The structure of streamers in N₂. I. fast method of space-charge dominated plasma simulation

A novel technique of simulation of low-temperature gas-discharge plasmas when space-charge effects are dominant is described. It is shown that the Poisson equation for electric field can be replaced by a much simpler current conservation law so that the solution would automatically obey the Poisson equation. A one-dimensional version of this method was tested on the problem of cathode region formation in pre-ionized atmospheric pressure nitrogen. A two-dimensional scheme for cylindrical coordinates is described. The method proposed allows one to simulate fully the two-dimensional problem of streamer dynamics in an over-volted gap on a personal computer, as described in the companion paper.