We examine the mapping of magnetospheric and ionospheric electric fields in a kinetic model of magnetospheric-ionospheric electrodynamic coupling proposed for the aurora by Chiu and Cornwell (1980). A new feature is the generalization of the kinetic current potential relationship to the return current region (identified as a region where the parallel potential drop from magnetosphere to ionosphere is positive); such a return current always exists unless the ionosphere is electrically charged to grossly unphysical values. We are able for the first time to give a coherent phenomenological picture of both the low-energy return current and the high-energy precipitation of an inverted V. The mapping between magnetospheric and ionospheric electric fields is phrased in terms of a Green's function that acts as a filter, emphasizing magnetospheric latitudinal spatial scales of order (when mapped to the ionosphere) 50-150 km. We identify this length as roughly the overall size of the inverted V region. Roughly speaking, this scale length, when multiplied by the perpendicular electric field just above the ionosphere, gives the magnitude of the parallel potential drop between the ionosphere and equatorial magnetosphere. A precise relation between these quantities is given-for the first time-in the body of the paper; previous two-dimensional kinetic models have taken the parallel potential drop as an assumed input.