Linac Coherent Light Source (LCLS) accelerator system Jitter model Feedback model

Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004Miniworkshop on XFEL Short Bunch, SLAC, July 26 – 30, 2004

Juhao Wu, SLACJuhao Wu, SLAC

Feedback and CSRFeedback and CSR

[email protected]@SLAC.Stanford.EDU

LCLS Feedback Study and CSR as Diagnostic Tool

Juhao WuJuhao WuStanford Linear Accelerator CenterStanford Linear Accelerator Center

ICFA Miniworkshop on XFEL Short Bunch Measurement and Timing, SLACJuly 29, 2004

LCLS Feedback Study and CSR as Diagnostic Tool

Juhao WuJuhao WuStanford Linear Accelerator CenterStanford Linear Accelerator Center

ICFA Miniworkshop on XFEL Short Bunch Measurement and Timing, SLACJuly 29, 2004

Linac Coherent Light Source (LCLS) accelerator system Linac Coherent Light Source (LCLS) accelerator system Jitter modelJitter model Feedback modelFeedback model

Coherent Synchrotron Radiation (CSR) as diagnostic toolCoherent Synchrotron Radiation (CSR) as diagnostic tool Bunch length: Gaussian and double-horn structureBunch length: Gaussian and double-horn structure MicrobunchingMicrobunching

DiscussionDiscussion

Linac Coherent Light Source (LCLS) accelerator system Linac Coherent Light Source (LCLS) accelerator system Jitter modelJitter model Feedback modelFeedback model

Coherent Synchrotron Radiation (CSR) as diagnostic toolCoherent Synchrotron Radiation (CSR) as diagnostic tool Bunch length: Gaussian and double-horn structureBunch length: Gaussian and double-horn structure MicrobunchingMicrobunching

DiscussionDiscussion





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





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)

We need a feedback systemWe need a feedback system Courtesy of P. Emma

Courtesy of P. Emma






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

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






Linac

RF

Wakefield (structure wake)

Bend (2rd order map)

Linac

RF

Wakefield (structure wake)

Bend (2rd order map)

]cos[ kzeVEE

0/2

0)( szea

cZzw

56656 TRzz





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) 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)

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)

Courtesy of P. KrejcikCourtesy of P. Krejcik





LCLS Feedback AlgorithmLCLS Feedback AlgorithmLCLS Feedback AlgorithmLCLS Feedback Algorithm

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

IdI

VdVI

dI

d

IdI

VdVI

dI

VdVI

dI

d

EdE

VdVE

dE

d

EdE

VdVE

dE

VdVE

dE

d

IdI

VdVI

dI

VdVI

dI

d

EdE

VdVE

dE

VdVE

dEVdV

EdE

E

dE

I

dI

E

dE

I

dI

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

MCO MCO OGMCC 1 beforeafterOGMCC 1 beforeafter

We are linearlinear

We are linearlinear





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





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 0.0

/

/arg

off

on

EE

EE

Integral Gain helps!Integral Gain helps!

I:0.5I:0.5





Bode Plot (Bode Plot (I/I)I/I)Bode Plot (Bode Plot (I/I)I/I)

off

on

II

II

/

/log20 10

off

on

II

II

/

/log20 10

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

0.0

/

/arg

off

on

II

II 0.0

/

/arg

off

on

II

II

Integral Gain helps!Integral Gain helps!

I:0.5I:0.5





LCLS Accelerator System Jitter MeasurementLCLS Accelerator System Jitter MeasurementLCLS Accelerator System Jitter MeasurementLCLS Accelerator System Jitter Measurement

Courtesy of P. Emma

Courtesy of P. Emma

Peaks around 0.08 and 1.7 Hz





[%])(

)1(1.060

)27.1sin(1.0)208.0sin(

1, H

randn

step

step

N

jj tt

ttt

V

dV

][)(

)1(1.060

)27.1sin(1.0)208.0sin(

1,

H

randn

step

step

N

jjtt

tttd

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 with stepstep :)( Nt





LCLS Feedback PerformanceLCLS Feedback PerformanceLCLS Feedback PerformanceLCLS Feedback Performancefeedback offfeedback off feedback on (Integral gain:0.5Integral gain:0.5)feedback on (Integral gain:0.5Integral gain:0.5)

%60.0/

%;21.0/

std

EE

EE %60.0/

%;21.0/

std

EE

EE

%09.0/

%;0007.0/

std

EE

EE %09.0/

%;0007.0/

std

EE

EE

%5.8/

%;10.0/

std

II

II %5.8/

%;10.0/

std

II

II %4.608/

%;0.169/

std

II

II %4.608/

%;0.169/

std

II

II

ps

ps

std 15.0

;003.0

t

t ps

ps

std 15.0

;003.0

t

t

ps

ps

std 6.1

;5.0

t

t ps

ps

std 6.1

;5.0

t

t





Coherent Synchrotron RadiationCoherent Synchrotron RadiationCoherent Synchrotron RadiationCoherent Synchrotron Radiation CSR as nondestructive diagnostic tool For a group of Ne electrons

