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SettingLinear Focusing Field
Self-Consistent Focusing
Focusing field in modulator simulations
Jun Ma, Roman Samulyak, Kwangmin Yu
Department of Applied Mathematics and Statistics
Stony Brook University
2016.2.18
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
Numerical setting
Domain
Transversal : 4e-3m (14 × Debyelength) open boundary
Longitudinal : 2e-5m (20 × Debyelength) periodic boundary
Grid number : 20 per Debye length
Electron
Gaussian in x, y
Uniform in z
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
k=3e+11 V/m2
k=1e+9 V/m2
k=1e+8 V/m2
Linear focusing field
~E0(x) =me
e
σ2
r20
(x − x0)
G. Bell et al., VLASOV AND PIC SIMULATIONS OF A
MODULATOR SECTION FOR COHERENT ELECTRON
COOLING, Proceedings of 2011 Particle Accelerator Conference,
New York, NY, USA, MOP067.
Implemented as
~E = k~x
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
k=3e+11 V/m2
k=1e+9 V/m2
k=1e+8 V/m2
Transversal velocity distribution, k=3e+11 V /m2
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
k=3e+11 V/m2
k=1e+9 V/m2
k=1e+8 V/m2
Transversal velocity distribution, k=3e+11 V /m2
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
k=3e+11 V/m2
k=1e+9 V/m2
k=1e+8 V/m2
Transversal number distribution, k=3e+11 V /m2
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
k=3e+11 V/m2
k=1e+9 V/m2
k=1e+8 V/m2
Transversal number distribution, k=3e+11 V /m2
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
k=3e+11 V/m2
k=1e+9 V/m2
k=1e+8 V/m2
Transversal velocity distribution, k=1e+9 V /m2
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
k=3e+11 V/m2
k=1e+9 V/m2
k=1e+8 V/m2
Transversal velocity distribution, k=1e+9 V /m2
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
k=3e+11 V/m2
k=1e+9 V/m2
k=1e+8 V/m2
Transversal number distribution, k=1e+9 V /m2
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
k=3e+11 V/m2
k=1e+9 V/m2
k=1e+8 V/m2
Transversal number distribution, k=1e+9 V /m2
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
k=3e+11 V/m2
k=1e+9 V/m2
k=1e+8 V/m2
Transversal velocity distribution, k=1e+8 V /m2
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
k=3e+11 V/m2
k=1e+9 V/m2
k=1e+8 V/m2
Transversal velocity distribution, k=1e+8 V /m2
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
k=3e+11 V/m2
k=1e+9 V/m2
k=1e+8 V/m2
Transversal velocity distribution, k=1e+8 V /m2
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
k=3e+11 V/m2
k=1e+9 V/m2
k=1e+8 V/m2
Transversal number distribution, k=1e+8 V /m2
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
k=3e+11 V/m2
k=1e+9 V/m2
k=1e+8 V/m2
Transversal number distribution, k=1e+8 V /m2
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
k=3e+11 V/m2
k=1e+9 V/m2
k=1e+8 V/m2
Transversal number distribution, k=1e+8 V /m2
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
Without SmoothingWith Smoothing
Self-consistent focusing
Estimate expansion velocity
Subtract expansion effect
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
Without SmoothingWith Smoothing
Expansion velocity
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
Without SmoothingWith Smoothing
Expansion velocity
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
Without SmoothingWith Smoothing
Expansion velocity
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
Without SmoothingWith Smoothing
Transversal velocity distribution
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
Without SmoothingWith Smoothing
Transversal velocity distribution
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
Without SmoothingWith Smoothing
Transversal velocity distribution
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
Without SmoothingWith Smoothing
Transversal velocity distribution
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
Without SmoothingWith Smoothing
Transversal number distribution
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
Without SmoothingWith Smoothing
Transversal number distribution
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
Without SmoothingWith Smoothing
Transversal number distribution
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
Without SmoothingWith Smoothing
Transversal number distribution
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
Without SmoothingWith Smoothing
Expansion velocity
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
Without SmoothingWith Smoothing
Expansion velocity
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
Without SmoothingWith Smoothing
Transversal velocity distribution
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
Without SmoothingWith Smoothing
Transversal velocity distribution
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
Without SmoothingWith Smoothing
Transversal number distribution
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
SettingLinear Focusing Field
Self-Consistent Focusing
Without SmoothingWith Smoothing
Transversal number distribution
Jun Ma, Roman Samulyak, Kwangmin Yu Focusing field in modulator simulations
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