1. Collective Effects in the Driver of the Wisconsin Free-Electron Laser (WiFEL) Robert Bosch, Kevin Kleman and the WiFEL team Synchrotron Radiation Center University of Wisconsin-Madison Juhao Wu SLAC National Accelerator Laboratory September 27, 2010

2. Outline I. The Wisconsin FEL II. Two-stage compression A.Macroscopic effects B.Microbunching C.Beam spreader III. Single-stage compression IV. Shot noise V. Using CSR to remove chirp VI. CSR effect in recirculating linac driver VII. Summary

3. WiFEL is a planned user facility with 3 FELs driven by a 1.7 GeV e-beam and 3 FELs at 2.2 GeV. A superconducting photoinjector and linac provide 200-pC parabolic bunches with peak current of 50 A. Magnetic bunch compression in- creases the current to 1 kA for the FELs. Collective effects in the driver must be considered.

4. Scientific Demand for a VUV/Soft Xray FEL Diffraction, VUV/X-ray light; e.g., for coherent imaging at nanometer-scale Highest energy-resolution beamlines Tool for advanced nanotechnology patterning Subpicosecond pulses for pump-probe experiments; e.g., for femtochemistry High flux for resonant inelastic X-ray scattering (photon in, photon out) Coherent synchrotron radiation in the infrared from bunches as a whole

5. UW FEL Layout

6. The FEL design fits in a field that is owned by the University of Wisconsin, across the street from SRC.

7. UV Hall 1.7 GeV Seed lasers Undulators 180 – 550 eV 20 – 180 eV 4.6 – 40 eV Master laser oscillator Fiber link synchronization Injector laser Pump lasers End stations Ebeam switch 2.2 GeV Seed lasers Undulators 80 – 550 eV 250 – 750 eV 300 – 900 eV SRF Linac Injector X-ray Hall Pump lasers End stations Ebeam dump RF power supplies Fiber link synchronization All undulators operate simultaneously at repetition rate up to 1 MHz each. Total number of undulators set by budget. Synchronization to ~10 fs. UW FEL Layout Courtesy Bill Graves

8. Figure courtesy of R. Legg 200-MHz superconducting rf gun

9. Superconducting Linac Linac is based on CW superconducting modules. CW SRF is currently in use at Jlab, SNS, Stanford, Daresbury, Rossendorf, BESSY CW SRF linac at Rossendorf

10. Magnetic Bunch Compression: Injectors Make 10’s Amps but FEL Need Kiloamps

11. Initial design: 2-stage bunch compressor with chicanes at 215 MeV and 485 MeV. Factor-of-twenty compression gives 1 kA output current. 1.7 GeV  = -17.8° Injector 3 Modules  = 9°  = 50.6° L2 15 Modules BC1 R 56 = -87 mm BC2 R 56 = -18 mm 3.9 GHz Cavities (10) 36.3 MV, 180° 215 MeV L1 2 Modules 485 MeV Gun 4 MeV 251.3 MeV BC1 compresses by a factor of 8, while BC2 compresses by a factor of 2.5

12. Lattice functions plotted from 4 MeV to 1.7 GeV

13. Compression of a parabolic bunch without collective effects. 100,000 particles are tracked by ELEGANT. 4 MeV BC1 entrance BC1 exitBC2 entrance BC2 exit1.7 GeV Tail 

14. Longitudinal wakefields affect the compression. The ELEGANT code simulates the effects. An approximate analytic model provides fast 1. Estimate of the minimum initial bunch length that can be compressed without an upright tail. 2. Trial-and-error compensation of wakes by adjusting rf parameters. 3. Jitter estimates. 4. Microbunching gain.

15. Analytic model The bunch is frozen outside of the chicanes. Longitudinal impedances act upon frozen bunches. Longitudinal impedances within the chicanes are represented by effective impedances. Emittance effects are included in the effective impedances.

