Numerical Study of the Streamer Dynamics Based on Integral and Differential Photoionization Models

Abstract

Photoionization, the same as impact ionization, is one of the key processes affecting the development of streamers of both polarities in air and nitrogen–oxygen mixtures. To study the streamer dynamics in detail, a series of numerical experiments are being conducted in this work. The computational algorithm is based on a drift–diffusion model, in which the photoionization term is calculated in two ways: using an integral model (the Zheleznyak approach) and a differential model (a set of Helmholtz equations). The problems are solved in an axisymmetric setting in a cylindrical coordinate system on a uniform Cartesian grid. A constant potential difference of 25 kV is applied to plane circular electrodes with the radius of \({l_r} = 0.2\;{\text{cm}}\) located at a distance of \({l_z} = 0.5\;{\text{cm}}\). The interelectrode gap is filled with nitrogen under normal conditions with a small oxygen admixture of 0.05%. In all problems, the results obtained using both photoionization models are compared (the closeness of the solutions found is noted). The photoionization process is studied by the example of a cathode-directed streamer, and the photoionization and impact ionization rates are analyzed by simulating a two-headed streamer. The dynamics of a cylindrical discharge initiated at the anode from a ring of quasi-neutral plasma is studied.