本論文之目的，為研究在相對論磁流體力學架構下波與震波的物理性質。在考慮電漿為均勻的情況下，我們推導出廣義的磁流體力學波色散關係，而此色散關係可以包含等溫／絕熱，壓力均向／壓力非均向，以及非相對論／超相對論等極限條件。我們發現，如同在非相對論磁流體力學之結果，壓力的非均向性可導致慢波的異常現象如相速逆轉以及密度與磁場關係的同相性，也會發生在相對論磁流體模型中。此外，我們也導出相對論磁流體理論中救火管及磁鏡不穩定的臨界條件。而在相對論磁流體震波的研究方面，我們推導出震波的跳躍條件，並得出六種震波型式的解，包含快速震波，慢速震波以及四種中速震波。 In this thesis the characteristics of hydromagnetic waves and shocks are studied within the framework of relativistic magnetohydrodynamics (RMHD) theory. The general dispersion relations are derived for linear MHD waves propagating in homogeneous ultrarelativistic plasmas with isotropic and gyrotropic pressures. The characteristics of fast, intermediate and slow waves are examined in detail and the formulations cover various limits such as isothermal/adiabatic, isotropic/anisotropic and nonrelativistic/ultrarelativistic cases. As in the nonrelativistic anisotropic MHD model, the phase speed inversion and the density-magnetic field anomaly for slow waves may occur in the relativistic MHD model. Both fire-hose and mirror instabilities may be generated in the gyrotropic plasma when the temperature anisotropy becomes sufficiently large and the instability criteria are derived. The relativistic MHD shocks are studied by solving the associated jump conditions and six types of relativistic MHD shocks including fast, slow and four intermediate shocks are identified.
