CSR Benchmark Test-Case Results

1. CSR Benchmark Test-Case Results Paul Emma SLAC January 14, 2002 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 B2 B3 B1 B4 ‘CSR-altered’ bx ‘linear’ bx hx-max 267 mm ‘linear’ hx

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

7. Line-Charge Validity Is transverse bunch size small ? B2 B3 B1 B4 x3/(Rs2) << 1 (Derbenev et. al.)

8. CSR may be over-estimated in present tracking… s s s s (s- s) Rj3/24 fields evaluated and immediately applied, without including longer bunch at retarded position  over-estimate? R R j

9. Final s-d phase space (gaussian input) sE/E0 = 0.716 %  bunch head ss = 20.3 mm

10. Energy Spread and Emittance (gaussian) B2 B4 B3 B1 E /E0 -0.043% sd 0.021% B2 B4 B3 B1 gex 1.52 mm

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

12. Chicane CSR-wake Movie (gaussian)

13. Chicane CSR-integrated-wake (gaussian)

14. Final x-x Phase Space (gaussian input) ge 1.52 mm geCSR 0.145 mm ge0 = 1.00 mm bopt 1.37 m aopt-1.10

15. Final x-x Phase Space (gaussian & optimalb0, a0) emittance growth can be reduced by choosing matchedb-functions ge 1.15 mm geCSR 0.145 mm bbopt aaopt ge0 = 1.00 mm

16. Beta and emittance (gaussian & optimalb0, a0) too big? bmin 0.6 m bbopt aaopt gex 1.15 mm

17. CSR wakefields (gaussian  bend-1 to drift-2) bend-1 (10) 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

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

19. Compressing Uniform Distribution rise/fall ‘time’ > R/g3 0.1 Å

20. Final s-d phase space – Uniform input dist. sE/E0 = 0.720 % ss = 20.2 mm

21. Now add incoherent synch. rad. in each bend (sE/E0)ISR 1.910-5 sE/E0 = 0.720 % less structure on bunch ss = 20.2 mm

22. Energy Spread and Emittance (uniform dist.) E /E0 -0.046% sd 0.007% emittance growth reduced compared to gaussian gex 1.12 mm

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

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

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

26. CSR wakefields (uniform dist.  bend-1 to drift-2) bend-1 (10) 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

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

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

29. Final s-d phase space - Single-Bend sE/E0 = 0.011 % ss = 20.1 mm

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

31. CSR-Wake Movie - Single-Bend

32. Try a Double-Chicane (two ‘test’-chicanes) hx 244 mm -I hx 107 mm R56= -21 mm R56= -4 mm ss 200 mm E0 = 5 GeV ss 50 mm ss 20 mm

33. CSR Energy Loss, Spread, and Emittance (double-chicane) E /E0 -0.052% energy loss and spread are larger than for a single-chicane sd 0.028% projected emittance growth is greatly reduced using double-chicane single-chicane double-chicane gex 1.01 mm

34. Final s-d phase space (double-chicane) sE/E0 = 0.712 % ss = 20.4 mm projected emittance growth is much smaller, but micro-bunching is worse