The Computation of the Magnetic Field of any Axisymmetric Current Distribution—with Magnetospheric Applications

Abstract

It is shown that the vector potential A of the magnetic field of any axisymmetric electric current distribution can be expressed in the form ∑ A n (r) P 1 n (cos θ). This series is used to compute the field of two model magnetospheric ring currents; the field of one of these was previously determined by double integrations by Akasofu, Cain & Chapman. The calculation of the functions A n (r) does not require double integrations. The two sets of results are in good agreement. The first term in the series for A gives the external magnetic moment of the ring current. The magnetic field energy is calculated for the field as a whole and for each term in the series for A. The field isointensity lines are drawn, and also the field lines for the ring current and for its field combined with that of the geomagnetic dipole. They illustrate the considerable distortion of the field in the magnetosphere during magnetic storms. The series for A may also be helpful in calculating the paths of cosmic rays in the deformed magnetosphere. The numerical convergence of the results is improved by the use of CesÀro summation.