Linac Coherent Light Source (LCLS) accelerator system Jitter model Longitudinal feedback model

Juhao Wu

Feedback & CSR [email protected]

Oct. 12 – 13, 2004

LCLS Longitudinal Feedback with CSR as

Diagnostic Tool

Juhao WuJuhao WuStanford Linear Accelerator CenterStanford Linear Accelerator Center

LCLS FAC Meeting, SLACOct. 12, 2004

Linac Coherent Light Source (LCLS) accelerator system Jitter modelLongitudinal feedback model

Coherent Synchrotron Radiation (CSR) as diagnostic toolBunch length: Gaussian, step, and double-horn structureDetector

Discussion

Juhao Wu


Oct. 12 – 13, 2004

LCLS Accelerator SystemLCLS Accelerator SystemLCLS Accelerator SystemLCLS Accelerator System

Electron beam at birth: peak current ~ 100 ampereXFEL calls for very high peak current ~ several kilo ampereCompress the bunch, and accelerate the bunch

Electron beam at birth: peak current ~ 100 ampereXFEL calls for very high peak current ~ several kilo ampereCompress the bunch, and accelerate the bunch

Bunch Compressor; Linac AcceleratorBunch Compressor; Linac Accelerator

Juhao Wu


Oct. 12 – 13, 2004

klystron phase rms klystron phase rms 0.07 0.07°°(20 sec)(20 sec)

klystron ampl. rms klystron ampl. rms 0.06 0.06%%(60 sec)(60 sec)

measured RF performancemeasured RF performance

X-bandX-band XX--

Jitter budget (< 1 minute time-scale)Jitter budget (< 1 minute time-scale)Jitter budget (< 1 minute time-scale)Jitter budget (< 1 minute time-scale)

Do we need a feedback system?

Juhao Wu


Oct. 12 – 13, 2004


LCLS accelerator system model (P. Emma): a 5-stage linac-bend segments

LCLS accelerator system model (P. Emma): a 5-stage linac-bend segments

L0

RFgun

L3L2X

i i = 1= 1 i i = 2= 2 i i = 3= 3 i i = 4= 4 i i = 5= 5

bends of zero strength at bends of zero strength at ii = 2 = 2

DL1DL1 BC1BC1 BC2BC2 DL2DL2L1

Juhao Wu


Oct. 12 – 13, 2004


Linac

RF

Wakefield (structure wake) (K. Bane)

Chicane and Dog-leg (2rd order map)

Linac

RF

Wakefield (structure wake) (K. Bane)

Chicane and Dog-leg (2rd order map)

]cos[ kzeVEE

0/2

0)( szea

cZzw

56656 TRzz

SLACSLAC S-Band: S-Band:ss00 1.32 mm 1.32 mm

aa 11.6 mm 11.6 mmzz < ~6 mm < ~6 mm

Juhao Wu


Oct. 12 – 13, 2004

SPPS Accelerator System Jitter MeasurementSPPS Accelerator System Jitter MeasurementSPPS Accelerator System Jitter MeasurementSPPS Accelerator System Jitter Measurement

Courtesy of P. Emma

Peaks around (f1 =0.08) and (f2 =1.7) Hz

Data rate 10 Hz, not 120 Hz

Peaks around (f1 =0.08) and (f2 =1.7) Hz

Data rate 10 Hz, not 120 Hz

Juhao Wu


Oct. 12 – 13, 2004

H randn step

step

o

N

jj tt

B

A

B

A

tB

Atf

B

Atf

B

A

dV

dV

%)()1(

)2sin()2sin(

1,

5

5

4

4

3

32

2

21

1

1

LCLS Accelerator System Jitter ModelLCLS Accelerator System Jitter ModelLCLS Accelerator System Jitter ModelLCLS Accelerator System Jitter Model

We model the jitter as the follows:We model the jitter as the follows:

time run total and rand

Hz Hz with

stepstep :)(

;60/1;1.0

;1;7.1;08.0

334422

551121

Nt

BABABA

BABAff

Juhao Wu


Oct. 12 – 13, 2004

LCLS Performance (No Feedback )LCLS Performance (No Feedback )LCLS Performance (No Feedback )LCLS Performance (No Feedback )

‘free’ machine‘free’ machine %50.0/

%;26.0/

std

EE

EE %50.0/

%;26.0/

std

EE

EE

%7.1564/

%;4.247/

std

II

II %7.1564/

%;4.247/

std

II

II

ps

ps

std 4.1

;5.0

t

t ps

ps

std 4.1

;5.0

t

tAt undulator entranceAt undulator entrance

Juhao Wu


Oct. 12 – 13, 2004

LCLS Feedback System SchematicLCLS Feedback System SchematicLCLS Feedback System SchematicLCLS Feedback System Schematic

