Paul EmmaPaul EmmaSLACSLAC

January 14, 2002January 14, 2002

BERLINBERLIN

CSR Benchmark CSR Benchmark Test-Case ResultsTest-Case Results

CSR WorkshopCSR Workshop

Chicane CSR Test-CaseChicane CSR Test-Case

Use line-charge CSR transient model described in LCLS-TN-01-12…(Stupakov/Emma, Dec. 2001)

[same now used in Elegant]

…based onTESLA-FEL-96-14(Saldin et al., Nov. 1996)

Use line-charge CSR transient model described in LCLS-TN-01-12…(Stupakov/Emma, Dec. 2001)

[same now used in Elegant]

…based onTESLA-FEL-96-14(Saldin et al., Nov. 1996)

((TT566566 included, no ISR included, no ISR** added) added)

* incoherent synchrotron radiation

Initial Gaussian Distribution Prior to ChicaneInitial Gaussian Distribution Prior to Chicane

ss = 200 = 200 mm

EE//EE00 = 0.72 % = 0.72 %

bunch headbunch head

perfectly linear perfectly linear correlationcorrelation

EE00 = 5 GeV = 5 GeV

Second Order Compression Included: Second Order Compression Included: TT566566

TT566566 33RR5656/2/2

after drift-3after drift-3

before drift-3before drift-3

leads to slight bunch leads to slight bunch shape distortionshape distortion

/mm

Beta and Dispersion FunctionsBeta and Dispersion Functions

‘‘linear’ linear’ xx

‘‘linear’ linear’ xx

‘‘CSR-altered’ CSR-altered’ xx

B1B1 B2B2 B3B3 B4B4

x-maxx-max 267 mm 267 mm

Bunch Length and Bunch Length and RR5656

B1B1 B2B2 B3B3 B4B4

B1B1 B2B2 B3B3 B4B4

ss = 20 = 20 mm

ss00 = 200 = 200 mm

RR5656 = = 25 mm25 mm

Line-Charge ValidityLine-Charge Validity

(Derbenev et. al.)(Derbenev et. al.)

B1B1 B2B2 B3B3 B4B4

Is transverse bunch size small ?Is transverse bunch size small ?

xx33/(/(RRss

22) << 1) << 1

((ssss) ) RR33/24/24

RR

ssss

ssss

fields evaluated fields evaluated and and immediatelyimmediately applied, without applied, without including longer including longer bunch at retarded bunch at retarded position position over- over-estimate?estimate?

RR

CSR may be over-estimated in CSR may be over-estimated in present tracking…present tracking…

Final Final ss-- phase space (gaussian input) phase space (gaussian input)

ss = 20.3 = 20.3 mm

EE//EE00 = 0.716 % = 0.716 %

bunch headbunch head

Energy Spread and Emittance (gaussian)Energy Spread and Emittance (gaussian)

B1B1 B2B2 B3B3 B4B4

B1B1 B2B2 B3B3 B4B4

xx 1.52 1.52 mm

0.021%0.021%

0.043%0.043%

Total RMS Relative Energy Spread (including ‘chirp’)Total RMS Relative Energy Spread (including ‘chirp’)

B1B1 B2B2 B3B3 B4B4

Chicane CSR-wake Movie (gaussian)Chicane CSR-wake Movie (gaussian)

Chicane CSR-integrated-wake (gaussian)Chicane CSR-integrated-wake (gaussian)

Final Final xx--xx Phase Space (gaussian input) Phase Space (gaussian input)

1.52 1.52 mm

00 = 1.00 = 1.00 mmCSRCSR 0.145 0.145 mm

optopt 1.37 m 1.37 m

optopt 1.101.10

Final Final xx--xx Phase Space (gaussian & Phase Space (gaussian & optimaloptimal 00, , 00))

1.15 1.15 mm

00 = 1.00 = 1.00 mm

CSRCSR 0.145 0.145 mm

optopt

optopt

emittance growth can be emittance growth can be reduced by choosing reduced by choosing matchedmatched -functions-functions

Beta and emittance (gaussian & Beta and emittance (gaussian & optimaloptimal 00, , 00))

xx 1.15 1.15 mm

optopt

optopt

too big?too big? minmin 0.6 m 0.6 m

bend-1 (bend-1 (10)10)LL = 0.4 m = 0.4 m

drift-1 (drift-1 (20)20)LL = 5 m = 5 m

bend-2 (bend-2 (10)10)LL = 0.4 m = 0.4 m

drift-2 (drift-2 (10)10)LL = 1 m = 1 m

CSR wakefields (gaussian CSR wakefields (gaussian bend-1 to drift-2) bend-1 to drift-2)

