Asymptotic analysis of a simple ionization kinetics of air flows at atmospheric pressure . Draft version , 14 February 2005

The purpose of this paper is to propose and analyze a simplified model for plasma generation in air flows at atmospheric pressure. The starting point is a model previously proposed by Lowke [21], enriched with a loss term which schematically takes into account the drag of the metastable and ionized species by the flow. An asymptotic analysis of this model confirmed by numerical simulations is proposed and shows that plasma generation is a three time-scale process. Eventually, the existence of the plasma over long time scales depends on the value of the flow velocity relative to a threshold value, which can be approximately computed analytically. A procedure for generating a plasma at atmospheric pressure in air at low energetic cost is also suggested.