Generalized Paschen's Curves for Extraterrestrial Atmospheric Electricity

In (Riousset et al., 2020, DOI: 10.1016/j.icarus.2019.113506), we investigate putative and confirmed lightning events in the solar system by comparing the conventional breakdown threshold, Ek, in three planetary atmospheres (Earth, Mars, and Venus). The study shows how minor active components can dramatically reduce Ek locally. It further confirms the role of environmental factors (e.g., atmospheric composition) in facilitating the initiation of atmospheric discharges. Here, we continue this work through a study of the importance of geometrical factors in the sustainability of Townsend’s (1905, DOI: 10.1038/062340b0) discharges. The widely accepted Paschen's law describes these events as non-thermal, self-sustained discharges occurring in high voltage, low current, and low-pressure conditions between two parallel plate electrodes (e.g., Raizer et al., 1997, ISBN: 978-3540194620). This paper develops a new formalism adapted to cylindrical and spherical geometries and an experimental setup for its validation. We demonstrate how a simple change in the geometry results in equations requiring numerical solutions and transforming the Paschen’s curves and Stoletov’s points into surfaces and curves, respectively. We compare our work to the peer-reviewed literature and in-house experiments and explore the impact on modeling initiation and propagation of discharges in non-Earth-like environments. Lastly, we conclude on the role of such studies for risk assessments in planetary exploration.