A Simple Analytical Method of Gas Discharge Based on Logistic Model

Abstract

Current research on gas discharge theory has made significant development in terms of numerical simulation, but its analytical description of streamer mechanism remains overly simplified, as it is still based on the electron avalanche model characterized with the exponential growth and infinite breakdown current. This paper presents a simple analytical method of gas discharge based on the classic logistic model and covers four aspects. First, it gives the exact definition of generation and mortality rate of electron number, establishes a logistic differential equation and a logistic iteration model for streamer mechanism, and derives deterministic analytical and iterative solution. Second, we also extend the mortality rate to include negative value, thus allowing the logistic model to describe both exponential growth and S shape growth scenarios, and provide criteria for categorizing spark breakdown, Townsend discharge, and stable discharge (glow, arc, aka saturated streamer). Third, the logistic differential model can be transformed into an iterative model. From that we derive the criteria for evaluating discharge instability. Last, although our model is 1-D, but it is still practical and easy to use given its clear analytical expression of underlying physical mechanism.