地磁脈動(geomagnetic pulsations)為地球磁場之持續突發的擾動現象，其發生與磁流體波於非均勻之太空電漿環境之傳播有著密不可分之關係。本論文應用理想磁流體(Ideal Magnetohydrodynamics; Ideal MHD)方程式探討磁流體波於非均勻電漿之傳播，並發展出一套有系統的模式計算方法分析所推導出之波動方程式。透過計算二階微分波動方程式之特徵值，以及繪製快波、中速波、慢波、以及尖端波等四個特徵速度隨空間的變化情形，可分析各種電流片結構中存在的穩定與不穩定非連續特徵波。本研究分別以壓力均向與非均向 Harris 型式的對稱與非對稱電流片結構進行模式計算與分析。其結果顯示，當電漿壓力具非均向性時，電流片中可存在不穩定的非連續特徵波及共振現象，其發展條件為磁鏡不穩定或救火管不穩定發生之臨界條件。在實際應用方面，本研究利用磁場最小差異量法(Minimum Variance Analysis; MVA)及DeHoffmann-Teller座標分析，分別針對THEMIS人造衛星穿越地球磁層頂電流片之觀測資料，將移除擾動後之背景結構進行計算。結果顯示，兩組磁層頂穿越資料在特定的傳播方向上，皆存在非連續磁流體特徵波。

The persistent burst of magnetic variation in Earth’s space environment as shown in the magnetic field observation is called geomagnetic pulsations. It is well known that geomagnetic pulsations are resulted from the magnetohydrodynamic (MHD) waves propagating in non-uniform space and magnetospheric plasma environment. This study develops a systematic calculation method by solving the eigenvalues of the second-order wave equations derived based on the ideal MHD equations and analyzing the spatial profiles of four MHD characteristic speeds (fast, intermediate, slow and cusp) to obtain the stable and unstable discrete eigenmodes in general planar current sheet structures. Model calculations and analyses for various types of isotropic and anisotropic, symmetric and asymmetric Harris-type current sheets are presented. The results show that in anisotropic plasmas the current sheet may support unstable discrete modes and resonances which occur at the mirror or fire-hose instability thresholds. We have also applied the model calculations to the Earth’s magnetopause current sheet by analyzing two crossing events observed by the THEMIS spacecraft along with the analyses of minimum variance analysis and DeHoffmann-Teller frame and obtained the corresponding discrete eigenmode structures.

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