A New Computer Simulation of Avalanche Evolution and Its Transition Into Anode- and Cathode-Directed Streamers in Short Uniform Field Gaps

Abstract

A new method based on the charge simulation technique is proposed for computing the electric field in a short uniform field gap with space charge and without space charge of avalanches growing in the gap. The self-space-charge field of the avalanche is evaluated to result in field enhancement ahead of the avalanche due to electrons at its head and behind the avalanche due to positive ions in its wake. Also, a criterion is proposed for calculating the breakdown voltage and time-to-breakdown when the primary avalanche crosses the gap. The criterion is based on self-recurrence of the avalanche by secondary processes, and the most dominant one is the photoemission at the cathode. The condition of transition of the primary avalanche to anode- and cathode-directed streamers is formulated where the avalanche is chocked by its self-space-charge field. The number of electrons starting avalanche chains forming the streamers is evaluated in the gas ahead and behind the primary avalanche by photoionization and at the cathode by photoemitted electrons. The present computed values of the breakdown voltage of air at different pressures and N2 at atmospheric pressure as well as the time-to-breakdown in air at atmospheric pressure agree satisfactory with those recorded experimentally. The computed temporal variation of the size of the primary avalanche as influenced by its self-space-charge field agrees with that reported in the literature at different $E/N$ values. The computed current waveforms of the primary avalanche and its successor chains agree reasonably with those measured and those calculated using a finite-element method.