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 undulator radiation generated by ultra-relativistic positron channelling along a crystal plane, which is periodically bent. The bending might be due to either the propagation of a transverse acoustic wave through the crystal, or the static strain as it occurs in superlattices. The periodically bent crystal serves as an undulator. We investigate the dependence of the intensities of both the ordinary channelling and the undulator radiations on the parameters of the periodically bent channel with simultaneous account for the de-channelling effect of the positrons. We demonstrate that there is a range of parameters in which the undulator radiation dominates over the channelling one and the characteristic frequencies of both types of radiation are well separated. This result is important, because the undulator radiation can be used to create a tunable source of x-ray and γ-radiation.