Computer Simulation of Electrical Breakdown in Gases; Avalanche and Streamer Formation

Abstract

This paper presents a new method for the simulation of electrical-breakdown phenomena, and plasma phenomena where both binary electron-neutral-gas-molecule collisions and collective interactions among charged particles are important. Elastic, exciting, and ionizing electron-neutral-gas-molecule collisions are included using a Monte Carlo technique. Electron-ion pairs are released in ionizing collisions. The simulation also includes the release of electron-ion pairs by photoionization. Collective interactions (space-charge effects) are included using a one-dimensional-plasma model which regards the charged particles as charge sheets. Poisson's equation is solved in one dimension based on the positions of the charge sheets to find the accelerating forces on the sheets. The method is used to simulate the growth of electron avalanches and anode- and cathode-directed streamers in nitrogen-filled parallel-plane gaps. Avalanche-simulation results are used to calculate values for the drift velocity and the ionization coefficient in nitrogen. The calculated values for these quantities agree with experimental values over a wide range of $\frac{E}{p}$, the applied electric field divided by the pressure. Velocities for anode- and cathode-directed streamers are calculated based on the streamer-simulation results. The calculated streamer velocities agree with available experimentally measured streamer velocities. The streamer-simulation results also show that photoionization is the essential mechanism for streamer formation and growth.