Henry R. Radoski

Axisymmetric Plasmasphere Resonances: Toroidal Mode

The usual magnetohydromagnetic approach is used to investigate axisymmetric perturbations in a plasma permeated by a static dipole field. The model plasmasphere used has stationary, perfectly reflecting boundaries concentric with the dipole, and the plasma density is assumed to be spherically symmetric. The poloidal wave equation is reduced to a hierarchy of coupled differential equations in the radial variable. The toroidal wave equation is solved exactly using a density law which gives a good order of magnitude fit to recent whistler data. Because the extent of the plasma is finite, the eigenperiods are everywhere finite, including the poles. The stretched string model of vibrating lines of force is derived using the Wentzel‐Kramers‐Brillouin approximation, which fortuitously gives the exact periods for the density law utilized. Two unusual results are the prediction of shorter periods in the polar zones than at some high middle latitudes and discontinuous eigenperiods across the line of force which jus...

Poloidal Hydromagnetic Plasmaspheric Resonances

Under conditions of axisymmetry, the vector hydromagnetic wave equation of an infinitely conducting, stationary plasma permeated by a magnetic dipole field decouples into independent toroidal and poloidal modes. A general treatment is provided of the poloidal mode for a wide variety of radial and latitude‐dependent plasma densities. A harmonic decomposition of the poloidal wave equation is made, resulting in radial equations which are coupled except for the special case where the Alfven speed is latitude independent. Exact solutions are obtained in the latter case, and these are used to provide a general solution to the coupled equations for the general case. The method is applied to a model plasma confined between spherical surfaces concentric with the dipole. Resonance periods are calculated for the separable case with various positions of the outer plasma boundary. Periods are also obtained for a spherically symmetric density, and an evaluation of earlier approximate studies of this case is made.

Latitude‐Dependent Plasmasphere Oscillations

For a perfectly conducting plasma magnetized by a dipole field, the magnetohydrodynamic toroidal mode describes waves which propagate energy along the field lines. This characteristic causes the resonance oscillations of this mode to be strongly latitude‐dependent. The periods of these oscillations are determined for a generalized plasma density of the form ρ = ρ0(a/r) s D(φ) and compared with previously obtained results for the poloidal or isotropic mode. A discussion is provided of the validity of the model plasmasphere and the conditions for experimental observation.