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研究生: 鄭印呈
Jheng, Yin-Cheng
論文名稱: 應用時域有限差分法模擬微波電漿診測
FDTD Simulation of Microwave Plasma Diagnostics
指導教授: 陳秋榮
Chen, Chio-Zong
學位類別: 碩士
Master
系所名稱: 理學院 - 太空天文與電漿科學研究所
Institute of Space, Astrophysical and Plasma Sciences(ISAPS)
論文出版年: 2011
畢業學年度: 99
語文別: 英文
論文頁數: 87
中文關鍵詞: 時域有限差分法電漿微波診測
外文關鍵詞: FDTD, Plasma, Microwave diagnostics
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  • 微波診測是一種常見的非侵入式電漿診測工具。在本篇論文中,我們運用時域有限差分法模擬電磁波在磁化電漿中傳播,電磁波於磁化電漿內部會受到電漿密度與磁場的不均勻而產生色散,並有不同的傳播特性。本模型是由Maxwell equations,再加上電流密度在cold magnetized plasma中響應之方程式所架構的.此模型可以模擬微波在Ordinary mode和Extraordinary mode 中傳播及反射。在干涉計模型中,我們運用微波干涉計原理測量相位變化,進而得到電漿平均密度。在反射計模型中,我們採用超短脈衝行進於Ordinary mode和Extraordinary mode並完成重建電漿密度分佈的問題。重建電漿密度需要知道截止頻率所對應的反射時間,我們採用了三種方法對反射信號進行時頻分析,並比較了其結果。

    Microwave diagnostics are relatively common nonintrusive plasma diagnostic tools. In this thesis, we present simulation studies of microwave diagnostics of plasmas by solving the full wave equations by using a finite-difference time-domain method. The simulation model is based on the Maxwell’s equations and the fluid equations of cold magnetized plasmas, which describes the ordinary and extraordinary modes and their propagation in plasmas. We present results of simulations on (1) the interfelometry measurement of the line-integrated plasma density by measuring the phase shift of monochromatic incident waves; (2) reflectometry measurement of plasma density profiles by using of ultra-short pulse probing waves based on O-mode and X-mode propagation. In the reflectometry measurement, we apply three different methods to process the spectral analysis of the phase delay of the reflected signals. The simulation results demonstrate that the determination of plasma density from ultra-short pulse reflectometry is relatively robust.

    Content 致謝 2 摘要 3 Abstract 4 CHAPTER 1 Introduction 7 1.1 What is plasma 7 1.2 Nuclear fusion 7 1.3 Plasma diagnosis 10 1.4 Thesis organization 11 CHAPTER 2 Microwave diagnostics 12 2.1 High-frequency electromagnetic waves in cold plasmas 13 2.1.1 Governing equations 13 2.1.2 Cold plasma dielectric tensor 14 2.1.3 Cold plasma dispersion relation 16 2.2 Wentzel-Kramers-Brillouin approximation 20 2.3 Interferometry theory 22 2.4 Reflectometry theory 24 2.4.1 Reflectometry theoretical basis 25 2.4.2 Density profile reconstruction method 26 CHAPTER 3 The finite-difference time-domain method 31 3.1 Numerical formulation 31 3.2 Numerical stability condition 37 3.3 Wave excitation source 39 3.3.1 Sinusoidal waveform 39 3.3.2 Gaussian Waveform 40 3.3.3 Normalized Derivative of a Gaussian waveform 41 3.3.4 Cosine-modulated Gaussian waveform 42 3.4 Mur’s Absorbing Boundary Condition 42 CHAPTER 4 Numerical formulation of EM wave propagation in magnetized plasmas 45 4.1 Numerical formulation using FDTD scheme 45 4.2 Numerical scheme of current density computation 48 4.3 Numerical accuracy 50 CHAPTER 5 Full-wave simulation 54 5.1 1D full-wave simulation of interferometry 54 5.1.1 Simulation model 54 5.1.2 Simulation results 56 5.1.3 Comparison of full wave simulation with W.K.B method 59 5.2 1D full-wave simulation of ultra-short pulse reflectometry 61 5.2.1 Code description and simulation results 61 5.2.2 Spectral analysis of reflected signal 64 5.2.3 Density profile reconstruction using the O-mode 71 5.2.4 Fluctuation measurement 73 5.2.5 Density profile reconstruction using the X-mode 75 Chapter 6 Summary and conclusion 80 References 82 Appendix A : FDTD updating equations 83 Appendix B: Numerical dispersion relation equation 86

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