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

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.