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Linac Coherent Light Source (LCLS) accelerator system Jitter model Longitudinal feedback model

LCLS Longitudinal Feedback with CSR as Diagnostic Tool Juhao Wu Stanford Linear Accelerator Center LCLS FAC Meeting, SLAC Oct. 12, 2004. Linac Coherent Light Source (LCLS) accelerator system Jitter model Longitudinal feedback model Coherent Synchrotron Radiation (CSR) as diagnostic tool

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Linac Coherent Light Source (LCLS) accelerator system Jitter model Longitudinal feedback model

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  1. LCLS Longitudinal Feedback with CSR as Diagnostic ToolJuhao WuStanford Linear Accelerator CenterLCLS FAC Meeting, SLACOct. 12, 2004 • Linac Coherent Light Source (LCLS) accelerator system • Jitter model • Longitudinal feedback model • Coherent Synchrotron Radiation (CSR) as diagnostic tool • Bunch length: Gaussian, step, and double-horn structure • Detector • Discussion

  2. LCLS Accelerator System • Electron beam at birth: peak current ~ 100 ampere • XFEL calls for very high peak current ~ several kilo ampere • Compress the bunch, and accelerate the bunch Bunch Compressor; Linac Accelerator

  3. X- X-band Jitter budget (< 1 minute time-scale) measured RF performance klystron phase rms  0.07° (20 sec) klystron ampl. rms  0.06% (60 sec) • Do we need a feedback system?

  4. i = 3 i = 4 i = 1 i = 2 i = 5 RF gun L0 L1 L2 L3 X DL2 DL1 BC1 BC2 bends of zero strength at i = 2 LCLS Accelerator System • LCLS accelerator system model (P. Emma): a 5-stage linac-bend segments

  5. LCLS Accelerator System • Linac • RF • Wakefield (structure wake) (K. Bane) • Chicane and Dog-leg (2rd order map) SLAC S-Band: s0 1.32 mm a 11.6 mm z < ~6 mm

  6. SPPS Accelerator System Jitter Measurement Peaks around (f1 =0.08) and (f2 =1.7) Hz Data rate 10 Hz, not 120 Hz Courtesy of P. Emma

  7. LCLS Accelerator System Jitter Model • We model the jitter as the follows:

  8. LCLS Performance (No Feedback ) ‘free’ machine At undulator entrance

  9. LCLS Feedback System Schematic Courtesy of P. Krejcik • Observables: • Energy: E0 (at DL1), E1 (at BC1), E2 (at BC2), E3 (at DL2) • CSR power bunch length: z,1 (at BC1), z,2 (at BC2) • Controllables: • Voltage: V0 (in L0), V1 (in L1), V2 (effectively, in L2) • Phase: 1 (in L1), 2 (in L2 ), 3 (in L3)

  10. LCLS Feedback Algorithm We arelinear

  11. LCLS Feedback System • LCLS feedback model • Include Proportional gain, Integral gain, and Derivative gain (PID): Integral gain helps at the low frequency regime • Cascade scheme: we need to keep the off-diagonal elements in the M-matrix • Pulse rep rate: 120 Hz

  12. Bode Plot (E/E) Integral Gain helps! P:0.2 P:0.2; I:0.5 I:0.5 • Similar Bode Plot for (I / I)

  13. LCLS Feedback Performance (Use CSR P / P) feedback off feedback on (Integral gain:0.5) At undulator entrance

  14. Coherent Synchrotron Radiation • CSR as nondestructive diagnostic tool • For a group of Ne electrons • CSR spectrum Single electron • Form factor

  15. Wake-induced Cubic term • Longitudinal phase-space before BC2 Blue: only L2 Black: L2 + L1 (with BC1) Red: L2 + L1+ wake (with parabolic dist.) Wake with parabolic dist. leads to the double-horn

  16. Wake for parabolic distribution • For a parabolic distribution, the induced wake is

  17. Wake-induced Cubic term • Longitudinal phase-space change due to BC2 Blue: after BC2 Red: before BC2 Wake with parabolic dist. leads to the double-horn

  18. Current profile after BC2 • Wake-induced double-horn structure With Laser-Heater ( ) Laser-Heater smears out the double-horn, however …

  19. Bunch spectrum after BC2 • Sharp-edge induces high freq. component Red: with Laser-Heater ( ) Black: Gaussian with same Blue: Step [J. Galayda] with same

  20. Integrated CSR Power • Detector matters Red solid curve: Gaussian with same z Black dashed curve: Step with same z Red dots: Real with Laser-Heater

  21. Integrated CSR Power • Stay in the low frequency regime Red solid curve: Gaussian with same z Black dashed curve: Step with same z Red dots: Real with Laser-Heater

  22. Integrated CSR Power • Stay in the low frequency regime • Pyroelectric Detector? • Detector with fixed , the integrated power

  23. Discussion • Given the jitter budget and the SLAC linac jitter, our calculation shows that a longitudinal phase space Feedback system is mandatory!!! • Studied the energy and bunch length feedback • Low frequency jitter is not hard to correct • Need understanding on a more realistic jitter model • Need measurement from A-line? • CSR: a good candidate for the bunch length measurement; easy to be implemented into the feedback

  24. Acknowledgement Collaboration with P. Emma Help and discussion with L. Hendrickson, M. Hogan, Z. Huang, P. Krejcik, M. Ross, et al. Thank committee for the invitation

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