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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2403.13174 |
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| _version_ | 1866908278418571264 |
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| author | Strauss, Walter A. Suzuki, Masahiro |
| author_facet | Strauss, Walter A. Suzuki, Masahiro |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13174 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ionized Gas in an Annular Region Strauss, Walter A. Suzuki, Masahiro Analysis of PDEs Mathematical Physics 35M33, 35B32, 35B35, 76X05 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. |
| title | Ionized Gas in an Annular Region |
| topic | Analysis of PDEs Mathematical Physics 35M33, 35B32, 35B35, 76X05 |
| url | https://arxiv.org/abs/2403.13174 |