWO-COLOUR PHOTOIONIZATION EXPERIMENTS AT
FLASH
M. Meyer, LIXAM, Orsay

Abstract
Photoionization processes induced by femtosecond extremeultraviolet (XUV) pulses of the Free Electron Laser in Hamburg (FLASH at DESY) were investigated in He, Ar, Kr
and Xe by means of photoelectron spectroscopy. The wellknown photoionization cross sections of rare gases enabled
us to determine for each individual FEL pulse the importance of higher orders (0.5 - 1%) of the fundamental wavelength (32, 25 or 13.7 nm)1 . In a second series of experiments, the FEL was combined with a synchronized optical laser of 12 ps or 120 fs temporal width. ATI (Above
Threshold Ionization) processes induced by the optical laser
are giving rise to ’sidebands’ in the photoelectron spectrum.
Their intensity exhibits a characteristic dependence on therelative time delay between both pulses and provides an inherent time marker for time-resolved pump-probe experiments. The results are in excellent agreement with theoretical predictions and allow a first analysis of two-colour
ionization processes2 . Finally, the temporal stability, i.e.
the jitter of the FEL pulses with respect to the optical laser,
was determined by measuring cross correlation curves withthe ps- (523 nm) or the fs-laser (800 nm).

PAPER NOTAVAILABLE

1 S. Düsterer et al., Opt. Lett. 31, 1750 (2006)
2 M. Meyer et al., Phys. Rev. A (Rap. Comm.) submitted.

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FRBAU03

ULTRAFAST COHERENT DIFFRACTION IMAGING WITH X-RAY FREEELECTRON LASERS*
H. N. Chapman#, S. Bajt, A. Barty, W.H. Benner, M.J. Bogan, M. Frank, S.P. Hau-Riege,
R.A. London, S. Marchesini, E. Spiller, A. Szöke, B.W. Woods, LLNL, Livermore, CA 94550,
U.S.A.
J. Hajdu†, M. Bergh, F. Burmeister, C. Caleman, G. Huldt, F.R.N.C. Maia, M.M. Seibert,
D. van der Spoel, U. Uppsala, S-75124 Uppsala, Sweden.
S. Boutet, K.O. Hodgson, SSRL, SLAC, Menlo Park, CA 94305, U.S.A.
D.A. Shapiro, CBST, UC Davis, Sacramento, CA 95817, U.S.A.
Abstract
The ultrafast pulses from X-ray free-electron lasers will
enable imaging of non-periodic objects at near-atomic
resolution [1].
These objects could include single
molecules, protein complexes, or virus particles. The
specimen would be completely destroyed by the pulse in a
Coulomb explosion, but that destruction will only happen
after the pulse. The scattering from the sample will give
structural information about the undamaged object. There
are many technical challenges in carrying out such
experiments at an XFEL. We are addressing some ofthese challenges with experiments at the FLASH soft-Xray FEL at DESY.

SINGLE PARTICLE IMAGING
The success of crystallography lies in its ability toovercome radiation damage by spreading the X-ray doseover many (> 109) identical copies of the molecule and by
taking advantage of the strong signal that arises from thecoherent superposition of X-rays within Bragg spots.
However, by performing measurements with ultrashortpulses, we can apply crystallographic techniques to nonrepetitive structures (including cells, viruses, and single
macromolecules). The radiation dose required for such
“diffraction imaging” will be orders of magnitude above
the steady-state damage threshold of about 200–4000
photons/Å2 (depending on sample size and wavelength)[2]. Even so, the high-angle (high-resolution) scatteringfrom a single molecule will be extremely weak since,

unlike diffraction from a crystal, there will be no coherent
addition of scattering from many identical unit cells. We
expect that the proposed XFELs will provide enoughphotons per pulse to give a measurable atomic-resolution
signal.
Atomic-resolution imaging of biological objects with
X-rays will necessarily be “lensless”; a diffraction patternis recorded and a computer reconstruction algorithm
performs the image formation step, replacing the role of alens. Although the phase (wavefront) of the diffraction
pattern is not recorded, it is possible to reconstruct thecomplex-valued image of a finite object from the far-field
diffracted intensity. For single molecules and other nonperiodic objects, the diffracted intensity is not confined to
Bragg spots as it is for crystals. This allows an“oversampling” of the diffraction pattern, and thecollection of information not accessible in a
crystallographic experiment [3,4]. The “shrinkwrap”
algorithm [5] is a particularly robust and practical methodof using this information and performing 2D and 3D
image reconstructions [6].

