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CSR Benchmark Test-Case Results - DESY · Paul Emma SLAC January 14, 2001 CSR Benchmark Test-Case...
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Paul Emma Paul Emma SLAC SLAC January 14, 2001 January 14, 2001 BERLIN BERLIN CSR Benchmark CSR Benchmark Test Test - - Case Results Case Results CSR Workshop CSR Workshop
Transcript of CSR Benchmark Test-Case Results - DESY · Paul Emma SLAC January 14, 2001 CSR Benchmark Test-Case...
Paul EmmaPaul EmmaSLACSLAC
January 14, 2001January 14, 2001
BERLINBERLIN
CSR Benchmark CSR Benchmark TestTest--Case ResultsCase Results
CSR WorkshopCSR Workshop
B2 B3
∆L ∆LLcLB LB LB LB
B1 B4θ
Lf
−θ
Chicane parameter s symbol value unit
Bend�magnet�length�(not�curved�length)� LB 0.5� m�
Drift�length�(projected;�B1-B2�&�B3-B4)� ∆L 5� m�
Drift�length�(B2-B3)� Lc 1.0� m�
Post-chicane�drift�length�(after�B4)� Lf 2.0� m�
Bend�angle�per�dipole�magnet� |θ|� 2.770� deg�
Bend�radius�of�each�dipole�magnet� |R|� 10.35� m�
Momentum�compaction�factor� R56� −25.0� mm�
2nd-order�momentum�compaction�factor� T566� +37.5� mm�
Total�projected-length�of�chicane� Ltot 13.0� m�
Vertical�half-gap�of�bend�magnets� g 12.5� mm�
Electron beam par ameters symbol value unit Nominal�energy� E0 5.0� GeV�
bunch�charge� q 0.5�&�1.0� nC�
Incoherent�rms�relative�energy�spread� (∆E/E0)u-rms� 2.0� 10−6�
Linear�energy-z�correlation� a +36.0� m−1�
Total�initial�rms�relative�energy�spread� (∆E/E0)rms� 0.720� %�
Initial�rms�bunch�length� σzi 200� µm�
Final�rms�bunch�length� σzf 20� µm�
Initial�rms�norm.�emittances� γεx,y 1.0,�1.0� µm�
Initial�beta-functions�at�1st�bend�entrance� βx0,y0� 40,�13� m�
Initial�α-functions�at�1st�bend�entrance� αx0,y0� +2.6,�
+1.0�
�
Chicane�CSR�TestChicane�CSR�Test--CaseCase
Use�line-charge�CSR�γ → ∞transient�model�described�in�LCLS-TN-01-12…(Stupakov/Emma,�Dec.�2001)
[same�now�used�in�Elegant]
…based�onTESLA-FEL-96-14(Saldin�et�al.,�Nov.�1996)
Use�line-charge�CSR�γ → ∞transient�model�described�in�LCLS-TN-01-12…(Stupakov/Emma,�Dec.�2001)
[same�now�used�in�Elegant]
…based�onTESLA-FEL-96-14(Saldin�et�al.,�Nov.�1996)
((TT566566 included,�no�ISRincluded,�no�ISR** added)added)
*��incoherent�synchrotron�radiation
−1 0 1
−2
0
2
s /mm
∆E/E
0 [%]
0 5000 10000 15000
−2
0
2
∆E/E
0 [%
]
N
−1 0 10
0.5
1
1.5
2
s /mm
f(s)
[1/
mm
]
Longitudinal distribution (σs0
= 200 µm)
Energy distribution (σE/E
0 = 0.72 %)
Initial�Gaussian�Distribution�Prior�to�ChicaneInitial�Gaussian�Distribution�Prior�to�Chicane
σσss =�200�=�200�µµmm
σσEE//EE00 =�0.72�%=�0.72�%
←← bunch�headbunch�head
perfectly�linear�perfectly�linear�correlationcorrelation
EE00 =�5�GeV=�5�GeV
Second�Order�Compression�Included:�Second�Order�Compression�Included:�TT566566
TT566566 ≈≈ −−33RR5656/2/2
−0.1 −0.05 0 0.05 0.10
0.5
1
1.5
2
2.5
s /mm
λ(s)
(ar
b.)
