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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.13174 |
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Table of Contents:
- We consider a plasma that is created by a high voltage difference $λ$, which is known as a Townsend discharge. We consider it to be confined to the region $Ω$ between two concentric spheres, two concentric cylinders, or more generally between two star-shaped surfaces. We first prove that if the plasma is initially relatively dilute, then either it may remain dilute for all time or it may not, depending on a certain parameter $κ(λ, Ω)$. Secondly, we prove that there is a connected one-parameter family of steady states. This family connects the non-ionized gas to a plasma, either with a sparking voltage $λ^*$ or with very high ionization, at least in the cylindrical or spherical cases.