16. Longitudinal Impedance Formulas Longitudinal space charge (LSC) Linac geometric impedance Steady-state coherent synchrotron radiation (CSR) in magnets Coherent edge radiation (CER) downstream of magnets

17. Effective impedances from beginning of bunch compressor BC1 before BC1 between BC1 and BC2 after BC2, up to 1.7 GeV initial wavelength of modulation

18. Tracking simulations show that macroscopic wake effects upon the 1.7-GeV bunch are approximated by resistive impedances. LiTrack with resistors ELEGANT with coherent radiation Trapezoidal bunch Gaussian bunch Parabolic bunch

19. Upright bunch tails in phase space at 1.7 GeV are predicted by formulas for resistive impedances. LiTrack with resistors ELEGANT with coherent radiation Trapezoidal bunch Gaussian bunch Parabolic bunch

20. Fast 1-D compressor adjustment for design optimization with CSR/CER and wakes of the injector, harmonic cavities, and linacs for 200-pC parabolic bunches ELEGANT simulation (slow) LiTrack with coherent radiation approximated by resistors (fast)

21. 4 MeV BC1 entrance BC1 exitBC2 entrance BC2 exit1.7 GeV ELEGANT simulation of the adjusted compression.

22. Microbunching Input current and energy modulations at the entrance of BC1 cause output modulations at 1.7 GeV. Formulas for the growth of modulations are obtained. ELEGANT tracking of 4 million particles agrees with the formulas. Evaluation of the formulas is much faster than tracking simulations.

23. Analytic modeling (curves) and ELEGANT simulations (dots) predict microbunching gain for a trapezoidal bunch. Trapezoidal bunch with 3-keV Gaussian energy distribution and 1-micron normalized emittance Trapezoidal bunch with 10-keV laser-heater energy distribution and 1-micron normalized emittance

24. Analytic modeling (curves) and ELEGANT simulations (dots) predict microbunching gain for low emittance. Trapezoidal bunch with 3-keV Gaussian energy distribution and 0.1-micron normalized emittance

25. Analytic modeling (curves) also approximates ELEGANT simulations of a parabolic bunch (dots). Parabolic bunch with 3-keV Gaussian energy distribution and 1-micron normalized emittance Parabolic bunch with 10-keV laser-heater energy distribution and 1-micron normalized emittance

26. Analytic modeling (curves) approximates ELEGANT simulations of a parabolic bunch (dots) that is heated by 10-keV in a laser-heater simulation. Parabolic bunch heated by 10 keV in a laser heater simulation. Normalized emittance is 1 micron 3-keV initial Gaussian energy distribution After 10-keV heating in a laser heater simulation

27. The effect of the beam spreader upon microbunching gain for a 3-keV Gaussian energy distribution. Solid lines and dots are analytic and simulated gain from the chicane entrance through the beam spreader; dashed lines and open dots are gain without a beam spreader. (a) Original spreader design with R56 = 950 microns. (b) Revised spreader design with R56 = 38.5 microns.

28. Single-stage factor-of-twenty bunch compressor, with rf parameters optimized for 200-pC parabolic bunches. In comparison with 2-stage compression, the required harmonic-cavity voltage is much larger, and the dechirping phase in the final linac is larger. 1.7 GeV  = -18.5° Injector 5 Modules  = 40° L1 15 Modules BC1 R 56 = -100 mm 3.9 GHz Cavities (10) 45 MV, 180° 400 MeV Gun 4 MeV 445 MeV

30. RF parameters of the 1-stage compressor adjusted for coherent radiation and wakes of the injector and linac L1, for 200-pC parabolic bunches. The output of a low-R56 beam spreader is shown. Tail 

31. The effect of the beam spreader upon microbunching gain for a 3-keV Gaussian energy distribution. Solid lines and dots are analytic and simulated gain from the chicane entrance through the beam spreader; dashed lines and open dots are gain without a beam spreader. (a) Original spreader design with R56 = 950 microns. (b) Revised spreader design with R56 = 38.5 microns.

32. The microbunching gain is more than an order of magnitude lower with single-stage compression than with two-stage compression. With a low-R56 spreader, the microbunching is not increased. Single-stage compression with a low-R56 spreader provides the best FEL performance since a colder bunch can be compressed. Laser-heating may not be required.

33. Current and energy modulations at the FEL from shot noise, according to an analytical calculation that assumes linear gain for an initially parabolic bunch with 3-keV Gaussian energy spread. (a) Two-stage bunch compressor. (b) One-stage bunch compressor. The one-stage compressor with low-R56 spreader satisfies the FEL requirements that modulations with wavelengths shorter than the bunch should be smaller than 10% for current and 3x10 -4 for energy modulations.

