Radiation of fast positrons interacting with periodic microstructure on the surface of a crystal

Highlights: • New tunable crystalline source of X-ray radiation is described. • Radiation is emitted by the channeling relativistic particles. • A set of crystal plates offers more effective monitoring of the photon energy. • Formulae describing the radiation properties are obtained. - Abstract: Radiation of positrons passing through a set of equidistant crystal plates is calculated. Each plate is of thickness of half of the particle trajectory period at planar channeling in a thick crystal. Positively charged particle entering the first plate at an angle smaller than the critical channeling angle is captured into channeling mode and changes the direction of its transversal velocity to reversed. Between the half-wave plates the particle moves along a straight line. The proposed setup can be realized as a set of equidistant ridges on the surface of a single crystal. 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 particular direction is discrete, and the frequency of the first harmonic and the number of harmonics in the spectrum depend 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 in the crystal.