The formation of an electric discharge between electrodes with opposite charges in an air environment is considered. A mathematical model is proposed that describes the evolution of the discharge based on drift equations for the densities of free charge carriers — electrons and ions — in a given electromagnetic field. The model is formulated in terms of generalized functions. A generalized solution is obtained that is suitable for use in numerical algorithms based on the particle method.

discharge, electron, ionized gas, impact ionization, kinetic equation, electric field, distribution function, particle method

Mathematical modelling in actual problems of science and technics