The electron generator of an X-ray tube has a cathode (2) and an electrode system. The latter accelerates electrons coming from the cathode (2). An electron multiplier (4) is connected after the cathode (2). The electrons from the electron multiplier (4) are preferably focussed onto a target (8) by a focussing electrode system (10). The electron multiplier (4) may be a multichannel plate or a stack of plates with holes in. The electron multiplier (4) is preferably controllable and may have channels which are controlled by a control device. The cathode (2) may be a glow cathode or a photocathode. It may be controlled by a beam source (14) which may be a light source and may emit light pulses. A beam absorption layer may be connected in front of the electron multiplier.