The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

Introduction to Free Electron Laser on Electron/Positron Storage Rings
Hiroyuk.i HAMAUVSOR Facility, Institute for Molecular Science, 38 Nishigo-Naka, Myodaiji, Okazaki 444, Japan
Abstract

Free electron lasers (FELs) have been developed
as new radiation (including microwave region)
sources for various fields. Here we are going tobriefly introduce current research activities anddevelopments on storage ring based free electron laser(SRFEL) where the gain is relatively low and target
wavelength is rather short. Peculiarity of SRFEL ispointed out by showing some experimental data of
the UVSOR-FEL. Future prospect and importance ofdedicated storage ring are discussed.
1 Introduction

The FEL oscillation was first demonstrated 20
years ago [ 1 ]. The FELs has been proposed as
powerful light sources for the wide spectral range
with tunability and coherence. Actually a lot offacilities for users are spread over the world with theinfrared FELs based on linear accelerators. For the
short wavelength FELs, there is, however, an
important fact in the progress of the FEL physics andtechnology. Although electron/positron storage ringhas seemed to be a suitable FEL driver for the shortwavelength region such as UV, VUV and XUV, the
SRFEL has not qualified for expected performancesyet.
The first oscillation of the SRFEL in the visible
region was performed on the ACO storage ring,
Orsay, in 1983 [2]. The very small storage ring, ACO,
was constructed as a collider more than 30 years ago.
The FEL experiment was done after the ACO finished
its initial role for the particle physics. The success of
the ACO was followed by the VEPP3 storage ring,
Novosibirsk, in 1988 and the spectral range was
extended down to 240 nm [3]. This record of theshortest wavelength had been not broken until 1996.
Notwithstanding the long history, the progress of

SRFELs seems to be slow, while evolution qf theconventional lasers for the wavelength, the power andthe pulse width has been very rapid. The mattershould be discussed is what difficulties against thedevelopment of the SRFEL are.
2 SRFEL, present and past

On a post machine of the ACO, the Super-ACO,
the first lasing was obtained 1989 [4], and the activityof the FEL experiment has been continued. The
Super-ACO FEL is probably in the most advanced
stage for the study of SRFEL dynamics and also foruser program. In Japan, the first lasing was achievedon the TERAS ring, ETL, Tsukuba, in 1991 [5], which
was followed by another lasing on the UVSOR ring,
Okazaki, in 1992 [6]. In 1993, a lasing was obtained on
the first dedicated storage ring, NIJI-IV, Tsukuba [7].
In 1996, the latest lasing news was coming from Duke
University, Durham, where a new dedicated storage
ring was constructed by J.M.J Madey and his group[8]. The Duke storage ring was designed withconsideration of optimization to the SRFEL. Anotherdedicated ring, DELTA, is under commissioning at
Dortmund, Germany [9].
Table 1 is a glance of the SRFEL facilities. Only
facilities who have installed at least optical cavities arelisted. One can immediately notice that the average
output power is rather low. Although there are manydifferences in characteristics among the SRFELs, suchas pulse structure and repetition rate, the low output
power generally results from relatively low gain andthen low transmission rate of cavity mirrors because
higher beam energy is required to obtain the shortwavelength FEL, meanwhile the gain drops quickly
with increasing the beam energy.
In order to secure enough gain even with thehigh energy beam, very long undulator is necessary.
Consequently the dedicated storage rings like theTable 1 List of SRFEL Facilities and Typical Parameters of FEL
Ring

Location

Activi:£'
Perio

Beam
Ener~

(Me
A 0
rsay France
1978-1987 240
VEPP3*
Novosibirsk(Russia)
1978-1994 350
1988Su~erACO Orsay (France)
600&800
TE AS*
Tsukuba Uapan)
1988-1992 230
UVSOR
Okazaki Uapan)
1988500&600
NIJI-IV
1990Tsukuba Ua£an)240
Duke
Durham (U A)
1989500
DELTA
Dortmund (Germany) 1989< 1000
* Storage ring itself or FEL project was already shut down.

