Gedalin [Phys. Rev. E 47, 4354 (1993)] derived a dispersion relation for linear waves in relativistic anisotropic Magnetohydrodynamics (MHD). This dispersion relation is used to point out the regions where the relativistic anisotropic MHD leads to new results that cannot be obtained using usual collisional relativistic MHD. This is highlighted by plotting a Fresnal ray surface. Conditions for the onset of firehose and mirror instabilities are also indicated. Such a study can be applied to astrophysical features such as pulsar winds, propagation of cosmic rays, etc.

The plasma in several physical situations such as movement of electrons along the geomagnetic field lines in the magnetosphere, the movement of the ionosphere, propagation of cosmic rays, etc., can be appropriately simulated by a drifting relativistic model. Keeping this in view, a general dispersion relation for magnetohydrodynamic (MHD) waves has been derived in a laboratory stationary coordinate system with respect to which plasma is drifting with a velocity which need not be small compared with the speed of light. This dispersion relation gives several earlier well-known results for MHD waves supported by an ideal relativistic plasma. The characteristic equation for arbitrary direction of propagation with reference to the ambient magnetic field is quite unwieldy. So, the detailed discussion is confined to the special cases when the propagation vector is along or across the magnetic field. However, wherever feasible, approximate solutions for arbitrary direction of propagation have also been discussed.

An inviscid, unbounded, collisionless, gravitating, rotating and heat conducting anisotropic plasma medium which is drifting is considered. The medium is assumed to be embedded in a strong magnetic field. A general dispersion relation is derived using normal mode analysis and its various limiting cases are discussed, compared with similar earlier results for a non-drifting model, and some disagreements are indicated. The dispersion relation reveals the existence of five waves. These different wave modes are discussed in some particular cases analytically. It is found that in the case of parallel propagation all the five waves propagate. When the axis of rotation is across the magnetic field, the modified entropy wave and the modified anisotropic Alfven wave are independent of rotation, gravitation and heat flux. It is shown that the drift velocity has no effect on the stability of these waves but their phase velocities are found to be altered by the drift velocity; the forward propagating modes being increased and the backward modes decreased. The other three waves are affected by gravitation, rotation, drift and parallel component of the heat flux. It is further shown that only two waves propagate in the perpendicular direction. The propagating wave modes in this particular direction are not affected by the drift velocity since wave normal is transverse to the direction of flow.