We present Cluster measurements of large amplitude electric fields correlated with intense downward field-aligned currents, observed during a nightside crossing of the auroral zone. The data are reproduced by a simple model of magnetosphere-ionosphere coupling, which, under different conditions, can also produce a divergent electric field in the downward current region or a correlation between electric and perturbed magnetic fields. We conclude that a strong electric field associated with intense downward field-aligned current, such as this observation, is a signature of ionospheric plasma depletion caused by the downward current. The results are some of the strongest evidence to date that the ionosphere actively influences the structure and dynamics of black auroras.