MHD wave propagation in a relativistic and uniformly drifting plasma

In this work a set of relativistic MHD equations is used to describe waves in an ideal plasma drifting uniformly along the magnetic field with respect to a laboratory stationary coordinate system. The basic equations of interest are derived from the relativistic Vlasov equation in the Minkowski space. Then the corresponding dispersion relation is found. This dispersion relation gives several earlier results when it is analyzed and reduced to various limits. An important result is that an arbitrary value of a drift velocity introduces asymmetry in propagation when the wave normal is along the direction of the magnetic field, but when it is perpendicular to direction of the magnetic field, symmetry is not disturbed. Another important finding of this thesis is that in the special case when the drift velocity is absent and the wave is along the magnetic field, all the three modes are found to propagate with two of them being identical with the Alfv`en speed, while the third mode propagates with the sound speed. Moreover, in the absence of the magnetic field the drift velocity causes instability.