1. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 Juhao Wu Stanford Linear Accelerator Center 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 Bunch length: Gaussian, step, and double-horn structure Detector Discussion

2. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 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 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. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 klystron phase rms  0.07° (20 sec) klystron ampl. rms  0.06% (60 sec) measured RF performance X-band X-X-X-X- Jitter budget (< 1 minute time-scale) Do we need a feedback system?

4. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 LCLS Accelerator System LCLS accelerator system model (P. Emma): a 5-stage linac-bend segments L0 RF gun L3L2 X i = 1 i = 2 i = 3 i = 4 i = 5 bends of zero strength at i = 2 DL1 BC1BC2 DL2 L1

5. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 LCLS Accelerator System Linac RF Wakefield (structure wake) (K. Bane) Chicane and Dog-leg (2rd order map) Linac RF Wakefield (structure wake) (K. Bane) Chicane and Dog-leg (2rd order map) SLAC S-Band: s 0  1.32 mm a  11.6 mm z < ~6 mm

6. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 SPPS Accelerator System Jitter Measurement Courtesy of P. Emma Peaks around (f 1 =0.08) and (f 2 =1.7) Hz Data rate 10 Hz, not 120 Hz Peaks around (f 1 =0.08) and (f 2 =1.7) Hz Data rate 10 Hz, not 120 Hz

7. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 LCLS Accelerator System Jitter Model We model the jitter as the follows:

8. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 LCLS Performance (No Feedback ) ‘free’ machine At undulator entrance

9. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 LCLS Feedback System Schematic Observables: Energy: E 0 (at DL1), E 1 (at BC1), E 2 (at BC2), E 3 (at DL2) CSR power bunch length:  z,1 (at BC1),  z,2 (at BC2) Controllables: Voltage: V 0 (in L0), V 1 (in L1), V 2 (effectively, in L2) Phase:  1 (in L1),  2 (in L2 ),  3 (in L3) Observables: Energy: E 0 (at DL1), E 1 (at BC1), E 2 (at BC2), E 3 (at DL2) CSR power bunch length:  z,1 (at BC1),  z,2 (at BC2) Controllables: Voltage: V 0 (in L0), V 1 (in L1), V 2 (effectively, in L2) Phase:  1 (in L1),  2 (in L2 ),  3 (in L3) Courtesy of P. Krejcik

10. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 LCLS Feedback Algorithm linear We are linear

11. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 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 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. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 Bode Plot (  E/E) P:0.2; I:0.5 P:0.2 Integral Gain helps! I:0.5 Bode Plot  I / I Similar Bode Plot for (  I / I)

13. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 LCLS Feedback Performance (Use CSR  P / P) feedback off Integral gain:0.5 feedback on (Integral gain:0.5) At undulator entrance

14. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 Coherent Synchrotron Radiation CSR as nondestructive diagnostic tool For a group of N e electrons CSR spectrum CSR as nondestructive diagnostic tool For a group of N e electrons CSR spectrum Form factor Single electron

15. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 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. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 Wake for parabolic distribution For a parabolic distribution, the induced wake is

17. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 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. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 Current profile after BC2 Wake-induced double-horn structure With Laser- Heater ( ) Laser-Heater smears out the double-horn, however …

19. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 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. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 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. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 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. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 Integrated CSR Power Stay in the low frequency regime Pyroelectric Detector? Detector with fixed , the integrated power Stay in the low frequency regime Pyroelectric Detector? Detector with fixed , the integrated power

23. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 DiscussionDiscussion 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 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. Juhao Wu Feedback & CSRjhwu@SLAC.Stanford.EDU Oct. 12 – 13, 2004 AcknowledgementAcknowledgement 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 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