1. ‘S2E’ Study of Linac for TESLA XFEL P. Emma SLAC  Tracking  Comparison to LCLS  Re-optimization  Tolerances  Jitter  CSR Effects

2. L = 6 m L = 9 m  rf =  38° L = 330 m  rf =  43° L = 550 m  rf =  10° BC-1 L = 6 m R 56 =  36 mm BC-2 L = 22 m R 56 =  22 mm DL-2 R 56 = 0 DL-1 R 56  0 undulator L =120 m 6 MeV  z  0.83 mm    0.1 % 150 MeV  z  0.83 mm    0.10 % 250 MeV  z  0.19 mm    1.8 % 4.54 GeV  z  0.022 mm    0.76 % 14.35 GeV  z  0.022 mm    0.01 %...existing linac L0 rf gun L3L1 X Lh L =0.6 m  rf =  L2 L  16 m  rf   40° L  72 m  rf   40° L  850 m  rf = 0° BC-2 L  14 m R 56 =  36 mm BC-3 L  18 m R 56 =  11 mm undulator L =? m 6 MeV  z  2.0 mm    0.1 % 120 MeV  z  0.5 mm    2.0 % 375 MeV  z  0.1 mm    1.4 % 1.64 GeV  z  0.020 mm    0.5 % 20.5 GeV  z  0.020 mm    0.01 % L3L0 Lh L  1.4 m  rf =  rf gun 3.9 L1 BC-1 L  4 m R 56 =  76 mm L = 8 m  rf   22° L2 LCLS TESLA-XFEL (parameters only approximate)

3. Twiss parameters along TESLA-XFEL BC1 BC2 BC3 undulator

4. Bunch length and energy spread along TESLA-XFEL E/EE/EE/EE/E ssss

5.  -bunching exaggerated by noise, but gain may be large (see modulated beam study below). BC1+ BC2+ BC3+

6. Longitudinal phase space at end of TESLA-XFEL  -bunching exaggerated by noise (see modulation study below)  x  1.3  3.6  m

7. Slice emittance at end of TESLA-XFEL

8. Slice energy spread at end of TESLA-XFEL  E /E < 0.01%

9. slice 4D centroid osc. amplitude Twiss slice mismatch amplitude Sliced Bunch Analysis I pk  x,y E/E0E/E0E/E0E/E0  /  /

10. Quad alignment tolerances Quad roll-angle tolerances 1 mm 10 mrad

11. Longitudinal-only simulation with LiTrack (200k in 66 seconds) no CSR

12.  0 = 0.2°  0 = 0 I pk  11 kA I pk  6 kA Test rf phase sensitivity:

13. gun-timing charge |  E/E| < 0.1% |  t i | < 0.13 ps |  Q/Q| < 4% gun-timing charge |  I pk /I pk | < 12% Scan gun-laser timing and charge, monitoring energy and peak current

14. gun-timingcharge |  t i |< 0.13 ps |  Q/Q|< 4% 3.9-phase3.9-voltage |  h |< 0.05° |  V h /V h |< 0.3% L0-phaseL0-voltage |  0 |< 0.07° |  V 0 /V 0 |< 0.08% L1-phaseL1-voltage |  1 |< 0.05° |  V 1 /V 1 |< 0.21%

15. L2-phaseL2-voltage L3-phaseL3-voltage |  2 |< 1.1° |  V 2 /V 2 |< 1.6% |  V 3 /V 3 |< 0.1% |  3 |< 2.2° This suggests an increase of the 3.9-GHz voltage  Note 2 nd -order chirp after BC2 System is very sensitive with large 11-kA spike at head (T. Limberg)…

16. LiTrack with 3.9-GHz voltage raised from 16.6 MV to 21.0 MV previous distribution no spikes

17.  0 = 0.2°  0 = 0 I pk  5.5 kA I pk  4.5 kA With 21-MV 3.9-GHz rf, again testing rf phase sensitivity: …much less sensitive

