Download - r esults from measurement and simulation
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results from measurement and simulation
methods (LW, PIC, Astra) and setup
About LW & Astra Simulations of The Pitz Gun
comparison LW Astra
more analysis of LW results
about Astra results: sensitivity to numerical parameters
about approaches: some analytical calculations
second inspection
summary
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results from measurement and simulation
see: DESY/TEMF Meeting - Status 2011http://www.desy.de/xfel-beam/data/talks/files/03-Gjonaj_Erion_DESY_16.12.2011_new.pdf
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methods (LW, PIC, Astra) and setup
LW = Lienard Wichertexact solution of Maxwell problem (based on retarded trajectory)no spatial meshnumeric integration of EoM; fixed time step
higher order PIC; PIC = particle in cell
exact numerical approach for Maxwell problemspatial mesh & time stepnumeric integration of EoM; fixed time step
extensive convergence test in 2010carefull comparison in 2011
simulation of PITZ injectorfor z <= 5 cmAstra
approximation based on uniform motion rz - Poisson approach; spatial meshnumeric integration of EoM; variable time step
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methods (LW, PIC, Astra) and setup
setup
bunch charge = 1 nCbunch length = 21.5 psec (Lt=0.0215 rt=0.002)
rms-radius = (radius/2) = 0.2 … 0.6 mm
MaxE = 60.58 MV/mphi = 223.386 deg (or auto phase = -1.404 deg) E0 = 41.6 MV/m
estimated SC limitation (DC field and planar diode)2
00limitSC REQ
Rrms/mm = 0.20.30.40.5
QSC-limit/nC = 0.1850.4170.7411.157
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comparison LW Astra
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comparison LW Astra
rms laser spot size = 0.6 mm, slice properties
-3 -2 -1 0 1 2 3 4
x 10-3
0
0.5
1
1.5x 10
-6
-3 -2 -1 0 1 2 3 4
x 10-3
7
7.5
8
8.5
9
9.5
10
10.5
11x 10
5
-3 -2 -1 0 1 2 3 4
x 10-3
0
500
1000
1500
2000
2500
3000LW
-3 -2 -1 0 1 2 3 4
x 10-3
0
0.5
1
1.5x 10
-6
-3 -2 -1 0 1 2 3 4
x 10-3
0
500
1000
1500
2000
2500
3000
-3 -2 -1 0 1 2 3 4
x 10-3
7
7.5
8
8.5
9
9.5
10
10.5
11x 10
5Astra
see also: s2e-seminar 2011-Feb-07http://www.desy.de/xfel-beam/data/talks/files/2011_02_s2e_Gun_TEMF_Auswertung.pdf
(z-mean(z))/m
norm. (hor;vert) emittance / m c0pz / eV rms{c0pz}/ eV
(z-mean(z))/m (z-mean(z))/m
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comparison LW Astra
rms laser spot size = 0.6 mm
i
i
zzqzq
iqQ
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comparison LW Astra
rms laser spot size = 0.6 mm
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comparison LW Astra
rms laser spot size = 0.4 mm
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comparison LW Astra
rms laser spot size = 0.3 mm
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comparison LW Astra
rms laser spot size = 0.2 mm
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more analysis of LW results
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more analysis of LW results
rms laser spot size = 0.6 mmr/m
z/m
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more analysis of LW results
rms laser spot size = 0.5 mmr/m
z/m
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more analysis of LW results
rms laser spot size = 0.4 mmr/m
z/m
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more analysis of LW results
rms laser spot size = 0.3 mm (0.5MP; dt=0.1psec)r/m
z/m
aliasing
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more analysis of LW results
rms laser spot size = 0.2 mmr/m
z/m
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more analysis of LW results
micro modulation0.2mm;
0.3mm;
0.4mm;
0.5mm;
0.6mm;r/m
z/m
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more analysis of LW results
rms laser spot size = 0.3 mmsimulation with more particles
0.5M 1M
r/m
z/m
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more analysis of LW results
rms laser spot size = 0.3 mm; calc. with different time step
0.2mm/9=22.2um;
pz
907.037.2
μm 14 tv
1mm/24=42um;
dt = 0.10 psecdt = 0.05 psec
r/m
z/m
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this bunch needs more compression !
