1. XFEL Oscillator in ERLs
R. Hajima
Japan Atomic Energy Agency
March 4, 2010.

2. X-ray FEL Oscillator Typical electron beam parameters for XFELO
K-J. Kim et al., PRL (2008), PRST-AB (2009)
Typical electron beam parameters for XFELO
Energy, charge, emittance, repetition are similar to ERL beams.
R. Hajima

3. ERL Injector Performance
design example
Ultimate Injector
8 pC, 0.1 mm-mrad will be feasibly
obtained.
500-kV DC gun, 3-D pulse shaping,
and 10-MeV SCA.
80 pC, 0.1 mm-mrad will be obtained.
750-kV DC gun, 3-D pulse shaping,
and 10-MeV SCA.
R. Hajima et al.
Compact ERL CDR (2008)
I.V. Bazarov et al., PRST-AB (2005)
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4. Integration of XFELO and ERL
Beam dump
ERL Gun
FEL Gun
Location
Operation mode
straight section of the loop
additional branch
independent
concurrent
From the ERL side,
XFELO adds a new feature with minor modification
ERL and XFELO provides complimentary X-rays
Injector
share an ERL injector
use a FEL injector
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5. Growth of emittance and energy spread in a loop
E=5 GeV, r=25m, “half arc” = TBA x 15
coherent SR
for 20pC/2ps
tuning of cell-to-cell phase advance
 negligible emittance growth
incoherent SR
FEL gain is preserved
energy spread after FEL lasing
Energy recovery is preserved
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6. XFELO lasing at 5-GeV?
0.1nm XFELO with a 5-mm gap Halbach-type undulator
7 GeV, lw=1.88cm, gap=5mm, aw=  l=0.1nm
5 GeV, lw=1.43cm, gap=5mm, aw=0.59  l=0.1nm
assuming same peak current and same mode area,
1-D gain for 5 GeV beam is “0.65 x 1-D gain for 7 GeV”
further gain reduction due to the emittance effect.
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7. XFELO with 5 and 7-GeV ERLs
0.3
1Å X-FELO
analytical estimation
of small-signal FEL gain
Energy
5 GeV
7 GeV
charge
20 pC  st
2 ps
sE/E
1e-4 aw
0.59
1.0 lu
1.43 cm
1.88 cm Nu
3000
b*=ZR
10 m en
0.1 mm-mrad
gain
14 %
22 %
0.25
7 GeV
0.2
small-signal FEL gain
0.15
0.1
5 GeV
0.05
0.1
0.15
0.2
0.25
0.3
normalized emittance (mm-mrad)
The above calculations are based on a Halbach-type undulator.
DELTA undulator gives 1.4 times larger FEL gain.
R. Hajima

8. Velocity bunching in an ERL main linac
Injector
SCA #1
SCA #2
SCA #3
Velocity bunching for a SASE-FEL injector
Velocity bunching for an ERL light source
Velocity bunching for an X-FELO
(1) no additional component is required
(2) only 2-3% SCAs are used for the velocity bunching
(3) residual energy spread is smaller than magnetic compression
(4) moderate emittance growth for low bunch charge
L. Serafini and M. Ferrario, AIP-Porc. (2001)
H. Iijima, R. Hajima, NIM-A557 (2006).
R. Hajima, N. Nishimori, FEL-2009
R. Hajima

9. Gain reduction by bandwidth mismatch
K-J. Kim et al., PRL 100, (2008).
growth rate
of the m-th mode
gain
loss
cavity length
detuning
bandwidth mismatch
bandwidth of the Bragg mirrors = 12 meV
12 meV
In the following calculations,
we choose
reflectivity and phase shift
for a cavity round trip
R. Hajima

10. Example of the velocity bunchingst E
Energy (MeV)
bunch length (ps)
z (m)
velocity bunching 1 2 3 4 5 6 7 8 9 10 15 20 25 30
injector
merger
SCA #1
SCA #2
PARMELA simulation
bunch charge q = 7.7 pC
velocity bunching
bunching in 8 cavities
injection 10.9 MeV, 1.3 ps, -85 deg.
gradient Eacc = 8.5 MV/m
4 cavities
4 cavities
emittance growth by
chromatic aberration
0.2
0.4
0.6
0.8 1
1.2 5 10 15 20 25 30 2 ex sx
1.6 ey sy
beam size (mm)
1.2
norm. emittance (mm-mrad)
0.8
0.4
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z (m)
z (m)