Observables: Energy: E0 (at DL1), E1 (at BC1), E2 (at BC2), E3 (at DL2) CSR power bunch length: z,1 (at BC1), z,2 (at BC2)

Controllables: Voltage: V0 (in L0), V1 (in L1), V2 (effectively, in L2)

Phase: 1 (in L1), 2 (in L2 ), 3 (in L3)

Observables: Energy: E0 (at DL1), E1 (at BC1), E2 (at BC2), E3 (at DL2) CSR power bunch length: z,1 (at BC1), z,2 (at BC2)

Controllables: Voltage: V0 (in L0), V1 (in L1), V2 (effectively, in L2)

Phase: 1 (in L1), 2 (in L2 ), 3 (in L3)

Courtesy of P. KrejcikCourtesy of P. Krejcik

Juhao Wu


Oct. 12 – 13, 2004

MC

d

d

V

dV

d

V

dV

V

dV

d

d

V

dV

d

V

dV

V

dV

d

EdE

d

EdE

VdV

EdE

d

EdE

VdV

EdE

VdV

EdE

d

PdP

VdVP

dP

d

PdP

VdVP

dP

VdVP

dP

d

EdE

VdVE

dE

d

EdE

VdVE

dE

VdVE

dE

d

PdP

VdVP

dP

VdVP

dP

d

EdE

VdVE

dE

VdVE

dEVdV

EdE

E

dE

P

dP

E

dE

P

dP

E

dE

E

dE

M

3

2

2

1

1

0

3

2

2

1

1

0

3

3

2

3

2

3

1

3

1

3

0

3

2

2

2

2

1

2

1

2

0

2

2

2

2

2

1

2

1

2

0

2

1

1

1

1

0

1

1

1

1

1

0

1

0

0

3

2

2

1

1

0

0

0

000

000

00000

LCLS Feedback AlgorithmLCLS Feedback AlgorithmLCLS Feedback AlgorithmLCLS Feedback Algorithm

MCO OGMCC 1 beforeafter

We are linearlinear

We are linearlinear

Juhao Wu


Oct. 12 – 13, 2004

LCLS Feedback SystemLCLS Feedback SystemLCLS Feedback SystemLCLS 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

Juhao Wu


Oct. 12 – 13, 2004

Bode Plot (Bode Plot (E/E)E/E)Bode Plot (Bode Plot (E/E)E/E)

off

on

EE

EE

/

/log20 10

off

on

EE

EE

/

/log20 10

P:0.2; I:0.5P:0.2; I:0.5P:0.2P:0.2

0.0

/

/arg

off

on

EE

EE

Integral Gain helps!Integral Gain helps!

I:0.5I:0.5

Similar Bode PlotBode Plot for (I / II / I) Similar Bode PlotBode Plot for (I / II / I)

Juhao Wu


Oct. 12 – 13, 2004

LCLS Feedback Performance (Use CSR LCLS Feedback Performance (Use CSR P / P)P / P)LCLS Feedback Performance (Use CSR LCLS Feedback Performance (Use CSR P / P)P / P)

feedback offfeedback off feedback on (Integral gain:0.5Integral gain:0.5)feedback on (Integral gain:0.5Integral gain:0.5) %50.0/

%;26.0/

std

EE

EE %50.0/

%;26.0/

std

EE

EE

%09.0/

%;0007.0/

std

EE

EE %09.0/

%;0007.0/

std

EE

EE

%5.10/

%;12.0/

std

II

II %5.10/

%;12.0/

std

II

II

%7.1564/

%;4.247/

std

II

II %7.1564/

%;4.247/

std

II

II

ps

ps

std 16.0

;003.0

t

t ps

ps

std 16.0

;003.0

t

t

ps

ps

std 4.1

;5.0

t

t ps

ps

std 4.1

;5.0

t

t

At undulator entranceAt undulator entrance

Juhao Wu


Oct. 12 – 13, 2004

dd

IdFN

dd

Idee

dd

Id

e

N

j

c

Rnitie

j

j

02

22

02

2

1

ˆ2

Coherent Synchrotron RadiationCoherent Synchrotron RadiationCoherent Synchrotron RadiationCoherent Synchrotron Radiation

