A practical guide to modeling low-current quasi-stationary gas discharges: Eigenvalue, stationary, and time-dependent solvers

The work is concerned with the modeling of low-current quasi-stationary discharges, including the Townsend and corona discharges. The aim is to develop an integrated approach suitable for the computation of the whole range of existence of a quasi-stationary discharge from its inception to a non-stationary transition to another discharge form, such as a transition from the Townsend discharge to a normal glow discharge or the corona-to-streamer transition. This task includes three steps: (i) modeling of the ignition of a self-sustaining discharge, (ii) modeling of the quasi-stationary evolution of the discharge with increasing current, and (iii) the determination of the current range where the quasi-stationary discharge becomes unstable and the non-stationary transition to another discharge form begins. Each of these three steps is considered in some detail with a number of examples, referring mostly to discharges in high-pressure air.