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研究生： 黃榮達
Huang, Jung-Da
論文名稱： 由百萬伏特能量離子驅動的相對論電磁離子迴旋不穩定性之研究
Study of Relativistic Electromagnetic Ion Cyclotron Instabilities Driven by MeV Ions
指導教授： 陳寬任
Chen, K. R.
學位類別： 碩士
Master
系所名稱： 理學院 - 物理學系
Department of Physics
論文出版年： 2002
畢業學年度： 90
語文別： 英文
論文頁數： 64
中文關鍵詞： 電漿
外文關鍵詞： physics, fusion, plasma
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    • 在外加磁場中傳遞和被百萬伏特之快速離子驅動的相對論離子迴旋電磁波不穩定性是本篇主要的發現. 利用kinetic theory和MHD可得完整的色散關係方程式, 利用數值和分析計算, 色散關係方程式求其解可了解其物理條件, 成長速度和波頻率。

    　　The relativistic instability of electromagnetic ion cyclotron waves propagating across the magnetic field driven by fast ions of MeV energy is investigated. Both kinetic theory and MHD theory are employed to derive the dispersion relation. The conditions, growth rates, and wave frequencies are studied by analytical and numerical calculation of the dispersion relation.
    　　The relativistic instability is reactive, as in contrast to the inversed Landau instability. In addition to a cubic instability, there is a special quadratic instability. While the maximum growth rate of all know instabilities is determined by their drives (e.g., the fast ion density), the threshold of the quadratic instability is determined by the fast ion density; but, its maximum growth is independent of the fast ion density and is determined by the slow ion density instead.
    　　Due to the wave magnetic field is much larger than the electric field, the dielectric constant of the cold plasma part is large. The instabilities are two-gyro-stream type and are raised due to the coupling of the first order pole of slow ions and the second order pole of fast ions. The wave frequency of the cubic instability is close to the harmonic fast ion cyclotron frequency and the maximum growth is with a 1/3 power of fast ion density. However, when the slow ion density is low, the wave frequency is very close to the slow ion harmonic cyclotron frequency and, thus, the cubic term in the dispersion relation can be neglected and the dispersion relation becomes quadratic so as the instability.
    　　The relativistic quadratic instability has some special characteristics. It occurs when the ions’ frequency mismatch can be canceled by the coefficient of the relativistic second order pole of fast ions; that is, there is a threshold of fast ion density for the instability. But, the maximum growth rate depends on the slow ion density (not fast ion density). The higher is the slow ion density; the higher is the maximum growth rate, the lower is the fast ion density threshold, and the smaller is the mismatch of the wave and fast ion harmonic cyclotron frequencies.

    Contents Abstract… … … … … … … … … … … … … … … .....… … … … ..(2) Symbol Table… … … … … … … … … … … … … … … … … … ...(6) 1. Introduction… … … … … … … … … … … … … … … … … … (8) 2. MHD Dispersion Relation of The Electromagnetic Ion Cyclotron Wave… … … … … … … … … … … … … … … … .(11) 2.1 Introduction… … … … … … … … … … … … … … … ....(11) 2.2 Mode feature and dispersion relation from MHD… .(11) 2.3 Compare with Coppi’s result… … … … … … … … … .(16) 2.4 Characteristic of the cold electromagnetic wave… ...(18) 3. Kinetic Theory… … … … … … … … … … … … … … … … ..(20) 3.1 Introduction… … … … … … … … … … … … … … … ...(20) 3.2 Two-gyro-stream instability… … … … … … … … … ..(20) 3.3 Dielectric tensor… … … … … … … … … … … … … … (23) 3.4 Dispersion relation from kinetic theory… … … … … (24) 3.5 Compare with MHD … … … … … … … … … … … … (29) 3.6 Instability Analysis… … … … … … … … … … … … … (30) 4. Numerical Result… … … … … … … … … … … … … … … ..(35) 4.1 Introduction… … … … … … … … … … … … … … … .(35) 4.2 Cubic instability… … … … … … … … … … … ..… … ..(35) 4.3 Quadratic instability… … … … … … … … … … ..… … (44) 4.4 Transition from the quadratic instability to cubic by increase slow ion density… … … … … … … … ..… … .(58) 5. Conclusion… … … … … … … … … … … … … … … … .… … (62) 6. Reference… … … … … … … … … … … … … … … … … ...… (64)

    1. F. Chen, Introduction of Plasma Physics
    2. K. R. Chen, Physics Latter A 181, 308 (1993)
    3. K. R. Chen, Phys. Plasma 7, 844 (2000)
    4. K. R. Chen, Phys. Plasma 7, 857 (2000)
    5. K. R. Chen, Phys. Rev. Lett. 72, 3534 (1994)
    6. K. R. Chen, Physics Latter A 247, 319 (1998)
    7. B. Coppi, S. Cowley and F. Kulsrud, Phys. Fluids 29, 4060 (1986)
    8. K. R. Chen, ” Role of Relativity in Dynamics of MeV Alpha Particles in Magnetized Plasmas”, Physical Society Republic of China (2002)
    9. K. R. Chen, “Plasma Physics Class Note”, (2000)

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