1. 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

2. 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

3. 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

4. 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)

5. 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

6. LCLS feedback algorithm
M -1- feedback
matrix

7. 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

8. 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)

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

10. 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

11. 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:

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

13. 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

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

15. Monitor resolution
BPM resolution  [25, 40] m  energy resolution  [1.0, 1.7]×10 –  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

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

17. 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

18. 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

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

20. 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)

21. 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.

22. Diode detector
Diode detector (WD-06)  spectral response; For BC1: 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)

23. 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.