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

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 $\omega_1$ depends on the plasma frequency and the thickness of the radiator foils. The height and width of the peak depend on the collimation angle $\vartheta_c$. The height of the peak for given $\vartheta_c$ is proportional to N. Selecting parameters one can have the source of X-rays of desired frequency with rather good monochromaticity.