sFLASH SASE interference
description
Transcript of sFLASH SASE interference
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sFLASH SASE interferencesetup & optics
rough estimation
1d estimation
3d estimation
summary
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setup & opticsfrom
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q 0.3 nC
estimated electron beam properties
estimated photon beam properties
Ipeak 1.5 kC
E 585 MeVErms 150 keVn 1.5 µm
modulator undulatorK = 4.3
L = 1.45 m
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0
220
~
PPKLcm L
I
uu
modulation amplitude
keV 550150
FLASH @ 19 nmundulator
laser
2rms
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x / my / m
quadsundulators
vertical correctors
chicane 1 chicane 2 chicane 3
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1 2
(1) - energy modulation
rough estimation
kA 2.4 66.0
ˆrefc1,5612
krII
keV 550150
(saturation)
(2) - conversion to density modulation, chicane 1, r56c1 = 220 µm
kA 5.11 I
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2 3
(23) - discrete impedance, L 23 m, av 10 m
if linear:
cFiZZ r
r
22
0
2
2exp2
duu
uF k 4.3Z from
ekrZI
ref
c1,5612
15 amplification of energy modulation
(3) - chicane 1, r56c3 = 170 µm
eZIkr
II
ref
1c3,56
2
3
ˆˆ
10 amplification of density modulation
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k 4.2Z(34) - discrete impedance, L 16 m, av 10 m
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1d estimation
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1 2 3 4 5
1 discrete modulation12 discrete impedance, L = 2.6 m, av = 10.6 m2 discrete longitudinal dispersion, chicane 1, r56 = 220 µm23 discrete impedance, L = 4.7 m, av = 10.1 m3 discrete longitudinal dispersion, chicane 2, r56 = 3 µm34 discrete impedance, L = 17.7 m, av = 7.7 m4 discrete longitudinal dispersion, chicane 3, r56 = 170 µm45 discrete impedance , L = 16.3 m, av = 9.8 m
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40E6 macro particles
space charge interaction: discrete, 1d
energy modulation: discrete in middle of modulator
no CSR interaction
next slide: explore linear domain
initial modulation amplitude keV 20
initial uncorrelated energy spread keV 10 keV 150 rms
1d estimation
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longitudinal phase space current
keV 20
keV 10 rms
MeV 2 kA 1ˆ I
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MeV 2
same, but Erms = 150 keV
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keV 100
keV 150 rms
MeV
MeVnon linear !!!
~ 3 MeVrms energy spread
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keV 500
keV 150 rms
MeV
MeVnon linear !!!
~ 3.5 MeVrms energy spread
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~ 3.5 MeV rms energy spread
keV 500
~ 2 MeV rms
3D
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3d estimation20E6 macro particles
space charge interaction: full 3d Poisson solver
equidistant mesh: 15 µm × 15 µm × 800 nm/(10)
step width: 2 cm (beam-line coordinate)
modulation: Emod = 250 keV discrete in middle of modulator (= instantaneous)
no CSR interaction
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Emod = 250 keV3D Calculation
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current
bunc
h co
ordi
nate
/ m
beam line coordinate / m
-6-4
-20
24
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x 10-5
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-20
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x 10-5
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Emod = 250 keV3D Calculation
after chicane 1 before chicane 2
Curr
ent /
A_
rms /
eV
/
eV
bunch coordinate / m
rms spread in 400 nm “slice” rms spread in 400 nm “slice”
~ 2.5 m
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after chicane 2 before chicane 3
Emod = 250 keV3D Calculation
Curr
ent /
A_
rms /
eV
/
eV
bunch coordinate / m
rms spread in 400 nm “slice” rms spread in 400 nm “slice”
~ 14.6 m
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after chicane 3 before SASE undulator
Emod = 250 keV3D Calculation
Curr
ent /
A_
rms /
eV
/
eV
bunch coordinate / m
rms spread in 400 nm “slice” rms spread in 400 nm “slice”
~ 14.2 m
~ 2 MeV rms
50 µm, 170 fsec
15 µm, 50 fsec
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curr
ent /
A
bunch coordinate 1E-4 / m beam line coordinate / m
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Emod = 250 keV3D Calculation
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current/A
beam linecoordinate/ m
bunch coordinate/ m
current/A
beam line coordinate/ m
“side view”
period of plasma oscillation
120 m
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summarymodulator:
1d estimation (without plasma osc.):
3d estimation:
gain length (Ming Xie)
keV 550150 2rms
linear gain ~ 100
saturation even with minimal modulationMeV 5.33rms
MeV 2rms plasma oscillations, period 120 m
m 29MeV 3
m 11MeV 2
rms
rms
g
g
L
L
weak amplification in 30 m SASE undulator
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First Shot at Statistics
• Assume laser pulse eliminates lasing within FWHM completely• Take a few hundred SASE simulation results (0.25 nC) and apply the above • Let the ‘laser pulse’ jitter by about 100 fs
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s[um]
P[G
W]
P(s) at z=14 m
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Comparison to Observation
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The rough estimate Observed behavior
Electron macro pulse number
Ener
gy in
pho
ton
pulse