1. Some Simulations for the Proposed Hard X-Ray Self- Seeding on LCLS J. Wu J. Wu et al. Feb. 25, 2011

2. Possible experiment at LCLS DESY’s scheme for 8 keV HXRSS –Low charge 20 pC, 0.4 mm-mrad emittance, slice energy spread 1.3 MeV –Plan to take the section 15 undulator out to implement the chicane and single crystal Numerical Simulation –with ideal electron bunch –with start-to-end electron bunch Additional details –Energy tuning –X-ray angular divergence

3. Ideal simulation SASE FEL performance 13-46.8,14-50.4,15-54

4. SASE FEL at exit of Und.13 Plan to take out the 15 th undualtor, SASE FEL from the exit of 13 undulator on the single crystal –We reserve the 14 th for safety consideration

5. Single crystal monochromator FEL spectrum after the single-crystal monochromator

6. Single crystal monochromator FEL after the single-crystal monochromator

7. Self-seeded FEL at exit of und 10 There are 18 undualtors after the monochromator –FEL at the exit of 10 undulator (no tapering) – minimum bandwidth 2.8E-5

8. Maximum power with taper Taper the 18 undualtors after the monochromator –Taper starts at 25 m, quadratic taper of 2 % –At the end of 18 undulator (60 m magnetic length), FEL power reach 100 GW (< 1 mJ for low charge 20 pC)

9. Self-seeded FEL at exit of Und 18 There are 18 undualtors after the monochromator –FEL at the exit of 18 undulator 1.0E-4

10.  Start-to-end e  bunch: und.-comp. t (s) z (  m)  (  m) Courtesy of Y. Ding

11. Start-to-end simulation SASE FEL performance –Taper starts at 25 m, quadratic taper of 2 % 13-51.9,14-55.8,15-60

12. S-2-E electron bunch Simulation with S-2-E electron bunch –SASE @ 132 m, blue: raw data, green, smoothed data (2%), red: Gaussian fit FWHM BW: 2.5E-3 FWHM BW: 3.3E-3

13. Start-to-end simulation Seeded FEL (5 MW seed) performance 13-51.9, 18-72

14. S-2-E electron bunch Simulation with S-2-E electron bunch –P seed = 5 MW @ 15 m, blue: raw data, red: Gaussian fit FWHM BW: 2.5E-3 FWHM BW: 9.4E-4 FWHM BW: 1.1E-4 FWHM BW: 1.3E-4

15. S-2-E electron bunch Simulation with S-2-E electron bunch –P seed = 5 MW @ 15 m

16. S-2-E electron bunch Simulation with S-2-E electron bunch –P seed = 5 MW @ 51.9 m, blue: raw data, green, smoothed data (0.25%), red: Gaussian fit FWHM BW: 2.5E-3 FWHM BW: 9.4E-4 FWHM BW: 1.1E-4 FWHM BW: 2.6E-4

17. S-2-E electron bunch Simulation with S-2-E electron bunch –P seed = 5 MW @ 51.9 m

18. S-2-E electron bunch Simulation with S-2-E electron bunch –P seed = 5 MW @ 72 m, blue: raw data, green, smoothed data (0.1%), red: Gaussian fit FWHM BW: 2.5E-3 FWHM BW: 9.4E-4 FWHM BW: 1.1E-4 FWHM BW: 2.8E-4

19. S-2-E electron bunch Simulation with S-2-E electron bunch –P seed = 5 MW @ 72 m

20. FEL Energy Tuning The plan is to have a tuning range from 1.4 Å to 1.6 Å Rocking curve: –The bandwidth in the rocking curve depends on |C = cos(2  B )| for  - polarization, and |C = 1| for  - polarization

21.  - polarization

22.  - polarization

23. 8 keV energy-jitter case Spectrum on the left, temporal profile on the right –  =1.4 Å; Bragg angle: 51.72 o –  - polarization

24. 8 keV on-energy case Spectrum on the left, temporal profile on the right –  =1.5 Å; Bragg angle: 57.25 o –  - polarization

25. 8 keV energy-jitter case Spectrum on the left, temporal profile on the right –  =1.6 Å; Bragg angle: 63.78 o –  - polarization

26. 8 keV energy-jitter case Spectrum on the left, temporal profile on the right –  =1.4 Å; Bragg angle: 51.72 o –  - polarization

27. 8 keV on-energy case Spectrum on the left, temporal profile on the right –  =1.5 Å; Bragg angle: 57.25 o –  - polarization

28. 8 keV energy-jitter case Spectrum on the left, temporal profile on the right –  =1.6 Å; Bragg angle: 63.78 o –  - polarization

29. Maximum power with taper Taper the 18 undualtors after the monochromator –Taper starts at 25 m, quadratic taper of 2 % –Divergence along the undulator

30. Self-seeded FEL at exit of 18 undulators There are 18 undulators after the monochromator –FEL at the exit of 18 undulator

31. Angular divergence To incorporate the x-ray beam divergence into dynamic theory of diffraction We take a phenomenological approach, we define the effective Darwin width as where  is the FWHM beam divergence Then we follow the derivation in dynamic theory of diffraction by introducing an effective deviation parameter

32. Angular divergence The transmitted intensity is then with and t being the crystal thickness.

33. Rocking curve Left plots for  - polarization, and right plots for  - polarization –The red curve is for ideal parallel incident beam, the blue is for rms  x’ = 2  rad, and the green is for rms  x’ = 4  rad.

34. On-going work Refine the S-2-E simulation for 20 pC Optimize the tapering Simulation for 40 pC case Find out the minimum seed power to dominate the SASE in the second undulator