Finite-element analysis of monopolar ionized fields including ion diffusion

This paper aims at analysis of the monopolar ionized field in conductor-to-plane configurations. An iterative finite-element technique is used to solve Poisson's equation. Two algorithms are proposed for satisfying the current continuity condition and updating the space-charge density. The first algorithm is a modified method of characteristics, which neglects ion diffusion. The second algorithm is based on application of Kirchhoff's current-balance law at each node of the finite-element grid and takes ion diffusion into account. The proposed method of solution has been applied for laboratory and full-scale models of monopolar transmission lines. The calculated V-I characteristics, current-density and electric field profiles at the ground plane agreed well with those measured experimentally in comparison with previous calculations. Fast convergence and simplicity in programming characterize the proposed method.