______________________________________________*Work supported by U.S. Department of Energy (DOE) under Contract
W-7405-Eng-48 to the University of California, Lawrence Livermore
National Laboratory; the National Science Foundation Center for
Biophotonics, University of California, Davis, under Cooperative
Agreement PHY 0120999; The National Center for Electron
Microscopy and the Advanced Light Source, Lawrence Berkeley Lab,
under DOE Contract DE-AC02-05CH11231; Natural Sciences andEngineering Research Council of Canada; the U.S. Department ofEnergy Office of Science to the Stanford Linear Accelerator Center; theEuropean Union (TUIXS); The Swedish Research Council; The
Swedish Foundation for International Cooperation in Research andHigher Education; and The Swedish Foundation for Strategic Research.
#henry.chapman@llnl.gov†
janos.hajdu@xray.bmc.uu.se

New Science at FELs

Figure 1: Schematic diagram of a single-particle
diffraction imaging experiment at an XFEL.

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A full 3D reconstruction can be achieved fromdiffraction patterns taken from many different
orientations of the structure. With an XFEL, a complete
data set will require identical copies of the object exposedto the beam one by one, which may be injected into thevacuum environment of the experiment and pass throughthe beam path at a random orientation. With identicalsamples it will possible to sort diffraction patterns to findthose of similar orientation that can then be averaged.
The averaging step will be important in order to improve
the signal to noise ratio (SNR) and hence improve
resolution. The critical step in the analysis becomesfinding the minimum dose that is required not to image aparticle, but to infer its orientation. Hence any methodthat can be employed to fix a particle’s orientation, suchas laser alignment [7,8] will have a big impact on the
success of the technique.
A concept of the single-particle diffraction experimentis shown in Fig. 1. Some of the challenges we face todevelop this technique include: understanding theinteraction of the specimen and the FEL pulse todetermine how short a pulse is required to overcome
radiation damage; methods to focus X-ray FEL pulses tobelow 0.1 micron focal spots to achieve high intensity;
development of high-dynamic range, low noise, and fastarea detectors; methods of delivering purified samples
into the beam without containers or substrates; handlingthe large data stream from the detectors and performing
the classification and averaging of the diffraction data;
and developing robust 3D imaging techniques.

RESOLUTION LIMITS
Radiation Damage
Radiation damage significantly limits the resolution of
conventional imaging experiments. Damage is caused byenergy deposited into the sample by the probes used for
imaging (photons, electrons, neutrons, etc.). Cooling canslow down sample deterioration, but it cannot eliminate
damage-induced sample movement during conventional
measurements [9-12]. Ultra short x-ray pulses from X-ray
free-electron lasers offer the possibility to extend theconventional damage limits, and will allow the imaging of
non-crystalline biological (and other) materials. Forproteins, simulations based on molecular dynamics (MD)[1, 13, 14], hydrodynamic [15, 21], and on plasma models[16] indicate that if very short (100 fs or less) and very
intense x-ray pulses are available ( 106 photons/Å2 on
the sample), then a single scattering pattern could berecorded from a single protein molecule in the gas phase
before radiation damage manifests itself and ultimately
destroys the sample (Figure 2).
The hydrodynamic (HD) model can be computed fast
on a computer, as compared with MD models. However,the MD models are potentially more accurate since theytreat the microscopic atom-atom and atom-electroninteractions in greater detail. The general approach at ourlaboratories is to use HD for simulations of the soft x-ray
experiments at FLASH and to quickly explore new

806

Figure 2: MD simulation of radiation-induced Coulomb
explosion of a small protein (lysozyme). White balls: H,
Gray: C, Blue: N, Red: O, Yellow: S. Integrated X-ray
intensity: 3x1012 (12 keV) photons/100 nm diameter spot
(corresponding to 3.8 x 108 photons/nm2, or 3.8 x 106
photons/Å2 on the sample) in all cases. (a) Protein
exposed to a 2 fs FWHM X-ray pulse, and disintegration
followed in time. The atomic positions in the first two
structures (before and after the pulse) are practically
identical at this pulse length due to an inertial delay in the
explosion. (b) Lysozyme exposed to the same number ofphotons as in (a) but the pulse FWHM is now 10 fs. The
images show the structure at the beginning, in the middle
and near the end of the X-ray pulse. (c) Behaviour of theprotein during a 50 fs FWHM X-ray pulse. It is also
apparent from the figure that during the Coulomb
explosion, hydrogen ions and highly ionised sulphurs are
the first to escape the immediate vicinity of the protein (at12 keV, the photoelectric cross section for sulphur isabout fifty times larger than that for carbon). Based on
Neutze at al. [1].
concepts for molecular imaging at XFELs, whiledeveloping an advanced MD model including electrons
for more accurate simulations of the x-ray-moleculeinteraction for XFELs.
The basic assumption of the HD model is that the
sample can be described by a liquid-like continuum ofmatter rather than considering individual atoms. This
gives a simplified description of the average effects of xray material interaction and atomic motion, which thenpermits calculations even on very big samples. The model
further assumes that the particle is spherically symmetric,
reducing the mathematical model to one dimension plus
time. The model assumes that the motion of the atoms
within the molecule is solely in the radial direction. The
electrons and the atoms are treated as separate,
structureless, fluids that interact through the Coulomb

