High-voltage ionized gas with spherical cathode emission

Walter A. Strauss; Masahiro Suzuki

doi:10.3934/dcds.2026119

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2026, Volume 57: 24-52. Doi: 10.3934/dcds.2026119

This volume Previous Article Modica type estimates and curvature results for overdetermined $ p $-Laplace problems Next Article Extremal values of $ L^2 $-Pohozaev manifolds and their applications

High-voltage ionized gas with spherical cathode emission

Walter A. Strauss^1, , and
Masahiro Suzuki^2,

1.
Department of Mathematics and Lefschetz Center for Dynamical Systems, Brown University, USA
2.
Department of Computer Science and Engineering, Nagoya Institute of Technology, Japan

^*Corresponding author: Walter A. Strauss
^*Corresponding author: Walter A. Strauss

Received: January 18, 2026

Early access: June 17, 2026

Published online: June 17, 2026

The second author is supported by JSPS KAKENHI Numbers 21K03308 and 25K00915.

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Abstract

We consider a plasma that is created by a high voltage difference, which is known as a Townsend gas discharge. The plasma is confined to the region between two concentric spheres, one of which is a cathode and the other an anode. Ion-electron pairs are created by collisions inside the plasma. Additional electrons enter the plasma by collisions of ions with the cathode. We prove under certain conditions that there are many steady states exhibiting gas discharge, beginning with a 'sparking' voltage. In fact, there is an analytic one-parameter family of them that connects the non-ionized gas to a plasma with arbitrarily high ionization or arbitrarily high potential, or else the family ends at an 'anti-sparking' voltage.

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Mathematics Subject Classification: Primary: 76X05; Secondary: 35M33, 35B32, 35B35.

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