Total spectrum of photon emission by an ultra-relativistic positron channelling in a periodically bent crystal

We present the results of numerical calculations of the channelling and und ulator radiation generated by ultra-relativistic positron channelling along a crystal plane, which is periodically bent. The bending might be due to e ither the propagation of a transverse acoustic wave through the crystal. or the static strain as it occurs in superlattices. The periodically bent cry stal serves as an undulator. We investigate the dependence of the intensiti es of both the ordinary channelling and the undulator radiations on the par ameters of the periodically bent channel with simultaneous account for the de-channelling effect of the positrons. We demonstrate that there is a rang e of parameters in which the undulator radiation dominates over the channel ling one and the characteristic frequencies of both types of radiation are well separated. This result is important, because the undulator radiation c an be used to create a tunable source of x-ray and gamma-radiation.