An intense terahertz radiation sourceat the Compact ERL

Kentaro Haradaa*, Miho Shimadab, Ryoichi Hajimac,
aKEK-PF, 1-1, Oho, Tsukuba, Ibaraki 305-0801, Japan (*kentaro.harada@kek.jp)b
UVSOR, IMS, NINS, 38 Nishigo-Naka, Myodaiji, Okazaki 444-8585, Japanc
ERL Development Group, JAEA, 2-4 Shirane Shirakata, Tokai-mura, Naka-gun, Ibaraki 319-1195

Japan ERL Collaboration
T. Kasuga, T. Agoh, A. Enomoto, S. Fukuda, K. Furukawa, T. Furuya, K. Haga, K. Harada,
S. Hiramatsu, T. Honda, K. Hosoyama, M. Izawa, E. Kako, H. Kawata, M. Kikuchi, Y. Kobayashi,
M. Kuriki, T. Mitsuhashi, T. Miyajima, T. Naito, S. Nagahashi, T. Nogami, S. Noguchi, T. Obina,
S. Ohsawa, M. Ono, T. Ozaki, S. Sakanaka, H. Sasaki, S. Sasaki, K. Satoh, M. Satoh, T. Shioya,
T. Shishido, T. Suwada, M. Tadano, T. Takahashi, Y. Tanimoto, M. Tawada, M. Tobiyama,
K. Tsuchiya, T. Uchiyama, K. Umemori, S. Yamamoto
High Energy Accelerator Research Organization (KEK), Oho, Tsukuba, Ibaraki 305-0801, Japan
R. Hajima, H. Iijima, N. Kikuzawa, E. J. Minehara, R. Nagai, N. Nishimori, M. Sawamura
ERL Development Group, Japan Atomic Energy Agency (JAEA), Tokai, Naka, Ibaraki 319-1195, Japan
A. Ishii, I. Ito, H. Kudoh, N. Nakamura, H. Sakai, T. Shibuya, K. Shinoe, H. Takaki
Synchrotron Radiation Laboratory, Institute for Solid State Physics (ISSP-SRL), University of Tokyo,
Kashiwanoha, Kashiwa, Chiba 277-8581, Japan
M. Katoh, A. Mochihashi, M. Shimada
UVSOR Facility, Institute for Molecular Science, National Institutes of Natural Sciences,
Myodaiji-cho, Okazaki, Aichi 444-8585, Japan
H. Hanaki, H. Tomizawa
Japan Synchrotron Radiation Research Institute (JASRI/SPring-8)
Kouto, Mikazuki-cho, Sanyo-gun, Hyogo 679-5198, Japan(Authors of the status report for PAC07)

Intense terahertz radiation source at the Compact ERL・・・・・・・・

Beam energy 65MeV, Beam current 77pC x 1.3GHz = 100mA
Bunch length >0.1ps （～59fs r.m.s.）
Bending curvature radius 1m
Vertical aperture of vacuum duct ～5cm
Terahertz radiation:～0.16meV (cut-off of vacuum duct) < photons available < ～10meV (critical energy)
including 4meV (1THz)
Flux density is about 1016～1018 [photons/s/mrad2/0.1%b.w.]
Integrated energy: a few µJ/pulse
for the horizontal photon acceptance over 100mrad
Peak electric field reaches the order of MV/cm
for the focused spot size of 100µm x 100µm.

Overview of ERL・ Review of CSR formulae
・ Bunch compression
・ Expected CSR spectrum calculation・Lattice of the Compact ERL (ERL test facility)
・Chicane(circumference adjuster)

1st arc(bunchcompression)

Recirculation pathExtractor

Beam dumpLong straight section

Main acceleration
module No.2

Main acceleration
module No.1

2nd arc

MergerInjector
acceleration
cavityElectrongun

InjectorWhy ERL?
・・・・・

The beam quality is determined by the equilibrium of the radiation excitation and damping
at the synchrotron.
The bigger the ring, the smaller the emittance. In order to achieve diffraction limit at thehard X-ray region, the circumference of the ring become huge. (10pmrad ～ 10keV)
It is difficult to achieve the short bunch length at the synchrotron. (The large bunchcharge is especially very hard.)
The photocathode DC electron gun can make electron beam with ultra-small transverse(normalized) emittance and ultra-short bunch length. The beam passes the recirculation
path only once and free from the radiation equilibrium.
The beam power is huge (for example, 100mA x 5GeV = 500MW), and the energy recovery
is inevitable for the RF system and the beam dump.

