基于FDTD的一維時變等離子體中電磁波傳播特性研究

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摘 要
等離子體是自然界中廣泛存在的一種特殊的復雜色散介質，具有眾多獨特的性質和重要的利用價值。關于非時變等離子體的研究已經(jīng)取得了大量的研究成果，且廣泛應用于多個領域。本文基于FDTD方法研究了一維磁化等離子體和非磁化等離子體的電磁波傳播特性，得到相關結論。
研究了適用于計算一維磁化時變等離子體和一維非磁化時變等離子體問題的時域有限差分（FDTD）方法，通過選取一維諧振腔模型和參數(shù)，將時變等離子體中瞬變的情形理論分析結果與FDTD數(shù)值仿真結果相比較，驗證了所用FDTD方法的正確性。研究了推導出截斷瞬變等離子體的修正的近似完全匹配層（M-NPML）吸收邊界的時域有限差分方法（FDTD）迭代式。通過選取半空間等離子體模型和參數(shù)，將該FDTD數(shù)值解與解析解進行對比，驗證了所用FDTD方法的正確性。在此基礎上,在頻域中分析了一維瞬變等離子體板的電磁波散射特性，發(fā)現(xiàn)了瞬變等離子體板反射波的頻率漂移規(guī)律。

關鍵詞：時域有限差分方法；瞬變等離子體；頻率漂移；近似完全匹配層


Research of transmission characteristics for 1 D
time-varying plasma by FDTD method
ABSTRACT
Plasma is a kind of special complex dispersion medium and widely existed in nature. It has many unique features and very important use value. The research of time-invariant plasma has a lot of achievements and widely used in various fields. In this paper, characteristics of electromagnetic wave in the magnetized time-varying plasma and un-magnetized time-varying plasma are researched based on finite difference time domain (FDTD) method, some important conclusions are obtained.
The one-dimensional finite difference time domain method for magnetized time-varying plasma and un-magnetized time-varying plasma are researched. This FDTD algorithm has been verified by using one dimensional cavity model and parameters through comparing the FDTD numerical solution and the time-varying of transient plasma theory analysis results. The Modified Nearly Perfectly Matched Layer (M-NPML) method to truncate the transient plasma is presented by using Finite Difference Time Domain (FDTD) method. This FDTD algorithm has been verified by using a half-space plasma model through comparing the FDTD numerical solution and theoretical solution. On the basis of the work we have done, the scattering characteristics of electromagnetic wave by a sudden-created plasma slab in the frequency domain are analyzed. The frequency drift phenomena for the reflected wave of a sudden-created plasma slab and other useful conclusions are obtained.

Keyword: finite difference time domain method;transient plasma ;frequency drift;
approximate perfectly matched layer;

目 錄
第一章 緒論 1
1.1選題背景及研究意義 1
1.2國內外研究概況及其進展 4
1.3本文的主要工作及結構安排 6
1.4 本章小結 6
第二章 一維時變等離子體的FDTD算法 7
2.1一維時變磁化等離子體的FDTD算法 7
2.2一維時變非磁化等離子體的FDTD算法 13
第三章 一維瞬變等離子體的算法驗證與數(shù)值分析 16
3.1 一維瞬變等離子體電磁特性解析解的推導 16
3.2 FDTD算法驗證與數(shù)值分析 28
3.3 本章小結 33
第四章 一維瞬變等離子體的電磁波散射特性研究 34
4.1截斷瞬變等離子體修正的一維M-NPML吸收邊界條件 34
4.2吸收邊界條件算法正確性的驗證 35
4.3基于FDTD的一維瞬變等離子體電磁散射特性研究 36
4.3.1 瞬變非磁化無損耗等離子體板情形下的頻譜分析 36
4.3.2 瞬變磁化無損耗等離子體板情形下的頻譜分析 37
4.4本章小結 40
第五章 總結和展望 41
附錄A 42
主要參考文獻 45
致謝 50