| Project/Area Number |
18K03364
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 12020:Mathematical analysis-related
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| Research Institution | Nagoya Institute of Technology |
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Principal Investigator |
Suzuki Masahiro 名古屋工業大学, 工学(系)研究科(研究院), 准教授 (30587895)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | プラズマ境界層 / Bohm条件 / Debye長 / 準中性極限 / 放電 / 火花電圧 / 安定性・不安定性 / 分岐解析 / シース / Bohm 条件 / Debye 長 / 境界層 / プレシース |
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| Outline of Final Research Achievements |
In the real world, artificially produced plasmas are widely used. In such applications, a plasma is generated using a gas discharge, and a boundary layer appears around materials which the plasma contacts with. The analysis of discharge and boundary layer are important in plasma physics and engineering. To analyze the the process of the formation of the boundary layer, we have shown that the solution of the Euler-Poisson system can be approximated by the sum of the outer and inner solutions. From the behavior of the inner solution, the process of the formation can be understood immediately. Moreover, we have analyzed the Morrow model to investigate the fundamental process of discharge generation. It has been shown that the trivial steady-state solution is stable for voltages which are less than the sparking voltage, and the trivial steady-state solution is unstable for voltages which are greater than the sparking voltage.
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| Academic Significance and Societal Importance of the Research Achievements |
プラズマ境界層が定常解に対応することは数学的に検証されていたが,境界層の発展過程は明らかにされていなかった．本研究では，数学解析及び数値解析を通じて，その一部を解明することに成功した．また，Townshend理論による火花電圧を，最新のモデル方程式を用いて再導出することができた．これらの成果は,プラズマの諸現象を理解する上で,プラズマ工学・物理学にも利するものである．また，微分方程式に対する新たな解析手法を生み出すことができ，非線形偏微分方程式論の発展にも貢献した．
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