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.

Akhiezer, A. I.; I. A. Akhiezer, R. V. Polovin, A. G. Sitenko, K. N. Stepanov, Plasma Electrodynamics, Pergamon Press, Oxford, 1975.
Appl, S. and M. Camenzind, Shock conditions for relativistic MHD jets, Astron. Astrophys. J., 206, 258, 1988.
Asseo, E. and D. Beaufils, Role of the pressure anisotropy in the relativistic pulsar wing, Astrophys. Space Sci., 89, 133, 1983.
Baker, D. N., J. E. Borovsky, B. Gregory and J. A. Eilek, The collective emission of electromagnetic waves from astrophysical jets - Luminosity gaps, BL Lacertae objects, and efficient energy transport, Astrophys. J., 326, 110, 1988.
Berdichevsky, Daniel B.; Szabo, Adam; Lepping, Ronald P.; Viñas, Adolfo F. and Mariani, F., Interplanetary fast shocks and associated drivers observed through the 23rd solar minimum by Wind over its first 2.5 years, J. Geophys. Res., 105, A12, 27289, 2000.
Beskin, V. S., A. V. Gurevich and Ya. N. Istomin, Physics of the Pulsar Magnetosphere, Cambridge, New York, 1993.
Ballard, K. R. and A. F. Heavens, First-order Fermi acceleration at oblique relativistic magnetohydrodynamic shocks, Mon. Not. R. Astr. Soc., 251,438, 1991.
Blandford, R. D. and M. J. Rees, A ''twin-exhaust'' model for double radio sources, Mon. Not. R. Astr. Soc., 169, 395, 1974.
Bolton et al., Ultra-relativistic electrons in Jupiter''s radiation belts, Nature, 415, 987, 2002.
Chatterjee, S. and J. M. Cordes, Bow shocks from neutron stars: scaling laws and hubble space telescope observations of the guitar nebula, Astrophys. J., 575, 2002.
Chao, J. K., Intermediate shocks: observations, Adv. Space Res., 15, 521, 1995.
Chao, J. K., L. H. Lyu, B. H. Wu, A. J. Lazarus, T. S. Chang and R. P. Lepping, Observations of an intermediate shock in interplanetary space, J. Geophys. Res., 98, 17443, 1993.
Chew, G., M. Goldberger and F. Low, The Boltzmann equation and the one-fluid hydromagnetic equations in the absence of particle collisions, Proc. Roy. Soc. London, Ser. A 236, 112, 1956.
Chou, M. and L. N. Hau, Magnetohydrodynamic waves and instabilities in homogeneous gyrotropic ultrarelativistic plasma, Astrophys. J., 611, 1200, 2004.
Cissoko, M., Waves and discontinuities in relativistic anisotropic magnetohydrodynamics, Ann. Inst. Henri Poincaré XXII (1), 1, 1975.
Double, G. P., M. G. Baring, F. C. Jones and D. C. Ellison, Magnetohydrodynamic jump conditions for oblique relativistic shocks with gyrotropic pressure, Astrophys. J., 600, 485, 2004.
De Hoffmann, F. and E. Teller, Magneto-Hydrodynamic Shocks, Phys. Rev., 80, 692, 1950.
Gebretsadkan, W. B. and G. L. Kalra, Propagation of linear waves in relativistic anisotropic magnetohydrodynamics, Phys. Rev. E 66, 057401, 2002.
Gedalin, M., Relativistic hydrodynamics and thermodynamics of anisotropic plasmas, Phys. Fluids B, 3, 1871, 1991.
Gedalin, M., Linear waves in relativistic anisotropic magnetohydrodynamics, Phys. Rev. E, 47, 4354, 1993.
Gupta, N. D. S., Synchrotron motion with radiation damping, Phys. Lett A. 32, 103, 1970.
Hasegawa, A., Plasma Instabilities and Nonlinear Effects, Springer-Verlag, New York, 94, 1975.
Hau, L. N., Nonideal MHD effects in the magnetosheath, J. Geophys. Res., 101, 2655, 1996.
Hau, L. N. and C. A. Lin, Wave propagation in an inhomogeneous anisotropic plasma, Phys. Plasmas, 2, 294, 1995.
Hau, L. N. and B. U. Ö. Sonnerup, On structure of resistive MHD intermediate shocks, J. Geophys. Res., 94, 6539, 1989.
Hau, L. N. and B. U. Ö. Sonnerup, On slow mode waves in anisotropic plasmas, Geophys. Res. Lett. 20, 1763, 1993.
Hau, L. N., T. D. Phan, B. U. Ö. Sonnerup and G. Paschmann, Double-polytropic closure in the magnetosheath, Geophys. Res. Lett., 20, 2255, 1993.
Hau, L. N., A note on the energy laws in gyrotropic plasmas, Phys. Plasmas, 9, 2455, 2002.
Hazeltine, R. D. and S. M. Mahajan, Fluid description of relativistic magnetized plasma, Astrophys. J., 567, 1262, 2002.
Hellinger, P. and H. Matsumoto, New kinetic instability: Oblique Alfvén fire hose, J. Geophys. Res., 105, A5, 10519, 2000.