5-GeV ERL for the Future Light Source in Japan

Machine parameters
Beam energy

5 GeV

Light source parameters

Averaged beam current

100 mASpectrum range

30 eV – 30 keV

Circumference

1253 mBrilliance from ID’s（for 0.1 nm)

1021 – 1023

ph/s/0.1%/mm2/mrad2

Averaged flux

> 1016 ph/s/0.1%

Normalized emittance εn1 - 0.1 mm·mrad

Beam emittance at 5 GeV

100 - 10 pm·rad

Energy spread (r.m.s.)

4×10-5

Bunch length (r.m.s.)

1 - 0.1 ps

RF frequency

1.3 GHz

Accelerating gradient

10 – 20 MV/m

Bunch length (rms)(short pulse mode)< 100 fs

Number of insertion
devices

20 – 30

Plan of the 5-GeV ERL at KEK Tsukuba Campus

What’s difficult? -R&D planDevelopment of key components•••

DC photocathode gun (ultra low emittance, large charge, long lifetime...)1.3 GHz CW laser (high power, very stable, not too expensive...)Superconducting cavities & cryostats(HOM dumped, high power for injector...)Construction of ERL test facility• Testing critical components under beams• Proof of predictions on accelerator physics issues– Space charge effects (especially for low energy)– CSR effects (impacts on emittance, energy spread, and bunch length)– Instabilities (ion trapping, RW-BBU, HOM-BBU)– Beam loss mechanism, etc.
Testing SC cavities for main linac,studying the instabilities, CSR,
optimizing bunch compression.

Test facility with a return loop

Planned Compact ERL (ERL test facility)
In the East Counter Hall at KEK.

Approved to use the building.

Tentative parameters
Initial goal
Circumference of recirculation path

Final goal
69m

TBA 2 cells

Lattice of recirculation path
Injection beam energy

MeV

510～15Injection (=dumped) beam power

kW500

1000～Beam energy after acceleration

MeV

65

160～200modules

12

Normalized transverse emittance (r.m.s.) mm⋅mrad

10.1

Beam current

mA

10100Bunch length (r.m.s.)

ps1～2～0.1

no1

Number of Main acceleration module（1 module = 9cell cavity x 4）

Insertion devices

Feasibility for the limited user operation
Main difference between test ERL and 5GeV ERL
・・・・・

Beam energy:
Circumference:
Bunch length:
Normalized emittance :Averaged current:

60MeV vs. 5GeV
70m
vs. 1.2km
1ps ～ >0.1ps
no difference!
1mm⋅mradno difference!
10mA～100mA
no difference!

Candidates for the user operation: terahertz CSR and Inverse Compton Scattering
CSR
・ For terahertz CSR, the bunch length is essential.
・ The beam energy of 60MeV is sufficient without unnecessary higher energy photons.
・ It is suitable for the test ERL to use intense terahertz radiation source.
Inverse Compton Scattering
・ For 800nm laser with 60MeV electron beam, 90°inverse Compton scattering can generate
short pulsed hard X-ray of the energy 42keV.
・ For 5GeV ERL, however, the radiation from the undulator is short pulsed. The number ofthe photons is extremely large.

