Radiation of the magneto-crystalline undulator

The radiation at grazing incidence of relativistic positively charged particles on the crystal surface in the presence of magnetic field is studied theoretically. The magnetic field is supposed to be parallel to the surface. Dependent on the initial conditions the particle can be captured in the channeling mode and perform periodic oscillations along the surface of the crystal. The spectrum, angular distribution and polarization of radiation are calculated. The emission spectrum of a single particle is discrete and it extends up to very large numbers of harmonics. If the magnetic field is much weaker than the electric field of atoms, the frequency range of radiation of the particle beam does not depend on magnetic field and is defined solely by the energy of the particles and by the surface averaged potential, though the frequency of the first harmonic is defined only by the magnetic field. In case of channeled positrons the characteristic energy of the emitted photons is of order 10γ^3/2 (eV), where γ is the particle relativistic factor. The main part of radiation is bound to a narrow cone and is polarized largely orthogonal to the surface of the crystal. (paper)