Derivation of a simple engineering equation for the minimum voltage of inverted fireball onset
This paper describes the derivation of a simple engineering equation to calculate the minimal necessary bias voltage for the onset of an inverted fireball. The calculation uses the electron density in the absence of an inverted fireball as well as the grid constant and the working gas species as input parameters. It will be shown that the interplay between ionsation potential, dissociation potential (for molecular working gases), as well as the electron density in the background plasma, play an important role in the necessary minimum bias on the fireball electrode. Some of the most common working gases and their relevant parameters will also be listed in this paper. This should give experimentalists and engineers a practical equation that can be used to quickly determine the most important electrical properties of the anode that is used to trap the inverted fireball. Thus, the planning and design of experimental setups or technological devices will be made much less time-consuming and, thus, more convenient.