Applicability limit and time-marching algorithm of special relativistic MHD models extended by two-fluid effects

Relativistic magnetohydrodynamic (RMHD) equations are considered inappropriate for plasmas in low-density, small-scale, or collision-less situation. Koide (ApJ 2009) proposed a generalized RMHD model incorporating Hall and inertia effects to address wider situations. However, the applicable conditions of such the generalized RMHD models remain ambiguous, because all these models need to assume proper charge neutrality and its validity is not formulated clearly. By using the method of dominant balance, we have identified the applicable ranges of proper charge neutrality and generalized RMHD models in a parameter space of physical scales. As a result, relativistic Hall MHD (RHMHD) is found to be valid in wide ranges of density and magnetic field, while relativistic extended MHD (including inertia effect) has a limited applicability.

We have also considered numerical algorithm to solve the RHMHD equations. Unlike RMHD, RHMHD needs to solve the time evolution of the electric field additionally, but it allows us to explicitly derive all the primitive variables in terms of the time-evolving variables. Since the recovery of primitive variables is a computationally expensive part of RMHD simulation, RHMHD is potentially solved at a lower computation cost than RMHD.