The invention relates to an X-ray source that is provided with a liquid metal target and an electron source (3) for the emission of an electron beam (4) through a window (23) of a duct section (51) wherethrough the liquid metal target flows in the operating condition. The X-ray source is notably characterized in that the duct section (51) is formed by a first duct segment (10, 20) that includes the window (23) and wherethrough the liquid metal target flows, and by a second duct segment (30, 40) wherethrough a cooling medium flows and which is connected to the first duct segment in such a manner that the area in which the electron beam acts on the first duct segment is cooled.