about micro bunching investigation for dogleg with ... · δe q = gaussian / parabula laser heater:...
TRANSCRIPT
![Page 1: About Micro Bunching Investigation for DOGLEG with ... · δE q = gaussian / parabula laser heater: perfect match of particle and optical beam initial current Ctot I 5 kA = (0.1 nC](https://reader031.vdocuments.us/reader031/viewer/2022040723/5e34409e5c49612fd262a192/html5/thumbnails/1.jpg)
About Micro BunchingInvestigation for DOGLEG with Longitudinal Dispersion
Remark: Micro Bunching in FLASH
XFEL bunch Compression System
Working Points
DOGLEG without Sextupoles
LGM (= linear gain model using integral equation method)
Detailed Comparison for 0.1 nC Working Point
Results and Comparison
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f.i. 1st October 2010, 02:20
0.65nC
Remark: Micro Bunching in FLASH
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micro-bunching increases energy spread and affects emittance
example: energy spread ∫ ′≈ dzZIeE~δ
XFEL, from BC1 (@ 500 MeV) to BC2 (@ 2 GeV)
Ω′∫ k 10~dzZ
A 500~~I
100% ofI ~ 500 A
↓MeV 5~Eδ
↓
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energy spread ∫ ′≈ dzZIeE~δ
XFEL, from BC2 (@ 2 GeV) to 17.5 GeV
Ω′∫ k 10~dzZ
A 500~~I
10% ofI ~ 5 kA
↓MeV 5~Eδ
↓
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( ) ( )( ) ( ) ( )∫B
dSSGSBKBGBG0
0 ,+=
( )( ) ( )( )BkLHBG =0
( ) ( ) ( ) ( ) ( )( ) ( ) ( )( )( )SLBLkH
eSE
SZSIBkjqSBK SB −
′−= ←
ref
56,
( ) ( )5601
1
←+=
ShqcSC
( ) ( )( )SparametersZSZ ,, ωω ′=′
( ) ( )∫ ( ) ( )( )
( )
′′×′= ⊥u
0
0
0u
000u
000 exp,
ηηψψη η x
x
jVxxdxddxVH t
transversephase space
longitudinalphase space
longitudinal impedancecompression:
chirp
optics
(local) current
emittance
LGM (= linear gain model using integral equation method)
laser heater
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XFEL Bunch Compression System
BC0BC1
BC2
3 stage bunch compression system:
5 MeV gun 1nC, 50 A130 MeV BC0 → ~ 100 A
500 MeV BC1 → ~ 1 kA2 GeV BC2 → ~ 5 kA
DOGLEG
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DOGLEG without Sextupoles
!// *******************************************************!// * XFEL Injector Dogleg as two FRFR arcs: *!// *-----------------------------------------------------*!// * 20 m length along linac axis, 2.75 m beam offset, *!// * 20.253 m lenght along reference orbit and r56 = 0. *!// *-----------------------------------------------------*!// * Created: 08 February 2011 (without sextupoles) *!// *******************************************************
no sextupoles16 bending magnets16 quadrupolesr56/mm = 30 (reduce strength of BC0!)
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Working Points (from Beam Dynamics Homepage, Jan 2010)
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Detailed Comparison for 0.1 nC Working Point
initial RMS energy spread ( )nC 1
keV 2q
qE =δ gaussian / parabula
laser heater: perfect match of particle and optical beam
initial currenttotC
IkA 5= (0.1 nC → Ctot = 870)
normalized emittancenC 1
q µm 1=nε
1) adjust laser amplitude for MeV 1totend =×= CEE δδ
2) adjust laser amplitude for ( ) end100,max ESG δω →=
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Detailed Comparison for 0.1 nC Working Point
beta function: typical = 20 m, real optic for DOGLEG, BC0 ... BC2
BC0
BC1 BC2
DOG-LEG
optics without DOGLEG optics with DOGLEG
calculation ends after BC2(or no longitudinal dispersion beyond that is)
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Detailed Comparison for 0.1 nC Working Point
gain(S) without DOGLEG gain(S) with DOGLEG
adjust laser amplitude for MeV 1totend =×= CEE δδ1.5 THz (initial wavelength 0.2 mm)
after DOGLEG, BC0, BC1, BC2
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Detailed Comparison for 0.1 nC Working Point
gain(f) without DOGLEG gain(f) with DOGLEG
adjust laser amplitude for MeV 1totend =×= CEE δδ
after DOGLEG, BC0, BC1, BC2, maximum
LH spectrum
too many curves →
1.5 THz
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Detailed Comparison for 0.1 nC Working Point
gain(f) without DOGLEG gain(f) with DOGLEG
adjust laser amplitude for MeV 1totend =×= CEE δδ
after BC2, maximum
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Detailed Comparison for 0.1 nC Working Point
gain(f) without DOGLEG gain(f) with DOGLEG
adjust laser amplitude for ( ) end100,max ESG δω →=
2.2end =MeVEδ2.3end =MeVEδ
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Detailed Comparison for 0.1 nC Working Point
gain(f) withoutgain(f)
with DOGLEG
adjust laser amplitude for ( ) end100,max ESG δω →=
2.2end =MeVEδ2.3end =MeVEδ
parabola energy profile before LH
gaussian energy profilegaussian energy profile
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Results and Comparison
charge(case) / nC
without dogleg δE = 1MeVwithout dogleg Gmax = 100with dogleg δE = 1MeVwith dogleg Gmax = 100
( )∫∞
=0
2
2
22 ωω
πdG
eIIrms