CSR Benchmark TestCase Results

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CSR Benchmark Test-Case Results
Paul Emma SLAC January 14, 2002 BERLIN
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)
(T566 included, no ISR added)
incoherent synchrotron radiation
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Initial Gaussian Distribution Prior to Chicane
perfectly linear correlation
sE/E0 0.72
? bunch head
ss 200 mm
E0 5 GeV
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Second Order Compression Included T566
T566 ? -3R56/2
leads to slight bunch shape distortion
after drift-3
before drift-3
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Beta and Dispersion Functions
B2
B3
B1
B4
CSR-altered bx
linear bx
hx-max ? 267 mm
linear hx
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Bunch Length and R56
B2
B3
B1
B4
ss0 200 mm
ss 20 mm
B1
B2
B3
B4
R56 -25 mm
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Line-Charge Validity
Is transverse bunch size small ?
B1
B2
B3
B4
?x3/(R?s2) ltlt 1
(Derbenev et. al.)
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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
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Final s-d phase space (gaussian input)
sE/E0 0.716
? bunch head
ss 20.3 mm
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Energy Spread and Emittance (gaussian)
B1
B2
B3
B4
??E ?/E0 ? -0.043
sd ? 0.021
B2
B4
B1
B3
gex ? 1.52 mm
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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)
ge ? 1.52 mm
geCSR ? 0.145 mm
ge0 1.00 mm
bopt ? 1.37 m aopt ? -1.10
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Final x-x? Phase Space (gaussian optimal b0, a0)
emittance growth can be reduced by choosing
matched b-functions
ge ? 1.15 mm
geCSR ? 0.145 mm
b ? bopt a ? aopt
ge0 1.00 mm
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Beta and emittance (gaussian optimal b0, a0)
too big?
bmin ? 0.6 m
b ? bopt a ? aopt
gex ? 1.15 mm
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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
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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
drift-4 (?20) ?L 2 m
bend-4 (?20) ?L 0.4 m
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Compressing Uniform Distribution
rise/fall time gt R/g 3 ? 0.1 Å
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Final s-d phase space Uniform input dist.
sE/E0 0.720
ss 20.2 mm
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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
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Energy Spread and Emittance (uniform dist.)
??E ?/E0 ? -0.046
sd ? 0.007
emittance growth reduced compared to gaussian
gex ? 1.12 mm
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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.)
ge ? 1.12 mm
geCSR ? 0.07 mm
ge0 1.00 mm
bopt ? 3.9 m aopt ? -0.51
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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
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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
drift-4 (?20) ?L 2 m
bend-4 (?20) ?L 0.4 m
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Betatron Amplitude per Bunch Slice
gaussian
l(s)
uniform
l(s)
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Final s-d phase space - Single-Bend
sE/E0 0.011
ss 20.1 mm
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Energy Spread and Emittance Single Bend
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CSR-Wake Movie - Single-Bend
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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
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CSR Energy Loss, Spread, and Emittance
(double-chicane)
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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