Mathematical Model and Numerical Methods for Understanding Instability Phenomena in Rarefied Plasmas

Reference No.	2025a046
Type/Category	Grant for General Research-Short-term Joint Research
Title of Research Project	Mathematical Model and Numerical Methods for Understanding Instability Phenomena in Rarefied Plasmas
Principal Investigator	Rei Kawashima（Department of Electrical Engineering・Associate Professor）
Research Period	October 27,2025. - October 31,2025.
Keyword(s) of Research Fields	Plasma processing, Ion engine, Plasma simulation, Anisotropic diffusion problem, Discrete maximum principle, Structure-preserving scheme
Abstract for Research Report	Rarefied plasma flows are critical in applications such as semiconductor manufacturing and ion thrusters for satellites. These systems use magnetic fields to control plasma flow, but self-excited instabilities in strongly magnetized plasmas pose a major challenge. These instabilities disrupt magnetic confinement, limiting device performance. Traditionally, stability analysis using perturbation models has been used to predict instabilities. However, there is increasing recognition of the need to examine not just instability onset but also subsequent changes in flow states and energy structures. This has created demand for fluid and continuum models that can support such analyses. This study aims to analyze the mathematical structures of governing equations related to plasma instabilities in rarefied plasmas and to develop numerical methods that reduce numerical oscillations while preserving energy conservation. In fluid-model-based instability analysis, special attention is given to the anisotropic diffusion problem in magnetized electron fluid models, identifying key equation characteristics crucial for instability studies. For kinetic instabilities, this research focuses on analyzing the Boltzmann or Vlasov equation using continuum models, seeking to develop numerical methods that inherently maintain energy conservation. The proposed electron fluid and continuum models will be integrated and applied to practical plasma devices to assess their effectiveness. Through this work, we aim to establish a mathematical framework that accurately describes instability development and energy structure evolution in various plasma sources. Additionally, by leveraging these models and simulation techniques, this research seeks to contribute to new technologies that enhance magnetic confinement and control plasma turbulence.
Organizing Committee Members (Workshop) Participants (Short-term Joint Usage)	Rei Kawashima（Shibaura Institute of Technology・Associate Professor） Daisuke Tagami（Kyushu University・Associate Professor） Tokuhiro Eto（The University of Tokyo・Postdoctoral Researcher）