Centrifugally driven instability of a rotationally dominated magnetodisc

Abstract

The dynamics of a rorationally dominated magnetodisc is considered on the basis of linearized MHD. The treatment is prompted by the concern that the dominant theoretical view on this subject is based on the reduced framework of interchange motion, in which changes in magnetic field are suppressed. A realistic perturbation of a magnetodisc generally does not satisfy this constraint, and the changing magnetic field is expected to stabilize any small‐amplitude perturbation. We reexamine the problem in an idealized slab magnetodisc geometry but with dynamical terms fully installed in the MHD equations. We find that the traditional interchange instability, essentially a centrifugal buoyancy regulated by the ionosphere, is not a proper solution for a thin magnetodisc. For short‐wavelength modes the actual situation of instability comes to resemble what is known in the literature as magnetic buoyancy, i.e., a centrifugally driven motion moderated by the strong local magnetic field. Physically, the instability results as the rotational effects couple the Alfvén and slow modes; density perturbations formed by the latter are in turn driven radially by centrifugal buoyancy. The instability is manifest even for a perfectly uniform density distribution and for the characteristic parameters near the Io torus, dominates over the contribution from a radial density gradient. The theory of centrifugally driven radial diffusion is considered with this instability as the mechanism of eddy formation. This consideration gives a mass transport rate of ∼ 103 kg/s and a density profile n ∼ L−4 near the Io torus, both in good agreement with observations. Further computational works need to be carried out to compare our model with more detailed in situ observations.