  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.
