On an electromagnetic calculation of ionospheric conductance that seems to override the field line integrated conductivity

The ionospheric conductance is the major quantity that determines the interaction of the magnetosphere with the ionosphere, where the magnetosphere is the large region of space affected by Earth's geomagnetic field, and the ionosphere is its electrically conducting inner boundary, lying right on the edge of the atmosphere. Storms and substorms in space dissipate their energy through ionospheric currents, which heat the atmosphere and disrupt satellite orbits. The ionospheric conductance has, heretofore, been estimated using the staticized physics known as electrostatic theory, which finds that it can be computed by integrating the zero-frequency conductivity along the lines of Earth's geomagnetic field. In this work we test this supposition by deriving an electromagnetic solution for collisional plasma, and applying it to obtain a first-ever fully-electromagnetic calculation of ionospheric conductance. We compare the results to the field line integrated conductivity, and find significant differences on all scales investigated. We find short-wavelength, mode-mixing, and wave-admittance effects that were completely unexpected. When this theoretical result is matched with recent observational findings for the scale of the magnetosphere-ionosphere coupling-interaction, there results a situation where small- to intermediate-scale effects really may contribute to global modeling of the Sun-Earth system.