High-Voltage Ionized Gas with Spherical Cathode Emission

TL;DR

This paper analyzes plasma formation between concentric spheres under high voltage, proving the existence of multiple steady states including sparking and anti-sparking conditions, with implications for understanding gas discharge phenomena.

Contribution

It provides a mathematical proof of multiple steady states in Townsend gas discharge confined between spherical electrodes, including the existence of a continuous family of solutions.

Findings

Multiple steady states exist for Townsend gas discharge.

A one-parameter family of solutions connects non-ionized gas to highly ionized plasma.

Solutions end at an anti-sparking voltage under certain conditions.

Abstract

We consider a plasma that is created by a high voltage difference, which is known as a Townsend gas discharge. The plasma is confined to the region between two concentric spheres, one of which is a cathode and the other an anode. Ion-electron pairs are created by collisions inside the plasma. Additional electrons enter the plasma by collisions of ions with the cathode. We prove under certain conditions that there are many steady states exhibiting gas discharge, beginning with a `sparking' voltage. In fact, there is an analytic one-parameter family of them that connects the non-ionized gas to a plasma with arbitrarily high ionization or arbitrarily high potential, or else the family ends at an `anti-sparking' voltage.