Page 1
CSR Calculation for TTF2
1. method2. no CSR, ϕrf = 8 deg3. CSR “projected”, optics = option 1 & 2, ϕrf = 8 deg4. CSR “projected”, optics = option 1 & 2, ϕrf = 12 deg5. CSR “projected”, optics = option 1, ϕrf = 7 deg6. some LOLA pictures7. conclusion / remarks
ϕrfon crest
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1. method
from: Commissioning of TTF2 Bunch Compressor For The Femptosecond (fs) FEL Mode Operation, Yujong Kim
ASTRA distribution (xfel.1200.001.txt)1nC, 200000 particles
1) extract rf (longitudinal momentum)2) add ACC1 rf as required
3) calculate Twiss parameters fromcore of bunch (particles between ±2mm)use transport matrix for matching torequired values (Nina Golubeva)
( )rf
rfacc cos
cos)(ϕ
ϕ+= ksVsV
m 809.2 012.0m 174.20 619.4
=−===yy
xx
βαβα
ϕrf
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MeVrefEE −
deg 8rf =ϕ
mmz
mmz
AI
particles at entrance of BC1horizontal vs. longitudinal
mz
mxe.g.
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particles at entrance of BC1(“slices” with 5000 particles)
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method …
from: Commissioning of TTF2 Bunch Compressor For The Femptosecond (fs) FEL Mode Operation, Yujong Kim
4) calculate BC2 with projected methodsub-bunch length:
reference plane = 1 m after BC
2
R = 1.614955 mr56 = -0.181496 mt586 = 0.296575 m
ms
µmσ
3
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from: Commissioning of TTF2 Bunch Compressor For The Femptosecond (fs) FEL Mode Operation, Yujong Kim
5) transformation from exit BC2 to entrance BC3:
longitudinal: add rf-field and wake of two modules
transverse: use transport matrixoption 1: αx=-0.284, βx= 0.976m µx=0.328*2π to αx=-0.284, βx= 0.976m µx=1.427*2π
αy= 2, βy=31.037m µy=1.427*2π αy= 2, βy=30.021m µy=1.465*2π
option 2: … to αx=-0.495, βx=17.150m µx=1.478*2παy=-0.152, βy=19.719m µy=1.830*2π
method …
on crest
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from: Commissioning of TTF2 Bunch Compressor For The Femptosecond (fs) FEL Mode Operation, Yujong Kim
6) calculate BC3 with projected methodsub-bunch length = 3 µm
reference plane = 1 m after BC
R = 5.695 m
r56 = -0.041226 mt586 = 0.064860 m
method …
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12
3
4
5
6
4
5
6
12
3
4
5
6
MeVrefEE −
mmz
before BC2 1m after BC2 1m after BC3
12
34
5
6
4
5
6
deg 8rf =ϕoptics = option 12. no CSR
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4
5
6
4
5
6
12
3
4
5
6
MeVrefEE −
mmz
before BC2 1m after BC2 1m after BC3
mmz
AI
deg 8rf =ϕoptics = option 1no CSR
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4
5
6
12
3
4
5
6
4
5
6
12
3
4
5
6
before BC2 1m after BC2 1m after BC31
23
4
5
6
MeVrefEE −
mmz
deg 8rf =ϕoptics = option 13. CSR “projected”
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220
before BC2 1m after BC2 1m after BC3
mmz
AI 44
MeVrefEE −
mmz
deg 8rf =ϕoptics = option 1CSR “projected”
1400
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long. phase space in BC3
1 2 34 5
6
MeVrefEE −
mmz
1 2
3
4 5 6
deg 8rf =ϕoptics = option 1
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MeVrefEE −
mmz
mmz
AI
longitudinal horizontal“top”
mmz
mmx
mmx
mradx′
x
z
deg 8rf =ϕoptics = option 1CSR “projected”
1400
all particles:emittance/um = 10.1rms-length/um = 722rms-energy spread/keV = 1450
“black” particles:emittance/um = 4.13rms-length/um = 5.6rms-energy spread/keV = 476
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longitudinal “top” horizontal
MeVrefEE −
mmz
mmx
mmz
mradx′
mmx
mmz
AI
z
x
deg 8rf =ϕoptics = option 2CSR “projected”
907
all particles:emittance/um = 10.6rms-length/um = 722rms-energy spread/keV = 1419
“black” particles:emittance/um = 3.63rms-length/um = 6.8rms-energy spread/keV = 418
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230
before BC2 1m after BC2 1m after BC3
mmz
AI 46
MeVrefEE −
mmz
854
deg 12rf =ϕoptics = option 14. CSR “projected”
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deg 12rf =ϕoptics = option 1CSR “projected”
MeVrefEE −
mmz
longitudinal horizontal“top”
mmz
mmx
mmx
mradx′
x
z
all particles:emittance/um = 10.55rms-length/um = 339rms-energy spread/keV = 1380
“black” particles:emittance/um = 4.56rms-length/um = 13.0rms-energy spread/keV = 324
mmz
AI
854
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MeVrefEE −
mmz
longitudinal horizontal“top”
mmz
mmx
mmx
mradx′
x
zmmz
AI
637
deg 12rf =ϕoptics = option 2CSR “projected”
all particles:emittance/um = 10.74rms-length/um = 338rms-energy spread/keV = 1380
“black” particles:emittance/um = 5.43rms-length/um = 13.8rms-energy spread/keV = 313
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240
before BC2 1m after BC2 1m after BC3
mmz
AI
36.5
MeVrefEE −
mmz
1430
deg 7rf =ϕoptics = option 15. CSR “projected”
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MeVrefEE −
mmz
longitudinal horizontal“top”
mmz
mmx
mmx
mradx′
x
z
deg 7rf =ϕoptics = option 1CSR “projected”
mmz
AI
1430
all particles:emittance/um = 3.38rms-length/um = 923rms-energy spread/keV = 880
“black” particles:emittance/um = 2.06rms-length/um = 4.2rms-energy spread/keV = 256
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6. some LOLApictures
deg 8rf =ϕoptics = option 1
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deg 12rf =ϕoptics = option 1
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7. conclusion / remarks1. settings and beam parameters only known to a certain precision
2. CSR model for TTF2 with space charge in ACC1,“projected” method in BC2 & BC3,transport matrix for BC2 → BC3,ACC4 → undulator not considered jet
3. ASTRA calculations for BC2 → BC3 and ACC4 → undulator in preparation“projected” CSR calculations in ASTRA in principle possible
4. “3D” CSR calculations with full- & over-compression difficult(variable sub-bunch needed due to long tails ↔ meshed green’s function)“projected” CSR calculations need better smoothing/filter-algorithms
5. qualitative understanding of compression process,complicated interaction of “full” compressed part to rest of bunch
6. qualitative agreement with LOLA pictures
7. optics “option 1” and “weak over-compression” in BC2 seems preferable