1. CSR Benchmark Test-Case Results
Paul Emma
SLAC
January 14, 2001
BERLIN
CSR Workshop

2. Chicane CSR Test-Case
Use line-charge CSR    transient model described in LCLS-TN-01-12…
(Stupakov/Emma, Dec. 2001)
[same now used in Elegant]
…based on
TESLA-FEL-96-14
(Saldin et al., Nov. 1996)
(T566 included, no ISR* added)
* incoherent synchrotron radiation

3. Initial Gaussian Distribution Prior to Chicane
perfectly linear correlation
sE/E0 = 0.72 %
 bunch head
ss = 200 mm
E0 = 5 GeV

4. Second Order Compression Included: T566
/mm
T566  -3R56/2
leads to slight bunch shape distortion
after drift-3
before drift-3

5. Beta and Dispersion Functions
‘CSR-altered’ bx
‘linear’ bx
hx-max  267 mm
‘linear’ hx

6. Bunch Length and R56 ss0 = 200 mm ss = 20 mm R56 = -25 mm B1 B2 B3 B4

7. Final s-d phase space (gaussian input)
sE/E0 = %
 bunch head
ss = 20.3 mm

8. Energy Spread and Emittance (gaussian)B1 B2 B3 B4
E /E0  %
sd  0.021% B1 B2 B3 B4
gex  1.52 mm

9. Total RMS Relative Energy Spread (including ‘chirp’)B1 B2 B3 B4

10. Chicane CSR-wake Movie (gaussian)

11. Chicane CSR-integrated-wake (gaussian)

12. Final x-x Phase Space (gaussian input)
ge  1.52 mm
geCSR  mm
ge0 = 1.00 mm
bopt  1.37 m
aopt  -1.10

13. Final x-x Phase Space (gaussian & optimal b0, a0)
emittance growth can be reduced by choosing optimal b-functions
ge  1.15 mm
geCSR  mm
b  bopt
a  aopt
ge0 = 1.00 mm

14. Beta and emittance (gaussian & optimal b0, a0)
too big?
bmin  0.6 m
b  bopt
a  aopt
gex  1.15 mm

15. CSR wakefields (gaussian  bend-1 to drift-2)
L = 0.4 m
drift-1 (20)
L = 5 m
Nbin = 600, smoothed over 4
bend-2 (10)
L = 0.4 m
drift-2 (10)
L = 1 m

16. CSR wakefields (gaussian  bend-3 to drift-4)
L = 0.4 m
drift-3 (40)
L = 5 m
bend-4 (20)
L = 0.4 m
drift-4 (20)
L = 2 m

17. Compressing Uniform Distribution

18. Final s-d phase space – Uniform input dist.
sE/E0 = %
ss = 20.2 mm

19. Energy Spread and Emittance (uniform)
E /E0  %
sd  0.007%
emittance growth reduced compared to gaussian
gex  1.12 mm

20. Chicane CSR-wake Movie – Uniform Dist.

21. Chicane CSR-integrated-wake – Uniform Dist.

22. Final x-x Phase Space (uniform input)
ge  1.12 mm
geCSR  0.07 mm
ge0 = 1.00 mm
bopt  3.9 m
aopt  -0.51

23. CSR wakefields (uniform  bend-1 to drift-2)
L = 0.4 m
drift-1 (20)
L = 5 m
Nbin = 600, smoothed over 4
bend-2 (10)
L = 0.4 m
drift-2 (10)
L = 1 m

24. CSR wakefields (uniform  bend-3 to drift-4)
L = 0.4 m
drift-3 (40)
L = 5 m
bend-4 (20)
L = 0.4 m
drift-4 (20)
L = 2 m

25. Betatron Amplitude per Bunch Slice
gaussian
l(s)
uniform
l(s)

26. Final s-d phase space - Single-Bend
sE/E0 = %
ss = 20.1 mm

27. Energy Spread and Emittance – Single Bend
steady-state
bend magnet
sd = 0.011%
(24ssR2)1/3

28. CSR-Wake Movie - Single-Bend

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