Fluid Description of Relativistic, Magnetized Plasma

Abstract

Many astrophysical plasmas and some laboratory plasmas are relativistic: either the thermal speed or the local flow speed (in a convenient frame) approaches the speed of light. Many such plasmas are also magnetized, in the sense that the thermal Larmor radius is smaller than gradient scale lengths. Relativistic MHD, conventionally used to describe such systems, requires the collision time to be shorter than any other timescale in the system. On this assumption, it uses the thermodynamic equilibrium form of the plasma pressure tensor, neglecting stress anisotropy as well as heat flow along the magnetic field. Beginning with exact moments of the kinetic equation, we derive a closed set of Lorentz-covariant fluid equations that allows for anisotropy and heat flow, as would pertain to a collisionless plasma, far from thermodynamic equilibrium. The heart of the derivation is the construction of the plasma stress tensor as the fully general solution to the energy-momentum conservation law in the case of dominant electromagnetic force.