Abstract: An electron gun includes a preferably non-metallic apertured grid with a flat upstream-facing surface closely spaced from and parallel to a flat emitting surface of a cathode. The grid aperture diverges in a downstream direction and has its peripheral wall contoured to shape the transverse cross-section of an emitted electron beam at a predetermined downstream location, preferably at the beam crossover. The peripheral wall of the grid aperture is devoid of sharp transitions, has a circular cross section to produce a circular beam crossover of minimum diameter, and has a convex segment extending from the upstream end of the aperture and joining a concave segment extending to the downstream end of the aperture. The convex first segment has a smaller radius of curvature than the second concave segment and has its center of curvature disposed substantially at the upstream facing surface.