r/m
z/m
0.6 mm
0.5 mm
0.4 mm
0.3 mm
0.2 mm
“micro bunching” vs. injection timecolor frequency = 2x 0.1psec
0.3 mm, half time step
dt = 0.10 psec
dt = 0.05 psec
more analysis of LW results
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0.2 mm, <z> = 10 mm
r/m
z/m
0.3 mm, <z> = 10 mm 0.6 mm, <z> = 10 mm
<z> = 20 mm <z> = 20 mm
<z> = 30 mm <z> = 30 mm
<z> = 40 mm
<z> = 50 mm50 mm
more analysisof LW results
different longitudinalposition
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more analysis of LW results
rms laser spot size = 0.3 mm; slice properties500k, 0.1psec
-5 -4 -3 -2 -1 0 1 2 3 4
x 10-3
0
0.5
1
1.5x 10
-6
-5 -4 -3 -2 -1 0 1 2 3 4
x 10-3
6
7
8
9
10
11
12x 10
5
-5 -4 -3 -2 -1 0 1 2 3 4
x 10-3
0
500
1000
1500
2000
2500
3000
(z-mean(z))/m
norm. (hor;vert) emittance / m c0pz / eV rms{c0pz}/ eV
(z-mean(z))/m (z-mean(z))/m
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-5 -4 -3 -2 -1 0 1 2 3 4
x 10-3
0
500
1000
1500
2000
2500
3000
-5 -4 -3 -2 -1 0 1 2 3 4
x 10-3
6
7
8
9
10
11
12x 10
5
-5 -4 -3 -2 -1 0 1 2 3 4
x 10-3
0
0.5
1
1.5x 10
-6
more analysis of LW results
rms laser spot size = 0.3 mm; slice properties1M, 0.1psec
(z-mean(z))/m
norm. (hor;vert) emittance / m c0pz / eV rms{c0pz}/ eV
(z-mean(z))/m (z-mean(z))/m
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-5 -4 -3 -2 -1 0 1 2 3 4
x 10-3
0
500
1000
1500
2000
2500
3000
-5 -4 -3 -2 -1 0 1 2 3 4
x 10-3
6
7
8
9
10
11
12x 10
5
-5 -4 -3 -2 -1 0 1 2 3 4
x 10-3
0
0.5
1
1.5x 10
-6
more analysis of LW results
rms laser spot size = 0.3 mm; slice properties500k, 0.05psec
(z-mean(z))/m
norm. (hor;vert) emittance / m c0pz / eV rms{c0pz}/ eV
(z-mean(z))/m (z-mean(z))/m
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about Astra results
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rms laser spot size = 0.6 mmno SC limitation
is it possible to provoke numerical microbunching?(fine mesh, big time step)
about Astra results: sensitivity to numerical parameters
Hammersley randommesh linestime step
rms laser spot size = 0.2 mmstrong SC limitation: late emission is pulsing
no: Astra is too clever; during emission it does not use the user defined time step
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rms laser spot size = 0.2 mmstrong SC limitation: late emission is pulsing
emitted particles 40.5%
pitzTT100x40
pitzTT100x40
r/m
z/m
about Astra results: sensitivity to numerical parameters
Nz Nr
psec 017.0t
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Hammersleyemitted particles 40.5%
pitzTT100x40
pitzN100x40
randomemitted particles 40.5%
pulsing (multiple fronts) is no artifact of pseudo random gen.
