Relativistic fluid equations of motion, equilibrium and stability of beams

A general relativistic fluid formulation has been obtained by Siambis in Ref. [1]. The set of relativistic fluid equations includes a general equation of state, which is Eq. 17 of [1], after the heat flow tensor is set equal to zero. The use of these equations, however, is hampered by the presence of additional fluid variables resulting from relativistic corrections. The systematic expansion and associated nice variables introduced by Newcomb in [2], have been utilized in the formulation of [1] to yield a compact set of relativistic fluid equations which is the relativistic generalization of the well-known non-relativistic set of fluid equations. Specifically a general relativistic equation of state is obtained, which can be reduced to much simpler forms for specific cases. Equilibrium constraints are obtained and discussed. A stability analysis has been carried out for the two-stream instability including relativistic thermal corrections. A new mode of beam oscillation has been found, the thermal-relativistic mode. This mode is a fast-wave mode and it interacts resonantly, under certain conditions, with the well-known positive energy beam fast wave.