The Dependence of the Polar Cap Potential on the Alfvén Mach Number and Dynamic Pressure

The non-linearity of the Cross Polar Cap Potential (CPCP) with respect to the solar wind electric field is a well-known phenomenon referred to as Polar Cap saturation in the literature. The reasons leading to this saturation, however, are still under debate. We have studied the Polar Cap saturation using the Polar Cap (PCN) index as a proxy for CPCP during different solar wind conditions. We performed a large-scale statistical study based on the solar wind measurements and the geomagnetic PCN index from 1986 to 2015 . The results are compared with existing saturation models to understand the different underlying mechanisms and to highlight the problems with existing models. Consistent with previous results, we find that the PCN saturates during low (< 4) Alfvén Mach number (MA) solar wind conditions. However, it does not saturate in an asymptotic manner, it keeps slowly increasing after the saturation point. The non-linearity between the PCN index and solar wind electric field is still clearly present for high MA periods only. The solar wind dynamic pressure seems to also have an effect on the PCN. If the electric field is kept constant, a higher pressure leads to higher PCN. On average, the highest PCN values are achieved for a combination of high pressure and high electric field. Our findings suggest that the Hill-Siscoe model constitutes a baseline mechanism leading to non-linearity in all Mach number regimes, but that under low Mach number the geoefficiency is further (and significantly) reduced owing to the impact of increased magnetosheath flow deflection.