1. LCLS Tracking Studies CSR micro-bunching in compressors
Superconducting wiggler can reduce effect
FEL gain evaluation after system tracking
LCLS Tracking Studies
Paul Emma
January 17, 2002
UCLA
CSR Workshop
LLNL

2. LCLS Accelerator and Compressor Schematic
7 MeV
z  0.83 mm
  0.2 %
150 MeV
z  0.83 mm
  0.10 %
250 MeV
z  0.19 mm
  1.8 %
4.54 GeV
z  mm
  0.76 %
14.35 GeV
z  mm
  0.02 %
Linac-X
L =0.6 m
rf=180 rf
gun
new
Linac-1
L =9 m
rf = -38°
Linac-2
L =330 m
rf = -43°
Linac-3
L =550 m
rf = -10°
Linac-0
L =6 m
21-1b
21-1d X
21-3b
24-6d
25-1a
30-8c
undulator
L =120 m
...existing linac
BC-1
L =6 m
R56= -36 mm
BC-2
L =22 m
R56= -22 mm
DL-1
L =12 m
R56 0
DL-2
L =66 m
R56 = 0
SLAC linac tunnel
undulator hall
(12/01/01)

3. LCLS Linac Layout
BC1
0.25 GeV
BC2
5.4 GeV
undulator
14.3 GeV

4. Compression Evolution using Elegant*
before BC1
after BC1
E = 250 MeV
sz  830 mm
E = 250 MeV
sz  190 mm
under-compression of head & tail from 3rd-order term
L2 wakes induce new 3rd-order correlation
over-compression of head and tail
before BC2
after BC2
E = 4.5 GeV
sz  190 mm
E = 4.5 GeV
sz  22 mm
* written by M. Borland, ANL/APS

5. 3rd-order energy-time correlation from injector
E0 = 150 MeV
energy ‘chirp’
1st, and 2nd-order correctable with S-band and X-band RF…
2nd-order fit
HEAD
3rd-order term remains…
3rd-order term generated with space charge and l(s) in gun-to-linac drift (C. Limborg)

6. Smoothed Parmela dist. input to LCLS
plus temporal smoothing
at 150 MeV, before any bends

7. LCLS bunch tracked to start of BC2
cubic correlation term generates head/tail spikes at end of chicane
CSR ON in upstream bends (BC1, etc)
CSR OFF in upstream bends (BC1, etc)
CSR in BC1 causes microbunching at entrance to BC2
…otherwise have smooth dist. at BC2 entrance

8. Superconducting Wiggler in LCLS…
10 cm
20 cm
5 cm
90 cm
Add Super-Conducting wiggler prior to BC2 to increase incoherent energy spread (×10)
SC wiggler
BC2 chicane
E0 = 4.54 GeV
sE/E0  3×10-5
Dex/ex0  7%
At BC2:
wiggler field limited by b-function
E1 = 14.3 GeV
sz0  195 mm
sz1  22 mm
(sz0/sz1)sE/E1  8.4×10-5
At Undulator:

9. Superconducting wiggler OFF
SC-wiggler OFF
Using Stupakov CSR model (based on Saldin et. al.) and Elegant tracking
SC-wiggler ON
CSR may still be over-estimated in present tracking

10. LCLS Distribution After BC2 Chicane
(SC-wiggler ON, CSR ON in upstream bends)
wiggler  310-5 incoherent energy spread
sE/E0 = %
 bunch head
ss = 24.8 mm
E0 = 4.54 GeV

11. LCLS Distribution After BC2 Chicane
(SC-wiggler OFF, CSR ON in upstream bends)
310-6 incoherent energy spread
sE/E0 = %
 bunch head
ss = 24.8 mm
E0 = 4.54 GeV

12. LCLS Distribution After BC2 Chicane
(SC-wiggler ON and CSR OFF in upstream bends)
wiggler  310-5 incoherent energy spread
sE/E0 = %
 bunch head
ss = 24.8 mm
E0 = 4.54 GeV
no CSR in upstream bends

13. LCLS Distribution After BC2 Chicane
(SC-wiggler OFF, CSR OFF in upstream bends)
310-6 incoherent energy spread
sE/E0 = %
 bunch head
ss = 24.8 mm
E0 = 4.54 GeV
no CSR in upstream bends

14. Final x-x Phase Space (LCLS input)
e/e0  2.5

15. Slice Mismatch and Oscillation (LCLS Input)

16. Slice Emittance (LCLS)

17. LCLS BC2 CSR-integrated-wake (tracked dist.)

18. Transverse RF deflector used to diagnose ‘slice’ emittance after BC2
screen at 6.2 MeV after BC2 with transverse-RF OFF
Transverse RF ON (V = 20 MV)

19. Sliced Beam After Injector and Linac Tracking
gex
gey
osc-amp/s
mismatch zx zy
Ming-Xie method
LG < 4 m

20. Summary
New awareness of CSR micro-bunching and new design optimization
Projected emittance doubles over linac, but slice parameters allow LG < 4 m
Projected emittance growth presents a diagnostics and tuning challenge (use transverse RF)
Stability studies and Genesis results  (see M. Borland talk…)