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姓名 王伯洲(Bo-Jhou Wang)  查詢紙本館藏   畢業系所 太空科學研究所
論文名稱 救火管不穩定性之磁流體力學理論
(MHD Theory of Fire-hose Type Instabilities)
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摘要(中) 無碰撞電漿在磁場作用下,沿著磁場方向的壓力( )可以與垂直磁場方向的壓力( )不同。若 ,則磁流體波中的Alfvén波會形成所謂的救火管不穩定性。傳統的救火管不穩定是不可壓縮且最大的成長速率是發生在沿著磁場傳播的方向上。Hellinger and Matsumoto [2000]以動力理論發現一可壓縮的,且最大成長速率是發生在斜向磁場方向之新型態的救火管不穩定性。此新型不穩定性之線性最大成長速率在特定的參數範圍內會大於傳統救火管不穩定之最大成長速率。
近年來,有關救火管不穩定的研究大都是基於動力理論及粒子模擬方法。本論文則以壓力非均向之磁流體理論探討救火管不穩定性之線性特性與模擬其非線性演化之過程。文中採用雙重多向性能量定律以封閉整個磁流體方程組,並首次證明在磁流體理論中,慢速波也會在 的情況下發生不穩定,形成可壓縮的新型救火管不穩定性。尤其當能量方程中的雙重多向性指數 及 之值分別為1/2與2時,此可壓縮救火管不穩定性發生的臨界條件與動力理論所得到的結果一致。另外,在某些參數條件與範圍內,新型救火管不穩定性之最大成長速率會大於傳統的救火管不穩定性,且發生在斜向傳播的方向上。非線性模擬結果顯示,傳統的救火管不穩定性之演化遵循線性救火管不穩定之臨界條件,而新的可壓縮救火管不穩定性之演化則遵循線性磁鏡不穩定臨界條件。此結果使得可壓縮救火管不穩定性舒減壓力非均向程度之能力優於傳統的救火管不穩定性。非線性霍爾磁流體模擬則顯示離子慣性效應會使得救火管不穩定性具有傳播的特性,並且因為霍爾電流的影響造成非共平面方向之磁場分量有大幅度的擾動。
磁流體理論及模擬不但與動力理論及粒子模擬之研究結果有許多的相似處,且對於救火管不穩定之形成機制與非線性演化趨向提供清楚的物理解釋。
摘要(英) In a homogeneous anisotropic plasma the magnetohydrodynamic (MHD) shear Alfvén wave may become the fire-hose instability for . This instability is incompressible and has maximum growth rate occurring for parallel propagation. Recently, Hellinger and Matsumoto [2000] found a new fire-hose instability based on the kinetic theory that is compressible and has maximum growth rate at oblique propagation. Moreover, the new fire-hose instability may grow faster than the standard fire hose in certain parameter regime.
This thesis examines the fire-hose type ( ) instabilities based on the linear and nonlinear gyrotropic MHD theory. It is shown that the slow-mode wave may become the compressible fire-hose instability for . In particular, with suitable choice of polytropic exponents in the energy equations, and , the linear instability criteria become the same as those based on the Vlasov theory in the hydromagnetic limit. Moreover, the compressible fire-hose instability may grow faster than the classical fire-hose instability and has maximum growth rate at oblique propagation in certain parameter regime. The nonlinear simulation results show that the classical fire-hose instability evolves toward the linear fire-hose stability threshold while the nonlinear marginal stability associated with the new fire hose is well below the condition of but complies with the linear mirror instability threshold for compressible Alfvén waves. The results also show that the compressible fire hose is more efficient at reducing pressure anisotropy than the standard fire hose. The effects of Hall currents on both types of fire-hose instability are also examined based on the nonlinear Hall MHD simulations. It is shown that the ion inertial effect may lead to propagating fire-hose instability and also large noncoplanar magnetic field component.
The MHD and Hall MHD results presented in this study show great similarities with those obtained from the kinetic theory and hybrid particle simulation and provide much clear physics for the linear and nonlinear fire-hose instabilities.
關鍵字(中) ★ 救火管不穩定性
★ 磁流體模擬
關鍵字(英) ★ Fire-hose Instabilities
★ MHD simulations
論文目次 Chinese Abstract i
English Abstract iii
Acknowledgement v
Contents vii
List of Figures ix
1. Introduction 1
2. Linear Theory of Fire-Hose Type Instabilities 14
2.1 Linear Vlasov Theory 14
2.2 Linear MHD Theory 20
2.3 Discussion 28
3. Nonlinear Evolution of Fire-Hose Type Instabilities 37
3.1 Review of Particle Simulation Results 38
3.2 Nonlinear Evolution of MHD Fire-Hose Type Instabilities 40
3.2.1 Case A: 41
3.2.2 Case B: 45
3.3 Discussion 48
4. The Effects of Hall Currents on Nonlinear Fire-Hose
Instabilities 68
4.1 Simulation Results 71
4.1.1 Case A: 71
4.1.2 Case B: 72
4.2 Discussion 74
5. Conclusion and Summary 84
References 87
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Wang, B.-J., 壓力非均向電漿中霍爾電流對震波形成之效應, 碩士論文, 國立中央大學太空科學研究所, 2000.
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指導教授 郝玲妮(Lin-Ni Hau) 審核日期 2005-10-4
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