Simulation of breakdown in air using cellular automata with streamer to leader transition

Abstract

We propose a new discrete stochastic model for computer simulation of the lightning process and the breakdown process in long gaps in gaseous dielectrics. In this model we used cellular automata. Two different states of a conductive structure that correspond to streamers and channels of very high conductivity (leader phase) are introduced. The conductivity of the streamers is assumed to be negligible in comparison with highly conductive channels. The electric-field potential is obtained by solving the Laplace equation in a region outside the equipotential, highly conductive part of the structure. As the streamer growth criteria we use two multi-element models in which several conductive bonds can arise at each time step. The growth is stochastic in time, and the probability of streamer formation is proportional to a certain function of local electric field r(E) that depends on the properties of the dielectric. If the energy released in a segment of the streamer is larger than a certain critical value, the streamer transforms to a highly conductive phase. Patterns of conductive trees are obtained in computer simulations of breakdown under various conditions.