Three-dimensional modelling of the DC glow discharge using the second order fluid model

Abstract

This paper presents the development of a three dimensional second order fluid model, used to properly describe a DC glow discharge, maintained by secondary emission at cathode, at low pressure, by using Cartesian geometry. The transport description of the charged species uses the corresponding first three moments of Boltzmann equation, coupled in a self-consistent way with Poisson equation. Some assumptions are required in order to simplify the numerical procedure. Thus, all transport equations are treated in the same manner, using classical drift-diffusion expression for fluxes. We used in this work, the Tchebychev distribution for the longitudinal positions, which gives dense grids near the electrodes in order to accurately resolve the sheaths and to speed up the computing time.