NNbinbin = 600, = 600,

smoothed over 4smoothed over 4

CSR wakefields (gaussian CSR wakefields (gaussian bend-3 to drift-4) bend-3 to drift-4)

bend-3 (bend-3 (20)20)LL = 0.4 m = 0.4 m

drift-3 (drift-3 (40)40)LL = 5 m = 5 m

bend-4 (bend-4 (20)20)LL = 0.4 m = 0.4 m

drift-4 (drift-4 (20)20)LL = 2 m = 2 m

Compressing Compressing UniformUniform Distribution Distribution

rise/fall ‘time’ > rise/fall ‘time’ > RR//33 0.1 Å 0.1 Å

ss = 20.2 = 20.2 mm

EE//EE00 = 0.720 % = 0.720 %

Final Final ss-- phase space – phase space – UniformUniform input dist. input dist.

Now add incoherent synch. rad. in each bendNow add incoherent synch. rad. in each bend

less structure less structure on bunchon bunch

ss = 20.2 = 20.2 mm

EE//EE00 = 0.720 % = 0.720 %

EE//EE00ISRISR 1.9 1.9101055

xx 1.12 1.12 mm

0.007%0.007%

0.046%0.046%

Energy Spread and Emittance (Energy Spread and Emittance (uniformuniform dist.) dist.)

emittance growth reduced compared to gaussianemittance growth reduced compared to gaussian

Chicane CSR-wake Movie (Chicane CSR-wake Movie (uniformuniform dist.) dist.)

Chicane CSR-integrated-wake (Chicane CSR-integrated-wake (uniformuniform dist.) dist.)

Final Final xx--xx Phase Space ( Phase Space (uniformuniform dist.) dist.)

1.12 1.12 mm

00 = 1.00 = 1.00 mmCSRCSR 0.07 0.07 mm

optopt 3.9 m 3.9 m

optopt 0.510.51

bend-1 (bend-1 (10)10)LL = 0.4 m = 0.4 m

drift-1 (drift-1 (20)20)LL = 5 m = 5 m

bend-2 (bend-2 (10)10)LL = 0.4 m = 0.4 m

drift-2 (drift-2 (10)10)LL = 1 m = 1 m

CSR wakefields (CSR wakefields (uniformuniform dist. dist. bend-1 to drift-2) bend-1 to drift-2)

NNbinbin = 600, = 600,

smoothed over 4smoothed over 4

CSR wakefields (CSR wakefields (uniformuniform dist. dist. bend-3 to drift-4) bend-3 to drift-4)

bend-3 (bend-3 (20)20)LL = 0.4 m = 0.4 m

drift-3 (drift-3 (40)40)LL = 5 m = 5 m

bend-4 (bend-4 (20)20)LL = 0.4 m = 0.4 m

drift-4 (drift-4 (20)20)LL = 2 m = 2 m

((ss))

Betatron Amplitude per Bunch SliceBetatron Amplitude per Bunch Slice

((ss))

gaussiangaussian

uniformuniform

Final Final ss-- phase space - phase space - Single-BendSingle-Bend

ss = 20.1 = 20.1 mm

EE//EE00 = 0.011 % = 0.011 %

Energy Spread and Emittance – Energy Spread and Emittance – Single BendSingle Bend

steady-state

steady-state

bend magnetbend magnet

= 0.011%= 0.011%

(24(24ssRR22))1/31/3

CSR-Wake Movie - CSR-Wake Movie - Single-BendSingle-Bend

Try aTry a Double Double-Chicane (two ‘test’-chicanes)-Chicane (two ‘test’-chicanes)xx 244 mm 244 mm

xx 107 mm 107 mm

ss 50 50 mm

ss 200 200 mm

ss 20 20 mm

I

RR5656 = = 21 mm21 mm RR5656 = = 4 mm4 mm

EE00 =

5 G

eV =

5 G

eV

CSR Energy Loss, Spread, and Emittance CSR Energy Loss, Spread, and Emittance ((doubledouble-chicane)-chicane)

0.028%0.028%

0.052%0.052%energy loss and spread are larger energy loss and spread are larger than for a single-chicanethan for a single-chicane

xx 1.01 1.01 mm

projected projected emittance growth emittance growth is greatly reduced is greatly reduced

using double-using double-chicanechicane

single-chicanesingle-chicane

double-chicanedouble-chicane

ss = 20.4 = 20.4 mm

EE//EE00 = 0.712 % = 0.712 %

Final Final ss-- phase space (double-chicane) phase space (double-chicane)

projected projected emittance emittance growth is growth is much smaller, much smaller, but micro-but micro-bunching is bunching is worseworse

projected projected emittance emittance growth is growth is much smaller, much smaller, but micro-but micro-bunching is bunching is worseworse