On the significance of the external circuit, Langmuir and Bohm criterion for the stability of plasma fireballs

Abstract

This paper is devoted to studying the influence of the external circuit as well as the Langmuir and Bohm criterion on the stability of plasma fireballs. A simple mathematical model is suggested that describes why plasma fireballs can get unstable up to the point where they start pulsating. The predictions of this model are compared to measured experimental data. Furthermore, it is argued that the Bohm criterion in particular determines whether a stable plasma fireball can be formed. This adds to the current understanding that fireballs are preliminarily formed due to a change in the space charge in front of a positively biased electrode in surrounding plasma. It is argued that the space charge distribution near the vicinity of the anode surface might play a role but that the initial stages of fireball formation are dominantly driven by the requirement of the double layer to satisfy Bohm’s sheath criterion and Langmuir’s criterion. The same holds for a collapsing fireball. This paper shows that if the Langmuir and the Bohm criterion are not satisfied simultaneously, a fireball cannot reach a stable state and will start pulsating with a frequency that is proportional to the square root of the mass of the working gas ions.