Radiation of the magneto-crystalline undulator

Abstract

Abstract. 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. IntroductionNew sources of X-ray and gamma radiation, consisting of the particle accelerators and precisely oriented mono-crystals are created on the basis of the channeling phenomenon. There is interest in developing a radiation source using the periodically deformed crystals. See, for example, the recent papers [1,2]. The channeled positrons are bound to the bent atomic crystal planes, and emit monochromatic radiation of a frequency which depends on the particles energy and the period of the crystal plate bending. Such a "crystalline undulator" was first proposed in [3,4], where the deformation of the crystal was proposed to be performed by an ultrasonic wave. There are also a number of projects of multi-crystal undulators where the particle is deflected successively in the opposite directions at passing through a series of mutually oriented ultrathin crystals (see, for example, [5]). The radiation generated in the crystal undulators can be harder than one can get in a magnetic undulator at the same energy of the positrons, since the period of the deformed crystal may be much smaller than the period of undulator magnetic field.A "magneto-crystalline undulator" which produces electromagnetic radiation by means of charged particles moving near the flat surface of a crystal in a magnetic field parallel to the surface was proposed in [6]. The positively charged particles at grazing incidence to the surface of the crystal are reflected from the surface and returning back by the magnetic field, if the field is orthogonal to the average velocity of the particles. The quantum energy levels of the particle transverse motion at the surface channeling in a magnetic field, and the possible frequency of radiation were also found in [7].