Numerical solution of hyperbolic equations for electron drift in strongly non-uniform electric fields

Abstract A comparison is made of solutions of the continuity equations for the motion of electrons and ions in a strong electric field using the methods of Euler, Runge-Kutta, Lax-Wendroff, characteristics and the flux-corrected transport (FCT) algorithm “Phoenical LPE Shasta” developed by Boris and Book( J. Comput. Phys. 20 (1976) , 397), with their flux limiter and with the new flux limiting algorithms developed by Zalesak ( J. Comput. Phys. 31 (1979) , 335). Results with and without ionization, and for uniform and non-uniform electric fields, are compared. Because ionization by electrons is strongly dependent on the electric field, considerable care needs to be taken to choose an optimum numerical scheme for non-uniform fields. For example, the calculation of the properties of corona discharges, or the cathode-fall of a glow discharge, requires fine spatial resolution. It is found that the Lax-Wendroff method and the method of characteristics give acceptable results; however, the Phoenical LPE Shasta algorithm with the flux limiting algorithm of Zalesak gives the best results, with the added advantage of suppressing spurious oscillations.