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

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

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.
251.3 MeV
215 MeV
4 MeV
Injector
3 Modules L1
2 Modules
485 MeV L2
15 Modules
1.7 GeV
Gun
BC1
R56 =
-87 mm
BC2
R56 =
-18 mm
f = -17.8°
f = 9°
f = 50.6°
3.9 GHz Cavities (10)
36.3 MV, 180°
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 exit
BC2 entrance
BC2 exit
1.7 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
LiTrack with coherent radiation
approximated by resistors (fast)
ELEGANT simulation (slow)

21. ELEGANT simulation of the adjusted compression.
4 MeV
BC1 entrance
BC1 exit
BC2 entrance
BC2 exit
1.7 GeV

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.
3-keV initial
Gaussian
energy
distribution
After 10-keV heating
in a laser heater
simulation
Parabolic bunch heated by 10 keV in a laser heater simulation. Normalized emittance is 1 micron

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.
4 MeV
445 MeV
400 MeV L1
15 Modules
Injector
5 Modules
1.7 GeV
Gun
BC1
R56 =
-100 mm
f = -18.5°
f = 40°
3.9 GHz Cavities (10)
45 MV, 180°

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
–NqZ0/πtb2, where N is the bunch population, q is the electron charge, Z0 is the impedance of free space, and tb is the bunch length in seconds.
The magnets should be separated by a distance exceeding ctb/(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
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.
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’ R56 = -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
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.
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. The FEL requirements are satisfied without a laser heater.
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
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

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

51. 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 R56 << 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.