Modeling Birkeland currents in the expanding/contracting polar cap paradigm

We present a simple mathematical model of the region 1 and 2 Birkeland current system intensities for differing dayside and nightside magnetic reconnection rates, consistent with the expanding/contracting polar cap paradigm of solar wind-magnetosphere-ionosphere coupling. The current intensities are shown to be dependent on the cross-polar cap potential, which is the average of the dayside and nightside reconnection rates. Current intensities are expected to maximize on the dayside or the nightside when magnetopause or magnetotail reconnection dominates. Current intensities are also dependent on the ionospheric conductance, the width of the merging gaps, the width of the ionospheric convection return flow region, and on the size of the polar cap.