Transcript LCLS Feedback Study and CSR as Diagnostic Tool

Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
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
Microbunching
Discussion
1
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
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
Bunch Compressor; Linac Accelerator
2
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
Jitter budget (< 1 minute time-scale)
measured RF performance
klystron phase rms  0.07°
(20 sec)
X-
X-band
klystron ampl. rms  0.06%
(60 sec)
We need a feedback system
3
Courtesy of P. Emma
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
LCLS Accelerator System
LCLS accelerator system model (P. Emma): a 5-stage linac-bend
segments
4
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
LCLS Accelerator System
Linac
RF
E  E  eV cos[  kz]
Wakefield (structure wake)
w( z ) 
Z 0c
a
2
e
 z / s0
Bend (2rd order map)
z  z   R56  T566 
5
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
LCLS Feedback System Schematic
Courtesy of P. Krejcik
Observables:
Energy: E0 (at DL1), E1 (at BC1), E2 (at BC2), E3 (at DL2)
Bunch length
Peak current: I1 (at BC1), I2 (at BC2)
Controllables:
Voltage: V0 (in L0), V1 (in L1), V2 (effectively, in L2)
Phase: 1 (in L1), 2 (in L2 ), 3 (in L3)
6
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
  dE  

 
  E 0 


dE  



  E 1 


dI  



  I 1 


  dE  


E 2 



  dI  
 

  I 2 
  dE  
 



  E 3 
  dE 
 

  E 0
  dV 

 
  V 0
  dE 
  E 
1
 
dV
 


 
V

0

dI


 

  I 1

dV 
 


  V 0

dE 
 


  E 2
  dV 
 

  V 0
  dI 

 
I

2

  dV 
  V 
0
 
  dE 

 
 E 3

dV 
 

 
  V 0
Feedback and CSR
LCLS Feedback Algorithm


0
0
 dE 


 E 1
 dV 


 V 1
 dI 


 I 1
 dV 


 V 1
 dE 


 E 2
 dV 


 V 1
 dI 


 I 2
 dV 


 V 1
 dE 


 E 3
 dV 


 V 1
 dE 


 E 1
 d 1
O  MC
 dI 


 I 1
 d 1
 dE 


 E 2
 d 1
 dI 


 I 2
 d 1
 dE 


 E 3
 d 1
0
0
0
0
0
0
 dE 


 E 2
 dV 


 V 2
 dI 


 I 2
 dV 


 V 2
 dE 


 E 3
 dV 


 V 2
 dE 


 E 2
 d 2
 dI 


 I 2
 d 2
 dE 


 E 3
 d 2







0





0






0






0



 dE  


 E 3 

 d 3 


0
We are linear
  dV  
  dV  


 
 
  V 0 
  V 0 




dV  
dV  






  V 1 
  V 1 




 d 1   M  d 1   MC
  dV  
  dV  


 
 
  V 2 
  V 2 
 d 

 d 

2 
2 


 d 

 d 

3 
3 


1
Cafter  Cbefore  GM O
7
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
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
8
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
Bode Plot (E/E)
 E / E on
20 log 10 
 E / E 
off





P:0.2
Integral Gain helps!
P:0.2; I:0.5
I:0.5
 E / E on 
  0 .0
arg 




E
/
E
off 

9
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
Bode Plot (I/I)
 I / I on
20 log 10 
 I / I 
off





P:0.2
Integral Gain helps!
P:0.2; I:0.5
I:0.5
 I / I on 
  0.0
arg 




I
/
I
off 

10
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
LCLS Accelerator System Jitter Measurement
Peaks
around 0.08
and 1.7 Hz
Courtesy of P. Emma
11
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
LCLS Accelerator System Jitter Model
We model the jitter as the follows:
dV
t
 sin( 0.08  2t )  0.1sin( 1.7  2t ) 
 0.1 randn (1)
V
60

N step
 H(t  tstep, j )
[%]
j 1
t
d  sin( 0.08  2t )  0.1sin( 1.7  2t ) 
 0.1 randn (1)
60

N step

H
(
t

t
)
[
]

step, j
j 1
with tstep    rand ( N step ) and  : total run time
12
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
LCLS Feedback Performance
feedback off
E / E  0.21 %;
feedback on (Integral gain:0.5)
E / E std  0.60 %
E / E  0.0007 %;
E / E std  0.09 %
I / I  169.0 %;
I / I std  608.4 %
I / I  0.10 %;
I / I std  8.5 %
t  0.5 ps;
t std  1.6 ps
t  0.003 ps;
t std  0.15 ps
13
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
Coherent Synchrotron Radiation
CSR as nondestructive diagnostic tool
For a group of Ne electrons
CSR spectrum
d 2I

dd
Ne

ˆ  2
nR j
it j i c
e e
j 1
d 2I0
dd
2
d
I0
2
2
 Ne F
dd
Form factor
F   n ( x, y , z ) e
2
ˆ 
ikz ikn  R
e
2
dxdydz
with
2
 n( x, y, z )dxdydz  1
  n( x, y, z )e ikz dxdydz
14
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
Linac Wake/Impedance
Linac wake Green function (K. Bane)
SLAC S-Band:
s0  1.32 mm
a  11.6 mm
s < ~6 mm
V(s)/MV/nC/m
ss
1 mm
500 m
250 m
100 m
50 m
25 m
To first order in 1/k
s/sFW
(capacitive)
15
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
Wake for parabolic distribution
For a parabolic distribution, the induced wake is


