The bright night-time aurorae that are visible to the unaided eye are caused by electrons accelerated towards Earth by an upward-pointing electric field. On adjacent geomagnetic field lines the reverse process occurs: a downward-pointing electric field accelerates electrons away from Earth. Such magnetic-field-aligned electric fields in the collisionless plasma above the auroral ionosphere have been predicted, but how they could be maintained is still a matter for debate. The spatial and temporal behaviour of the electric fields-a knowledge of which is crucial to an understanding of their nature-cannot be resolved uniquely by single satellite measurements. Here we report on the first observations by a formation of identically instrumented satellites crossing a beam of upward-accelerated electrons. The structure of the electric potential accelerating the beam grew in magnitude and width for about 200 s, accompanied by a widening of the downward-current sheet, with the total current remaining constant. The 200-s timescale suggests that the evacuation of the electrons from the ionosphere contributes to the formation of the downward-pointing magnetic-field-aligned electric fields. This evolution implies a growing load in the downward leg of the current circuit, which may affect the visible discrete aurorae.