Transition radiation as a source of quasi-monochromatic X-rays

The transition radiation (TR) from ultrarelativistic particles is considered. It is shown that performing collimation of the TR from the periodic N-foil stack (parameters of which are selected in a appropriate manner) one obtains the spectrum of the TR which has a form of a peak position of which ω1 depends on the plasma frequency and the thickness of the radiator foils. The height and width of the peak depend on the collimation angle ϑc. The height of the peak for given ϑc is proportional to N. Selecting parameters, one can have the source of X-rays of desired frequency with rather good monochromaticity. Relation with the undulator radiation is discussed.