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Output
Power
(mW)
<3
-100
2.5
-3
low
-10

Beam
Current
rnA
150
20
30
4
20
10
10

Ttfa~cal
am

(%)

0.2
10
2
0.5
1
>5
>10

The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

Duke ring and the DELTA, which equip long straightsection of more than 10 m, will play important roles
for future progress of the SRFEL
3 Fundamentals of FELs in low gain regime
Relativistic electrons which have the transverse
momentum with respect to propagation axis of theelectromagnetic wave are stimulated to emit photons
by the electric field of the optical wave (the pendulum
force). Generally the transverse momentum ofelectrons is led by periodic magnetic fields of the
wiggler (or undulator). Since the relativistic electron
longitudinally moves with the light velocity, there is aphase resonance condition between the electrons andoptical wave, which can be easily obtained as(1)

where .itn, It", and y are the wavelength of the opticalwave, the spatial period length of the undulator field
and the relative electron energy. For the fundamental
wavelength, the harmonic number, n, is 1. Here thedeflection parameter, K, is defined as K 2 =Kx 2 + KY 2
and Kx,y =0.934 Bx,y[11 Au[cm], where K is divided into
the horizontal and the vertical component, and B is
the peak magnetic field of the wiggler. The resonantcondition of eq. (1) is exactly same as the wavelengthof the undulator synchrotron radiation.
The energy gain or loss of electrons is governedby a following formula:

The phase of electron with respect to a potential of the
optical wave, <p, should satisfy the pendulum
equation,

The electron distribution in the phase spaceinside the optical wave is essential for the FEL gain.
However normally the phase space of the electron
bunch is much larger than the wavelength of the FEL,
therefore in the entrance of the undulator the electron
distribution in the phase space of the optical wave
packet is almost constant. If the electrons can becondensed into a phase where the electrons are
decelerated, the small signal gain would be enhanced.
An invention of the optical klystron by N.A.
Vinokurov et. al. was very revolutionary for the
SRFELs [11]. The optical klystron consists of two
undulator sections separated by a large wiggle ofmagnetic field which produce so-called dispersive
section. After passing through the first undulator, aphase advance of energy modulated electrons toward
high energy side in the dispersive section is slower
while that is fast for the low energy electrons.
Consequently at the entrance of the second undulator
the electron distribution with respect to the phase of
the optical wave is collected and forms "microbunch".
In other words, the energy modulation is converted tothe density modulation by the dispersive section in
the optical klystron. Figure 1 shows a spontaneous
spectrum from the optical klystron. The Madey's
theorem suggests a higher gain due to the steep slopeof a jagged-structure of the spectrum that results frominterference of two undulator radiations.
The phase space evolution in the optical klystronis shown in Fig. 2, where the undulator field is helicaland the electric field of circular polarized opticalwave. At the exit of the first undulator, the energy
modulation is caused, and then the electron density is
modulated by passing through the dispersive section.
The microbunched electrons loose their energy in thesecond undulator. As on can see in the figure at theexit of the optical klystron, total energy gain summingwhere e and m are the charge and the mass of theelectron, respectively, and E is the amplitude of theelectric field of the optical wave. In a case of which
the electron energy satisfies eq. (1) but individual
phase of electrons with respect to the electric field of
the optical wave is random, there is totally no energy
exchange between the optical wave and the electron
bunch. If the electron energy is slightly deviated fromthe resonance condition, there is energy gain or loss.
By evaluating the pendulum equation for the energy
exchange depending on the phase, one obtains thesmall signal gain curve is proportional to thederivative of the spontaneous spectrum, which isnamely Madey's theorem [10].

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- 300
;:,

cti

~ 200
C/)
c:

2
E

100

450

500

550

Wavelength (nm)Fig. 1 A spontaneous spectrum from thehelical optical klystron on the UVSOR.

The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

where N the period number of the undulator, N d theinterference order between the two undulators, Pe thepeak electron density, [JJ] the brightness factor of theradiation expressed by Bessel functions ( =1 for thecomplete circular polarization), and fmod and F1 are
the modulation factor and the filling factor comingfrom the energy spread of the beam and transverse
overlapping with the FEL and the electron,
respectively.

Entrance of HOK

1176 r-'"~,-.-.~,..,.-,c-r-T"...-~~,_,...,.,..,....,...,...,....,
1175?-1174

1173

-1

0

1

4 Bunch-heating and gain saturation

Exit of 1-st Undulator

1176 [""T""T..,...,...,-.-.~~~--,-,-,.-,-.,~~..,-.,...,.,..,As one presumes from Fig. 2, the phase rotationof electrons goes over n, the total energy gain may
exceed the loss, which leads the gain saturation. The
saturation is expected to be occurred at which the FEL
power density is more than - 100 WI m 2 for the
UVSOR-FEL, This huge power is roughly estimatedto be a 200 kW (!)average powerin the optical cavity.
However an actual saturation of the FEL power comes

