Resonance periods for lines of force in the guided mode for a simple model of the magnetosphere

A magnetosphere model which is axially symmetric around the dipole is considered at frequencies at which gyroresonance can be ignored. The equations for the electromagnetic field are separated into two groups, one of which describes a field which is perfectly guided by the static dipole field. The solutions to the second-order differential equation for the radial electric component are studied for the case in which the density is inversely proportional to the cube of the altitude from the center. Resonances are calculated for the closed magnetosphere above a perfectly conducting earth.