The invention relates to an electron gun for generating a flat electron beam, comprising a cathode with an emission surface which is curved about a central axis and which is designed to emit electrons. The electron gun further comprises an accelerating device for accelerating the electrons in a radial direction towards a target region on the central axis. Furthermore, the emission surface has a width in the azimuth direction and a height oriented perpendicularly to the width, said width being at least ten times greater than the height.