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系統識別號 U0026-1007201516511700
論文名稱(中文) 在低維度幾何中藉由迴旋動力標記粒子模擬低頻電漿波
論文名稱(英文) Low frequency plasma wave simulation by gyrokinetic marker particles in low dimensional geometry
校院名稱 成功大學
系所名稱(中) 太空與電漿科學研究所
系所名稱(英) Institute of Space and Plasma Sciences
學年度 103
學期 2
出版年 104
研究生(中文) 陳智民
研究生(英文) Chih-Min Chen
學號 LA6024012
學位類別 碩士
語文別 英文
論文頁數 64頁
口試委員 指導教授-西村泰太郎
口試委員-西田靖
口試委員-河森榮一郎
中文關鍵字 δf方法  迴旋動力理論  飄移波  電磁效應 
英文關鍵字 δf-method  gyrokinetic theory  drift-wave  electromagnetics 
學科別分類
中文摘要 在托卡馬克裡,為了解決長波長磁流體力學的不穩定性,我們發展了電磁迴旋動力模擬模型。我們從基礎的粒子模擬開始建立程式碼。首先,我們用基本的粒子網格法模擬朗道阻尼。然後,我們利用δf方法進一步發展程式碼並模擬電漿回聲,藉由這個方法可以減少統計雜訊的產生。

建立模擬的基礎後我們加入靜電迴旋動力模型的概念。利用絕熱電子的想法我們模擬了飄移波的不穩定性,在此模擬下頻率與密度梯度的相依性符合理論的預測;並且藉由朗道阻尼,不穩定性趨於飽和。為了追求電磁狀況下的粒子模擬,我們需要動力電子。因此我們模擬飄移波在磁鏡力下的運動狀況,得出在飽和狀況下須有較大的電場振幅,並且在相空間看到粒子的δf部分從束縛到穿透的加速過程。

最後我們更進一步在(x,p,t)座標下使用電磁迴旋動力理論,利用這個模型我們模擬了阿爾芬波在靜電極限的狀況也就是β_e等於零,即為粒子空間波,相依於離子與電子間質量比。但在(x,p,t)中,我們在數值上會遇到小項被大項掩蓋的問題,因此我們導出新方法在(x,v,t)座標。此方法中我們運用了一個荷姆赫茲方程式來解來自法拉第定律對時間微分的磁向量勢.
英文摘要 New electrostatic and electromagnetic gyrokinetic particle-in-cell (PIC) simulation methods are developed for future application of kinetic electron dynamics and long-wave-length magnetohydrodynamic instability in a fully three dimensional tokamak geometry. The PIC code is developed step by step. First, Landau damping of Langmuir wave is confirmed in “full- f” PIC. Second, by introducing the δf-method, Eulerian valuables of Vlasov equation is changed to Lagragian variables in the weight equations plus the equation of motion, the characteristics. Third, as one of the applications, simulation of plasma echo of the Langmuir wave by the δf-PIC is demonstrated by imposing two temporal impulsive electric fields.

Forth, benchmark computation of 1-D electrostatic drift-wave instability is performed. Variation of real frequency (and growth rates) as a function of density gradient matches with the linear theory of the drift-wave dispersion relation. Nonlinear saturation of the drift-wave due to Landau damping by kinetic electrons is demonstrated. Fifth, mirror force is given to simulate trapped electrons and ions. Electrostatic potential also saturates but with larger amplitude. Finally, in the new formulation of electromagnetic gyrokinetics, time derivative of Ampere’s law is incorporated to obtain inductive component in gyrokinetic equation (∂A/∂t) which originates from Faraday’s Law.
論文目次 摘要 I
Abstract II
誌謝 IV
Contents V
List of Figures VII
Chapter 1 Introduction 1
Chapter 2 Particle-In-Cell simulation 5
2-1 Normalization of Model Equation 7
2-2 Loading of Initial Distribution 9
2-3 Interpolated Weighting 12
2-4 Solving Poisson Equation 12
2-5 Demonstration of Wave-Particle Interaction 14
2-6 Benchmark of Landau Damping of Langmuir Waves 15
Chapter 3 δf-Method 20
3-1 Charge Density And Current Density in δf-PIC 22
3-2 Temporal Plasma-Wave Echo by δf-PIC 23
Chapter 4 Basic Concepts of Gyrokinetic Theory 26
4-1 Equations to time advance in Gyrokinetics 27
4-2 Gyro-averaging of Vlasov Equation 29
Chapter 5 Electrostatic Gyrokinetic Simulation in One Dimensional Geometry 30
5-1 Gyro-averaging in 1-D Geometry 30
5-2 1-D Electrostatic Equation of Motion 31
5-3 Drift-Wave Simulation in 1-D Geometry 33
5-4 Guiding Center Motion in a 3-D Toroidal Geometry 40
5-5 Drift-Wave Propagation in Non-Uniform Magnetic Field 44
Chapter 6 Development of Electromagnetic Gyrokinetics 49
6-1 A Formulation for Electromagnetic Gyrokinetics in (R,p,t) Space 50
6-2 A Proposed New Formulation for Electromagnetic Gyrokinetics in (R,v,t)Space 56
Chapter 7 Summary And Future Work 58
Reference 61
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