An asymptotic model for steady wire-to-wire corona discharges

The purpose of this paper is to propose a new model based on an asymptotic analysis for the modelling of steady wire-to-wire corona discharges. The concept consists in dividing the discharges into regions of two kinds: two thin ionization layers at the vicinity of the electrodes and a much larger ion-drift region. Introducing the length of the ionization layer ε and using an asymptotic analysis to define a truncated system, a simplified kinetic can be considered for each region which allows finding quasi-analytical solutions. The method is validated by comparison with a classical scheme and the results show good agreement with experiments. Finally, an example of parametric study of the discharge is presented. Indeed, the ability of the model to provide solutions at low computational cost allows quickly performing such a study and could be useful to experimenters in order to suggest new geometric settings or experimental setups.