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Proceedings of FEL 2006, BESSY, Berlin, Germany

FRBAU03energy and position to form a cloud around the positive
ions, leaving a neutral core and a positively charged outershell (similar to Debye shielding). This layer is ejected
first from the particle, and the Coulomb explosion
proceeds from the outside in. A rarefaction wave
propagates in from the surface at the sound speed, andhence the centre of the particle undergoes destruction
later. In the inner core, there is hardly any ion motion but
the high electron temperature leads to ionization andblurring of the electron density.
This behaviour has led to the proposal of a tamper as asacrificial layer that will delay the onset of damage on the
structure of interest [17]. The tamper may be a small
water or helium drop that surrounds the molecule, andwhich has a total mass comparable to that of themolecule. Modern electrospray techniques can precisely
control the amount of solvent left around the moleculeand can be used to select an optimum layer thickness.

Sample reproducibility and orientation

Figure 3: Intersection of two Ewald spheres with theircentrosymmetric opposites. Centrosymmetry gives anextra intersect as there are two common arcs ofintersection in each diffraction pattern (middle). The
patterns in the middle show the expected arcs ofintersections in two diffraction patterns from theexperimental pyramid X-ray diffraction data set from
Figure 10. Patterns at the bottom show these very lines ofintersections when the experimentally obtained patterns
are subtracted from each other pair wise (Huldt et al., in
preparation).
force and ionization processes. The short-range electronelectron interactions are treated as a hydrodynamic
pressure, and the long-range electron-electron andelectron-ion Coulomb interactions are determined fromthe continuous net charge of the electrons and ions. In thismodel, all forces act radially. The model further assumes
that the trapped electrons are thermalised among
themselves, and that they are inertia free, so that theyquickly relax to a force-free spatial equilibrium. Finally,
the x-ray matter interaction, atomic ionization processes,
and energy of the trapped electrons are described by timedependent rate equations. The model shows that at later
phases in an exposure, trapped electrons quickly relax in

New Science at FELs

Each particle (macromolecule) is exposed to the beam
only once, and disintegrates at the end of this process.
The diffraction pattern so recorded encodes a twodimensional projection image of the sample (and this may
provide sufficient information for some applications).
Three-dimensional imaging requires more than one view
from the sample. In addition, the signal-to-noise ratio of
raw diffraction images will probably be insufficient for ahigh-resolution reconstruction, and it will be necessary toobtain a redundant data set so that averaging can enhance
the signal. One could extend the depth of view from asingle exposure by various holographic techniques basedon external or internal reference beams, but a full threedimensional reconstruction will most likely require
reproducible samples exposed to the beam one-by one,and in different orientations. A “reproducible sample”(e.g. purified proteins) may contain heterogeneities,
different subgroups of sample, and distinct conformers ofthe molecule. How reproducible is a “reproducible
sample” and how well can we distinguish between similar
and dissimilar structures will affect resolution through a
B-factor-like component.
Conventional “single molecule” electron cryomicroscopy [18,19] faces similar challenges as thosedescribed here. The basic requirement for reconstruction
and/or signal averaging from many diffraction images isthe ability to tell whether two noisy diffraction patterns
represent the same view of the sample or two different
views [20]. Huldt et al. [20] have shown that a signal ofless than one photon per pixel would be sufficient tocorrelate diffraction images of identical particles
presenting the same view, assuming photon noise only.
Correlation-based methods to average and orient large
numbers of noisy, randomly oriented real-space images
have been successfully developed in the electron
microscopy community [18,19]. Diffraction patterns are
first classified into classes of like-orientation so that they
can be averaged to increase the signal relative to noise.
The average signal per diffraction pattern at the highest

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(a)

(c)

(b)

(d)