CSR spectrum

dd

IdFN

dd

Idee

dd

Id

e

N

j

c

Rnitie

j

j

02

22

02

2

1

ˆ2

Form factor

2

2ˆ2

),,(

),,(

dxdydzezyxn

dxdydzeezyxnF

ikz

Rnikikz

with

1),,( dxdydzzyxn





Linac Wake/ImpedanceLinac Wake/ImpedanceLinac Wake/ImpedanceLinac Wake/Impedance

(capacitive)

VV(( ss

)/M

V/n

C/m

)/M

V/n

C/m

ss//ssFWFW

1 mm1 mm

500 500 mm

250 250 mm

100 100 mm 50 50 mm 25 25 mm

s

Linac wake Green function (K. Bane)

SLACSLAC S-Band: S-Band:ss0 0 1.32 mm 1.32 mmaa 11.6 mm 11.6 mmss < ~6 mm < ~6 mm

To first order in 1/k





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

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]





Wake-induced Cubic termWake-induced Cubic termWake-induced Cubic termWake-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 Wake with parabolic dist. leads to the double-horn





Wake-induced Cubic termWake-induced Cubic termWake-induced Cubic termWake-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 Wake with parabolic dist. leads to the double-horn





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

Black: with Laser-Heater

( )

Red: without Laser-Heater

( )

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

keV 47E

keV 3E

m 21zm 21z





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 Black: with

Laser-Heater

( )


( )

Blue: Gaussian with same ( )

Green: Step with same ( )

keV 47E

keV 3E

m 21z

m 21z





CSR spectrum after BC2CSR spectrum after BC2CSR spectrum after BC2CSR spectrum after BC2

ISR power spectrum from a bending magnetfor an azimuthal milliradian of the electron orbit () and integrated over all the vertical angles

ISR power spectrum from a bending magnetfor an azimuthal milliradian of the electron orbit () and integrated over all the vertical angles

];[3

4

][][][1042.8)(

3

3/73/18

o

c A

IθP

for

mmAmpm /mm][W/mradisr

).()(2 isrcsr /mm][W/mrad Hence, PFNθP e

(m)(m) z z (mm)(mm) (mm)(mm) f (THz)f (THz) IIpeak peak (A)(A) PPcsrcsr(kW)(kW)

BC1BC1 2.42.4 0.190.19 0.190.19 1.61.6 400400 0.260.26

BC2BC2 14.514.5 0.0210.021 0.0210.021 14.314.3 34003400 75.275.2

Assuming |F|2=1%, /=1%, for 1 nC charge bunch Assuming |F|2=1%, /=1%, for 1 nC charge

bunch





Black: with Laser-Heater

( )


( )



keV 47E

keV 3E

m 21z

m 21z

CSR spectrum after BC2CSR spectrum after BC2CSR spectrum after BC2CSR spectrum after BC2 Fix detector Fix detector





CSR spectrum after BC2CSR spectrum after BC2CSR spectrum after BC2CSR spectrum after BC2 Fix detector Fix detector Black: with

Laser-Heater

( )


( )



keV 47E

keV 3E

m 21z

m 21z





Instability mechanismInstability mechanism

t

Energybi bf >> bi or G= bf/ bi >> 1k

R

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!

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!

t

Current modulation

1% 10%Gain=10





Microbunching after BC2Microbunching after BC2Microbunching after BC2Microbunching after BC2 Current profile with microbunching at 100/40 m Current profile with microbunching at 100/40 m

Black: with microbunching(20% at 100/40 m)

Red: without microbunching

m 21zm 21z





Bunch spectrum after BC2Bunch spectrum after BC2Bunch spectrum after BC2Bunch spectrum after BC2 Microbunching inf. in the bunch spectrum Microbunching inf. in the bunch spectrum

Black: with microbunching (20% at 100/40 m)




m 21z

m 21z










m 21z

m 21z





Microbunching after BC2Microbunching after BC2Microbunching after BC2Microbunching after BC2

Current profile with microbunching at 500/40 m Current profile with microbunching at 500/40 m



m 21zm 21z





Bunch spectrum after BC2Bunch spectrum after BC2Bunch spectrum after BC2Bunch spectrum after BC2 Microbunching inf. in the bunch spectrum Microbunching inf. in the bunch spectrum





m 21z

m 21z










m 21z

m 21z





Microbunching after BC1Microbunching after BC1Microbunching after BC1Microbunching after BC1

Current profile with microbunching at 500/4 m Current profile with microbunching at 500/4 m



m 190zm 190z





Bunch spectrum after BC1Bunch spectrum after BC1Bunch spectrum after BC1Bunch spectrum after BC1 Smooth parabolic distribution Smooth parabolic distribution




m 190z









m 190z





DiscussionDiscussionDiscussionDiscussion

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 correctHowever, 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 situationMicorbunching easier to be detected at BC1, because

The double-horn structure complicates situation

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 correctHowever, 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 situationMicorbunching easier to be detected at BC1, because

The double-horn structure complicates situation





To-do listTo-do listTo-do listTo-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

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





Acknowledgement Acknowledgement Acknowledgement Acknowledgement

Collaboration with P. Emma, L. Hendrickson, Z. Huang, P. Krejcik, et al.

Thank committee for the workshop and invitation

Linac Coherent Light Source (LCLS) accelerator system Jitter model Feedback model

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