after driftafter drift--33
before driftbefore drift--33
leads to slight bunch leads to slight bunch shape distortionshape distortion
0 2 4 6 8 10 12 14 160
10
20
30
40
S /m
T56
6 [m
]/m
m
0 2 4 6 8 10 12 14 160
0.1
0.2
S /m
η x [m
]
Horizontal dispersion (ηx)
0 2 4 6 8 10 12 14 160
10
20
30
40
S /m
β x [m
]
Horizontal Beta Function (βx, RED/dash=CSR)
Beta�and�Dispersion�FunctionsBeta�and�Dispersion�Functions
‘ linear’ �‘ linear’ �ηηxx
‘ linear’ �‘ linear’ �ββxx
‘CSR‘CSR--altered’ �altered’ �ββxx
B1B1 B2B2 B3B3 B4B4
ηηxx--maxmax ≈≈ 267�mm267�mm
0 2 4 6 8 10 12 14 160
0.05
0.1
0.15
0.2
S /m
σ z [m
m]
RMS bunch length
0 2 4 6 8 10 12 14 16−0.03
−0.02
−0.01
0
0.01
S /m
R56
[m
]
Momentum compaction factor (R56
)
Bunch�Length�and�Bunch�Length�and�RR5656
B1B1 B2B2 B3B3 B4B4
B1B1 B2B2 B3B3 B4B4
σσss =�20�=�20�µµmm
σσss00=�200�=�200�µµmm
RR5656 =�=�−−25�mm25�mm
−0.1 0 0.1−4
−2
0
2
s /mm
∆E/E
0 [%
]
ε/ε0= 1.520; ε
c/ε
0= 1.499
0 1 2
x 104
−4
−2
0
2
∆E/E
0 [%
]
N
−0.1 0 0.10
5
10
15
20
25
s /mm
f(s)
[1/
mm
]
Longitudinal distribution (σz=20.3 µm)
−0.1 0 0.1−0.06
−0.04
−0.02
0
0.02
s /mm
(∆E
/E0) C
SR [
%]
CSR−induced Energy Gradient
Energy distribution (σE/E
0=0.716 %)
Final�Final�ss--δδ phase�space�(gaussian�input)phase�space�(gaussian�input)
σσss =�20.3�=�20.3�µµmm
σσEE//EE00 =�0.716�%=�0.716�%
←← bunch�headbunch�head
0 2 4 6 8 10 12 14 161
1.2
1.4
1.6
S /m
γεx [
µm]
Bend−plane normalized emittance
0 2 4 6 8 10 12 14 160
0.02
0.04
S /m
−⟨∆
E/E
0⟩ and
⟨(∆E
/E0)2 ⟩1/
2 [%
]
CSR energy loss (DASH) and rms spread (SOLID) accumulated
Energy�Spread�and�Emittance�(gaussian)Energy�Spread�and�Emittance�(gaussian)
B1B1 B2B2 B3B3 B4B4
B1B1 B2B2 B3B3 B4B4
γεγεxx ≈≈ 1.52�1.52�µµmm
σσδδ ≈≈ 0.021%0.021%
�∆�∆ΕΕ ��//ΕΕ0 0 ≈≈ −−0.043%0.043%
0 2 4 6 8 10 12 14 16
0.714
0.716
0.718
S /m
σ E/E
0 /%
Total RMS Relative Energy Spread
Total�RMS�Relative�Energy�Spread�(including�‘chirp’)Total�RMS�Relative�Energy�Spread�(including�‘chirp’)
B1B1 B2B2 B3B3 B4B4
Chicane�CSRChicane�CSR--wake�Movie�(gaussian)wake�Movie�(gaussian)
Chicane�CSRChicane�CSR--integratedintegrated--wake�(gaussian)wake�(gaussian)
−30 −20 −10 0 10 20 30
−15
−10
−5
0
5
10
15
∆x /µm
