Geometrical optics method in the theory of channeling of high energy particles in crystals

The process of scattering of fast charged particles in thin crystals is considered in the transitional range of thicknesses, between those at which the channeling phenomenon is not developed and those at which it is realized. The possibility is shown of application of the methods of geometrical optics for description of the scattering process. The dependence is studied of the total scattering cross-section of ultrarelativistic positrons on target thickness in this range of crystal thicknesses. In the case of ultrarelativistic particles channeling the possibility is shown of the existence of an effect analogical to the Ramsauer-Townsend effect of conversion into zero of the total scattering cross-section at some values of crystal thickness. The important role is outlined of the Morse-Maslov index that enters into the wave function expression in the geometrical optics method.Comment: 6 pages, 2 figure

Transition radiation on semi-infinite plate and Smith-Purcell effect

The Smith-Purcell radiation is usually measured when an electron passes over the grating of metallic stripes. However, for high frequencies (exceeding the plasma frequency of the grating material) none material could be treated as a conductor, but ought to be considered as a dielectric with plasma-like permittivity. So for describing Smith-Purcell radiation in the range of high frequencies new theoretical approaches are needed. In the present paper we apply the simple variant of eikonal approximation developed earlier to the case of radiation on the set of parallel semi-infinite dielectric plates. The formulae obtained describe the radiation generated by the particles both passing through the plates (traditionally referred as "transition radiation") and moving in vacuum over the grating formed by the edges of the plates (traditionally referred as "diffraction radiation", and, taking into account the periodicity of the plates arrangement, as Smith-Purcell radiation).Comment: Submitted to Journal of Physics: Conference Serie

On spectral method in the axial channeling theory

The quantization of the transverse motion energy in the continuous potentials of atomic strings and planes can take place under passage of fast charged particles through crystals. The energy levels for electron moving in axial channeling regime in a system of parallel atomic strings (for instance, [110] strings of a silicon crystal) are found in this work for the electron energy of order of several tens of MeV, when a total number of energy levels becomes large (up to several hundreds). High resolution of the spectral method used for energy level search has been demonstrated. Hence this method could be useful for investigation of quantum chaos problem.Comment: 11 pages, 4 figures, presented on the conference "Channeling-2012", 23-28 September 2012 Alghero, Sardegna, Italy; accepted for publication in Nuclear Instruments and Methods

On the analogies between the processes of coherent radiation at collisions of relativistic particles with bunches of relativistic particles and crystals

At scattering of relativistic bunches of charged particles the effect of a significant amplification of radiation in the region of low radiated frequencies, when the spectral density is proportional to the square number of particles in the bunch, is possible. This effect holds both for head-scattered bunches, and bunches which scattered at a small angle between their axes of motion. At the same time with an increasing number of the particles in bunches the radiation is almost independent of the number of particles. The analogy of these effects and the effects of radiation at the passage of charged particles in matter is discussed. The analogy of the mechanisms of these radiation processes not only for coherent, but also for incoherent radiation, is shown. The possibility of usage of the coherent effect in radiation for monitoring charged particle beams is noted

On quantum spreading of a localized stationary flow of high energy particles

The study addresses the quantum spreading of a localized stationary flow of high energy particles. Results demonstrate that as particle energy increases, the spreading speed of the particle wave packet diminishes rapidly. Concurrently, increasing the energies stabilizes the initially localized packet, preserving its transverse form in a vacuum over extended distances. This allows substantial simplifications when using various approximate methods to calculate the wave function in an external field

Contribution of incoherent effects to the orientation dependence of bremsstrahlung from rapid electrons in crystal

The bremsstrahlung cross section for relativistic electrons in a crystal is split into the sum of coherent and incoherent parts (the last is due to a thermal motion of atoms in the crystal). Although the spectrum of incoherent radiation in crystal is similar to one in amorphous medium, the incoherent radiation intensity could demonstrate substantial dependence on the crystal orientation due to the electrons' flux redistribution in the crystal. In the present paper we apply our method of the incoherent bremsstrahlung simulation developed earlier to interpretation of some recent experimental results obtained at the Mainz Microtron MAMI.Comment: VIII International Symposium "Radiation from Relativistic Electrons in Periodic Structures" (RREPS-09) Zvenigorod, Russia, September 7-11, 200