A Generalized Townsend's Theory for Paschen Curves in Planar, Cylindrical, and Spherical Geometries in Planetary Atmospheres
Sponsor
This work was supported by the National Science Foundation (Grants CAREER-2047863 and EAR-2311331). The authors also acknowledge Embry-Riddle Aeronautical University Office of Undergraduate Research for supporting Mr. Jacob A. Engle's initial contribution to this work.
Published In
Journal of Geophysical Research-Atmospheres
Document Type
Citation
Publication Date
4-16-2024
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.
Rights
©2024 American Geophysical Union
Locate the Document
DOI
10.1029/2022JD038427
Persistent Identifier
https://archives.pdx.edu/ds/psu/41820
Publisher
American Geophysical Union
Citation Details
Riousset, J. A., Méndez Harper, J. S., Dufek, J., Nelson, J. P., & Esparza, A. B. (2024). A generalized Townsend's theory for Paschen curves in planar, cylindrical, and spherical geometries in planetary atmospheres. Journal of Geophysical Research: Atmospheres, 129, e2022JD038427. https://doi.org/10.1029/2022JD038427