Mathematical analysis on boundary layers of multicomponent plasmas

2018 Fiscal Year Final Research Report

• Project/Area Number: 26800067
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: Nagoya Institute of Technology (2015-2018); Tokyo Institute of Technology (2014)
• Principal Investigator: Suzuki Masahiro 名古屋工業大学, 工学(系)研究科(研究院), 准教授 (30587895)
• Research Collaborator: Takayama Masahiro
• Project Period (FY): 2014-04-01 – 2019-03-31
• Keywords: シース / Bohm条件 / Euler-Poisson方程式 / 定常解 / 3 次元円環領域 / 摂動半空間

Outline of Final Research Achievements

A boundary layer called a sheath appears around the wall where the plasma contacts. H. Bohm considered a plasma composed of electrons and a single kind of positive ion, and derive the Bohm condition for the formation of a sheath. Furthermore, K.-U. Riemann considered a plasma composed of electrons and various positive ions, and proposed the generalized Bohm condition. The motions of these plasmas can be described by the Euler-Poisson equation, and it can be understood that the sheath is a steady solution of the equation. We analyzed the existence and stability of the stationary solution under those Bohm conditions.

Free Research Field

関数方程式

Academic Significance and Societal Importance of the Research Achievements

EP 方程式から形式的に導出された Bohm 条件に対して，数学的に厳密な正当性を与えるなど，シースに関する数学理論を完成させることはシース現象の理解を深める助けとなろう. また, EP 方程式は双曲・楕円型連立方程式系に分類されるが，半導体中の電子流，熱輻射気体，自己重力をもつガス惑星などの現象を記述するモデルも双曲・楕円型連立系である．本研究で得られた解析手法は他のモデルにも応用可能であり，これらの数理物理モデルを一般化した双曲・楕円型連立系の数学理論を構築する契機となろう．