Quasi-neutral theory of positive columns in electronegative gases

Abstract

A theory of the positive column in electronegative gases based on fluid-type momentum equations to describe charged particle motion is presented. It is assumed that quasi-neutrality conditions prevail and the ion inertial terms are neglected. The positive ions are assumed to be created by electron collisions with neutral molecules and the negative ions to be formed by dissociative electron attachment and destroyed by detachment in reactions with neutral species. The mathematical formulation consists of a two-point boundary value problem involving two independent parameters, functions of collisional and transport data, and two eigenvalues. One of these is the central ratio of the negative ion density to the electron density, while the other is related to the ionisation-loss balance and embodies a discharge characteristic for the maintenance field. These eigenvalues and the radial density distributions of the charged species were calculated for a wide range of variation of the independent parameters. An application of the theory to a positive column in oxygen is given as an illustrative example.