Why doesn't the ring current injection rate saturate?

For low values of the solar wind electric field, the response of the polar cap potential is essentially linear, but at high values of VBs, the polar cap potential saturates and does not increase further with increasing VBs. On the other hand, the ring current injection rate does increase linearly with VBs and shows no evidence of saturating. If enhanced convection is the origin of the ring current, this poses a paradox. How can the polar cap potential, and thus convection, saturate when the ring current does not? We examine a possible explanation based on the reexamination of the Burton equation by Vasyliunas (2006). We show that this explanation is not a viable solution to the paradox since it would require a changing polar cap flux, and we demonstrate that the polar cap flux saturates (at around 1 GWb) as the polar cap potential saturates. Instead, we argue that during storms a quasi-steady reconnection region forms in the tail near the Earth. This reconnection region moves closer to the Earth for higher values of solar wind Bs, although the polar cap potential, the dayside merging and nightside reconnection rates, and the amount of open flux do not change much as a function of Bs once the polar cap potential has become saturated. As the neutral line moves closer, the volume per unit magnetic flux in the closed field line region is less. Flux tubes leaving the reconnection region in general have lower PVγ as Bs increases, and lower PVy flux tubes can penetrate deeper into the inner magnetosphere, leading to a corresponding greater injection of particles into the inner magnetosphere. Thus a reconnection region that is closer to Earth is more effective in creating a strong ring current. This leads to a continued dependence of the ring current injection rate on VBs, although the polar cap potential has saturated.