Bifurcations in the theory of current transfer to cathodes of dc discharges and observations of transitions between different modes

TL;DR

This paper investigates how bifurcations in steady-state solutions explain the transitions between different current transfer modes on cathodes in dc gas discharges, supported by experimental and numerical analysis.

Contribution

It links observed mode transitions to specific bifurcations of steady-state solutions and provides numerical confirmation matching experimental patterns.

Findings

Transitions between diffuse and spot modes involve pitchfork or fold bifurcations.

Experimental observations align with bifurcation theory predictions.

Numerical patterns conform to observed transition behaviors.

Abstract

General scenarios of transitions between different spot patterns on electrodes of dc gas discharges and their relation to bifurcations of steady-state solutions are analyzed. In the case of cathodes of arc discharges, it is shown that any transition between different modes of current transfer is related to a bifurcation of steady-state solutions. In particular, transitions between diffuse and spot modes on axially symmetric cathodes, frequently observed in the experiment, represent an indication of the presence of pitchfork or fold bifurcations of steady-state solutions. Experimental observations of transitions on cathodes of dc glow microdischarges are analyzed and those potentially related to bifurcations of steady-state solutions are identified. The relevant bifurcations are investigated numerically and the computed patterns are found to conform to those observed in the course of the corresponding transitions in the experiment.