Fluid model for relativistic, magnetized plasmas

Many astrophysical plasmas and some laboratory plasmas are relativistic: Either the thermal speed or the local bulk flow in some frame approaches the speed of light. Often, such plasmas are magnetized in the sense that the Larmor radius is smaller than any gradient scale length of interest. Conventionally, relativistic magnetohydrodynamics (MHD) is employed to treat relativistic, magnetized plasmas. However, MHD requires the collision time to be shorter than any other time scale in the system. Thus, MHD employs the thermodynamic equilibrium form of the stress tensor, neglecting pressure anisotropy and heat flow parallel to the magnetic field. Recent work has attempted to remedy these shortcomings. This paper re-examines the closure question and finds a more complete theory, which yields a more physical and self-consistent closure. Beginning with exact moments of the kinetic equation, we derive a closed set of Lorentz-covariant fluid equations for a magnetized plasma allowing for pressure and heat flow anisotropy. Basic predictions of the model, especially of the dispersion relation's dependence upon relativistic temperature, are examined.