A device for generating X-rays or electron beams is described. The cathode of the device is mounted on a ceramic insulator which becomes hot during operation, and the ceramic insulator is cooled by means of a fluid coolant flowing around the outside of the insulator at the remote end of the insulator, away from the cathode. The coolant conduit can be formed by flange rings, soldered directly on to the surface of the insulator, and the conduit may be shaped such that the coolant is in direct contact with the insulator. A method for manufacturing the device is also described.