∆x′ /
µrad
∆γεCSR
= 0.145 µm; βCSR
= 1.368 m; αCSR
= −1.099 (GRN=CSR,BLUE=nom,RED=tot)
Final�Final�xx--xx′′ Phase�Space�(gaussian�input)Phase�Space�(gaussian�input)
γεγε ≈≈ 1.52�1.52�µµmm
γεγε00 =�1.00�=�1.00�µµmmγεγεCSRCSR ≈≈ 0.145�0.145�µµmm
ββoptopt ≈≈ 1.37�m1.37�mααoptopt ≈≈ −−1.101.10
−30 −20 −10 0 10 20 30
−15
−10
−5
0
5
10
15
∆x /µm
∆x′ /
µrad
∆γεCSR
= 0.142 µm; βCSR
= 1.368 m; αCSR
= −1.131 (GRN=CSR,BLUE=nom,RED=tot)
Final�Final�xx--xx′′ Phase�Space�(gaussian�&�Phase�Space�(gaussian�&�optimaloptimal ββ00,�,�αα00))
γεγε ≈≈ 1.15�1.15�µµmm
γεγε00 =�1.00�=�1.00�µµmm
γεγεCSRCSR ≈≈ 0.145�0.145�µµmm
ββ ≈≈ ββoptopt
αα ≈≈ ααoptopt
emittance�growth�can�be�emittance�growth�can�be�reduced�by�choosing�reduced�by�choosing�optimal�optimal�ββ--functionsfunctions
0 2 4 6 8 10 12 14 161
1.2
1.4
1.6
S /m
γεx [
µm]
Bend−plane normalized emittance
0 2 4 6 8 10 12 14 160
100
200
300
400
S /m
β x [m
]
Horizontal Beta Function (βx, RED/dash=CSR)
Beta�and�emittance�(gaussian�&�Beta�and�emittance�(gaussian�&�optimaloptimal ββ00,�,�αα00))
γεγεxx ≈≈ 1.15�1.15�µµmm
ββ ≈≈ ββoptopt
αα ≈≈ ααoptopt
too�big?too�big? ββminmin ≈≈ 0.6�m0.6�m
−6 −4 −2 0 2 4 6−0.1
−0.05
0
0.05
0.1
s/σs
dE/d
(ct)
[M
eV/m
]
−6 −4 −2 0 2 4 6−0.08
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
0.08
s/σs
dE/d
(ct)
[M
eV/m
]
−6 −4 −2 0 2 4 6−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
s/σs
dE/d
(ct)
[M
eV/m
]
−6 −4 −2 0 2 4 6−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
s/σs
dE/d
(ct)
[M
eV/m
]
bendbend--1�(1�(÷÷10)10)∆∆LL =�0.4�m=�0.4�m
driftdrift--1�(1�(÷÷20)20)∆∆LL =�5�m=�5�m
bendbend--2�(2�(÷÷10)10)∆∆LL =�0.4�m=�0.4�m
driftdrift--2�(2�(÷÷10)10)∆∆LL =�1�m=�1�m
CSR�wakefields�(gaussian�CSR�wakefields�(gaussian� bendbend--1�to�drift1�to�drift--2)2)
NNbinbin =�600,�=�600,�smoothed�over�4smoothed�over�4
−6 −4 −2 0 2 4 6 8−2.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
s/σs
dE/d
(ct)
[M
eV/m
]
−4 −2 0 2 4 6 8−1.5
−1
−0.5
0
0.5
s/σs
dE/d
(ct)
[M
eV/m
]
−4 −2 0 2 4 6 8−3
−2
−1
0
1
2
3
s/σs
dE/d
(ct)
[M
eV/m
]
−4 −2 0 2 4 6 8−2
−1.5
−1
−0.5
0
0.5
s/σs
dE/d
(ct)
[M
eV/m
]
CSR�wakefields�(gaussian�CSR�wakefields�(gaussian� bendbend--3�to�drift3�to�drift--4)4)
