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We suggest a new type of the undulator radiation which is generated by anultra-relativistic particle channeled along a periodically bentcrystallographic plane or axis. The electromagnetic radiation arises mainly dueto the bending of the particle's trajectory, which follows the shape of thechannel. The parameters of this undulator, which totally define the spectrumand the angular distribution of the radiation (both spontaneous andstimulated), depend on the type of the crystal and the crystallographic plane(axis), on the type of a projectile and its energy, and on the shape of thebent channel, and, thus, can be varied significantly by varying thesecharacteristics.  As an example, we consider the acoustically induced radiation (AIR) which isgenerated by ultra-relativistic particles channeled in a crystal which is bentby a transverse acoustic wave. The AIR mechanism allows to make the undulatorwith the main parameters varying in wide ranges, which are inaccessible in theundulators based on the motion of particles in the periodic magnetic fields andalso in the field of the laser radiation. The intensity of AIR can be easilymade larger than the intensity of the radiation in a linear crystal and can bevaried in a wide range by varying the frequency and the amplitude of theacoustic wave in the crystal. A possibility to generate stimulated emission ofhigh-energy photons (in keV - MeV region) is also discussed.

Coherent radiation of an ultrarelativistic charged particle channelled in a periodically bent crystal