1. Paul Emma SLAC January 14, 2002 BERLIN CSR Benchmark Test-Case Results 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) 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) (T 566 included, no ISR * added) * incoherent synchrotron radiation

3. Initial Gaussian Distribution Prior to Chicane  s = 200  m  E /E 0 = 0.72 %  bunch head perfectly linear correlation E 0 = 5 GeV

4. Second Order Compression Included: T 566 T 566   3R 56 /2 after drift-3 before drift-3 leads to slight bunch shape distortion /mm

5. Beta and Dispersion Functions ‘linear’  x ‘linear’  x ‘CSR-altered’  x B1 B2 B3 B4  x-max  267 mm

6. Bunch Length and R 56 B1 B2 B3 B4 B1 B2 B3 B4  s = 20  m  s 0 = 200  m R 56 =  25 mm

7. Line-Charge Validity (Derbenev et. al.) B1 B2 B3 B4 Is transverse bunch size small ?  x 3 /(R  s 2 ) << 1

8. (s  s)  R  3 /24 R  s s s s fields evaluated and immediately applied, without including longer bunch at retarded position  over- estimate? R CSR may be over-estimated in present tracking…

9. Final s -  phase space (gaussian input)  s = 20.3  m  E /E 0 = 0.716 %  bunch head

10. Energy Spread and Emittance (gaussian) B1 B2 B3 B4 B1 B2 B3 B4  x  1.52  m    0.021%     0.043%

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

12. Chicane CSR-wake Movie (gaussian)

13. Chicane CSR-integrated-wake (gaussian)

14. Final x-x Phase Space (gaussian input)   1.52  m  0 = 1.00  m  CSR  0.145  m  opt  1.37 m  opt   1.10

15. Final x-x Phase Space (gaussian & optimal  0,  0 )   1.15  m  0 = 1.00  m  CSR  0.145  m    opt    opt emittance growth can be reduced by choosing matched  -functions

16. Beta and emittance (gaussian & optimal  0,  0 )  x  1.15  m    opt    opt too big?  min  0.6 m

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

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

19. Compressing Uniform Distribution rise/fall ‘time’ > R/   3  0.1 Å

20.  s = 20.2  m  E /E 0 = 0.720 % Final s -  phase space – Uniform input dist.

21. Now add incoherent synch. rad. in each bend less structure on bunch  s = 20.2  m  E /E 0 = 0.720 %  E /E 0  ISR  1.9  10  5

22.  x  1.12  m    0.007%     0.046% Energy Spread and Emittance (uniform dist.) emittance growth reduced compared to gaussian

23. Chicane CSR-wake Movie (uniform dist.)

24. Chicane CSR-integrated-wake (uniform dist.)

25. Final x-x Phase Space (uniform dist.)   1.12  m  0 = 1.00  m  CSR  0.07  m  opt  3.9 m  opt   0.51

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

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

28. (s) (s) Betatron Amplitude per Bunch Slice (s) (s) gaussian uniform

29. Final s -  phase space - Single-Bend  s = 20.1  m  E /E 0 = 0.011 %

30. Energy Spread and Emittance – Single Bend steady-state bend magnet   = 0.011% (24  s R 2 ) 1/3

31. CSR-Wake Movie - Single-Bend

32. Try a Double -Chicane (two ‘test’-chicanes)  x  244 mm  x  107 mm  s  50  m  s  200  m  s  20  m II R 56 =  21 mm R 56 =  4 mm E 0 = 5 GeV

33. CSR Energy Loss, Spread, and Emittance (double-chicane)    0.028%     0.052% energy loss and spread are larger than for a single-chicane  x  1.01  m projected emittance growth is greatly reduced using double-chicane single-chicane double-chicane

34.  s = 20.4  m  E /E 0 = 0.712 % Final s -  phase space (double-chicane) projected emittance growth is much smaller, but micro- bunching is worse