AbstractTheoretical studies indicate that electric potential saturation in a polar cap ionosphere is regulated by the limited reconnection rate at the magnetopause associated with field‐aligned currents (FACs), predicting the possible saturation of FACs under large interplanetary electric field (IEF). However, recent statistical studies have shown that observed FACs increase linearly with IEF. To reconcile this disparity, numerical experiments are conducted to explore the response of FACs under large IEF. Results show that FACs may exhibit either linear or saturated responses, depending on the Alfvén Mach number. The magnetospheric closure paths of region 1 currents differ significantly between the linear and saturated conditions. In the linear case, essential parts of the region 1 current extend toward dayside and connect to the magnetopause currents, whereas these parts of currents almost disappear in the saturation state. Saturation usually occurs under sub‐Alfvénic solar wind conditions, so the observed FACs generally grow linearly with IEF.