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- Title
A Generalized Townsend's Theory for Paschen Curves in Planar, Cylindrical, and Spherical Geometries in Planetary Atmospheres.
- Authors
Riousset, Jeremy A.; Méndez Harper, Joshua S.; Dufek, Josef; Nelson, Jared P.; Esparza, Annelisa B.
- Abstract
In this work, we focus on plasma discharges produced between two electrodes with a high potential difference, resulting in the ionization of the neutral particles supporting a current in a gaseous medium. At low currents and low temperatures, this process can create luminescent emissions: glow and corona discharges. The parallel plate geometry used in Townsend's theory lets us develop a theoretical formalism, with explicit solutions for the critical voltage effectively reproducing experimental Paschen curves. However, most discharge processes occur in non‐parallel plate geometries, such as discharges between particles in multiphase systems and between cylindrical conductors. Here, we propose a generalization of the classic parallel plate configurations to concentric spherical and coaxial cylindrical geometries in Earth, Mars, Titan, and Venus atmospheres. In a spherical case, a small radius effectively represents a sharp tip rod, while larger, centimeter‐scale radii represent blunted tips. In cylindrical geometries, small radii resemble thin wires. We solve continuity equations in the gap and estimate a critical radius and minimum breakdown voltage that allows the formation of a glow discharge. We show that glow coronæ form more easily in Mars's low‐pressure, CO2‐rich atmosphere than in Earth's high‐pressure, N2‐rich atmosphere. Additionally, we present breakdown criteria for Titan and Venus, two planets where discharge processes have been postulated. We further demonstrate that critical voltage minima occur at 0.5 cm⋅Torr for all three investigated geometries, suggesting easier initiation around millimeter‐size particles in dust and water clouds. This approach could be readily extended to examine other multiphase flows with inertial particles. Plain Language Summary: In this work, we focus on plasma discharges between two electrodes with a high voltage difference. The result is a conversion of the medium from an insulator to a conductor. At low currents and low temperatures, this process can create luminescent emissions: the so‐called glow and corona discharges. Here, we propose a generalization of Townsend's classic parallel plate configurations to concentric spheres and coaxial cylinders more likely to be encountered as particles in Earth, Mars, Venus, and Titan atmospheres. We computationally solve the continuity equations in the gap between objects and ultimately calculate critical electric fields for self‐sustained discharges. We show that glow coronæ form more easily in Mars's low‐pressure, carbon dioxide‐rich atmosphere than in Earth's high‐pressure, nitrogen‐rich atmosphere. Additionally, we present breakdown criteria for Titan and Venus. We further demonstrate that critical voltage minima occur near 0.5 cm ⋅ Torr for all three investigated geometries, suggesting easier initiation around millimeter‐size particles in dust and water clouds. Key Points: Numerical modeling lets us study glow coronæ around spherical and cylindrical electrodes based on Paschen theory in planetary atmospheresThe lowest requirements for discharge ignition occur at pressure×length‐scale products of 0.5 cm⋅Torr, independently of the geometryTownsend discharges are more easily ignited in low‐pressure and/or CO2‐rich atmosphere than in Earth's high‐pressure atmosphere
- Subjects
GLOW discharges; PLANETARY atmospheres; VENUSIAN atmosphere; PLASMA flow; BREAKDOWN voltage; MULTIPHASE flow; ATMOSPHERIC nitrogen
- Publication
Journal of Geophysical Research. Atmospheres, 2024, Vol 129, Issue 7, p1
- ISSN
2169-897X
- Publication type
Article
- DOI
10.1029/2022JD038427