Electrical breakdown of gases : the spatio-temporal growth of ionization in fields distorted by space charge

Abstract

A quantitative theoretical investigation is made of the spatio-temporal growth of ionization between plane parallel electrodes. A numerical method is described for integrating the ioniza­tion growth equations which enables the growth of the discharge to be traced from its initia­tion, in the uniform field region, as far as the transition to the glow discharge, involving space-charge-distorted fields, on the basis of the Townsend primary and secondary processes. A new method, more accurate than Poisson’s equation in one dimension, is used to calculate the field distortion. Experimental data in hydrogen are analyzed, and it is shown that the theoretically predicted curves of voltage collapse agree with those observed experimentally when the field distortion is taken into consideration. The magnitudes of the various Townsend secondary coefficients required to describe in detail the voltage collapse and the observed formative times of breakdown depend on the cross-sectional area of the discharge. Limiting values of the secondary coefficients are given.