Particle and fluid models for streamers: comparison and spatial coupling Li Chao 1 in cooperation with: W.J.M. Brok 2, U. Ebert 1,2, W. Hundsdorfer 1,

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Particle and fluid models for streamers: comparison and spatial coupling Li Chao 1 in cooperation with: W.J.M. Brok 2, U. Ebert 1,2, W. Hundsdorfer 1, and J.J.A.M. van der Mullen 2 1. Centrum voor Wiskunde en Informatica (CWI) A’dam 2. Eindhoven University of Technology (TU/E) Eindhoven

Streamers in laboratory [ Talk: Exploring streamer variability in experiments. T.M.P. Briels] Understand streamer dynamics. Here: electron dynamics in ionization front. For simplicity: Negative streamer in N 2 electronsnet charge Streamers in numerical simulation [Talk: Efficient fluid streamer simulations in 2D and 3D: methods and results. A. Luque]

Simulation models: advantages and disadvantages Fluid model Particles : electrons and ions Deterministic free flight between Monte Carlo Collisions Particle model Efficient computations in continuum approximation. Full physics : correct energies run away electrons perturbations for branching discrete particles in low density region but too many particles for CPU Compare and combine models! DriftDiffusion Ionization reaction E

Particle swarm experiments generate µ(E), D(E), α(E), and ε(E). Fluid model Particles : electrons and ions Deterministic free flight between Monte Carlo Collisions. Particle model DriftDiffusion Ionization reaction

Planar front in particle model: E=E + E=0 Periodic boundary condition Charge layer with charge: Streamer front planar approximation z E=E + E=0 Periodic boundary condition Charge layer with charge: Streamer front planar approximation z

Particle planar front simulation at 100 kV/cm E=E + E=0 Periodic boundary condition Charge layer with charge: Streamer front planar approximation z

1.The speeds are almost same. 2.The densities differ by 20%. Planar front simulation results comparison at 100 kV/cm Comparison of particle model with re-derived fluid model:

1.The speeds are almost same. 2.The densities differ by 20%. Planar front simulation results comparison at 100 kV/cm Comparison of particle model with re-derived fluid model:

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

z t1t1 t2t2 t3t3 Constant field E Swarm experiments: Energy overshoot because density decay length is similar to energy relaxation length. Field gradient is not important. avalanche front Same leading edge [C. Li et al. J. Appl. Phys ]

z (mm)

[C. Li et al., submitted (2007)] at 100 kV/cm

Improve fluid approximation: Adjust definition of mobility: 1.By mean displacement of swarm avalanche ZZ1Z1 Z2Z2 [N L Aleksandrov and I V Kochetov, J. Phys. D. 29 (1996) ] [G V Naidis, Tech. Phys. Lett. 23(6) (1997) 493.]

Adjust definition of mobility: 1.By mean displacement of swarm avalanche 2.By mean displacement of initially present particles ZZ1Z1 Z2Z2 Z2Z2 Improve fluid approximation: [N L Aleksandrov and I V Kochetov, J. Phys. D. 29 (1996) ] [G V Naidis, Tech. Phys. Lett. 23(6) (1997) 493.]

Adjust definition of mobility: 1.By mean displacement of swarm avalanche 2.By mean displacement of initially present particles 3.By averaging the local fluxes μ 1 ≥ μ 2 = μ 3 Improve fluid approximation: [N L Aleksandrov and I V Kochetov, J. Phys. D. 29 (1996) ] [G V Naidis, Tech. Phys. Lett. 23(6) (1997) 493.]

First VersionImproved version

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 1.Incorporate in 3D computations. 2.Include photo-ionization etc.