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CSR Benchmark Test-Case Results. Paul Emma SLAC January 14, 2002 BERLIN. CSR Workshop. Chicane 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 on TESLA-FEL-96-14

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csr benchmark test case results
CSR Benchmark Test-Case Results

Paul Emma

SLAC

January 14, 2002

BERLIN

CSR Workshop

chicane csr test case
Chicane 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 on

TESLA-FEL-96-14

(Saldin et al., Nov. 1996)

(T566 included, no ISR* added)

* incoherent synchrotron radiation

initial gaussian distribution prior to chicane
Initial Gaussian Distribution Prior to Chicane

perfectly linear correlation

sE/E0 = 0.72 %

 bunch head

ss = 200 mm

E0 = 5 GeV

second order compression included t 566
Second Order Compression Included: T566

/mm

T566 -3R56/2

leads to slight bunch shape distortion

after drift-3

before drift-3

beta and dispersion functions
Beta and Dispersion Functions

B2

B3

B1

B4

‘CSR-altered’ bx

‘linear’ bx

hx-max 267 mm

‘linear’ hx

bunch length and r 56
Bunch Length and R56

B2

B3

B1

B4

ss0 = 200 mm

ss = 20 mm

B2

B4

B3

B1

R56 = -25 mm

line charge validity
Line-Charge Validity

Is transverse bunch size small ?

B2

B3

B1

B4

x3/(Rs2) << 1

(Derbenev et. al.)

slide8

CSR may be over-estimated in present tracking…

s

s

s

s

(s- s) Rj3/24

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

R

R

j

final s d phase space gaussian input
Final s-d phase space (gaussian input)

sE/E0 = 0.716 %

 bunch head

ss = 20.3 mm

energy spread and emittance gaussian
Energy Spread and Emittance (gaussian)

B2

B4

B3

B1

E /E0 -0.043%

sd 0.021%

B2

B4

B3

B1

gex 1.52 mm

final x x phase space gaussian input
Final x-x Phase Space (gaussian input)

ge 1.52 mm

geCSR 0.145 mm

ge0 = 1.00 mm

bopt 1.37 m

aopt-1.10

final x x phase space gaussian optimal b 0 a 0
Final x-x Phase Space (gaussian & optimalb0, a0)

emittance growth can be reduced by choosing matchedb-functions

ge 1.15 mm

geCSR 0.145 mm

bbopt

aaopt

ge0 = 1.00 mm

beta and emittance gaussian optimal b 0 a 0
Beta and emittance (gaussian & optimalb0, a0)

too big?

bmin 0.6 m

bbopt

aaopt

gex 1.15 mm

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

bend-1 (10)

L = 0.4 m

drift-1 (20)

L = 5 m

Nbin = 600, smoothed over 4

bend-2 (10)

L = 0.4 m

drift-2 (10)

L = 1 m

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

bend-3 (20)

L = 0.4 m

drift-3 (40)

L = 5 m

drift-4 (20)

L = 2 m

bend-4 (20)

L = 0.4 m

compressing uniform distribution
Compressing Uniform Distribution

rise/fall ‘time’ > R/g3 0.1 Å

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

(sE/E0)ISR 1.910-5

sE/E0 = 0.720 %

less structure on bunch

ss = 20.2 mm

energy spread and emittance uniform dist
Energy Spread and Emittance (uniform dist.)

E /E0 -0.046%

sd 0.007%

emittance growth reduced compared to gaussian

gex 1.12 mm

final x x phase space uniform dist
Final x-x Phase Space (uniform dist.)

ge 1.12 mm

geCSR 0.07 mm

ge0 = 1.00 mm

bopt 3.9 m

aopt-0.51

csr wakefields uniform dist bend 1 to drift 2
CSR wakefields (uniform dist.  bend-1 to drift-2)

bend-1 (10)

L = 0.4 m

drift-1 (20)

L = 5 m

Nbin = 600, smoothed over 4

bend-2 (10)

L = 0.4 m

drift-2 (10)

L = 1 m

csr wakefields uniform dist bend 3 to drift 4
CSR wakefields (uniform dist.  bend-3 to drift-4)

bend-3 (20)

L = 0.4 m

drift-3 (40)

L = 5 m

drift-4 (20)

L = 2 m

bend-4 (20)

L = 0.4 m

betatron amplitude per bunch slice
Betatron Amplitude per Bunch Slice

gaussian

l(s)

uniform

l(s)

final s d phase space single bend
Final s-d phase space - Single-Bend

sE/E0 = 0.011 %

ss = 20.1 mm

energy spread and emittance single bend
Energy Spread and Emittance – Single Bend

(24ssR2)1/3

sd = 0.011%

steady-state

bend magnet

try a double chicane two test chicanes
Try a Double-Chicane (two ‘test’-chicanes)

hx 244 mm

-I

hx 107 mm

R56= -21 mm

R56= -4 mm

ss 200 mm

E0 = 5 GeV

ss 50 mm

ss 20 mm

csr energy loss spread and emittance double chicane
CSR Energy Loss, Spread, and Emittance (double-chicane)

E /E0 -0.052%

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

sd 0.028%

projected emittance growth is greatly reduced using double-chicane

single-chicane

double-chicane

gex 1.01 mm

final s d phase space double chicane
Final s-d phase space (double-chicane)

sE/E0 = 0.712 %

ss = 20.4 mm

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