Approximate solutions for the Vlasov--Poisson system with boundary layers
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909072245129216 |
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| author | Jung, Chang-Yeol Kwon, Bongsuk Suzuki, Masahiro Takayama, Masahiro |
| author_facet | Jung, Chang-Yeol Kwon, Bongsuk Suzuki, Masahiro Takayama, Masahiro |
| contents | We construct the approximate solutions to the Vlasov--Poisson system in a half-space, which arises in the study of the quasi-neutral limit problem in the presence of a sharp boundary layer, referred as to the plasma sheath in the context of plasma physics. The quasi-neutrality is an important characteristic of plasmas and its scale is characterized by a small parameter, called the Debye length.
We present the approximate equations obtained by a formal expansion in the parameter and study the properties of the approximate solutions.
Moreover, we present numerical experiments demonstrating that the approximate solutions converge to those of the Vlasov--Poisson system as the parameter goes to zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06928 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximate solutions for the Vlasov--Poisson system with boundary layers Jung, Chang-Yeol Kwon, Bongsuk Suzuki, Masahiro Takayama, Masahiro Mathematical Physics We construct the approximate solutions to the Vlasov--Poisson system in a half-space, which arises in the study of the quasi-neutral limit problem in the presence of a sharp boundary layer, referred as to the plasma sheath in the context of plasma physics. The quasi-neutrality is an important characteristic of plasmas and its scale is characterized by a small parameter, called the Debye length. We present the approximate equations obtained by a formal expansion in the parameter and study the properties of the approximate solutions. Moreover, we present numerical experiments demonstrating that the approximate solutions converge to those of the Vlasov--Poisson system as the parameter goes to zero. |
| title | Approximate solutions for the Vlasov--Poisson system with boundary layers |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2401.06928 |