Review of CSR formulaeFormulation for the CSRxyrnkzrrkr
E (λ ) is the electric field from the reference particle at the origin observed atthe detector. The electric field from k -th particle can be written as
2πi r rrrn k ⋅ rkλEk (λ ) = E (λ )e,rr
here nk is the unit vector from detector to the particle, rk the position of k -thparticle in the bunch. The total field strength from N particles can be written as
2πi r rNr 2 N 2πi nrk ⋅rrkrrnk ⋅rkλEtotal (λ ) = E (λ )∑ e λ、 Ptotal (λ ) ∝ E (λ ) ∑ e
k =1k =12N∑e

2πi r r 2nk ⋅rkλk =1N

2πi r r Nn j ⋅r jj =1k =1= ∑eλ∑e

2πi r rnk ⋅rkλN= N + ∑e

2πi r r r r
nk ⋅rk − n j ⋅r jλ()j≠kUsing the normalized distribution function of the particles of∫ S (r )dr = 1 , the numberof the particles between r and r + ∆r is NS (r )∆r (with zero transverse emittanceand symmetrical distribution of S (− r ) = S (r ) ).
N∑ej≠k2πi r r r rn k ⋅rk − n j ⋅r j(λ)

2πi r r rn ⋅( r − r ′ )= N ( N − 1) ∫ dr ∫ dr ′e λThus

2πi2z

S (r )S (r ′) ≈ N ( N − 1) ∫ dre λ S ( z ) .

Ptotal (λ ) = Pincoh (λ )(1 + ( N − 1) f (λ )) .
2πi2zλ()fλ=dzeS (z ) .
∫Here,For the “Gaussian” distribution, S ( z ) =1πσ ze z − σz 2、 f (λ ) = e πσ z − λ 2.

Reference ： E.B.Blum,”Observation of coherent synchrotron radiation at the Cornell linac”, NIM A307, (1991), pp568-576

f (x ) = e

1− x

2

10.8
0.6
0.4
0.2

2468

100.37 for x = 1 , and 0.99 for x = 10
For the bunch charge of 77pC, the number of the particles is 4.8x108 個. Thus if

λ = 2πσ z , the photon flux is increased by 108 times. ( λ = 2σ z is used as a criticalwavelength.)

Critical energy and critical angular divergence
Angular flux density of the synchrotron radiation can be written as
2d Pincoh
γ 2θ 23e γ  ω 222 2 =BesselK 1 (ξ )  .
1 + γ θ  BesselK 2 (ξ ) +2 23dωdΩ 16π ε 0 c  ωc 1+ γ θ
33


3
ω
3cγ 32 2 2
1 + γ θ , γ is the Lorentz factor, θ the observation
Here, ω c =, ξ =2ωc2ρ
222(())

angle, ε 0 the permittivity of vacuum, e the charge of an electron, and c the light speed.
From the argument of ξ , the critical frequency ωc and critical angular divergence θ c
is calculated. ωc is the frequency for ξ =1on axis. θ c is the divergence angle for21
31
31  2ωc   3c θ=ξ ≈ 1 with the case with ω << ωc and c γ  ω  =  ωρ  . （Usually, with ω >> ωc , the divergence angle when the flux become

1 2ωc1
is the critical angle, θ c =.）γ 3ωeReference ： J.D.Jackson “Classical Electrodynamics”

Shielding effect
Upper
plate

Lowerplateλλ2=2 cosθπk=πTE wave is transmitting between two perfectly conducting parallel
plate. The boundary condition is that the incident and reflectedwave compensate the electric field on the surface.
When the mode number and gap of the plate are fixed, the incident
angle is determined by the wavelength to satisfy the boundary
condition. The shorter the wavelength, the larger the incident angle.
When the incident wave perpendicular to the plate, the wave cannot

k g transmit. The usual cut-off wavelength is λ = 2h for thecincident angle of 90 degree.
For the synchrotron radiation, the divergence angle is limited by
the critical angle. Thus instead of 90 degree, we use critical angle
for the calculation of the cut-off wave length.

θh=mλ2 sin θ

λc = 2h sin θ c ~ 2hθ c = 23h 3πρ

~2h3

ρ .

