磁鏡不穩定性發生於電漿溫度非均向之環境中，其發生條件為：T_perp/T_para>1 且 β_perp/β_para>(1+β_perp)/β_para；此關係式中的T_perp與T_para分別表示垂直與平行於磁場的溫度，而電漿的beta為：β_perp,para=p_perp,para/(B^2/2μ_0)。磁鏡不穩定所產生的磁鏡波的現象已廣泛地被觀測到，如在太陽風、地球磁鞘、行星磁鞘與日鞘等區域中均有觀測的案例。磁鏡波的結構具有磁場的增加或減少，伴隨著電漿密度的減少或增加的特性；即兩者間具有反相位的關係。同樣的反相位關係亦可在溫度與磁場之間觀察到。研究顯示，線性的混合kinetic-MHD理論可以定量地解釋發生於地球磁鞘的磁鏡波之相位特性與熱力狀態。本論文研究之主要目的為，利用微觀動力數值模式驗證線性理論及觀測結果，並探討磁鏡不穩定性之非線性的演化過程。我們選擇了20組的β_perp與β_para參數值，作為混合粒子數值模式的初始條件，探討磁鏡不穩定性隨時間的演化，並比較粒子模式結果、線性Vlasov理論、以及6個磁鏡波的觀測案例，包含其成長率、相位關係、熱力狀態等。研究結果顯示，三者之間具有高度的一致性。我們比較雙重多向性能量定律與粒子模擬結果，得出γ_perp = 0.64±0.21與γ_para = 1.07±0.12 ，與線性理論預測及觀測所得到的 γ_perp<1與 γ_para≳1結果吻合。其中，非線性模擬結果可重建觀測個案，包括磁場等物理擾動量以及磁鏡波的波長等。統計的分析結果顯示，在模擬達飽和階段時，溫度非均向β_perp/β_para與β_para會呈現反相關，且滿足新的磁鏡不穩定性條件γ_para*β_para=β_perp^2/(2+γ_perp*β_perp)，其中γ_perp≈0.8，γ_para≈1.3。

Mirror instability may occur in anisotropic plasmas for the condition of T_perp/T_para>1 and β_perp/β_para>(1+β_perp)/β_para, where β_perp,para=p_perp,para/(B^2/2μ_0), T_perp and T_para are the two temperatures, perpendicular and along the magneic field, respectively. The mirror waves associated with the mirror instability have been widely observed in the solar wind, terrestrial magnetosheath, planetary magnetosheaths and heliosheath, etc. The important characteristic of the observed mirror wave structures is that the magneitic field is increased or decreased with the decreasing or increasing plasma density, or, there exists an anticorelation between these two quantities. In addition, the anticorrelation between the perpendicular temperature and magnetic field has also been observed. The present study first shows that the linear mixed kinetic-MHD theory can quantitatively describe the phase relations and thermodynamic conditions of the observed mirror waves in the terrestrial magnetosheath. Furthermore, it is shown that the theoretical predictions and mirror observations may be verified by the kinetic simulations of the time evolutions of proton mirror instability. We examine the proton mirror instability based on the hybrid particle simulations for twenty sets of initial β_perp and β_para values and the quantitative comparisons are made between the kinetic simulations, linear theory and mirror observations in terms of the growth rates, phase relations and thermodynamic conditions, etc. The results show that the simulations and observations are in high agreements with the theoreitcal predictions. In particular, the polyropic exponents in the saturated states of the kinetic simulations are in the ranges of γ_perp = 0.64±0.21 and γ_para = 1.07±0.12, which are consistent with theoretical predictions and mirror observations of γ_perp<1 and γ_para≳1. It is shown that the observed features, including various perturbations and wavelengths etc., may be reproduced by the nonlinear simulations. The analyses of statistical results indicate that the saturated temperature anisotropy β_perp/β_para and plasma β_para are anticorrelated and the relation may be fitted by the modified mirror instability threshold of γ_para*β_para=β_perp^2/(2+γ_perp*β_perp) with γ_perp≈0.8 and γ_para≈1.3.

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