Theory of Cowling channel formation by reflection of shear Alfven waves from the auroral ionosphere

We present the first complete formulation of the coupling between the ionospheric horizontal currents (including Hall currents) and the field-aligned currents (FAC) via shear Alfven waves, which can describe the formation of a Cowling channel without any a priori parameterization of the secondary (Hall polarization) electric field strength. Our theory reorganizes the Cowling channel by primary and secondary fields. Until now there are no theoretical frameworks, which can derive these separated components from observed or given total conductance, electric field, and FAC distributions alone. But when a given incident where Alfven wave is considered as the driver, the reflected wave can be uniquely decomposed into the primary and secondary components. We show that the reflected wave can, depending on actual conditions, indeed carry FAC that connect to divergent Hall currents. With this new method, we can identify how large the secondary electric field becomes, how efficiently the divergent Hall current is closed within the ionosphere, and how much of the Hall current continues out to the magnetosphere as FAC. In typical ionospheric situations, only a small fraction of FAC is connected to Hall currents at conductance gradients, i.e., the secondary field is relatively strong. But when conductances are relatively low compared with Alfven conductance and/or horizontal scales smaller than similar to 10 km, the Hall FAC may become significant.