During large geomagnetic storms the polar cap potential drop fluctuates, but its average value seldom reaches 150 kV and its peak value seldom reaches 200 kV. Since the quiet time potential drop is about 40 kV and since the interplanetary electric field (IEF) is greatly enhanced during storms, this relative constancy appears to be due to a saturation effect. This apparent saturation phenomenon has been previously noted but has not received much attention in the recent literature, in spite of its importance during magnetic storms and in spite of the fact that it seems not to be understood. The IEF and the polar cap potential drop appear to have a very linear relationship up to about 80 kV. At greater IEF the potential drop increases only slightly. We use the assimilative mapping of ionospheric electrodynamics procedure to illustrate this saturation on a case-by-case basis during a number of recent storms. We confirm using DE 2 data that the saturation of the potential drop is a real effect and is not an artifact of the measurement process. Observations of the plasmapause and the buildup of the ring current indicate a linear response to the IEF over a wide range of solar wind conditions. Thus the convection of the magnetospheric plasma and the injection of energy into the ring current seem not to be affected by this saturation. ¿ 2001 American Geophysical Union