  This paper is devoted to the investigation of the radiation energy losses of
an ultra-relativistic charged particle channeling along a crystal plane which
is periodically bent by a transverse acoustic wave. In such a system there are
two essential mechanisms leading to the photon emission. The first one is the
ordinary channeling radiation. This radiation is generated as a result of the
transverse oscillatory motion of the particle in the channel. The second one is
the acoustically induced radiation. This radiation is emitted because of the
periodic bending of the particle's trajectory created by the acoustic wave. The
general formalism described in our work is applicable for the calculation of
the total radiative losses accounting for the contributions of both radiation
mechanisms. We analyze the relative importance of the two mechanisms at various
amplitudes and lengths of the acoustic wave and the energy of the projectile
particle. We establish the ranges of projectile particle energies, in which
total energy loss is small for the LiH, C, Si, Ge, Fe and W crystals. This
result is important for the determination of the projectile particle energy
region, in which acoustically induced radiation of the undulator type and also
the stimulated photon emission can be effectively generated. The latter effects
have been described in our previous works.
