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We present the results of numerical calculations of the channelling andundulator radiation generated by an ultra-relativistic positron channellingalong a crystal plane, which is periodically bent. The bending might be dueeither to the propagation of a transverse acoustic wave through the crystal, ordue to the static strain as it occurs in superlattices. The periodically bentcrystal serves as an undulator. We investigate the dependence of theintensities of both the ordinary channelling and the undulator radiations onthe parameters of the periodically bent channel with simultaneous account forthe dechannelling effect of the positrons. We demonstrate that there is a rangeof parameters in which the undulator radiation dominates over the channellingone and the characteristic frequencies of both types of radiation are wellseparated. This result is important, because the undulator radiation can beused to create a tunable source of X-ray and gamma-radiation.

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