Model of development of the predischarge streamer in air-based on the long-line equation

A simplified mathematical model and algorithm for calculating a positive nonbranching streamer in air with separated description of the head and channel are developed. Due to one-dimensional formulation of the problem, the rate of streamer calculation is orders higher than the calculation rate for problems on streamer propagation based on the drift-diffusion approximation equations. A new method is suggested for describing the dynamics of the radius coordinate of the streamer head is offered. The results from the simplified model are compared, in terms of the main physical parameters, with estimates and experiments described in the literature, including one of the most recent experiments showing the complex pattern of streamer below propagation.