Figure 4: Resolution vs. radius for different X-ray fluences. (a) FOM for imaging conditions as a function of photon
energy. (b) X-ray fluence requirements to classify two-dimensional diffraction patterns of biological molecules
according to their orientation with 90% certainty. The curves are labeled with the X-ray fluence in units of photons in a
100 nm spot. (c) Plot of achievable resolution vs. molecule size for various pulse durations as limited by damage andclassification. Atomic resolution imaging is achievable with pulse durations less than 5 fs and fluences greater than 1012
photons per 0.1 micron spot size. (d) Pulse duration requirements are significantly relaxed for samples that give 10
times larger scattering signal (e.g. viruses or nanocrystals) [21].
resolution, required for classification, is found to be muchless than one photon per pixel, and an incident fluence of
108 ph/nm2 is sufficient to achieve atomic resolution forparticles greater than 15 nm radius [20].
Averaged diffraction patterns must be oriented withrespect to each other in 3D Fourier space, which may beachieved by the method of common lines, a techniquewidely used in electron microscopy, where themicrographs represent planar sections through the centerof the molecular transform. X-ray diffraction patterns arerecorded on the Ewald sphere and so two patterns ofdifferent orientations will intersect along an arc inreciprocal space that passes through the zero spatial
frequency. If the signal is strong enough for the line ofintersection to be found in two averaged images, it willthen be possible to establish the relative orientation ofthese patterns. We note that due to the curvature of thesections (especially at X-ray wavelengths), the common
arc will provide a three-dimensional fix rather than ahinge-axis. Moreover, since the electron density of theobject is real, its molecular transform exhibits
centrosymmetry. This symmetry ensures that we obtain808

two independent repeats of the common lines in the two
images. This feature provides redundancy for determining
sample orientation, and is unique to diffraction patterns(Figure 3).

Resolution for reproducible particles
A combination of results from the hydrodynamic
continuum model [15] with the diffraction patternclassification model of Huldt et al. [20] allows one to map
out the landscape of imaging resolution, molecule sizeand pulse requirements [21]. The results are shown in
Figure 4, which show that it will be possible to image
single molecules at very high resolutions with very shortpulse durations (atomic resolution with pulses less thanabout 5-10 fs).
First, the optimal photon energy for diffraction imaging
was estimated by maximizing a figure of merit (FOM),
defined as the ratio of signal minus noise to the radiation
damage. As shown in Figure 4a, for pulses shorter thanthe Auger decay time (~10 fs for C), the optimum photon
energy is 8 keV, and for longer pulses it is 13 keV,
although the peak FOM is much smaller. Figure 4b shows

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Proceedings of FEL 2006, BESSY, Berlin, Germany

FRBAU03the required x-ray fluence versus image resolution lengthand particle radius, required to achieve a large enoughdiffraction signal to classify the patterns. Figure 4c shows
the pulse length requirements for x-ray imaging biologicalmolecules with 12 keV photons, assuming no preorientation of the molecules. When the fluencerequirements are relaxed by orienting molecules withlaser fields, using nanocrystals containing only a small
number of molecules, or helical molecules, or icosahedral
virus particles up to 10-20 times longer pulses can be
tolerated, see Figure 4d.

IMAGE RECONSTRUCTION
A number of methods exist for recovering phases forobjects that have a finite size, or “support”. These include
oversampling of continuous molecular transforms [4,2225], holographic imaging methods [26-28], holographic
data evaluation methods [29,30], classical methods ofcrystallography, and techniques for phase extension fromlower resolution electron/X-ray cryo-microscopy images.
The past few years have seen the development of robustalgorithms in solving the phase problem throughoversampling the diffraction pattern, and this seems to bea most promising technique for the future. The 3D
diffraction transform of a non-periodic particle iscontinuous. Only the diffraction amplitudes are sampled
at discrete points by the pixellated detector and theprocess of classification. The measured diffraction
intensities are proportional to the modulus squared of theFourier transform of the wave exiting the object. On theirown, these diffraction intensities are insufficient to backtransform to form an image in real space. That inversion
requires knowledge of both the diffraction intensity andphase. If the diffraction pattern intensities are sampled
finely enough, then it is possible to solve for thediffraction pattern phases [22,23]. The solution to thisnon-linear inversion problem is usually obtained
iteratively by sequentially enforcing known constraints inreciprocal space and in real space. Specifically, in real
space we assert that the image has zero scattering strength
outside the area of the object’s boundary (called its
support) [23], whilst in reciprocal space the squared
modulus of the Fourier transform of the image must equal
the measured diffraction intensities. Such algorithms havenow been used successfully for image reconstruction in
X-ray diffraction experiments [4-6,31-34]. An example ofa reconstructed 3D image is shown in Figure 5.
The algorithms usually require that the support of theobject be known a priori, and the closer the support to theactual object boundary, the better the reconstruction. The
algorithm called SHRINKWRAP successively refines anestimate of the support from a current estimate of theimage [5]. This algorithm does not require the support tobe known and is remarkably robust at finding the smallest
image support that contains the majority of the image
intensity.

