Alfvén waves and wings in Hall magnetohydrodynamics

Abstract

The problem of a conducting body moving in a magnetized plasma when the electronic pressure and Hall terms in Ohm's law cannot be neglected is analyzed in the magnetohydrodynamic approximation. Since Alfvén wings are closely related to Alfvén waves, the influence of these terms in the propagation of Alfvénic perturbations of large amplitude is studied. Instead of linearizing the magnetohydrodynamic equations and searching monochromatic waves, the conditions that the group velocity be parallel to the background magnetic induction field, in the reference system in which the plasma is locally at rest, that the perturbation be incompressible, that the perturbations in velocity and the magnetic induction field be related, and that a magnitude connected to the pressure remain constant are imposed. It is shown that large‐amplitude Alfvén waves can propagate in homogeneous plasmas if a “polarization condition” on the current density is fulfilled. The value of their group velocity is different from the value that it takes when simple Ohm's law is used. On the other hand, the methodology of stream functions is used for the analysis of Alfvén wings. Their existence, when the Hall term in Ohm's law is relevant, is proved, and the relations among the plasma pressure, induction magnetic field, velocity, and electric current density in the wing are found. The present results can be applied, as an approximation, to spacecraft or space tethers moving in a circular orbit if one can consider that the density and the magnetic induction field do not change as the source is orbiting and if the influence of partial ionization can be neglected.