A computational study on the effects of fast-rising voltage on ionization fronts initiated in sub-mm air and CO\(_{2}\) gaps

Gas discharge and breakdown phenomena have become increasingly important for the development of an ever-growing number of applications. The need for compact and miniaturized systems within power, pulsed power, semiconductor, and power electronic industries has led to the imposing of significant operating electric field stresses on components, even within applications with low operating voltages. Consequently, the interest in gas discharge processes in sub-millimeter and microscale gaps has grown, as the understanding of their initiation and propagation is critical to the further optimization of these technologies. In this work, a computational study of primary ionization fronts has been conducted, which systematically investigated the role of voltage rate-of-rise in point-plane and point-point electrode geometries with an inter-electrode gap maintained at 250 \(\upmu\) $\mathrm{\mu }$ m and a needle radius of 80 \(\upmu\) $\mathrm{\mu }$ m. Using the hydrodynamic approach with the local mean energy approximation, along with simplified plasma chemistry, simulations have been performed under positive and negative ramp voltages, rising at 50, 25, 16.67, 12.5, and 10 kV/ns in synthetic air and in pure CO \(_{2}\) ${}_2$ . Results on the developed electric field, electron densities, and propagation velocities are presented and discussed. Effects on the cathode sheath thickness scaling with voltage rate-of-rise have been additionally analyzed, the mechanisms behind these effects and their potential impacts are discussed. The work conducted in this study contributes towards an increased understanding of the gas discharge process, under fast-transients and nonuniform electric fields, with relevance to microelectromechanical, power, and pulsed power system design.