1175?-11741173

1172 ......._.~-';-'--'--L"--'--'-~-!:-'-'--'-'~-'--'-'~-'-'-'w

-1

0

1

Exit of Dispersive Section

1176 r--'"'..,...,...,..,..,~.,--.-~~~.,..,...,..,..,~,..,..,r"l1175?-11741173

1175?- 1174

1173

1172 L.W.~-'--'-'--L"--'-'--''-'i-:L~~..J......_'--'-'~.._.__._j
-221
-220
-219
-218
qJ (X 1t)

Fig. 2 Phase space evolution of the electrons in thebucket of the optical wave along a helical optical
klystron. The initial electron energy of 600 MeV andthe energy spread of 3x104 and a very high power
density of the laser is employed to emphasize themotion of tne electrons.

over all electrons is negative, which is converted tostimulated photon emission.
From an analytical evaluation, the FEL gain with
an optical klystron is expressed as
Fig. 3 Start-up of lasing (upper) and the bunchheating. Q-start means tne frequency jump of the RFto synchronize the electron bunch to llie optical bunchso that the FEL interaction begins.

-29-The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

from a different mechanism on the storage ring.
Because the FEL photons are produced by thesame electron bunch turn-by-turn, the beam quality
such as the energy spread becomes no longer same as
an initial condition. As shown in Fig. 2, an amplitudeof the phase space oscillation increases and then it
becomes the large oscillation in synchrotron motion,
which is so-called "bunch heating". The gain
reduction due to the bunch-heating is much more
quicker, and then an average output power of the
UVSOR-FEL does not exceed a couple of mW, whichcorrespond to several W in the optical cavity (here themirror transmission is about 50 ppm).
The bunch-heating phenomena was clearlyobserved by a dual-sweep streak camera on the
UVSOR. Figure 3 shows time dependent evolution of
longitudinal intensity distributions of the FEL and theelectron bunch. The images were taken at the start-upof the lasing. At the high beam current (high gain),the laser light is coming quickly but also quickly
disappeared. This is obviously due to the gain
reduction induced by the bunch-heating. The bunch
length rapidly growth which results from an increaseof the energy spread of the beam. After the FEL is
killed by the bunch-heating, the gain recovers
gradually due to the synchrotron damping and the
FEL is back. We should note the saturation
mechanism in the FEL oscillation on the storage rings
is completely different from that on linac based FELs
where fresh beams can be supplied in the lasing
process.
On a very stable ring, the FEL intensity and theenergy spread of the beam would be in a certain
equilibrium state. This scenario for the saturated laser
power has been predicted by A. Renieri, which iswell-known as "Renieri's limit" [12].
5 How much power can be extracted
From a rise and fall of the FEL macropulse
shown in Fig. 3(upper), the gain reduction due to thebunch-heating was re-expressed in terms of the totalenergy of the produced photons S prod as

1.2

240

(a)

(b)

I • 18 mA/bunchs,. .o.smJ

180

~

·i

.e

Cl

fd tt f t t t r
++

• 120

"'I

0.4

60

SP'Od

(mJibunch)

BeamCurrent(rnA/bunch)

Fig. 4 The deduced FEL gain as a function of the total
extracted photon energy (a). Saturation energies for one
electron at various beam current (b).

1000
100 rnA/bunch

~

-

Duke

Qj
it

0
a. 100Q)

01--- s~l>~r~Aco

~

Q)

>

''

<(

~
>
al

10

I

I

~

UVSOR

£

1
0

500

1000

1500

Beam Energy (MeV)

Fig. 5 Expected maximum intracavity average powerof UV FEL at the beam current of 100 rnA/bunchplotted as a function of the beam energy. Solid lines
are available range of the beam energy and circles
indicate current operation energies for each facility.
(5)

where g 0 is the gain with no additional energy spreadand Ssat is namely the saturation energy. We cannotice eq. (5) is analogous to the population inversion
in conventional lasers. Experimental data is well
reproduced by the eq. (5) as shown in Fig. 4. It was
found out that experimental values of the saturationenergy for one electron were almost constant in awide range of the beam current, which means theoutput power of the FEL is restricted by the saturationenergy. Consequently the average output power PL isroughly estimated from analytical evaluations [13],where T, a and •. are the transmission rate of thecavity mirror, the round-trip cavity loss and thesynchrotron damping time, respectively. In the second
formula, PsR is synchrotron radiation power at a beamenergy Ebeam· Eq (6) is nothing but Renieri's limit.
From an investigation for an original form of Renieri's
limit, the saturation energy s.,at I ne is found to be
proportional to the beam energy and inversely
proportional to the period number of the undulator (for the optical klystron, it depends on the fieldstrength of the dispersive section).
Although the performance of the mirror is very
important factor for the FEL experiment, here let me
assume an ideal mirror a= 1% to estimate the average
power. The gain steeply drops as the beam en~rgy
increases (see eq. (4)), then the beam energy limitation
can be seen in Fig. 5. However the Duke-FEL has
extremely high potential. It is obvious that the very
high gain obtained by using a 7 m-long undulator on-30-

