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 the Birkeland currents, experience closure in the ionosphere, through the shell-current patterns, also known as the Pedersen and Cowley currents. Field aligned currents can be measured at an altitude of 800 km, farther, or closer, and can be reconstructed in the entire magnetosphere with 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 and numerical modelings of the shell currents are not easy tasks and require knowledge of the conductivity tensor in the ionosphere. We propose an alternative approach for the shell currents modeling. In this paper, we determine 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, for shell currents.