Electron gun with reduced heating of the grid

An electron gun comprising a cathode made of an emissive material with an active face emitting electrons through a control grid placed before the active face but having no contact with it and carried to a potential different from that of the cathode, the cathode and the control grid contributing to the creation of an electrical field, wherein the active face comprises emissive zones and non-emissive zones, the non-emissive zones being formed by grooves hollowed out of the emissive material, the electrical field having an intensity that is substantially zero at the bottom of the grooves, and wherein the control grid has solid parts that coincide with a projection of each of corresponding ones of said grooves in the direction of said cathode and said solid parts directly face the corresponding grooves.