Classification of extended MHD models for special relativistic plasmas using scale analysis

Relativistic magnetohydrodynamics (RMHD) has been widely used to analyze and simulate various cosmic phenomena. MHD conventionally represents a model that neglects certain terms of the two-fluid equations, such as the electron-inertia and Hall effects. On the other hand, when dealing with non-relativistic plasmas, extended MHD (XMHD) has been derived from the two-fluid equations by enforcing the quasi-neutrality condition and retaining the electron-inertia and Hall effects. XMHD has wider applicability than MHD, since MHD becomes invalid for low-density, small-scale or collision-less situations.

The counterpart of relativistic extended MHD (RXMHD) has been proposed by Koide (2009), in which “proper charge neutrality” is imposed. However, the precise conditions, under which this approximation holds, remain unclear. To clarify them, we start with the special relativistic two-fluid equations assuming cold and non-dissipative plasma and approximate them by means of the scale analysis. We present a hierarchical map of various approximate models, ranging from the two-fluid equations to RMHD, which are classified in terms of representative dimensionless parameters. This map includes RXMHD as well as relativistic Hall MHD, and the applicable ranges of these models are elucidated.