Field-dependent conductivity in non-uniform fields and its relation to electrical breakdown

A method is given for calculating the resulting field distribution when the conductivity is a function of the field strength. This is applied to a point-plane electrode system in an amorphous solid, with the assumption that the condictivity at low field-strengths is described by a relation due to Fröhlich. The results show that for polymethylmethacrylate with average fields of the order of 106 volt/cm, the reduction in maximum field-strength from that calculated for constant conductivity can be factor of five or more, the magnitude of the reduction depending on the degree of non-uniformity of the field. Energy-level data required for the calculation are given for glass, polyethylene, polymethylmethacrylate and several types of varnish, and incomplete data are given for chlorinated polyethylene polystyrene and polyisobutylene. The results are applied to breakdown in a non-uniform, and a method is suggested for determining experimentally whether breakdown occurs when the maximum stress reaches the intrinsic electric strength, or whether it is necessary for the intrinsic electric strength to be created over a given distance.