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The purpose of this paper is to clarify the flux conservation, magnetohydrodynamic and force-free approximations, for plasmas whose component species may be relativistically streaming, by paying particular attention to the conditions for their validity and to their interrelationships. All three approximations involve consideration of inertial effects, either in the generalized Ohm law or in the equation of motion of the plasma as a whole. All three imply that the electric field component parallel to the magnetic field is small. The significance of the approximations for pulsar magnetospheric theory is commented on.

Flux Conservation, Magnetohydrodynamic and Force-free Approximations for Relativistically Streaming Plasmas