Coronas and the space charge problem

Abstract

This paper presents a detailed analysis of a model for a positive corona discharge, and discusses the relationship between the model and the space charge equations which predict the macroscopic motion of charged ions in a gas. The study is restricted to the asymptotic behaviour of the discharge for large time, and it does not consider its initial or burst phases in detail. One prediction of this model is the existence of a steady state solution to the space charge equations that may lose stability to a travelling wave disturbance which then grows into a strongly pulsed oscillation. We compare some numerical calculations with an asymptotic analysis of the discharge and find good agreement.