CSR as nondestructive diagnostic tool For a group of Ne electrons

CSR spectrum

CSR as nondestructive diagnostic tool For a group of Ne electrons

CSR spectrum

Form factor Form factor

2

2ˆ2

),,(

),,(

dxdydzezyxn

dxdydzeezyxnF

ikz

Rnikikz

with

1),,( dxdydzzyxn

Single electronSingle electron

Juhao Wu


Oct. 12 – 13, 2004

Wake-induced Cubic termWake-induced Cubic termWake-induced Cubic termWake-induced Cubic term

Longitudinal phase-space before BC2 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

Juhao Wu


Oct. 12 – 13, 2004

Wake for parabolic distributionWake for parabolic distributionWake for parabolic distributionWake for parabolic distribution

For a parabolic distribution, the induced wake is For a parabolic distribution, the induced wake is

032

300

0

22/3

510

3

633252

12120615158)(

s

z

a

csNeLZH

se

eHzV

z

z

and [V]

with

[V]

Juhao Wu


Oct. 12 – 13, 2004

Wake-induced Cubic termWake-induced Cubic termWake-induced Cubic termWake-induced Cubic term

Longitudinal phase-space change due to BC2 Longitudinal phase-space change due to BC2

Blue: after BC2

Red: before BC2

Wake with parabolic dist. leads to the double-horn

Juhao Wu


Oct. 12 – 13, 2004

Current profile after BC2Current profile after BC2Current profile after BC2Current profile after BC2 Wake-induced double-horn

structure Wake-induced double-horn

structure

With Laser-Heater

( )

Laser-Heater smears out the double-horn, however …

keV 47Em 21zm 21z

Juhao Wu


Oct. 12 – 13, 2004

Bunch spectrum after BC2Bunch spectrum after BC2Bunch spectrum after BC2Bunch spectrum after BC2

Sharp-edge induces high freq. component Sharp-edge induces high freq. component Red: with Laser-Heater

( )

Black: Gaussian with same

Blue: Step [J. Galayda] with same

keV 47E

m 21z

m 21z

Juhao Wu


Oct. 12 – 13, 2004

Integrated CSR PowerIntegrated CSR PowerIntegrated CSR PowerIntegrated CSR Power

Detector matters Detector mattersRed solid curve: Gaussian with same z

Black dashed curve: Step with same z

Red dots: Real with Laser-Heater

o

z m

8.41,8.40,8.39

11,21,32

2

2,

THz )6,54.0(f

Juhao Wu


Oct. 12 – 13, 2004

Integrated CSR PowerIntegrated CSR PowerIntegrated CSR PowerIntegrated CSR Power Stay in the low frequency regime Stay in the low frequency regime

Red solid curve: Gaussian with same z

Black dashed curve: Step with same z

Red dots: Real with Laser-Heater

o

z m

8.41,8.40,8.39

11,21,32

2

2,

THz )4.0,24.0(f

Juhao Wu


Oct. 12 – 13, 2004

Integrated CSR PowerIntegrated CSR PowerIntegrated CSR PowerIntegrated CSR Power

Stay in the low frequency regime Pyroelectric Detector? Detector with fixed , the integrated power

Stay in the low frequency regime Pyroelectric Detector? Detector with fixed , the integrated power

2

22

3/4

3/110

det

2

4

,3

2,

3

21063.3),(

z

z rad

WINP

with

Juhao Wu


Oct. 12 – 13, 2004

DiscussionDiscussionDiscussionDiscussion

Given the jitter budget and the SLAC linac jitter, our calculation shows that a longitudinal phase space Feedback system is mandatory!!!

Studied the energy and bunch length feedbackLow frequency jitter is not hard to correctNeed understanding on a more realistic jitter modelNeed measurement from A-line?

CSR: a good candidate for the bunch length measurement; easy to be implemented into the feedback

Given the jitter budget and the SLAC linac jitter, our calculation shows that a longitudinal phase space Feedback system is mandatory!!!

Studied the energy and bunch length feedbackLow frequency jitter is not hard to correctNeed understanding on a more realistic jitter modelNeed measurement from A-line?

CSR: a good candidate for the bunch length measurement; easy to be implemented into the feedback

Juhao Wu


Oct. 12 – 13, 2004

Acknowledgement Acknowledgement Acknowledgement Acknowledgement

Collaboration with P. Emma

Help and discussion with L. Hendrickson, M. Hogan, Z. Huang, P. Krejcik, M. Ross, et al.

Thank committee for the invitation

Collaboration with P. Emma

Help and discussion with L. Hendrickson, M. Hogan, Z. Huang, P. Krejcik, M. Ross, et al.

Thank committee for the invitation

Documents

Linac Coherent Light Source (LCLS) accelerator system Jitter model Longitudinal feedback model