New Science at FELs

Figure 5: Coherent diffraction imaging and image
reconstruction [6]. Three-dimensional diffraction data
(middle) recorded from a test object (top), consisting of 50nm diameter gold balls on a silicon-nitride pyramid-shaped
membrane, at a wavelength of 1.6 nm, and a rendering of
the ab initio 3D image (bottom) reconstructed from thediffraction intensities to a resolution of 10 nm. The
diffraction data were obtained by rotating the specimen in
1° increments from -70° to +70°, and then interpolated onto
a 10243-element array. A quadrant of the diffraction dataset
has been removed for visualization in the central renderingof the 3D diffraction intensities. The gold balls seen in therendering of the 3D reconstructed image on the right fill theinside edges of the silicon-nitride pyramid. The scale bar is
1 micron.

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that does not obey the Bragg law, and hence are alsofiltered out.
Additionally, the mirror reflectivity
diminishes smoothly to zero at the edge of the hole, due
to roughness of the substrate at the edge. This “soft edge”
reduces scatter from the hole.
We have performed several experiments using thisapparatus, which will be reported on in forthcoming
publications.

REFERENCES

Figure 6: Schematic diagram of the diffraction camera for
FLASH experiments, which uses a multilayer-coatedmirror to reflect the diffraction pattern onto a CCD. The
intense direct beam passes through a hole in the mirror.

EXPERIMENTS AT FLASH
Experiments were carried out at FLASH (Free-electron
LASer at Hamburg, formerly known as the VUV-FEL).
During the experiments the machine operated at awavelength of 32 nm and in the ultrafast pulse mode of
25 ± 5 fs duration [36]. The pulses were focused to a
20 μm spot on the sample by an ellipsoidal mirror [37],achieving intensities up to about 1014 W/cm2. We carriedout experiments to demonstrate ultrafast coherent
diffraction imaging and to study the interaction of matterwith FEL pulses, in order to constrain our models todetermine ultimate resolution limits with XFELs.
Our experiments at FLASH depend critically on being
able to measure the forward scattering from samples withhigh sensitivity and low noise or parasitic scattering. The
main experimental challenge was to prevent the direct
beam from hitting the direct-detection CCD and toprevent out of band radiation (plasma emission from thesample) or non-sample scatter from obscuring thecoherent diffraction signals. We solved these problems
using a flat mirror oriented at 45° to the beam. The direct
beam passes through a hole in the mirror whereas thediffracted beam is reflected from the mirror onto a bare
CCD. The camera records diffraction angles between–15° to +15°, which requires a multilayer coating on the
mirror that varies in layer spacing by a factor of two overa distance of only 28 mm (Bajt et al, in preparation). The
multilayer coating was challenging because of the low
absorption length of materials at 32 nm wavelength. We
designed a coating consisting of three layers (Si, Mo, andB4C), which simultaneously met the requirements of low
stress, high reflectivity at 32 nm, and high reflectivity at
the characterization wavelength of 0.154 nm.
Anadvantage of the multilayer mirror is that it acts as a
bandpass filter both for wavelength and direction. Plasma
emission from the sample in the UV and visible ranges isrejected by the mirror. Stray light, from the scattering of
beamline optics for example, hits the mirror at an angle

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Proceedings of FEL 2006, BESSY, Berlin, Germany

THE PROPOSED EXPERIMENTAL PROGRAM AT LCLS
I. Lindau, MAX-lab, Lund;
R.W. Falcone, UCB, Berkeley, California

Abstract
I will discuss experiments planed for the LINAC Coherent
Light Source, which is under construction at the Stanford
Linear Accelerator Center. Experimental Teams have beenorganized, and construction of a range of instruments isunderway. The science program currently includes atomic
physics, femtochemistry, nanoscale dynamics in condensed
matter physics, structural studies on single particles andbiomolecules, and plasma and warm dense matter. New
ideas for experiments continue to emerge.

PAPER NOTAVAILABLE812

New Science at FELs