r/m
z/m
about Astra results: sensitivity to numerical parameters
rms laser spot size = 0.2 mmstrong SC limitation: late emission is pulsing
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Hammersleyemitted particles 41.9%
pitzTF200x40
pitzTFF1000x40
Hammersleyemitted particles 45.4%
r/m
z/m
about Astra results: sensitivity to numerical parameters
rms laser spot size = 0.2 mmstrong SC limitation: late emission is pulsing
Nz Nr Nz Nr
psec 017.0t psec 017.0t
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pitzTTfixed100x40
Hammersleyemitted particles 39.1%
Hammersleyemitted particles 40.5%
pitzTT100x40
not quite the same time
r/m
z/m
about Astra results: sensitivity to numerical parameters
rms laser spot size = 0.2 mmstrong SC limitation: late emission is pulsing
Nz Nr Nz Nr
psec 017.0t psec 050.0t
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still running: pitzTFFF, 10000x40pitzTFFR, 1000x200
pitzTFFF
pitzTFFR1000x200
r/m
z/m
about Astra results: sensitivity to numerical parameters
rms laser spot size = 0.2 mmstrong SC limitation: late emission is pulsing
psec 017.0t
pitzTFF1000x40
43.8% 45.4%
43.2%
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about Astra results: sensitivity to numerical parameters
pitzTFFF 10000x40
r/m
z/m
q/Q
z/m
z
dzzq0
10 mesh lines
q/Q = 0.05
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about Astra results: sensitivity to numerical parameters
result is extremelysensitive oninitial conditionsandboth mesh settings
no initial energy spread
caused by r-mesh
0.55eV initial energy spread
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about approaches
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about approaches: some analytical calculations
the planar diode
a three dimensional driven problem
exact solution of Maxwell problem tzz
tzEz ,1,
0
no explicit appearance of retarded time
exact solution of EoM
11
2
0
0
ttc
qEqEtz
tEE z ,0
with = slice index, t = ejection time of slice ,
otherwise0
if1,,, 2
RrR
tztzr
in the following: three different approaches to calculatecomparison for
t,rE tztzE zzz ,, eEe
acc0,0 EEz external field,
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about approaches: some analytical calculations
three approaches
“M” exact Maxwell solution
tzrtzr ,,,,M
“BUM” solution: bunch in uniform motion
“SUM” solution: slices in individual uniform motion
00BUM ,,,, tvttzrtzr with m
ptvv com0
and “com” = center of mass
dzzdtzrtzr~
,~,,, 0SUM 00,~~ tttzvzz withand z(v,t) the slice velocity
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about approaches: some analytical calculations
injection (z = 0)
mm 6mMV 60
nC 1
acc
icTE
q bunch chargeaccelerating fieldtime of injection (rectangular)
mm 1R (rms = 0.5 mm)
mct
mVzE
… planar diode__ SUM__ BUMx_ M
mm 6.0R (rms = 0.3 mm)
space chargelimitation
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space charge limitation
mVzE
mct
mct
mVzE
… planar diode__ SUM__ BUMx_ M
about approaches: some analytical calculations
injection (z = 0)
mm 4.0R (rms = 0.2 mm)
M calculates stronger field reduction than UM & BUM !
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mVzE
mz
mVzE
… planar diode__ SUM__ BUM__ M
about approaches: some analytical calculations
after injection (t > Ti )
mm 1mm 6
mMV 60nC 1
acc
RcT
Eq
i
bunch chargeaccelerating fieldtime of injection (rectangular)(rms = 0.5 mm)
iTt 5.1 53.0 iTt 5.2 43.1
mz
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mVzE
mz
mVzE
… planar diode__ SUM__ BUM__ M
about approaches: some analytical calculations
after injection (t > Ti )
iTt 5.3 82.1 iTt 5.4 24.2
mz
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second inspection
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second inspection
injection time / sec
injection radius / m
lost particles vs. accelerated particles (@ injection)
integrated charge accelerated particles lost particles
integrated charge accelerated particles lost particles
injection time / sec injection time / sec
0.2mm: ASTRA, lost particles = blue
injection time / sec
injection radius / m pitzTT100x40
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second inspection
lost particles vs. accelerated particles (@ injection)
integrated charge accelerated particles lost particles
injection time / sec
0.2mm: ASTRA, lost particles = blue
injection time / sec
injection radius / m pitzTT100x40
pitzTT 10000x40
notcalc.
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second inspection
injection time / sec injection time / sec
injection radius / m injection radius / m
lost particles vs. accelerated particles (@ injection)
integrated charge accelerated particles lost particles
injection time / sec
pitzTT100x40
![Page 46: r esults from measurement and simulation](https://reader035.vdocuments.mx/reader035/viewer/2022062410/568163e5550346895dd545be/html5/thumbnails/46.jpg)
second inspection
0.2mm: ASTRA, lost particles = blue
injection radius / m pitzTT100x40
injection time / sec
injection radius / m
mct
mVzE
… planar diode__ SUM__ BUMx_ M
mm 4.0R(rms = 0.2 mm)
correct numbers: q = 1nC Ti = 21.5 psec Eacc=41.61 MV/m
M-shielding should be stronger than BUM-shielding!
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summary
SC limited emission: differences between measurement and ASTRA
ASTRA incomplete modelpredicts strong SC limited emissionSC limited emissions needs extreme mesh resolution
(usually not fulfilled at end of emission)very sensitive to initial conditions (is it real physics?)SC shielding seems to agree with analytical model
LW should include all effectshas been benchmarked with PIC or vice versa (but: same tracker)less SC shielding: seems to agree with measurementproblems with boundary condition at injection (mirror-point-charge)micro modulation: related to time step and time of injectionanalytical model (Maxwell Poisson) predicts stronger shielding
measurement …?!