An x-ray radiator has a vacuum housing that can rotate around an axis, a cathode that thermionically emits electrons upon irradiation thereof by a laser beam, an anode that emits x-rays upon being struck by the electrons, an insulator that is part of the vacuum housing and that separates the cathode from the anode, electrodes or terminals to apply a high voltage between the anode and the cathode to accelerate the emitted electrons toward the anode to form an electron beam, a drive arrangement for rotation of the vacuum housing around its axis, an arrangement for cooling components of the x-ray radiator, and an arrangement that directs and focuses the laser beam from a stationary source that is arranged outside of the vacuum housing onto a spatially stationary laser focal spot on the cathode.