Radiation of particles in undulators with straight sections taking into account the medium polarization

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, Lp=2(L+L0), where L and L0 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 L0 one can tune the energy region of the emitted photons as well as their spectral distribution.