The II th Symposium on Accelerator Science and Technology, Harima Science Garden City, I997

the Duke ring leads the high saturation power. Since
the ratioT Ia is expected to be 0.01 using dielectric
multilayer mirrors, an average power of 1 W would be
extracted from the optical cavity at an 1 GeV
operation on the Duke ring.
6 SummaryThe expected power shown in Fig. 5 may be
widely fluctuated by the absolute value of the gain.
At the high beam current like 100 rnA/bunch, thebeam property becomes an important factor. In thecalculation, the gain at 100 rnA/bunch has been justextrapolated by optimistic prospects. However, forexample, the bunch lengthening reduces the peakcurrent, which appears as Pe in eq. (4), and a single
bunch instability, i.e., microwave instability, increases
the energy spread and also reduces the gain. Thesephenomena are ·surely kinds of the ring
characteristics, but have not been included in theestimation in Fig. 5. On the DELTA ring, they have
improved the shape of the vacuum chamber to reducea broad band impedance to avoid the bunch
lengthening and make a threshold current for
microwave instability very high. That is one ofapproaches from the accelerator physics.
The bunch-heating is originating from astochastic process of the energy modulation by the
FEL interaction and the synchrotron oscillation. If theenergy damping time is very fast, the gain saturation
would be slow. Otherwise the ring with zero
momentum compaction is realized, the stochastic
heating would be avoided. This was proposed as
isochronous storage ring FEL by D.A.G. Deacon [14].
An important point for progress of the SRFEL is theperformance of the SRFEL strongly depends on thestorage ring, in other words the progress of the SRFEL
itself is identical to that of the storage ring. For
instance, stochastic cooling of the beam recently· becomes subject to be frequently discussed. Sameissues such as forced damping will be included in the
future development of the SRFEL.
At the moment, the performance of the SRFEL
does not exceed that of the conventional lasers even
the Super-ACO FEL where they are now supplying
the FEL photons to user experiments. However both
dedicated rings of the Duke and the DELTA have justopened the door for new generation of the SRFEL.
The SRFEL has progressed on the old machines as aparasitic function so far. Although a lot of works
concerned in the SRFEL are left on those rings,
necessity of dedicated storage ring should be argued
to future development.

Acknowledgment
The author thanks Dr. M.-E. Couprie (SuperACO, LURE), Prof. V. Litvinenko (Duke University),
Dr. D. Nolle (University of Dortmund), Dr. T.
Yamazaki (ETL) and all people in the SRFEL society
for letting us have opportunities to discuss many
subjects and exchange information together.
The works on the UVSOR-FEL are partly. supported by a Grant-Aid for Scientific Research from
the Ministry of Education, Science, Sports andCulture, Gr. No. 08640518.
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Ramian, H.A. Schwettman and T.l. Smith, Phys. Rev.
Lett. 38, (1977) 892.
[2] M. Billardon, P. Elleaume, J.M. Ortega, C. Bazin,
M. Bergher, M. Velghe, D.A.G. Deacon, Y. Petroff,
K.E. Robinson and J.M.J. Madey, Phys. Rev. Lett. 51{1983) 1652.
[3] G.N. Kulipanov, I.V. Pinaev, V.M. Popik, A.N.
Skrinsky, A.S. Sokolov and N.A. Vinokurov, Nucl.
Instr. and Meth. A296 (1990) 1.
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1301.

[5] K. Yamada, T. Yamazaki, S. Sugiyama, T.
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Chiwaki and R. Suzuki, Nucl. Instr. and Meth. A318
(1992) 33.
[6] S. Takano, H. Hama and G. Isoyama, Nucl. lnstr.
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[8] V. Litvinenko, private communication.
[9] "DELTA", a status report, DELTA group, Instituteof Physics, University of Dortmund, 1990.: Dirk Nolle,
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