Model of a global electric circuit with conditions at magnetic conjugate points of the upper boundary of the atmosphere in the non-stationary case

A new analytical representation of the electric potential is obtained for the classical non-stationary model of the global electrical circuit of the atmosphere, occupying a spherical layer, the conductivity of which increases exponentially along the radius. The boundary conditions of the model take into account the relationship between the values of the electric potential and current at magnetically conjugate points of the upper boundary of the atmosphere. Using the obtained representation, the potential distribution for a current dipole in a spherical layer is analyzed. New asymptotic formulas for the electric potential of a current dipole at t→∞ at each point of the spherical layer are obtained. An analytical expression for the Green’s function of the corresponding initial-boundary value problem is found.