bendbend--3�(3�(÷÷20)20)∆∆LL =�0.4�m=�0.4�m
driftdrift--3�(3�(÷÷40)40)∆∆LL =�5�m=�5�m
bendbend--4�(4�(÷÷20)20)∆∆LL =�0.4�m=�0.4�m
driftdrift--4�(4�(÷÷20)20)∆∆LL =�2�m=�2�m
−0.4 −0.2 0 0.2 0.40
5
10
15
20
25
s /mm
f(s)
[1/
mm
]
Longitudinal distribution function
Compressing�Compressing�UniformUniform DistributionDistribution
−0.04−0.02 0 0.02 0.04
−1
0
1
s /mm
∆E/E
0 [%
]
ε/ε0= 1.118; ε
c/ε
0= 1.102
0 5000 10000
−1
0
1
∆E/E
0 [%
]
N
Energy distribution (σE/E
0=0.720%)
−0.04−0.02 0 0.02 0.040
5
10
15
20
25
s /mm
f(s)
[1/
mm
]
Long. dist. (σz=20.2 µm)
−0.04−0.02 0 0.02 0.04
−0.05
0
0.05
s /mm
(∆E
/E0) C
SR [
%]
CSR−induced Energy Gradient
σσss =�20.2�=�20.2�µµmm
σσEE//EE00 =�0.720�%=�0.720�%
Final�Final�ss--δδ phase�space�phase�space�–– UniformUniform input�dist.input�dist.
0 2 4 6 8 10 12 14 161
1.2
1.4
1.6
S /m
γεx [
µm]
Bend−plane normalized emittance
0 2 4 6 8 10 12 14 160
0.02
0.04−
⟨∆E
/E0⟩ a
nd ⟨(
∆E/E
0)2 ⟩1/2 [
%]
CSR energy loss (DASH) and rms spread (SOLID) accumulated
γεγεxx ≈≈ 1.12�1.12�µµmm
σσδδ ≈≈ 0.007%0.007%
�∆�∆ΕΕ ��//ΕΕ0 0 ≈≈ −−0.046%0.046%
Energy�Spread�and�Emittance�(Energy�Spread�and�Emittance�(uniformuniform))
emittance�growth�reduced�compared�to�gaussianemittance�growth�reduced�compared�to�gaussian
Chicane�CSRChicane�CSR--wake�Movie�wake�Movie�–– UniformUniform Dist.Dist.
Chicane�CSRChicane�CSR--integratedintegrated--wake�wake�–– UniformUniform Dist.Dist.
−30 −20 −10 0 10 20 30
−15
−10
−5
0
5
10
15
∆x /µm
∆x′ /
µrad
∆γεCSR
= 0.069 µm; βCSR
= 3.872 m; αCSR
= −0.508 (GRN=CSR,BLUE=nom,RED=tot)
Final�Final�xx--xx′′ Phase�Space�(Phase�Space�(uniformuniform input)input)
γεγε ≈≈ 1.12�1.12�µµmm
γεγε00 =�1.00�=�1.00�µµmmγεγεCSRCSR ≈≈ 0.07�0.07�µµmm
ββoptopt ≈≈ 3.9�m3.9�mααoptopt ≈≈ −−0.510.51
−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
s/σs
dE/d
(ct)
[M
eV/m
]
−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−0.08
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
0.08
s/σs
dE/d
(ct)
[M
eV/m
]
−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
s/σs
dE/d
(ct)
[M
eV/m
]
−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
s/σs
dE/d
(ct)
[M
eV/m
]
