Numerical Methods for Two-Dimensional Analysis of Electrical Breakdown in a Non-uniform Gap

A finite difference procedure used to analyze the two-dimensional evolution of the charged particle densities and electrostatic potential during the initial stages of electrical breakdown between a wire and a plane is described. The diffusion flux equations for the charged particle densities and poison's equation of the electrostatic potential contitute a set of coupled, two-dimensional, time dependent, nonlinear equations that govern the breakdown phenomena. In this paper, we have the problem by two different procedures: (a) a finite difference method that combines upwind difference scheme (USD) for drift terms, central difference scheme (CDS) for the diffusion terms, and implicit time integration; and (b) a method that combines CDS for drift terms, for the diffusion terms, and implicit time integration. In each case, Crank-Nicolson time integration has aslo been tried. It is concluded that method (a) is most suitable for discharge breakdown problems.