An x-ray tube has a cathode that generates free electrons; an anode on which the free and accelerated electrons strikes so that x-ray radiation is generated; a cooling channel with coolant flowing therethrough to cool the anode; a vacuum region between the cathode and the anode; and an exit window through which the x-ray radiation exits from the x-ray tube. The anode is fashioned as a transmission anode; with the transmission anode arranged between the vacuum region and the cooling channel, with the cooling channel arranged between the transmission anode and the exit window; so the useful x-ray radiation passes through the coolant.