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Paul Emma SLAC January 14, 2002 BERLIN CSR Benchmark Test-Case Results CSR Workshop

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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) 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) (T 566 included, no ISR * added) * incoherent synchrotron radiation

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Initial Gaussian Distribution Prior to Chicane s = 200 m E /E 0 = 0.72 % bunch head perfectly linear correlation E 0 = 5 GeV

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Second Order Compression Included: T 566 T 566 3R 56 /2 after drift-3 before drift-3 leads to slight bunch shape distortion /mm

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Beta and Dispersion Functions ‘linear’ x ‘linear’ x ‘CSR-altered’ x B1 B2 B3 B4 x-max 267 mm

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Bunch Length and R 56 B1 B2 B3 B4 B1 B2 B3 B4 s = 20 m s 0 = 200 m R 56 = 25 mm

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Line-Charge Validity (Derbenev et. al.) B1 B2 B3 B4 Is transverse bunch size small ? x 3 /(R s 2 ) << 1

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(s s) R 3 /24 R s s s s fields evaluated and immediately applied, without including longer bunch at retarded position over- estimate? R CSR may be over-estimated in present tracking…

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Final s - phase space (gaussian input) s = 20.3 m E /E 0 = 0.716 % bunch head

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Energy Spread and Emittance (gaussian) B1 B2 B3 B4 B1 B2 B3 B4 x 1.52 m 0.021% 0.043%

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Total RMS Relative Energy Spread (including ‘chirp’) B1 B2 B3 B4

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Chicane CSR-wake Movie (gaussian)

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Chicane CSR-integrated-wake (gaussian)

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Final x-x Phase Space (gaussian input) 1.52 m 0 = 1.00 m CSR 0.145 m opt 1.37 m opt 1.10

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Final x-x Phase Space (gaussian & optimal 0, 0 ) 1.15 m 0 = 1.00 m CSR 0.145 m opt opt emittance growth can be reduced by choosing matched -functions

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Beta and emittance (gaussian & optimal 0, 0 ) x 1.15 m opt opt too big? min 0.6 m

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bend-1 ( 10) L = 0.4 m drift-1 ( 20) L = 5 m bend-2 ( 10) L = 0.4 m drift-2 ( 10) L = 1 m CSR wakefields (gaussian bend-1 to drift-2) N bin = 600, smoothed over 4

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CSR wakefields (gaussian bend-3 to drift-4) bend-3 ( 20) L = 0.4 m drift-3 ( 40) L = 5 m bend-4 ( 20) L = 0.4 m drift-4 ( 20) L = 2 m

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Compressing Uniform Distribution rise/fall ‘time’ > R/ 3 0.1 Å

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s = 20.2 m E /E 0 = 0.720 % Final s - phase space – Uniform input dist.

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Now add incoherent synch. rad. in each bend less structure on bunch s = 20.2 m E /E 0 = 0.720 % E /E 0 ISR 1.9 10 5

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x 1.12 m 0.007% 0.046% Energy Spread and Emittance (uniform dist.) emittance growth reduced compared to gaussian

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Chicane CSR-wake Movie (uniform dist.)

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Chicane CSR-integrated-wake (uniform dist.)

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Final x-x Phase Space (uniform dist.) 1.12 m 0 = 1.00 m CSR 0.07 m opt 3.9 m opt 0.51

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bend-1 ( 10) L = 0.4 m drift-1 ( 20) L = 5 m bend-2 ( 10) L = 0.4 m drift-2 ( 10) L = 1 m CSR wakefields (uniform dist. bend-1 to drift-2) N bin = 600, smoothed over 4

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CSR wakefields (uniform dist. bend-3 to drift-4) bend-3 ( 20) L = 0.4 m drift-3 ( 40) L = 5 m bend-4 ( 20) L = 0.4 m drift-4 ( 20) L = 2 m

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(s) (s) Betatron Amplitude per Bunch Slice (s) (s) gaussian uniform

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Final s - phase space - Single-Bend s = 20.1 m E /E 0 = 0.011 %

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Energy Spread and Emittance – Single Bend steady-state bend magnet = 0.011% (24 s R 2 ) 1/3

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CSR-Wake Movie - Single-Bend

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Try a Double -Chicane (two ‘test’-chicanes) x 244 mm x 107 mm s 50 m s 200 m s 20 m II R 56 = 21 mm R 56 = 4 mm E 0 = 5 GeV

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CSR Energy Loss, Spread, and Emittance (double-chicane) 0.028% 0.052% energy loss and spread are larger than for a single-chicane x 1.01 m projected emittance growth is greatly reduced using double-chicane single-chicane double-chicane

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s = 20.4 m E /E 0 = 0.712 % Final s - phase space (double-chicane) projected emittance growth is much smaller, but micro- bunching is worse

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