Structures at the electrodes of gas discharges

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Abstract
A phenomenological model is developed to explain single spots or regular patterns of spots at the electrode of gas discharges. The electrodic discharge parts are described by bistable layers, governed by a time-dependent Ginsburg-Landau equation or reaction-diffusion equation; the space between the electrodic layers is taken into account by a resistive region. The steady state of a bi- stable layer is characterized by an S-shaped voltage-current density characteristic. If one bistable layer dominates the interelectrodic space, one single spot may occur. A resistive region may help to stabilize a system of spots and causes a Coulombic interaction of the spots. From a Lyapunov function, equations of motion of the spots can be derived. An initial system of spots relaxes to a stable or metastable state. Experimentally found patterns of anode spots in a glow discharge can be reproduced.