Why is it necessary to dissipate the heat of the anode in an X-ray tube? I understand that in an X-ray tube electrons collide with the anode which then deflects them out of the window producing X-rays and that this anode is rotated to dissipate heat. But why is it necessary? I imagine the cathode filament will get far hotter but this is not rotated. Is the dissipation of heat connected to the release of X-rays?
 A: The electron beam power is (voltage) x (current), only a small fraction of which actually generates X-rays. Most of those watts end up dissipated as heat when they collide with the anode. This heating is manageable in small X-ray machines running at low power for short periods of time but for big industrial X-ray tubes (~1.5 million volts) the anode is hollow and is cooled by running water through it.
A: There are multiple types of X-ray tubes used, e.g., in crystallography, and the one using a rotating anode is one (but not the only) type being used.  The advantage compared to a "conventional" X-ray tube in a diffractometer is the higher brightness of this source of radiation, i.e. number of photons suitable for the diffraction experiment per unit of time. The temperature on the focus of the anode of the rotating anode reaches about ${2500\,^\circ{}\mathrm{C}}$.  The higher brightness is useful because it allows to shorten the time to collect the data; more importantly however to record in sensible time useful data for the protein crystals which are both i) much smaller than the "small molecule crystals" routinely characterized by in-house single crystal diffractometers and ii) for most of their atoms consist of weakly diffracting matter only.
The cooling (both for the conventional, as for the rotating anode) however is only an attempt to extend the time the anode may be used. This is not made to alter e.g., the wavelength of the X-ray radiation harvested.
