Normal modes in magnetized two-fluid spin quantum plasmas

Abstract

We extend the classical two-fluid magnetohydrodynamic (MHD) formalism to include quantum effects such as electron Fermi pressure, Bohm pressure, and spin couplings. At scales smaller than the electron skin-depth, the Hall effect and electron inertia must be taken into account, and can overlap with the quantum effects. We write down the full set of two-fluid quantumMHD(QMHD)and analyse the relative importance ofthese effects in the high-density environments of neutron star atmospheres and white dwarf interiors, finding that for a broad range of parameters all these effects are operative. Of all spin interactions we analyse only the spin-magnetic coupling, as it is linear in h(stroke) and consequently it is the strongest spin effect. We re-obtain the classical two-fluidMHD dispersion relations corresponding to the magnetosonic and Alfvén modes,modified by quantum effects. In the zero-spin case, for propagation parallel to the magnetic field, we find that the frequency of the fast mode is due to quantum effects modified by electron inertia, while the frequency of the Alfvén-slow sector has no quantum corrections. For perpendicular propagation, the fast-mode frequency is the same as for the parallel propagation plus a correction due only to classical two-fluid effects. When spin is considered, a whistler mode appears, which is due to two-fluid effects plus spin-magnetic interaction. There are no modifications due to spin for parallel propagation of magnetosonic and Alfvén waves, while for perpendicular propagation a dispersive term due to spin arises in the two-fluid expression for the fast magnetosonic mode.