Applicability criteria of proper charge neutrality and special relativistic MHD models extended by two-fluid effects

The applicability of relativistic magnetohydrodynamics (RMHD) and its generalization to two-fluid models (including the Hall and inertial effects) is systematically investigated by using the method of dominant balance in the two-fluid equations. Although proper charge neutrality or quasi-neutrality is the key assumption for all MHD models, this condition is difficult to be met when both relativistic and inertial effects are taken into account. The range of application for each MHD model is illustrated in the space of dimensionless scale parameters. Moreover, the number of field variables of relativistic Hall MHD (RHMHD) is shown to be greater than that of RMHD and Hall MHD. Nevertheless, the RHMHD equations may be solved at a lower computational cost than RMHD in the limit of cold plasma, since root-finding algorithm, which is the most time-consuming part of the RMHD code, is no longer required to compute the primitive variables.