Abstract: An electron gun having a field emission cathode is provided with a focusing magnetic lens. In the vicinity of the cathode, a pole piece is defined by two parts. The orifice of the part closer to the cathode is smaller than that positioned downstream. The air gap between the two parts is small and the filament of the cathode extends up to a distance of from about 1.5 to 3 mm from the median plane of the air gap. The excitation of the coil of the focusing magnetic lens is provided such that the image of the electronic source is substantially positioned at the level of the orifice of an intermediate electrode surrounding at least the magnetic lens.