Compressible Hall magnetohydrodynamics in a strong magnetic field

Plasma dynamics becomes anisotropic in the presence of a strong background magnetic field, a feature that may be exploited to yield reduced fluid models. The reduced Hall-magnetohydrodynamics model derived in a recent work by Gomez et al. [Phys. Plasmas 15, 102303 (2008)], reflecting two-fluid effects such as the Hall current and the electron pressure, is extended to account for a crucial aspect of the role of the plasma compressibility, i.e., the compression of the guide field. This reduced model constitutes therefore a description of the two-fluid plasma dynamics in a strong external magnetic field, which can be used also for values of the plasma pressure parameter β of the order of unity or smaller.