LCLS Longitudinal Feedback System and Bunch Length Monitor Juhao Wu Stanford Linear Accelerator Center LCLS DOE Review, February 08, 2006 LCLS longitudinal feedback system Motivation Observables and controllables (actuator) Multi-stage cascade, PID scheme Jitter model Issues Relative bunch length monitor Coherent Radiation Optical setup Discussion

Jitter budget (< 1 minute time-scale) X-band X- 0.50 measured RF performance klystron phase rms  0.07° (20 sec) klystron ampl. rms  0.06% (60 sec) LINAC RF meets all specifications for 2 second P. Emma & R. Akre

Jitter measurement (> 1 minute time-scale) R. Akre Phase 22-6 1.2 Deg pp Amplitude 22-6 0.20%pp Amplitude 22-7 0.43%pp Phase 22-7 1.2 Deg pp 14 minutes data taken using the SCP correlation plot However, LINAC RF is out of specs in 1 minute  need feedback

LCLS feedback system schematic BPM BLM Observables (6): Energy: E0 (at DL1), E1 (at BC1), E2 (at BC2), E3 (at DL2) Coherent Radiation power bunch length: z,1 (at BC1), z,2 (at BC2) Controllables (6): Voltage: V0 (in L0), V1 (in L1), V2 (effectively, in L2) Phase: 1 (in L1), 2 (in L2 ), 3 (in L3)

LCLS accelerator system model Linac RF Wakefield (structure wake) (K. Bane) Chicane and Dog-leg (2rd order map) V  = 0 at accelerating crest k = 2p/l eV z  eV SLAC S(X)-Band: s0  1.32 (0.77)mm a  11.6(4.72) mm z < ~6 mm e- z

LCLS feedback algorithm M -1- feedback matrix

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-1-feedback matrix Equivalent to the so-called Multi-stage Cascade Pulse rep rate: 120 Hz

Similar Bode plot for (I / I) 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)

SPPS accelerator system jitter measurement Peaks around (f1=0.08) and (f2 =1.7) Hz Data rate  10 Hz, not 120 Hz P. Emma

LCLS accelerator system jitter model We model the LINAC voltage / phase jitter as the follows Two characteristic frequencies, linear drift, white noise (sets the tolerance), and step-function jitter tolerance

Injector jitter mapping into LINAC Use C. Limborg’s PARMELA results (with Schottky effect) for injector Laser DV/V Dj Dt DNe / Ne e- bunch Gun Cell L0A L0B Dt, h, sz, d Cathode At injector exit, the jitter is then modeled as:

LCLS gun jitter model Similarly, the charge / Laser timing jitter at cathode:

LCLS Feedback Performance (Use CSR P / P) feedback off feedback on (Integral gain:0.5) P. Emma’s 1-1 timing map With toroid With gun charge / timing jitter At undulator entrance

Gun timing jitter and energy feedback Dt with energy feedback without energy feedback P. Emma Energy feedback in chicanes causes 1-to-1 gun-timing to final timing jitter!

Monitor resolution BPM resolution  [25, 40] m  energy resolution  [1.0, 1.7]×10 – 4  much better than required BLM resolution BC2  more critical 3 sets of simulation ○ BC1 jitter, BC2 perfect ◊ BC2 jitter, BC1 perfect × BC1 and BC2 jitter

L1 adjustment to compensate Lx jitter Lx phase jitter + 5o, voltage fixed L1 adjustment: phase +2.1o, voltage - 2.1 % Similarly Lx voltage jitter + 5 %, phase fixed L1 adjustment: phase +0.61o, voltage 0.18 %

Coherent radiation as bunch length monitor Coherent Radiation (CR) as nondestructive diagnostic tool Synchrotron, Edge, and Diffraction Radiation For a group of Ne electrons CR spectrum Single e- Form factor  bunch length information

Coherent enhancement and bunch length information CSR at BC1 and BC2 Parameters at BC1 and BC2  (m) z (mm)  (mm) f (THz) Ipeak (A) BC1 2.4 0.19 1.2 0.25 400 BC2 14.5 0.021 0.13 2.3 3400 Coherent enhancement and bunch length information CSR pulse energy can be as much as J

Current profile after BC2 Wake-induced double-horn structure I (kA)

Bunch spectrum after BC2 Sharp-edge induces high freq. component. However, low freq. region (< 2 THz) independent of shape Similarly, for BC1 parabolic distribution  low freq. region (< 400 GHz) Non-Gaussian? Fine low freq. region Black: double-horn Blue: Gaussian with same Red: Step with same f (THz)

Schematic optical setup for BC1 detector CDR CER 4.0 in. ~20 in QM12 1.5 in. BX14 e- 0.6 in. 3.0 in. 5° 8.0 in. <6.0 in. ~9.0 in. CSR 12.7 in.

Diode detector Diode detector (WD-06)  spectral response; For BC1: 1.76 mm <  < 2.72 mm (110 to 170 GHz) Black: Parabolic Blue: Gaussian with same z Red: Step with same z free space Edet (mJ/mrad-arc) sz (mm) Beam pipe cutoff (2 cm radius pipe 1/2 signal, but similar slope)

Discussion Jitter budget and the SLAC linac jitter  a longitudinal phase space Feedback system is needed! Studied the energy and bunch length feedback Low frequency jitter is not hard to correct A more realistic jitter model for the LINAC and Injector CR: good candidate for bunch length measurement; easily implemented into the feedback system Stay in low frequency region Optical setup: beam pipe cutoff, mirror reflectivity, window CR BLM resolution 5% X-band compensated by S-band Thanks to P. Emma, L. Hendrickson, Z. Huang, R. Akre, E. Bong, T. Borden, D.H. Dowell, M. Dunning, J. Galayda, M. Hogan, R. Ischebeck, P. Krejcik, C. Limborg, H. Loos, A. Lumpkin, P. Muggli, M. Ross, D. Schultz, G. Travish, et al.