A magnetospheric energy principle extended to include neutral atmosphere

Abstract

The problem of ideal magnetohydrodynamic stability of plasmas in a magnetosphere-atmosphere system, in which the unperturbed magnetic field is assumed to be perpendicular to the plasma-atmosphere interface (ionospheric surface), is investigated by means of an extended magnetospheric energy principle. The derivation of the principle and conditions under which it applies to a real terrestrial magnetosphere is given. In the principle, the atmosphere is considered to be a very heavy and compressible gas with finite pressure. A thin ionospheric layer is taken into account as boundary conditions, but energetics within it are neglected. The solid-earth surface is assumed to be a perfectly conducting wall for perturbations. For a perturbation that satisfies either rigid or horizontally free boundary conditions at the plasma-atmosphere interface, the self-adjointness of the force operator is satisfied and an extended magnetospheric energy principle can be developed on the basis of the extended energy principle for fusion plasmas. These two boundary conditions are shown to be realized in the magnetosphere when the ionospheric conductivity is either very large or very small. Whereas in fusion plasmas the perturbed magnetic energy in the vacuum makes a stabilizing contribution to the potential energy, in the magnetosphere the perturbed magnetic energy in the atmosphere makes no such stabilizing contribution. This is due to the difference of the assumed field configurations of the magnetospheric and fusion plasmas. The ionospheric surface makes a destabilizing negative contribution to the potential energy owing to a horizontal plasma displacement on the spherical ionospheric surface. The method is applied to magnetospheric ballooning and interchange instabilities. The existence of a new type of magnetospheric interchange instability is shown and its structure in the magnetosphere-atmosphere system is clarified. Possible consequences of the instabilities and their relevance to magnetospheric physics are discussed.