Holm, D. D. and B. A. Kupershmidt, Hamiltonian theory of relativistic magnetohydrodynamics with anisotropic pressure, Phys. Fluids, 29, 3889, 1986.
Jackson, J. D., Classical Electrodynamics, John Wiley & Sons, New York, 1998.
Kasper, J. C., A. J. Lazarus and S. P. Gary, Wind/SWE observations of firehose constraint on solar wind proton temperature anisotropy, Geophys. Res. Lett, 29, 20, 2002.
Kennel, C. F., R. D. Blandford and C. C. Wu, Structure and evolution of small-amplitude intermediate shock waves, Phys. Fluids., B2, 253, 1990.
Kennel, C. F. and F. V. Coroniti, Confinement of the Crab pulsar’s wind by its supernova remanant, Astrophys. J., 283, 694, 1984.
Kennel, C. F., R. D. Blandford and P. Coppi, MHD intermediate shock discontinuities. I - Rankine-Hugoniot conditions, J. Plasma Phys., 42, 299, 1989.
Komissarov, S. S., Numerical simulations of relativistic magnetized jets, Mon. Not. R. Astr. Soc., 308, 1069, 1999.
Landau, L. D. and E. M. Lifshitz, Fluid mechanics, Elsevier Butterworth-Heinemann, Oxford, 1956.
Lightman, A. P., W. H. Press, R. H. Price and S. A. Teukolsky, Problem Books in Relativity and Gravitation, Princeton University Press. Princeton, New Jersey, 1975.
Lichnerowicz, A., Relativistic Hydrodynamics and Manetohydrodynamics, Benjamin, New York, 1967.
Longair M. S., High Energy Astrophysics, Cambridge University Press, 1994.
Lyutikov, M., On the nature of eclipses in binary pulsar J0737-3039, Mon. Not. R. Astr. Soc., 353, 1095, 2004.
Majorana, A. and A. M. Anile, Magnetoacoustic shock waves in a relativistic gas, Phys. Fluids, 30, 3045, 1987.
Manchester, R. N., B. M. Gaensler, S. L. Staveley,M. J. Kesteven and A. K. Tzioumis, Imaging of the radio remnant of SN 1987A at 12 mm wavelength, Astrophys. J., 628, 131, 2005.
Norman, M. L., K. H. A. Winkler, L. Smarr, and M. D. Smith, Structure and dynamics of supersonic jets, Astron. Astrophys., 113, 285, 1982.
Parker, E. N., Dynamical Instability in an Anisotropic Ionized Gas of Low Density, Phys. Rev., 109, 1874, 1958.
Pelliazzoni, A., F. Mattana, S. Mereghetti, A. De Luca, P. Caraveo and M. Coni, Pulsar Bow-Shocks, Mem. S. A. It. Suppl., 5,195, 2004.
Piran, T., Gamma-ray bursts and the fireball model, Phys. Rep., 314, 575, 1999.
Post, R. F. and W. A. Perkins, Velocity-space plasma instabilities observed in a mirror machine, Phys. Rev. Lett. 6, 85, 1961.
Punsly, B., Black Hole Gravitohydromagnetics, Springer-Verlag, Berlin Heidelberg, 2001.
Rossi, B. and S. Olbert, Introduction to the Physics of Space, McGraw-Hill, New York, 1970.
Seon, J., L. A. Frank, W. R. Paterson, J. D. Scudder, F. V. Coroniti, S. Kokubun and T. Yamamoto, Observations of slow-mode shocks in Earth’s distant magnetotail with the Geotail spacecraft, J. Geophys. Res., 101, 27,383, 1996.
Synge, J. L., The Relativistic Gas, North-Holland Publishing Company, Amsterdam, 1957.
Taussig, R., Dynamics of Ionized Gas, Academic Press, New York, 1975.
Tsikarishvili, E. G., J. G. Lominadze and A. D. Rogava, General-relativistic hydrodynamics of a collisionless plasma in a strong magnetic field, Phys. Rev. A 46, 1078, 1992.
Tsikarishvili, E. G. and A. D. Rogava, Linear hydromagnetic waves in an ultrarelativistic, collisionless plasma with a pressure anisotropy, Phys. Rev. E 50, 3050, 1994.
Tsikarishvili, E. D., A. D. Rogava and D. G. Tsiklauri, Relativistic hot stellar wins with anisotropic pressure, Astrophys. J., 439, 822, 1995.
Wang, B. J. and L. N. Hau, MHD aspects of fire-hose type instabilities, J. Geophys. Res., 108, A12, 1463, 2003.
Webb, G. M., G. P. Zank and J. F. Mckenzie, Relativistic oblique Magnetohydrodynamic shocks, J. Plasma Phys., 37, 117, 1987.
Wu, C. C., On MHD intermediate shocks, Geophys. Res. Lett., 14, 668, 1987.
Zhang, B. and S. Kobayashi, Gamma-ray burst early afterglows: reverse shock emission from an argitrary magnetized ejecta, Astrophys. J., 628, 315, 2005.