Number of photons and brilliance of the radiation from a crystalline undulator

The scheme for accurate quantitative treatment of the radiation from a crystalline undulator in presence of the dechanneling and the photon attenuation is presented. The number of emitted photons and the brilliance of electromagnetic radiation generated by ultra-relativistic positrons channeling in a crystalline undulator are calculated for various crystals, positron energies and different bending parameters. It is demonstrated that with the use of high-energy positron beams available at present in modern colliders it is possible to generate the crystalline undulator radiation with energies from hundreds of keV up to tens of MeV region. The brilliance of the undulator radiation within this energy range is comparable to that of conventional light sources of the third generation but for much lower photon energies.