11. Optimum design of the velocity bunching
injector
merger
SCA #1
SCA #2
bunch charge q = 7.7 pC
velocity bunching
bunching in 6 cav. + on-crest 2 cav.
injection 10.9 MeV, 1.3 ps, -90 deg.
gradient Eacc = 8.5 MV/m
at the SCA#2 exit
E = 27.7 MeV, st = 380 fs, sE = 250 keV
ex = 0.16 mm-mrad, ey = 0.13 mm-mrad 10 30 9 25 8 st 7 20 6 E
bunch length (ps) 5
Energy (MeV) 15 4 3
velocity bunching 10 2 5 1 5 10 15 20 25 30
z (m) 2
0.2
0.4
0.6
0.8 1 5 10 15 20 25 30 ex ey
z (m)
norm. emittance (mm-mrad)
1.6 sx
1.2 sy
beam size (mm)
0.8
0.4 5 10 15 20 25 30
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z (m)

12. Phase plot at the SCA #2 exit
R. Hajima

13. Enhancement of the FEL gain by velocity bunching
0.8
for 5-GeV, 1-Å X-FELO
0.7
0.6
with velocity bunching
0.5
7.7 pC, 0.38 ps, sE/E=5x10-5
small-signal FEL gain
0.4
0.3
0.2
without velocity bunching
20 pC, 2 ps, sE/E=10-4
0.1
0.1
0.15
0.2
0.25
0.3
normalized emittance (mm-mrad)
Significant enhancement of the FEL gain by velocity bunching.
Gain~40% is possible even with emittance growth during the bunching.
R. Hajima

14. Simulation of XFELO (5 GeV with velocity bunching)
saturation
After the saturation:
pulse duration
t=1.2 ps (FWHM)
photons/pulse (intra cavity)
Np = 2x1010
photons/pulse (extracted)
Np = 7x108
R. Hajima

15. 2-Loop Design of 5-GeV ERL
HOM-damped cavity
high threshold current of HOM BBU
allows 2-loop configuration.
TESLA　(HOM:5×2)
ERL　(HOM:6×2)
R. Hajima

16. Possible Scheme for Combining ERL and XFELO
5 GeV ERL for SR use : accelerate 2 times
7.5 GeV recirculating linac for XFELO : accelerate 3 times
Optional
We can switch two operation modes by introducing an orbit bump having lrf/2= 11.5 cm.
S. Sakanaka, talk at PF-ISAC (2010)
R. Hajima

17. Growth of emittance and e-spread for 3-pass 7.5-GeV
1st-loop: E=2.5 GeV, r=8.66m, 2x14-cell FODO
2nd-loop: E=5 GeV, r=25m, TBAx30-cell
Den
DsE
1st loop (2.5 GeV)
8pC/400fs pC/2ps
incoherent SR
0.029 mm-mrad
34 keV keV
coherent SR
assumed to be compensated
37 keV keV
2nd loop (5 GeV)
0.027 mm-mrad
130 keV keV
53 keV keV
acceptable for FEL
DsE/E = 2 x 10-5
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18. Stability of SRF A/A< 2·10-5 P < 0.01 deg Cornell LLRF System
Demonstrated:
Exceptional field stability at QL = 106 to 108
Lorentz-force compensation and fast field ramp up
Piezo microphonics compensation with ~20 Hz bandwidth
A/A< 2·10-5
P < 0.01 deg
M. Liepe, ERL-09
energy stability << FEL gain band width
This requirement is fulfilled by current LLRF technology.
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19. Conclusions Hard X-ray ERL can accommodate XFELO.
we can extend the frontier of X-ray beam parameters
0.1nm-XFELO is feasibly realized at
5-GeV ERL with velocity bunching
7.5-GeV beam from a 2-loop 5-GeV ERL
an ERL injector is shared, no major modification is needed
XFELO can be installed either at a loop or a branch.
however, beam loss in a long narrow duct might be a problem for a XFELO in a loop
In the Japanese collaboration, XFELO is considered as a part of 5-GeV hard X-ray ERL.
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