Electric potential in the Earth's ionosphere: a numerical model

Modeling of the global distribution of the electric potential in the Earth's ionosphere is based on the solution of the 2-D equation of electric current continuity in the ionosphere-magnetosphere current circuit. Potential distribution is described by the boundary value problem for an elliptic system of partial differential equations on the spherical shell approximating the ionosphere which is divided into three subregions with nonlocal boundary conditions. Implementation of the boundary conditions, which reflect the continuity of the overall current circuit and the equation of potential at the boundaries of the polar caps, leads to the mutual dependence of the potential distribution inside the northern and southern caps and their influence on the potential distribution in the mid-latitude region. The problem is solved by an iterative method with a regularizing operator which is inverted using separation of variables and the fast Fourier transform with respect to the azimuthal variable and the sweep method with respect to the latitudinal one.