Determination of vertical profiles of shell currents in the ionosphere

Abstract. In previous works, we found Euler potentials for the combined magnetic field of Earth's dipole, field-aligned currents, ring current, and the magnetopause surface currents (represented by Dungey's term) in the magnetosphere. Field-aligned currents, also known as Birkeland currents, experience closure in the ionosphere through the shell current patterns, also known as Pedersen and Cowley currents. Field-aligned currents can be measured at an altitude of around 800 km and can be reconstructed in the entire magnetosphere by means of tracing along the magnetic-field lines. The determination of shell currents is more difficult. They can only be measured in the ionosphere because they form a closure of field-aligned currents in the ionosphere. Analytical modeling and numerical modeling of the shell currents are not easy tasks and require knowledge of the conductivity tensor in the ionosphere. We propose an alternative approach for shell current modeling. In this paper, we determine the current density distribution in a finite-thickness ionosphere. Our system consists of the ionosphere, a region above it (outer region), and a region below it (inner region). The dipole field is present in the entire system. In addition, there is a field generated by the field-aligned currents in the outer region. We search for a continuation of these currents into the ionosphere, that is, for shell currents.