Ionospheric elementary current systems in spherical coordinates and their application

Two sets of basis functions in spherical coordinates are presented, in terms of which any given ionospheric current system, consisting of horizontal sheet currents and their accompanying field-aligned currents, can be expanded, regardless of any considerations on the ionospheric conductances or the electric field. The single basis functions are called elementary current systems. One basis function set is curl-free and poloidal, and causes a toroidal magnetic field that is restricted to the area above the ionosphere. The other one is divergence-free and toroidal, and causes a poloidal magnetic field which is sorely responsible for the magnetic effect of ionospheric currents below the ionosphere. The field-aligned currents are assumed to flow radially. The expansion presented is used on a model of a Cowling channel to decompose its Hall and Pedersen currents into their total divergence-free and curl-free parts. This application example shows how the analysis technique based on the elementary current expansion resolves the physically relevant primary and secondary currents inside the Cowling channel.