34. The lower microbunching gain with single stage compression and a low-R56 spreader is confirmed by the following simulations that approximate the amplified shot noise for an initial energy spread of 3 keV.

35. Amplified shot noise for two-stage compression followed by a beam spreader with R56 = 950 microns.

36. Amplified shot noise for two-stage compression followed by a beam spreader with R56 = 40 microns.

37. Amplified shot noise for single-stage compression followed by a beam spreader with R56 = 950 microns.

38. Amplified shot noise for single-stage compression followed by a beam spreader with R56 = 40 microns.

39. A beneficial application of collective effects: In the WiFEL single-stage compressor, the compressed bunch is accelerated 40 degrees off- crest to remove its energy chirp. Since this requires 30% more RF accelerating voltage than on-crest acceleration, an alternative method of removing the bunch’s energy chirp may be cost-effective. The wake of coherent synchrotron radiation (CSR) is one alternative method for removing the bunch chirp.

40. An analytic model predicts that a short bending magnet reduces the chirp of a rectangular bunch (in V/s) by –NqZ 0 /πt b 2, where N is the bunch population, q is the electron charge, Z 0 is the impedance of free space, and t b is the bunch length in seconds. The magnets should be separated by a distance exceeding ct b /(1-cosӨ), where c is the speed of light and Ө is the angle of deflection in a bending magnet. About 15 bending magnets are predicted to give a dechirped WiFEL bunch with on-crest acceleration of the compressed bunch.

41. Removing the chirp of a bunch with the wake of CSR. This chicane dechirper cell contains 8 short bending magnets.

42. Longitudinal phase space at the exit of the beam spreader for on-crest acceleration after single-stage compression. (a) No dechirping cells. (b)Two dechirping cells (16 bending magnets) at beam energy of 400 MeV. (c) Two dechirping cells at 1.7 GeV.

43. Simulations of shot noise show increased microbunching from the dechirping chicanes’ R 56 = -1 mm, for a bunch that is not heated by a laser heater. The FEL requirements are marginally satisfied without a laser heater, with initial energy spread of 3 keV. Dechirping by off-crest acceleration, no dechirping chicanes Dechirping by 4 dechirping chicanes at beam energy of 400 MeV Dechirping by 4 dechirping chicanes at beam energy of 1700 MeV

44. Removing the chirp of a bunch with the wake of CSR. This isochronous arc dechirper contains 3 bending magnets.

45. Longitudinal phase space at the exit of the beam spreader for on-crest acceleration after single-stage compression. (a)No dechirping arcs. (b) Four dechirping arcs (12 bending magnets) at beam energy of 400 MeV. (c) Four dechirping arcs at 1.7 GeV.

46. Simulations of shot noise show little increase in microbunching from the isochronous dechirping arcs, for a bunch that is not heated by a laser heater. The FEL requirements are satisfied without a laser heater. Dechirping by off-crest acceleration, no dechirping arcs Dechirping by 4 isochronous arcs at beam energy of 400 MeV Dechirping by 4 isochronous arcs at beam energy of 1700 MeV

47. CSR is also important in a recirculating-linac FEL driver. Lattice functions for a 1.7-GeV design with two 3-magnet isochronous arcs on each end, followed by a chicane for bunch compression.

48. Parameters for good compression with CSR effects have been found by trial-and-error tracking with the ELEGANT code. Here, a 200-pC bunch with initial length of 450 um compresses well with a linac phase of 17.2 degrees.

49. Q = 200 pC, initial length of 450 um, continued

52. Summary Collective effects must be considered in the WiFEL driver Longitudinal wakes were modeled with longitudinal impedances before and after each stage of compression. Resistive impedances in the longitudinal LiTrack code approximate macroscopic CSR/CER effects. This allows fast adjustment of rf parameters to compensate longitudinal wakes. Microbunching analytic model agrees with simulations. Microbunching gain is minimized with single-stage compression followed by a beam spreader with R 56 << 1 mm. Shot noise simulations suggest that a laser heater will not be required in this case. With a cold bunch, we expect better FEL performance. The compressed bunch may be dechirped with the wake of CSR. This reduces the expense for superconducting RF cavities. In a recirculating-linac design, CSR effects have been studied by tracking with ELEGANT. Trial and error has been used to find parameters for good compression in a chicane downstream of the recirculating linac.