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研究生： 蔡宗華
Tsai, Tsung-Hua
論文名稱： 不均勻磁場中百萬電子伏特Alpha粒子所激發之相對論靜電離子迴旋不穩定性
Relativistic Electrostatic Ion Cyclotron Instabilities Driven by MeV Alpha Particles in Non-uniform Magnetic Fields
指導教授： 陳寬任
Chen, Kuan-Ren
學位類別： 博士
Doctor
系所名稱： 理學院 - 物理學系
Department of Physics
論文出版年： 2009
畢業學年度： 97
語文別： 英文
論文頁數： 86
中文關鍵詞： 解析理論 、粒子模擬 、相對論 、離子迴旋 、不均勻 、靜電 、絕對不穩定性 、區域化
外文關鍵詞： particle-in-cell simulation, relativistic, ion cyclotron, non-uniformity, electrostatic, localized, analytic theory, absolute instability
相關次數： 點閱：139  下載：3 
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    • 此論文中, 我們考慮典型核融合的物理參數以研究不均勻 (與均勻) 磁化電漿中相對論離子迴旋不穩定性的特性。在均勻磁場下, 藉由迴旋動力學的方法, 我們先推導出了靜電波的色散方程並進一步地用解析與數值方式加以分析其中不穩定性的機制, 最後用流體與粒子混合模擬來檢驗。在這部份的研究中, 理論與模擬結果皆顯示出, 波與粒子簡諧迴旋頻率間的正向差值並不是驅動靜電相對論迴旋不穩定性的必要條件。而當磁場是不均勻的情況下, 我們藉由流體與粒子混合模擬, 觀察到即使當外加磁場強度的變化率大於alpha粒子的羅倫茲係數減一, 此不穩定性依然可以存活且能在外加磁場強度最小值附近激發起區域化波模。另外, 這不穩定性對快速離子的動態行為也有著相當重要的影響。為比較不均勻磁場的模擬結果, 我們考慮絕對不穩定性條件並對色散方程做微擾展開而發展出了一套系統化的解析理論。這理論預測出區域化波模將發生且侷限在磁場強度的最低點附近; 其中的靜電波模之空間結構, 成長率與頻率皆與模擬的觀察相當一致。

    In this dissertation, we would like to investigate the characteristics of relativistic ion cyclotron instability (RICI) in non-uniform (and uniform) magnetized plasmas with typical fusion parameters. When a uniform magnetic field is considered, an electro-static dispersion relation is derived from the gyro-kinetic method and further analyzed theoretically and numerically. A corresponding hybrid particle-in-cell simulation is performed to verify the theoretical analysis. In addition, through theory and simulation, we verify that a positive frequency difference between wave frequency and the harmonic cyclotron frequency should not be a necessary condition for driving electrostatic relativistic cyclotron instabilities. To study relativistic instability in a non-uniform magnetic field, we employ hybrid particle-in-cell simulations and observe that this kind of instability can survive even when the magnetic variation is much greater than the Lorentzs factor of α-particles minus one and that it is able to excite localized modes around the minimum of an external magnetic field. Also, such instability plays an important role with regard to affecting the dynamics of the fast ions. An analytic theory based on expansion around the condition of absolute instability has been developed and predicts that there will be localized eigenmodes forming and bounded around the magnetic minimum; the spatial structures, growth rates and frequencies of the electrostatic modes observed are in good agreement with the simulation results.

    摘要 i Abstract iii Acknowledgements vii 1 Introduction 1 1.1 Background and development of relativistic ion cyclotron instability (RICI) 2 1.2 Electron cyclotron interactions and two-gyro-streams . . . . . . . . . . 6 1.3 Dissertation overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2 RICI in a uniform magnetized plasma 15 2.1 Electrostatic dispersion relation derived by gyro-kinetic theory . . . . . 15 2.2 Analytic and numerical studies . . . . . . . . . . . . . . . . . . . . . . 28 2.3 Hybrid particle-in-cell simulations . . . . . . . . . . . . . . . . . . . . . 32 2.4 Frequency mismatch requirement . . . . . . . . . . . . . . . . . . . . . 36 3 RICI in a non-uniform magnetized plasma 39 3.1 Theory based on the expansion around the absolute instability condition 39 3.2 Localized eigenmodes driven by the relativistic α-particles . . . . . . . 42 3.3 Hybrid particle-in-cell simulations . . . . . . . . . . . . . . . . . . . . . 47 3.4 Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4 Conclusions and suggested future work 55 A Relativistic ion cyclotron code (RIC) 63 A.1 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 A.2 Data plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 A.3 Descriptions for program files . . . . . . . . . . . . . . . . . . . . . . . 72 A.4 Outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 B Description of the hybrid particle-in-cell code 75 B.1 Structure plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 B.2 Data plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 C The energy spread effect of the α-particles on the relativistic instabilities. 81

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