Magnetohydrodynamic waves and gravitational/centrifugal instability in rotating systems

Interchange motions of magnetic flux tubes are customarily regarded as one of the main contributors to radial plasma transport in planetary magnetospheres, particularly in those magnetospheres, like the Jovian and Saturnian ones, where the centrifugal force is known to play an important role. However, so far, interchange motions have been treated only under a variety of simplifying assumptions which are not always justified. In this paper, we present a rigorous treatment of the interchange instability within the broader context of magnetohydrodynamic waves. After reviewing the existing work on the magnetospheric interchange instability, we derive the full wave equation for magnetohydrodynamic perturbations in the presence of external forces, magnetic field curvature, and overall rotation, and we proceed to a detailed examination of their dispersion relation and stability condition in the one-dimensional case when the equilibrium parameters vary in a single direction normal to the magnetic field. We then focus on the so-called "quasi-interchange'' modes, which, by definition, represent all the modes driven by gravitational or magnetic buoyancy (or a combination of both), including, in particular, the interchange mode. We demonstrate that they leave the total pressure virtually unchanged, slightly perturb the plasma density and the magnetic field, and generally give rise to motions both perpendicular and parallel to the background field lines.