Reference ： S.Heifets, A.Michailichenko, ”On the Impedance Due to Synchrotron Radiation”, Proc. of PAC 1991, p458

Parameters・ Intensity

Ptotal (λ ) = Pincoh (λ )(1 + ( N − 1) f (λ )) 、 f (λ ) = e 2πσ z − λ 2・ Critical angular frequency of the photon

3cγ 3
ωc =2ρ
・ Critical angular frequency for CSR

ωc −csr =πcσz(λc−csr = 2σ z )・ Shielded angular frequency for CSR

ωcut −off = πcρh3

・ Thus CSR is generated between ωcut −off < ω < ωc −csr (< ωc ) .

3 hλcut − off = 2ρ 

On-axis flux dencity [photons/sec/mrad 2/0.1%b.w.]

Spectrum from the bending magnet 77pC,1.3GHz,ρ=1m
1.E+191.E+181.E+170.01ps1.E+160.1ps
1.E+15Enhancement by the coherence
1.E+141ps(bunch length (ps))
3cm
1.E+134cm
1.E+125cm
1.E+116cm
7cm
1.E+10
1.E+09150MeV
1.E+0890MeV 120MeV
60MeV
1.E+0730MeV
Cut-off energy by
1.E+06
Beam energy (MeV)
the vacuum duct
1.E+05(Full gap)
1.E+04
1.E+030.00001 0.0001
0.001
0.01
0.1
110100
Photon Energy [eV]1000

Angular divergence and polarization
2d Pincoh
3e γ  ω γ 2θ 222
2 2 
1 + γ θ  BesselK 2 (ξ ) +=BesselK 1 (ξ ) 
32 2
1+ γ θdωdΩ 16π ε 0 c  ωc 33222()

Horizontally
polarized

Verticallypolarized・ Terahertz radiation has large angular divergence due to the low energy.
・ Of-axis vertically polarizing photons has some intensity and available for the users.

Vertical angular divergence and polarity of the photons
Angular divergence and polarization
77pC, 1.3GHz, ρ=1m, photon energy 0.01eV

Angular divergence and polarization
77pC, 1.3GHz, 60MeV, photon energy 1meV
1.E+18Flux density [photons/s/mrad /0.1%b.w]

1.E+17

1.E+172

Flux density [photons/s/mrad2/0.1%b.w]

1.E+181.E+16

1.E+15

1.E+14150MeV Horizontal polarization

1.E+16

1.E+15

1.E+14150MeV Vertical polarization

r=1m vertical

60MeV Horizontal polarization

r=5m horizontal

60MeV Vertical polarization
1.E+13-0.05

r=1m horizontal

-0.03
-0.01
0.01
0.03
vertical divergence angle [rad]r=5m vertical
0.05

1.E+13-0.05

-0.03
-0.01
0.01
0.03
vertical angular divergence [rad]0.05

Acceptance of the photons
・ Because the terahertz radiation has small γ, the aperture angle of the beam line is importantin order to capture the large number of the photons.
・ At the BL6B of the UVSOR, the first mirror is fixed in the vacuum duct of the bending
magnet.
・ The effect of the wake field may be severe.

Reference： UVSOR BL6B Introduction pdf（left）, IMS meeting ”赤外放射光の現状と将来計画”, S.Kimura(right)

Bunch compression

Bunch compression
・ Even if the ultra-short bunch could be generated at the electron gun, the bunch lengthis rapidly lengthened because of the velocity spread, space charge, and CSR effect.
・ The higher the beam energy, the weaker the bunch lengthening effect.
・ In order to make the bunch length smaller than about 1ps, the bunch compression after
the acceleration is inevitable.
・ For the bunch compression, we use the RF curvature effect.
・ The momentum deviation δ = ∆P P makes the difference of the orbit length as∆z = R56δ + T566δ 2 + U 5666δ 3 .
・ Off-crest acceleration at the main linac generate the energy correlation in the bunch.

