Abstract
In some undulators, in particular, in the recently proposed crystalline undulators the particle trajectories after each bending can have straight sections of length not much less than the period of the undulator, L p =2( L+ L 0), where L and L 0 are the projections on the direction of the particle average motion of arcs with alternating sign of curvature radius R and of the straight sections, respectively. The properties of the radiation produced by relativistic particles in such devices are studied theoretically taking into account the dielectric constant of the medium. This polarization effect results in energy threshold of the radiation, which for realistic crystalline undulators is in GeV region. Varying L 0 one can tune the energy region of the emitted photons as well as their spectral distribution.
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