The results from a numerical study on the formation and dynamics of the localized, diverging perpendicular electric fields found in the nightside auroral magnetosphere are presented. These fields are frequently observed inside the downward magnetic field-aligned current (FAC) channels where the electrons flow upward from the ionosphere. The present study focuses on one particular example of the dynamics of such structures that was recorded by the Cluster spacecrafts on 14 January 2001. Simulations show that the localized, divergent electric fields observed by Cluster can be provided by the interactions between downward FACs and the ionosphere. Conditions promoting the formation of these fields include low ionospheric conductivities and solitary downward current channels. Numerical simulations are used to explain the dynamics of the currents and electric fields observed by the Cluster satellites during this event and also show that such electric fields are not normally detected in the upward current channels.