Coherent radiation of an ultra-relativistic charged particle channeled in a periodically bent crystal

We suggest a new type of the undulator radiation which is generated by an ultra-relativistic particle channeled along a periodically bent crystallographic plane or axis. The electromagnetic radiation arises mainly due to the bending of the particle's trajectory, which follows the shape of the channel. The parameters of this undulator, which totally define the spectrum and the angular distribution of the radiation (both spontaneous and stimulated), 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 the bent channel, and, thus, can be varied significantly by varying these characteristics. As an example, we consider the acoustically induced radiation (AIR) which is generated by ultra-relativistic particles channeled in a crystal which is bent by a transverse acoustic wave. The AIR mechanism allows to make the undulator with the main parameters varying in wide ranges, which are inaccessible in the undulators based on the motion of particles in the periodic magnetic fields and also in the field of the laser radiation. The intensity of AIR can be easily made larger than the intensity of the radiation in a linear crystal and can be varied in a wide range by varying the frequency and the amplitude of the acoustic wave in the crystal. A possibility to generate stimulated emission of high-energy photons (in keV - MeV region) is also discussed.