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arXiv · 2403.13174

Ionized Gas in an Annular Region

Walter A. Strauss·Masahiro Suzuki
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Abstract

We consider a plasma that is created by a high voltage difference $\lambda$, which is known as a Townsend discharge. We consider it to be confined to the region $\Omega$ 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 $\kappa(\lambda, \Omega)$. 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 $\lambda^*$ or with very high ionization, at least in the cylindrical or spherical cases.

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Walter A. Strauss, Masahiro Suzuki. 2024-03-19. Ionized Gas in an Annular Region. https://arxiv.org/abs/2403.13174

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