Computation of magnetic fields within source regions of ionospheric and magnetospheric currents

A general method of computing the magnetic effect caused by a predetermined three-dimensional external current density is presented. It takes advantage of the representation of solenoidal vector fields in terms of toroidal and poloidal modes expressed by two independent series of spherical harmonics. In order to rest the method, it is applied to two ionospheric-magnetospheric model current densities. The first example assumes a special large-scale current system which has an analytical solution for the magnetic field everywhere. In the second example, the results for a model current distribution that is of small-scale at high latitudes are compared with a direct integration using Biot-Savart's law. It is demonstrated that the method provides a fast and numerically stable determination of the magnetic field both outside and inside the current density.