“…where n represents number density, u velocity, m mass, e charge, P pressure tensor, G gravity, E electric field, B magnetic field, j can represent either ions or neutrals with E and B dropping from the momentum equation for the neutrals, and the righthand terms represent production, loss, and collisions as discussed in Gardner and Schunk (2005). Empirical model inputs for the convection electric fields (Weimer, 2001) and electron precipitation (Hardy et al, 1985) are used in order to allow for ion convection in the polar cap and ion heating in the auroral oval, respectively.…”