Transition from Townsend to glow discharge: subcritical, mixed or supercritical

TL;DR

This paper investigates the transition from Townsend to glow discharge through numerical simulations and analytical expansions, revealing subcritical, supercritical, and mixed behaviors depending on system parameters, and enhances understanding of discharge pattern formation.

Contribution

It provides a comprehensive numerical and analytical study of the Townsend to glow discharge transition, identifying different transition behaviors based on system size and secondary emission.

Findings

Transition can be subcritical, supercritical, or mixed.

Small system sizes favor supercritical or mixed transitions.

Analytical small current expansion matches numerical results well.

Abstract

The full parameter space of the transition from Townsend to glow discharge is investigated numerically in one space dimension in the classical model: with electrons and positive ions drifting in the local electric field, impact ionization by electrons ($\alpha$ process), secondary electron emission from the cathode ($\gamma$ process) and space charge effects. We also perform a systematic analytical small current expansion about the Townsend limit up to third order in the total current that fits our numerical data very well. Depending on $\gamma$ and system size pd, the transition from Townsend to glow discharge can show the textbook subcritical behavior, but for smaller values of pd, we also find supercritical or some intermediate ``mixed'' behavior. The analysis in particular lays the basis for understanding the complex spatio-temporal patterns in planar barrier discharge systems.