A simulation method of DC discharge using separation of variables

A simulation method based on separation of variables for DC discharge is developed by analyzing various physical mechanisms with exponential dependencies inherent in the governing equations. The advantages of the developed method are simplicity, which does not require processes such as matrix inversion, and that it ensures numerical stability at large time step. The present method is applied to a one-dimensional theoretical model of Ar discharge, and the results are compared with those of the previously developed dielectric relaxation scheme (DRS) that had already been compared and verified with other several methods. While the DRS method, which has similar advantages, uses current as the input variable, the current method uses voltage as the input condition, and the electric field is directly calculated under that voltage condition through Gauss’ law rather than through Poisson’s equation. Summarizing the analysis of the simulation results, the accuracy is acceptable, and the saturation speed is faster with the present method.