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Development of nonlinear extended MHD simulation technique for free boundary plasma

Research Project

Project/Area Number 21K03498
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 14010:Fundamental plasma-related
Research InstitutionTohoku University

Principal Investigator

Hirota Makoto  東北大学, 流体科学研究所, 准教授 (40432900)

Project Period (FY) 2021-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2023: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2022: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2021: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Keywords磁気流体力学 / 自由境界問題 / 二流体プラズマ / 数値シミュレーション
Outline of Research at the Start

磁気流体力学(MHD)は磁場閉じ込め核融合プラズマや宇宙プラズマの巨視的なスケールの現象を理解するために広く用いられている。しかし、プラズマが真空領域と接しているような自由境界問題、あるいはプラズマ密度がほぼゼロである領域を含む問題は現実に数多く存在するが、数値計算でMHD方程式を解くのが技術的に困難とされる。本研究ではMHD方程式において無視されている微視的スケールの物理(二流体効果)を取り入れた拡張MHD方程式を解くことにより、このような真空中のプラズマの運動を適切にシミュレーションをする技法を構築する。

Outline of Final Research Achievements

In the peripheral region where plasma contacts vacuum, a physically correct solution cannot be obtained by MHD, since the MHD approximation breaks down as the density decreases. In this study, we investigated a method using an extended MHD model that includes two-fluid effects in addition to the conventionally used pseudo-vacuum model. Specifically, we analyzed Z-pinch equilibrium and numerically calculated the equilibrium solution for a plasma surrounded by a vacuum region. When the plasma changes adiabatically, the interface becomes a singular surface, and we proposed a method to regularize this singularity in numerical calculation. Furthermore, in the extended MHD model, it was found that an equilibrium state cannot be obtained unless a small amount of viscosity exists in the vacuum region. Then, the extended MHD can handle free boundary problems.

Academic Significance and Societal Importance of the Research Achievements

磁場閉じ込め核融合プラズマや天体プラズマは、真空領域によって囲まれていることが多く、外側に向かって密度は徐々に下がっていく。プラズマの運動を記述する磁気流体力学(MHD)は古くから用いられてきたが、密度がゼロになると物理的に正しくなくなり、数値計算も非常に不安定になることが長年の問題となっている。本研究の成果は、MHDをより物理的に正しい形に拡張することで、真空領域を含めた数値解析が可能になることを提案しており、核融合研究や天体物理などの様々な問題に応用ができると期待される。

Report

(4 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • Research Products

    (13 results)

All 2023 2022 2021

All Presentation (13 results) (of which Int'l Joint Research: 7 results,  Invited: 1 results)

  • [Presentation] Extended magnetohydrodynamic approach to plasma-vacuum interface2023

    • Author(s)
      Makoto Hirota
    • Organizer
      7th Asia-Pacific Conference on Plasma Physics
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Extended MHD solutions with plasma-vacuum interface2023

    • Author(s)
      Makoto Hirota
    • Organizer
      27th Workshop on MHD Stability Control
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Extended MHD equilibrium having boundary layer at plasma-vacuum interface2023

    • Author(s)
      Makoto Hirota
    • Organizer
      65th Annual Meeting of the APS Division of Plasma Physics
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Classification of extended MHD models for special relativistic plasmas using scale analysis2023

    • Author(s)
      Shuntaro Yoshino, Makoto Hirota, Yuji Hattori
    • Organizer
      65th Annual Meeting of the APS Division of Plasma Physics
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Extended MHD solutions for plasma-vacuum interface that is singularly perturbed by electron inertia2023

    • Author(s)
      Makoto Hirota
    • Organizer
      RIMS Workshop on "Mathematical Analysis in Fluid and Gas Dynamics"
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 拡張磁気流体力学におけるプラズマ-真空界面の特異摂動解析2023

    • Author(s)
      廣田 真
    • Organizer
      日本物理学会 第78回年次大会
    • Related Report
      2023 Annual Research Report
  • [Presentation] 特殊相対論的プラズマの拡張MHD近似の物理的適用性とラグランジアンの探索2023

    • Author(s)
      吉野舜太郎, 廣田真, 服部裕司
    • Organizer
      日本物理学会 第78回年次大会
    • Related Report
      2023 Annual Research Report
  • [Presentation] Theoretical and Numerical Properties of Extended MHD: Importance of Electron Inertia2023

    • Author(s)
      Makoto Hirota
    • Organizer
      US-Japan MHD Workshop on "MHD activity measurement and control in long-pulse operations towards DEMO"
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research
  • [Presentation] Application of extended magnetohydrodynamic model to plasma-vacuum systems2022

    • Author(s)
      Makoto Hirota
    • Organizer
      64th Annual Meeting of the APS Division of Plasma Physics
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research
  • [Presentation] 自由境界プラズマの解析に対する拡張MHDモデルの適用2022

    • Author(s)
      廣田 真
    • Organizer
      第27回数値トカマク実験(NEXT)研究会
    • Related Report
      2022 Research-status Report
  • [Presentation] 圧縮性拡張MHDシミュレーションにおける自由境界プラズマ平衡2022

    • Author(s)
      廣田 真
    • Organizer
      NIFS共同研究「高ベータトーラスプラズマ研究会」
    • Related Report
      2022 Research-status Report
  • [Presentation] 圧縮性拡張MHD方程式の数値シミュレーション技法2022

    • Author(s)
      廣田 真
    • Organizer
      日本物理学会第77回年次大会
    • Related Report
      2021 Research-status Report
  • [Presentation] 散逸的拡張MHDシミュレーションにおける境界条件の実装2021

    • Author(s)
      廣田 真
    • Organizer
      日本物理学会2021年秋季大会
    • Related Report
      2021 Research-status Report

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Published: 2021-04-28   Modified: 2025-01-30  

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