1. LCLS Longitudinal Feedback and Stability Requirements
P. Emma
LLRF Review November 23, 2005
LCLS

2. Critical LCLS Accelerator Parameters
Final energy 13.6 GeV (stable to 0.1%)
Final peak current 3.4 kA (stable to 12%)
Transverse emittance 1.2 mm (stable to 5%)
Final energy spread 10-4 (stable to 10%)
Bunch arrival time (stable to 150 fs)
(stability specifications quoted as rms)

3. FEL Power Sensitivity to e- Beam
12% DIpk/Ipk  20% DP/P
0.1% DE/E  0.2% Dlr/lr

4. Electron Bunch Compression
d  DE/E d d
under-compression
szi
‘chirp’ z z z sz
sdi
V = V0sin(kz)
Dz = R56d
RF Accelerating
Voltage
Path-Length Energy-
Dependent Beamline

5. Compression Stabilityd Df
d z
RF phase jitter becomes bunch length jitter…
Compression factor:

6. Phase and Bunch Length Stability Example (not LCLS)

7. Machine Schematic with Parameters
6 MeV
z  0.83 mm
  0.05 %
135 MeV
z  0.83 mm
  0.10 %
250 MeV
z  0.19 mm
  1.6 %
4.30 GeV
z  mm
  0.71 %
13.6 GeV
z  mm
  0.01 %
Linac-X
L =0.6 m
rf= -160 rf
gun
23-m
Linac-1
L 9 m
rf  -25°
Linac-2
L 330 m
rf  -41°
Linac-3
L 550 m
rf  0°
Linac-0
L =6 m
undulator
L =130 m
...existing linac
21-1b
21-1d X
21-3b
24-6d
25-1a
30-8c
BC1
L 6 m
R56 -39 mm
BC2
L 22 m
R56 -25 mm
DL1
L 12 m
R56 0
LTU
L =275 m
R56  0
1 X-klys.
3 klystrons
1 klystron
26 klystrons
45 klystrons
SLAC linac tunnel
research yard

8. Correlated or Uncorrelated Errors?
Suppose the mean RF phase of all 26 Linac-2 klystrons changes by: 0.21°  |DIpk/Ipk|  12%
This may arise statistically with 26 random uncorrelated phase errors with rms spread of: f21/2 = 0.21°261/2 = 1.07°, or with 26 identical phase errors.
Since we don’t fully understand the correlations, we choose the conservative (smallest) tolerance of 0.21° rms/klys. and then reduce this by ~N, where N (=12) is the number of major error sources.

9. Phase, Amplitude, and Charge Sensitivities
parameter
|DE/E0| = 0.1%
|DI/I0| = 12%
|Dtf| = 100 fs
unit
Dti
1.6
4.4
1.5
psec
DQ/Q0 46
5.2 24 %
Df0
3.5
0.65
5.9
deg-S
DV0/V0
0.32
0.24
0.95
Df1
0.17
1.0
DV1/V1
0.29
0.25
0.78
DfX
5.5
1.4
7.6
deg-X
DVX/VX
2.0
1.2
6.3
Df2
0.54
0.21
0.084
DV2/V2
1.1
0.13
Df3
0.35
24.8 15
DV3/V3
0.15
5.7
8.6

10. Longitudinal Fast-Jitter Tolerance Budget
tolerances are rms values
X-band X-
0.50
laser timing (w.r.t. RF) 
laser energy 
mean phase of 2 klys. 
1 klys. 
1 X-klys. 
mean phase of 26 klys. 
mean phase of 45 klys. 
mean amp. of 2 klys. 
1 klys. 
1 X-klys. 
mean amp. of 26 klys. 
mean amp. of 45 klys. 

11. Jitter Simulations (Particle Tracking)
0.09%
0.004% Lg
96 fs
Pout
10%

12. LCLS Longitudinal Beam-Based Feedback
(stabilizes beam for jitter frequencies < Hz rep-rate) L0
gun L3 L2 X
DL1
BC1
BC2
DL2 L1
sz1 d1 1 V1
sz2 d2 2 V2 d3 V3 d0 V0
BPM
CSR detector
J. Wu, et al., PAC’05, May 16-20, 2005, Knoxville, TN.

13. CSR Relative Bunch Length Monitor
Red curve: Gaussian
Black curve: Uniform
Blue curve: ‘Real’
J. Wu, et al., PAC’05, May 16-20, 2005, Knoxville, TN.

14. LCLS Feedback Performance (use CSR P/P)
feedback off
DIpk/Ipk0 (%)
feedback on
J. Wu
(undulator entrance)

15. Feedback System Bode Plot at 120 Hz
J. Wu
Define fast-jitter as variations faster than 2 seconds
Slow drift occurs on time-scales > 2 seconds (to 24+ hr)

16. Slow Drift Tolerance Limits
(Top 4 rows for De/e < 5%, bottom 4 limited by feedback dynamic range)
Gun-Laser Timing
2.4*
deg-S
Bunch Charge
3.2 %
Gun RF Phase
2.3
Gun Relative Voltage
0.6
L0,1,X,2,3 RF Phase (approx.) 5
L0,1,X,2,3 RF Voltage (approx.)
(Tolerances are peak values, not rms)
* for synchronization, this tolerance might be set to 1 ps (without arrival-time measurement)

17. L1 adjustment: phase +2.1o, voltage -2.1%
Compensate X-band Phase Step Error...
jx (deg)
x-band phase
LX phase error = 5o
final energy
final peak current
L1 adjustment: phase +2.1o, voltage -2.1%
final arrival time
J. Wu

18. Gun Timing Jitter and Energy Feedback
Dtf
Dt0
Dt0
E > E0
E = E0
Dtf = Dt0
without energy feedback
with energy feedback