Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 1 Juhao Wu Stanford Linear Accelerator Center LCLS Feedback Study and CSR as Diagnostic Tool Juhao Wu Stanford Linear Accelerator Center ICFA Miniworkshop on XFEL Short Bunch Measurement and Timing, SLAC July 29, 2004 Linac Coherent Light Source (LCLS) accelerator system Jitter model Feedback model Coherent Synchrotron Radiation (CSR) as diagnostic tool Bunch length: Gaussian and double-horn structure MicrobunchingDiscussion Linac Coherent Light Source (LCLS) accelerator system Jitter model Feedback model Coherent Synchrotron Radiation (CSR) as diagnostic tool Bunch length: Gaussian and double-horn structure MicrobunchingDiscussion

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 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 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

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 3 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) We need a feedback system Courtesy of P. Emma

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 4 LCLS Accelerator System LCLS accelerator system model (P. Emma): a 5-stage linac-bend segments

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 5 LCLS Accelerator System Linac RF Wakefield (structure wake) Bend (2rd order map) Linac RF Wakefield (structure wake) Bend (2rd order map)

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 6 LCLS Feedback System Schematic Observables: Energy: E 0 (at DL1), E 1 (at BC1), E 2 (at BC2), E 3 (at DL2) Bunch length Peak current: I 1 (at BC1), I 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) Bunch length Peak current: I 1 (at BC1), I 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

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 7 LCLS Feedback Algorithm linear We are linear

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 8 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

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 9 Bode Plot (  E/E) P:0.2; I:0.5 P:0.2 Integral Gain helps! I:0.5

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 10 Bode Plot (  I/I) P:0.2; I:0.5 P:0.2 Integral Gain helps! I:0.5

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 11 LCLS Accelerator System Jitter Measurement Courtesy of P. Emma Peaks around 0.08 and 1.7 Hz

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 12 LCLS Accelerator System Jitter Model We model the jitter as the follows:

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 13 LCLS Feedback Performance feedback off Integral gain:0.5 feedback on (Integral gain:0.5)

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 14 Coherent Synchrotron Radiation CSR as nondestructive diagnostic tool For a group of N e electrons CSR spectrum Form factor

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 15 Linac Wake/Impedance (capacitive) V(s)/MV/nC/m s/  s FW 1 mm 500  m 250  m 100  m 50  m 50  m 25  m 25  m ss Linac wake Green function (K. Bane) SLAC S-Band: s0  1.32 mm a  11.6 mm s < ~6 mm To first order in 1/k

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 16 Wake for parabolic distribution For a parabolic distribution, the induced wake is

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 17 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

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 18 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

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 19 Current profile after BC2 Wake-induced double-horn structure Black: with Laser-Heater ( ) Red: without Laser-Heater ( ) Laser-Heater smears out the double-horn, however …

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 20 Bunch spectrum after BC2 Sharp-edge induces high freq. component Black: with Laser-Heater ( ) Red: without Laser-Heater ( ) Blue: Gaussian with same ( )

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 21 CSR spectrum after BC2 ISR power spectrum from a bending magnet for an azimuthal milliradian of the electron orbit (  ) and integrated over all the vertical angles ISR power spectrum from a bending magnet for an azimuthal milliradian of the electron orbit (  ) and integrated over all the vertical angles  (m)  z (mm) (mm) (mm) f (THz) I peak (A) P csr (kW) BC BC Assuming |F| 2 =1%,  / =1%, for 1 nC charge bunch

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 22 CSR spectrum after BC2 Fix  detector Black: with Laser-Heater ( ) Red: without Laser-Heater ( ) Blue: Gaussian with same ( )

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 23 CSR spectrum after BC2 Fix  detector Black: with Laser-Heater ( ) Red: without Laser-Heater ( ) Blue: Gaussian with same ( )

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 24 Instability mechanism t Energy bibi b f >> b i or G= b f / b i >> 1  k   R  Initial density modulation due to drive uv laser ripple  energy modulation through long. impedance Z(k), Energy modulation  density modulation by a chicane Growth of slice energy spread / emittance! Initial density modulation due to drive uv laser ripple  energy modulation through long. impedance Z(k), Energy modulation  density modulation by a chicane Growth of slice energy spread / emittance! t Current modulation 1% 10% Gain=10

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 25 Microbunching after BC2 Current profile with microbunching at 100/40  m Black: with microbunching (20% at 100/40  m) Red: without microbunching

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 26 Bunch spectrum after BC2 Microbunching inf. in the bunch spectrum Black: with microbunching (20% at 100/40  m) Red: without microbunching Blue: Gaussian with same ( )

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 27 Black: with microbunching (20% at 100/40  m) Red: without microbunching Blue: Gaussian with same ( ) CSR spectrum after BC2 Fix  detector

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 28 Microbunching after BC2 Current profile with microbunching at 500/40  m Black: with microbunching (20% at 500/40  m) Red: without microbunching

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 29 Bunch spectrum after BC2 Microbunching inf. in the bunch spectrum Black: with microbunching (20% at 500/40  m) Red: without microbunching Blue: Gaussian with same ( )

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 30 Black: with microbunching (20% at 100/40  m) Red: without microbunching Blue: Gaussian with same ( ) CSR spectrum after BC2 Fix  detector

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 31 Microbunching after BC1 Current profile with microbunching at 500/4  m Black: with microbunching (5% at 500/4  m) Red: without microbunching

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 32 Bunch spectrum after BC1 Smooth parabolic distribution Black: with microbunching (5% at 500/4  m) Red: without microbunching Blue: Gaussian with same ( )

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 33 Black: with microbunching (5% at 500/4  m) Red: without microbunching Blue: Gaussian with same ( ) CSR spectrum after BC1 Fix  detector

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 34 DiscussionDiscussion Given the jitter budge and the experiment measurement, a Feedback system is mandatory!!! So far, studied the energy and bunch length feedback Low frequency jitter is not hard to correct However, the white noise is hard to deal with; need sort out what is the real white noise content P. Emma’s ``too’’ new discovery about the timing jitter 1-to-1 transfer necessaries one more timing feedback CSR: a good candidate for the bunch length measurement; needed for the feedback; however The double-horn structure complicates situation Micorbunching easier to be detected at BC1, because The double-horn structure complicates situation Given the jitter budge and the experiment measurement, a Feedback system is mandatory!!! So far, studied the energy and bunch length feedback Low frequency jitter is not hard to correct However, the white noise is hard to deal with; need sort out what is the real white noise content P. Emma’s ``too’’ new discovery about the timing jitter 1-to-1 transfer necessaries one more timing feedback CSR: a good candidate for the bunch length measurement; needed for the feedback; however The double-horn structure complicates situation Micorbunching easier to be detected at BC1, because The double-horn structure complicates situation

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 35 To-do list Implement the CSR-based bunch length diagnostic into the feedback simulation code Implement the timing feedback Sort out the real white noise component Create a more realistic jitter model Need to weight gain differently for different loop Implement the CSR-based bunch length diagnostic into the feedback simulation code Implement the timing feedback Sort out the real white noise component Create a more realistic jitter model Need to weight gain differently for different loop

Feedback and CSR Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004 Juhao Wu, SLAC 36 AcknowledgementAcknowledgement Collaboration with P. Emma, L. Hendrickson, Z. Huang, P. Krejcik, et al. Thank committee for the workshop and invitation