1. LSC/CSR Instability Introduction (origin of the instability) CSR/LSC
Z. Huang, M. Borland (ANL), P. Emma, J. Wu
C. Limborg, G. Stupakov, J. Welch
Introduction (origin of the instability)
CSR/LSC
Cure (laser heater)

2. Introduction
FEL instability in the undulator requires very “cold” electron beams (small emittance and energy spread)
Such a cold beam can be subject to other “undesirable” instabilities in the accelerator…
Bunch compression gives rise to a microbunching instability that may be harmful to LCLS
A laser heater at the end of LCLS injector can be used to add “incoherent” energy spread to control LSC/CSR instability while preserving the FEL lasing

3. How cold is the photoinjector beam?
Parmela Simulation
TTF measurement
3 keV
DE/E
·measured
simulation
mean
(sec)

4. Microbunching instability
Initial density modulation induces energy modulation through long. impedance Z(k), converted to more density modulation by a chicane  growth of local energy spread/emittance! bi
bf >> bi or G= bf/ bi >> 1
Z(k) DE
R56
Energy l l t
Current modulation
Gain=10
10% 1% t

5. LCLS accelerator systems
End of injector
SC wiggler at 4.5 GeV
DL1
DL2
Laser heater
at 135 MeV
Linac 1
Linac 2
Linac 3
BC1
BC2
At the end of injector, e-beam carries some residual density modulations which can be amplified in the downstream accel.
Sources of impedance: CSR in dipoles, longitudinal space charge (LSC) and linac wakefields in linacs
Landau damping options: a SC wiggler before BC2 at 4.5 GeV or a laser heater before DL1 at 135 MeV

6. Heating within FEL tolerance
FEL parameter r ~ 5×10-4, not sensitive to energy spread until sd ~ 1×10-4
M. Xie’s fitting formula
3 keV initial energy spread after compression = 120 keV,
corresponding to sd ~ 1×10-5 at 14 GeV
 can increase sd by a factor of 10 without FEL degradation

7. SC-wiggler damps bunching
CSR instability
energy profile
long. space
temporal profile
micro-bunching
sd  310-6
230 fsec
SC-wiggler damps bunching
sd  310-5

8. SC wiggler
SC wiggler increases sd 10 times at 4.5 GeV (BC2), suppresses the CSR gain
Initial modulation wavelength (mm)
Ineffective for LSC instability occurred earlier in the beamline

9. Longitudinal space charge
Current modulation
Energy modulation
Space charge oscillation at low energies (in the photoinjector), little accumulation in energy modulation

10. LSC instability
Acceleration in linacs freezes density modulation and accumulates energy modulation, amplified by the chicane
Saldin
Schneidmiller
Yurkov

11. LSC instability in LCLS
3 keV energy spread is too small to suppress the LSC instability in BC1, which could induce too much energy modulation in L2 before the wiggler
1×10-4
Elegant tracking of final energy spread with 1% initial density modulation
l0≈15 mm from 3 keV

12. Laser Heater
10 cm
50 cm
2 cm
q  5.7º
10 period undulator
10 cm
~120 cm
Laser-electron interaction in an undulator induces rapid energy modulation (at 800 nm), to be used as effective energy spread before BC1 (3 keV 40 keV rms)
Inside a weak chicane for easy laser access, time-coordinate smearing (Emittance growth is completely negligible)

13. P0 = 37 MW w0  3 mm large laser spot sx,y  200 mm P0 = 1.2 MW
matched spot
sx,y  200 mm
+60 keV
spread by laser transverse gradient
-60 keV
In Chicane
After Chicane
less uniform heating
more uniform heating

14. Microbunching Gain after Laser Heater
40 keV
large laser spot
matched laser spot

15. THE GOOD (w0 = 350 mm, P0 = 1.2 MW)
THE BAD ( w0 = 3 mm, P0 = 37 MW)
Final phase space for initial 15 mm seed
AND
THE UGLY (no heater)

16. Sliced final energy spread
No heater
w0 = 3 mm,
P0 = 37 MW
(c) w0 = 350 mm,
P0 = 1.2 MW

17. Choices of transverse laser profile
For an initial “white” noise spectrum, heating with a matched laser spot is generally more effective
Laser spot size may be used to “shape” the sliced energy distribution to suppress a particular range of modulation spectrum
A 60-fs section of the final phase space with initial150-mm seed
(w0 = 350 mm, P0 = 1.2 MW)
(w0 = 3 mm, P0 = 37 MW)

18. Summary
Microbunching instability driven by LSC, CSR and machine impedance can be a “nightmare” for LCLS
The photoinjector beam is too “cold” in energy spread, “heating” within the FEL tolerance (~10X) can damp the instability
SC wiggler is too late for the LSC instability occurs in the lower energy end of the linac (L1, BC1 and L2)
A laser heater can be effective to suppress the microbunching and is under technical design (R. Carr et al.)
It also adds flexible control of sliced energy spread to study FEL physics