18. gun-timingcharge |  t i |< 6.0 ps |  Q/Q|< 100% 3.9-phase3.9-voltage |  h |< 0.19° |  V h /V h |< 1.0% L0 phase L0 voltage |  0 |< 0.09° |  V 0 /V 0 |< 0.20% L1 phase L1 voltage |  1 |< 0.24° |  V 1 /V 1 |< 1.0%

19. L3 phase L3 voltage |  3 |< 2.2° |  V 3 /V 3 |< 0.1% L2 phase L2 voltage |  2 |< 0.49° |  V 2 /V 2 |< 1.4%

20. original adjusted3.9-GHz 3.9-GHz & X-band

21. Form ‘jitter budget’ based on uncorrelated jitter: degrees of X-band or 3.9-GHz 3.9-GHz & X-band h-

22. LiTrack Jitter Simulation of TESLA-XFEL using ‘jitter budget’ 6.7 minutes @ 5 Hz (no CSR)  I/I 0 ) rms  13%  E/E 0 ) rms  0.09%  /  /  0.18%  t) rms  0.2 ps energy energy spread peak current arrival time

23. No CSR Now test re-optimized setup with full 6D tracking (Elegant)

24. Elegant tracking with CSR (and increased 3.9-GHz voltage)  x  1.3  2.4  m  -bunching exaggerated by noise, but gain at  3  m may be large (see modulation study below) 4 keV injector slice energy spread

25. Elegant tracking with CSR and slice energy spread ×6 from gun  x  1.3  2.0  m  -bunching damped by large intrinsic energy spread (23 keV or  10  4 at undulator) 23 keV injector slice energy spread

26. slice  slice  E /E < 0.01%  -tron oscillation induced by CSR energy loss Full 6D Elegant tracking with increased 3.9-GHz voltage and “23 keV” …  x might be affected

27. = 500  m = 500  m A =  0.5% Add modulation on density and energy profile Use 10 6 macro-particles and quiet-start bunch population in x, x, z,  E/E at 120 MeV

28.  10  2 I pk  5 kA I pk  50 A 120 MeV 20.5 GeV CSR  -bunching in full TESLA-XFEL N = 10 6, bins = 500, transient 1D model, linear optics, matched  ’s, Q = 1 nC,  x = 1  m,  pk /  pk0  100,  E0 = 4 keV & 23 keV CSR off  E /E  10  4 at 20 GeV after BC’s linear optics

29. BC1 BC2BC3 Track full XFEL in 4D (x, x, z,  E/E) from pre-BC1 at 120 MeV to just past BC3 at 1.64 GeV using “CSR_calc” (PE) and linearly re-matching to proper  and energy chirp prior to each BC. re-match point

30. injector = 500  m, = 500  m, A = 0.5% post-BC1  123  m,  123  m, A  0.5% post-BC2  20  m,  20  m, A  6.0% post-BC3  6.6  m,  6.6  m, A  50%  E0 = 4 keV gain  100

31. injector = 500  m, = 500  m, A = 0.5% post-BC1  123  m,  123  m, A < 1.0% post-BC2  20  m,  20  m, A < 1.0% post-BC3  6  m,  6  m, A  3%  E0 = 23 keV gain  6

32.  E0 = 4 keV  E0 = 23 keV gain ~ 1 gain  150 = 250  m, = 250  m, A = 0.5%

33.   E0 = 4 keV   E0 = 23 keV TESLA-XFEL CSR Compound Gain Curve (no LSC) starting at 120 MeV

34.  Large  -bunching gain, even without longitudinal space charge – adding energy spread is very helpful  Charge jitter in XFEL much looser than LCLS  Some rf phase tolerances tighter than LCLS  Lack of longitudinal wakefield allows very linear compression, producing nearly uniform current profile – not possible in LCLS  Possibly better performance if BC3 were integrated into BC2?  Thanks especially to Yujong, Jean-Paul, and Torsten Final Comments