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Some Simulations for the Proposed Hard X-Ray Self-Seeding on LCLS

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

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Some Simulations for the Proposed Hard X-Ray Self-Seeding on LCLS

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

  2. Possible experiment at LCLS • DESY’s scheme for 8 keV HXRSS • Low charge 20 pC, 0.4 mm-mrademittance, 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 15thundualtor, • SASE FEL from the exit of 13 undulator on the single crystal • We reserve the 14thfor 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. d z (mm) t (s) (mm) 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 • Pseed= 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 • Pseed= 5 MW @ 15 m

  16. S-2-E electron bunch • Simulation with S-2-E electron bunch • Pseed= 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 • Pseed= 5 MW @ 51.9 m

  18. S-2-E electron bunch • Simulation with S-2-E electron bunch • Pseed= 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 • Pseed= 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(2qB)| for p - polarization, and |C = 1| for s - polarization

  21. p - polarization

  22. s - polarization

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

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

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

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

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

  28. 8 keV energy-jitter case • Spectrum on the left, temporal profile on the right • l =1.6 Å; Bragg angle: 63.78o • s - 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 W 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 p - polarization, and right plots for s - polarization • The red curve is for ideal parallel incident beam, the blue is for rms sx’ = 2mrad, and the green is for rms sx’ = 4mrad.

  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

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