Particle and fluid models for streamers: comparison and spatial coupling

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Particle and fluid models for streamers
comparison and spatial coupling
Li Chao1 in cooperation with W.J.M. Brok2, U.
Ebert1,2, W. Hundsdorfer1, and J.J.A.M. van der
Mullen2
1. Centrum voor Wiskunde en Informatica (CWI)
Adam 2. Eindhoven University of Technology
(TU/E) Eindhoven
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Streamers in laboratory
Streamers in numerical simulation
electrons
net charge
Talk Exploring streamer variability in
experiments. T.M.P. Briels
Talk Efficient fluid streamer simulations in 2D
and 3D methods and results. A. Luque
Understand streamer dynamics. Here electron
dynamics in ionization front. For simplicity
Negative streamer in N2
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Simulation models advantages and disadvantages
Fluid model
Particle model

• Particles electrons and ions
• Deterministic free flight between Monte Carlo
  Collisions

Drift
Diffusion
Ionization reaction
E
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Fluid model
Particle model
Particles electrons and ions Deterministic
free flight between Monte Carlo Collisions.
Particle swarm experiments generate µ(E), D(E),
a(E), and e(E).
Ionization reaction
Drift
Diffusion
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Planar front in particle model
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Particle planar front simulation at 100 kV/cm
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Comparison of particle model with re-derived
fluid model
Planar front simulation results comparison at 100
kV/cm

1. The speeds are almost same.
2. The densities differ by 20.

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Comparison of particle model with re-derived
fluid model
Planar front simulation results comparison at 100
kV/cm

1. The speeds are almost same.
2. The densities differ by 20.

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Energy overshoot

• higher energy larger ionization rate in
  front density discrepancy behind
• position of the model interface

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(No Transcript)
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z (mm)
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at 100 kV/cm
C. Li et al. , submitted (2007)
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Improve fluid approximation
N L Aleksandrov and I V Kochetov, J. Phys. D. 29
(1996) 1476-1483. G V Naidis, Tech. Phys. Lett.
23(6) (1997) 493.
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Improve fluid approximation
N L Aleksandrov and I V Kochetov, J. Phys. D. 29
(1996) 1476-1483. G V Naidis, Tech. Phys. Lett.
23(6) (1997) 493.

• Adjust definition of mobility
• By mean displacement of swarm avalanche
• By mean displacement of initially present
  particles

Z
Z1
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Improve fluid approximation
N L Aleksandrov and I V Kochetov, J. Phys. D. 29
(1996) 1476-1483. G V Naidis, Tech. Phys. Lett.
23(6) (1997) 493.

• Adjust definition of mobility
• By mean displacement of swarm avalanche
• By mean displacement of initially present
  particles
• By averaging the local fluxes

µ1 µ2 µ3
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Improved version
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• Conclusion and outlook
• Conclusion
• The fluid approximation is valid,
• except in the leading edge of the ionization
  front.
• Spatial coupling of fluid and particle model
  realized in 1D.
• Result relevant particle physics kept
• a) correct energies
• b) run away electrons
• c) perturbations for branching
• d) discrete particles in low density region
• but computational efficiency largely improved.
• Outlook
• Incorporate in 3D computations.
• Include photo-ionization etc.