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November  2007, 8(4): 735-772. doi: 10.3934/dcdsb.2007.8.735

A hierarchy of diffusion models for partially ionized plasmas

Isabelle Choquet 1, , Pierre Degond 2, and  Brigitte Lucquin-Desreux 3,

1. 

Department of Technology, Mathematics, and Computer Science, University West, Gärdhemsvägen 4, 461 39 Trollhättan, Sweden
2. 

Mathématiques pour l'Industrie et la Physique, CNRS UMR 5640, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 4
3. 

Laboratoire Jacques-Louis Lions, CNRS UMR 7598, Université Pierre et Marie Curie-Paris 6, 4 Place Jussieu, 75252 Paris Cedex 05, France

Received  October 2006 Revised  July 2007 Published  August 2007

Partially ionized plasmas corresponding to different ionization degrees are derived and connected one with each other by the diffusion approximation methodology. These plasmas are the following electrical discharges: a thermal arc discharge, glow discharges in local thermodynamic equilibrium -LTE- and in non-LTE, and a non-LTE glow discharge interacting with an electron beam (or flow).
Keywords: glow discharge, fluid limit, diffusion approximation, disparate masses, inelastic collisions, Hilbert expansion, impact ionization, Saha plasma., electron flow, Arc discharge, gas mixture.
Mathematics Subject Classification: 41A60, 76P05, 76X05, 82B40, 82C05, 82C70, 82D1.
Citation: Isabelle Choquet, Pierre Degond, Brigitte Lucquin-Desreux. A hierarchy of diffusion models for partially ionized plasmas. Discrete and Continuous Dynamical Systems - B, 2007, 8 (4) : 735-772. doi: 10.3934/dcdsb.2007.8.735
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