bendbend--1�(1�(÷÷10)10)∆∆LL =�0.4�m=�0.4�m
driftdrift--1�(1�(÷÷20)20)∆∆LL =�5�m=�5�m
bendbend--2�(2�(÷÷10)10)∆∆LL =�0.4�m=�0.4�m
driftdrift--2�(2�(÷÷10)10)∆∆LL =�1�m=�1�m
CSR�wakefields�(CSR�wakefields�(uniformuniform bendbend--1�to�drift1�to�drift--2)2)
NNbinbin =�600,�=�600,�smoothed�over�4smoothed�over�4
−2 −1 0 1 2 3−3
−2
−1
0
1
2
3
s/σs
dE/d
(ct)
[M
eV/m
]
−2 −1 0 1 2 3−1.5
−1
−0.5
0
0.5
1
s/σs
dE/d
(ct)
[M
eV/m
]
−2 −1 0 1 2 3−6
−4
−2
0
2
4
6
s/σs
dE/d
(ct)
[M
eV/m
]
−2 −1 0 1 2 3−2
−1.5
−1
−0.5
0
0.5
1
1.5
s/σs
dE/d
(ct)
[M
eV/m
]
CSR�wakefields�(CSR�wakefields�(uniformuniform bendbend--3�to�drift3�to�drift--4)4)
bendbend--3�(3�(÷÷20)20)∆∆LL =�0.4�m=�0.4�m
driftdrift--3�(3�(÷÷40)40)∆∆LL =�5�m=�5�m
bendbend--4�(4�(÷÷20)20)∆∆LL =�0.4�m=�0.4�m
driftdrift--4�(4�(÷÷20)20)∆∆LL =�2�m=�2�m
−0.04 −0.02 0 0.02 0.04 0.060
1
2
3
4
s /mm
(x2 +
[xα
+ x
′β]2 )1/
2 /(βε
)1/2 Sliced Normalized Centroid Offsets (σ
x units)
−0.05 0 0.05 0.10
1
2
3
4
s /mm
(x2 +
[xα
+ x
′β]2 )1/
2 /(βε
)1/2 Sliced Normalized Centroid Offsets (σ
x units)
λλ((ss))
Betatron�Amplitude�per�Bunch�SliceBetatron�Amplitude�per�Bunch�Slice
λλ((ss))
gaussiangaussian
uniformuniform
−0.1 0 0.1−0.04
−0.02
0
0.02
s /mm
∆E/E
0 [%
]
ε/ε0= 1.120; ε
c/ε
0= 1.037
0 5000 10000−0.04
−0.02
0
0.02
∆E/E
0 [%
]
N
Energy distribution (σE/E
0=1.1×10−4)
−0.1 0 0.10
5
10
15
20
s /mm
f(s)
[1/
mm
]
Longitudinal distribution (σz=20.1 µm)
−0.1 0 0.1−0.03
−0.02
−0.01
0
0.01
s /mm
(∆E
/E0) C
SR [
%]
CSR−induced Energy Gradient
Final�Final�ss--δδ phase�space�phase�space�-- SingleSingle--BendBend
σσss =�20.1�=�20.1�µµmm
σσEE//EE00 =�0.011�%=�0.011�%
Energy�Spread�and�Emittance�Energy�Spread�and�Emittance�–– Single BendSingle Bend
0 0.5 1 1.50
0.005
0.01
0.015
0.02
S /m−⟨∆
E/E
0⟩ and
⟨(∆E
/E0)2 ⟩1/
2 [%
]
CSR energy loss (DASH) and rms spread (SOLID) accumulated
0 0.5 1 1.51
1.2
1.4
1.6
1.8
S /m
γεx [
µm]
Bend−plane normalized emittance
⟨(∆E/E0 − ⟨∆E⟩/E
0)2⟩1/2
−⟨∆E⟩/E0
steadysteady--statestate
bend�magnetbend�magnet
σσδδ =�0.011%=�0.011%
(24(24σσssRR22))1/31/3
CSRCSR--Wake�Movie�Wake�Movie�-- SingleSingle--BendBend
LCLS�BC2�CSRLCLS�BC2�CSR--integratedintegrated--wake�(tracked�dist.)wake�(tracked�dist.)
