Monte-Carlo simulation of the ionization processes for discharges in the left branch of the Paschen curve

Abstract

The paper deals with the development of the simulation methods applied to the low-pressure discharges in which the reduced electric field E/p is extremely high and there exists a problem for the correct description of the ionization processes in the classical electron avalanches. Here we use the PIC/MC code xoopic for calculation of the impact ionization coefficient α, the electron drift velocity and the electron diffusion coefficient D in the electron avalanches in nitrogen. The range of calculations covers the ratio E/p ≤ 1000 V·(cm·Torr)−1. The simulation method was tested on a simple analytical model of an electron avalanche and showed good agreement in low and moderate E/p. It is shown that in conditions of high E/p the spatial distribution of electrons in the avalanche head based on the concepts of electron mobility during their drift motion and diffusion coefficient is not quite correct. The work confirmed that at the very low pressures pre-breakdown phenomena and the transition to the next stage of high-current breakdown cannot be based on ideas about classical electron avalanches.