We report the results of the first fully three-dimensional numerical simulation of a positive streamer in air in a 5 cm gap between a curved anode and a plane cathode. The formation of a negative radial field ahead of the streamer is found. This field leads to the formation of a current-free region in the streamer channel. The origin of the effect is discussed and the characteristic radius of this region is obtained. (C) 1998 Elsevier Science B.V.