V ( z )  H 8 15  15   6   3 / 2 e 



 2 5 2 3  3    e 





 120  12   2 

sz 

   6
 s0 
[V]
with
H 
3NeLZ 0cs03
10
5a 2s z3
16
[V]
and
z

s0
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
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
17
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
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, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
Current profile after BC2
Wake-induced double-horn structure
Black: with
Laser-Heater
s z  21 m
( s E  47 keV )
Red: without
Laser-Heater
( s E  3 keV )
Laser-Heater smears out the double-horn, however …
19
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
Bunch spectrum after BC2
Sharp-edge induces high freq. component Black: with
Laser-Heater
( s E  47 keV )
Red: without
Laser-Heater
( s E  3 keV )
Blue:
Gaussian
with same
( s z  21 m )
Green: Step
with same
( s z  21 m )
20
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
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
Pisr ( )[W/mrad θ/mm]  8.42 10 8  1 / 3[m]I [ Amp ]7 / 3[mm ]
for
  c 
4
o
[ A];
3
2
Hence, Pcsr ( )[W/mrad θ/mm]  Ne F Pisr ( ).
3
Assuming |F|2=1%, /=1%, for 1 nC charge bunch
 (m)
sz (mm)
 (mm)
f (THz)
BC1
2.4
0.19
0.19
1.6
400
0.26
BC2
14.5
0.021
0.021
14.3
3400
75.2
21
Ipeak (A) Pcsr(kW)
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
CSR spectrum after BC2
Fix  detector
Feedback and CSR
Black: with
Laser-Heater
( s E  47 keV )
Red: without
Laser-Heater
( s E  3 keV )
Blue:
Gaussian
with same
( s z  21 m )
Green: Step
with same
( s z  21 m )
22
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
CSR spectrum after BC2
Fix  detector
Feedback and CSR
Black: with
Laser-Heater
( s E  47 keV )
Red: without
Laser-Heater
( s E  3 keV )
Blue:
Gaussian
with same
( s z  21 m )
Green: Step
with same
( s z  21 m )
23
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
Instability mechanism
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!
R56
bi
Energy
Zk
E
bf >> bi or G= bf/ bi >> 1


Current modulation
t
Gain=10
1%
10%
t
24
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
Microbunching after BC2
Current profile with microbunching at 100/40 m
s z  21 m
Black: with
microbunching
(20% at
100/40 m)
Red: without
microbunching
25
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
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
( s z  21 m )
Green: Step
with same
( s z  21 m )
26
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
CSR spectrum after BC2
Fix  detector
Black: with
microbunching
(20% at 100/40
m)
Red: without
microbunching
Blue: Gaussian
with same
( s z  21 m )
Green: Step
with same
( s z  21 m )
27
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
CSR spectrum after BC2
Fix  detector
Black: with
microbunching
(20% at 100/40
m)
Red: without
microbunching
Blue: Gaussian
with same
( s z  21 m )
Green: Step
with same
( s z  21 m )
28
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
Microbunching after BC2
Current profile with microbunching at 500/40 m
s z  21 m
Black: with
microbunching
(20% at
500/40 m)
Red: without
microbunching
29
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
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
( s z  21 m )
Green: Step
with same
( s z  21 m )
30
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
CSR spectrum after BC2
Fix  detector
Black: with
microbunching
(20% at 500/40
m)
Red: without
microbunching
Blue: Gaussian
with same
( s z  21 m )
Green: Step
with same
( s z  21 m )
31
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
CSR spectrum after BC2
Fix  detector
Black: with
microbunching
(20% at 500/40
m)
Red: without
microbunching
Blue: Gaussian
with same
( s z  21 m )
Green: Step
with same
( s z  21 m )
32
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
Microbunching after BC1
Current profile with microbunching at 500/4 m
s z  190 m
Black: with
microbunching
(5% at 500/4
m)
Red: without
microbunching
33
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
Bunch spectrum after BC1
Smooth parabolic distribution
Black: with
microbunching
(5% at 500/4
m)
Red: without
microbunching
Blue: Gaussian
with same
( s z  190 m )
34
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
CSR spectrum after BC1
Fix  detector
Black: with
microbunching
(5% at 500/4
m)
Red: without
microbunching
Blue: Gaussian
with same
( s z  190 m )
35
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
CSR spectrum after BC1
Fix  detector
Black: with
microbunching
(5% at 500/4
m)
Red: without
microbunching
Blue: Gaussian
with same
( s z  190 m )
36
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
Discussion
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
37
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
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
38
Juhao Wu, SLAC
[email protected]
Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004
Feedback and CSR
Acknowledgement
Collaboration with P. Emma, L. Hendrickson, Z. Huang,
P. Krejcik, et al.
Thank committee for the workshop and invitation
39
Juhao Wu, SLAC
[email protected]