Integral equation for source of ionization in hollow cathode

TL;DR

This paper derives an integral equation for the ionization source in hollow cathodes, enabling simulation of the pendulum effect's influence on current-voltage characteristics in glow discharges.

Contribution

It introduces a novel integral equation based on a stationary kinetic model to analyze the pendulum effect in hollow cathode discharges.

Findings

Integral equation models ionization source in hollow cathodes.

The model predicts changes in current-voltage characteristics with anode transparency.

Applicable to self-consistent field calculations in plasma physics.

Abstract

To simulate the influence of pendulum effect in hollow cathode configuration on a current-voltage characteristic it is proposed to consider a plane glow discharge in one-dimensional space configuration with two plane parallel cathodes and one plane anode in the middle. A pendulum effect could be switched on or off, with consideration for the anode to be transparent or not for fast ionizing electrons. On the basis of a stationary kinetic equation for ionizing electrons an integral equation for a source of ionization is derived. This equation can be used as a component in self-consistent problem for field equations to calculate a current-voltage characteristic and to show how it changes in both cases - in presence or absence of anode transparency.