The investigation of electromagnetic interactions between regions surrounding the Earth. 1. Initial equations, the boundary conditions, the distribution of external currents and the methods of numerical solution
A numerical model is presented suitable for the study of the penetration of the global atmospheric electric field from the troposphere into the ionosphere. Equations are obtained in the plane-stratified approximation which permit us to use the same mathematical techniques in the atmosphere, the ionosphere and the magnetospheres. We take into account the anisotropy in the general case, the variation of conductivity of the medium and the temporal changes of the fields. The relationship between the electric and magnetic modes is taken into account by means of Ohm's law in anisotropic media, using the electrical conductivity sensor. The feasibility of the plane-stratified approximation is analysed by means of the analogous equations taking into account the spherical symmetry of the global electric field. Models of the external current distribution are discussed. The boundary conditions take into account the field attenuation into the conducting Earth and the field propagation into the magnetosphere as Alfven and magnetoacoustic waves. The methods of numerical solution of the equations obtained and their accuracy are described in brief.
