Minimum sparkover voltage characteristics in air, sulphur-hexafluoride, and some solid dielectrics: A macroscopic approach

Using a small number of plausible assumptions regarding the nature of the leader channel and the corona cloud in an electric discharge in a continuous medium, it is shown how a nonlinear first-order differential equation of the d’Alembert type can be derived which describes the history of the leader and corona cloud development in nondimensional terms. It is found that this solution can be used to derive a breakdown criterion which depends only on two material parameters, i.e., the minimum energy per unit length of the elongating leader channel and the average electric field in the corona cloud. These can be combined to form a single nondimensional parameter (Kekez number). The theory also shows how, for large gaps, the discharge must necessarily lead to the stepped-leader phenomenon. Comparison with experiments of other authors shows good agreement even for dielectrics of other than gaseous states of aggregation, where the concept of corona cloud requires some reinterpretation.