Title: Mathematical models of electrical discharges in air at atmospheric pressure: a derivation from asymptotic analysis

Authors: Pierre Degond, Brigitte Lucquin-Desreux

Addresses: Mathematiques pour l'Industrie et la Physique, UMR 5640 (CNRS-UPS-INSA), Universite Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France. ' Laboratoire Jacques-Louis Lions, CNRS UMR 7598, Universite Pierre et Marie Curie – Paris 6, B.C. 187, 4 Place Jussieu, 75252 Paris Cedex 05, France

Abstract: We derive some mathematical models describing electrical discharges at atmospheric pressure. We start from the coupled system of Euler–Maxwell equations for all species that we scale according to some relevant physical units. Among the nine dimensionless parameters that appear in this scaling, the mass ratio between the electrons and the heavy species plays a significant role. We then obtain various models, corresponding to different values of these parameters. In one of the steps of this hierarchy, both electrons and ions satisfy a mobility law; but this case, however, seems to correspond to non-realistic electron temperatures.

Keywords: electrical discharges; Euler–Maxwell equations; asymptotic analysis; quasineutrality; mobility laws; mathematical modelling; electrons; ions; air; atmospheric pressure.

DOI: 10.1504/IJCSM.2007.013764

International Journal of Computing Science and Mathematics, 2007 Vol.1 No.1, pp.58 - 97

Published online: 25 May 2007 *

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