δ=∆P/Pδ=∆P/P∆z = R56δ
R56 < 0zσzzσzEmittance growth and the bunch lengthening•••••

The energy spread is the cause of the emittance growth, the bunch lengthening
and the beam loss.
While the random energy spread (as the initial energy spread from the electrongun) cannot be corrected, the energy spread from the RF curvature and theCSR effect can be suppressed by the optics optimization.
The betatron tune shift and higher order optics distortion from the chromaticity
cause the vertical emittance growth. For the horizontal direction, the distortion ofthe dispersion function (higher order dispersion) is another cause for theemittance growth.
The distorted dispersion also brings about the bunch lengthening.
Thus the correction of the chromatic effect is the cure for both the emittance
growth and the bunch lengthening.

CSR wake potential・

“Linear part” of the CSR→ Energy change proportional to the orbit length in the bending magnets
beam

Acceleration
Deceleration

BWB

∆E

∆Etotal = 3W2 LbendzW1

B

W2

Acceleration depending
longitudinal position

onsthe∆E = Eentrance + Wsbend∆Etotal = 3W1Lbend∆E ∝ κ ∝ κζ ∝ ∆x

∆Ezzxxzz

xx′′ = −ρ+2W
δ 0 + κs=κδ = δ 0 + κsE0 ,ρ ,sss+ ρ 1 − cos δ 0 + ρ 2  − sin κρρρρρxssssx′ = − 0 sin + x0′ cos + δ 0 sin + ρ 1 − cos κρ
ρ
ρ
ρρ


x = x0 cos

 cos sρx s  1sin−′ x   ρρ δ0  = 0 δ CSR   0κ
 0
s+ x0′ ρ sin

ρ sin
cos
000s

ρs

ρss s s2 s ρ 1 − cos  ρ  − sin  ρ ρ ρ
ρ

 x 
sss   0 sin
ρ 1 − cos   x0′ sin
ρρ
ρ 


 δ 0 
100 δ CSR 01s κ 


001




ρ 1 − cosEnvelope matching technique for horizontal emittance compensation

ζx′ − ζ ′x = 0(κz = z1x′x′ϕζ , κ z = z ζ ′)ϕ1xφ(κz = z2ζ , κ z = z ζ ′)2φx

Optimizations with CSR wake potential
・ The initial beam parameters at the merger is the injected beam energy of 5MeV, the bunchcharge of 77pC, the bunch length of 1ps r.m.s., the transverse beam emittance 0.1mm⋅mradr.m.s., and the energy spread 0.01MeV r.m.s.
・ Optimizing RF phase, R56 by the linear optics and T566 by the sextupoles.
・ The effect of the horizontal emittance growth is not severe for the terahertz radiation.
For example, the diffraction limit emittance for the photons of 10meV (λ=120mm) is about
10mm⋅mrad at 65MeV that is the normalized emittance of 1215 mm⋅mrad.
・ By the optiomization,
RF phase : 109.6 degree
R56: -0.1m
T566: -0.97m.
Bunch length: 59fs r.m.s.
Horizontal projected emittance : 5.6mm⋅mrad

The longitudinal phase space distribution

100fs

Estimated flux density

Photon Flux Density [photons/sec/mrad2/0.1%b.w.]

1.E+18Enhancement by the CSR
effect1.E+15

1.E+12

1.E+09

1.E+06

1.E+03
1.E-05

Vacuum duct cut-off1.E-04

1.E-03

1.E-02
1.E-01
Photon Energy [eV]

1.E+00

1.E+01

1.E+02

Cconclusion
・・・・・・・・

Beam energy 65MeV, Beam current 77pC x 1.3GHz = 100mA
Bunch length >0.1ps （～59fs r.m.s.）
Bending curvature radius 1m
Vertical aperture of vacuum duct ～5cm
Terahertz radiation:～0.16meV (cut-off of vacuum duct) < photons available < ～10meV (critical energy)
including 4meV (1THz)
Flux density is about 1016～1018 [photons/s/mrad2/0.1%b.w.]
integrated energy : 4µJ/pulse
for the horizontal photon acceptance over 100mrad
Peak electric field is about 1 MV/cm
for the focused spot size of 100µm x 100µm.

Thank you very much.