Radiation of charged particles passing through a set of equidistant ridges on the surface of a single crystal is calculated. The ridges are rectangular in shape, each of thickness of half of the particle trajectory period at planar channeling in a thick crystal. Positively charged particle entering the first ridge with angle smaller than the critical channeling angle is captured into channeling and changes the direction of its transversal velocity to reversed. Between the half-wave ridges the particle moves along a straight line. Passing through such set of half-wave crystal plates the particle moves on quasi-undulator trajectories. Properties of the particle radiation emitted during their passage through such multicrystal undulator are calculated. The radiation spectrum in each direction is discrete, and the frequency of the first harmonic and the number of harmonics in the spectrum depends on the distance between the plates, on energy of the particles and on the averaged potential energy of atomic planes of the crystal. The radiation is bound to a narrow cone in the direction of the average particle velocity and polarized essentially in a plane orthogonal to the atomic planes of the crystal.
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