The influence of the dechannelling process on the photon emission by an ultra-relativistic positron channelling in a periodically bent crystal

Abstract

We investigate, both analytically and numerically, the influence of the dechannelling process on the parameters of undulator radiation generated by ultra-relativistic positron channelling along a crystal plane, which is periodically bent. The bending might be due either to the propagation of a transverse acoustic wave through the crystal, or due to the static strain as it occurs in superlattices. In either case the periodically bent crystal serves as an undulator which allows the generation of x-ray and γ-radiation. We propose a scheme for the accurate quantitative treatment of the radiation in the presence of dechannelling. The scheme includes: (a) the analytic expression for the spectral-angular distribution which contains, as a parameter, the dechannelling length; (b) the simulation procedure of the dechannelling process of a positron in periodically bent crystals. Using these we calculate the dechannelling lengths of 5 GeV positrons channelling in Si, Ge and W crystals, and the spectral-angular and spectral distributions of the undulator over broad ranges of the photons. The calculations are performed for various parameters of channel bending.

Simulation of ultra-relativistic electrons and positrons channeling in crystals with MBN Explorer

“…These calculations are performed by means of the Fortran code (which is not a part of MBN Explorer) built upon the revisited algorithm described earlier [24,30]. The basic formalism is summarized below in section II B.…”

<title>Number of photons and brilliance of the radiation from a crystalline undulator</title>

“…To calculate the dechanneling length one can either apply the diffusion theory to describe the multiple scattering 20,21 or carry out a computer simulation of the scattering process of the projectile from the crystal constituents. 5,22 Alternatively, to estimate L d (ε, C) one can use the approximate formulae. 2,22 For an ultra-relativistic positron the dechanneling length in straight channels (i.e.…”

“…More consistent treatment of the dechanneling process and of its influence on the parameters of the undulator radiation was carried out in Refs. 5,6, where a simple analytic expression for the spectral-angular distribution was derived which contains, as a parameter, the dechanneling length.…”

Feasibility of an Electron-Based Crystalline Undulator

“…Then, L d C introduces an upper limit on the length of a crystalline undulator. Indeed, it was demonstrated [3,10] that in the limit L L d the intensity of radiation is not defined by the expected number of undulator periods L=, but rather is formed in the undulator of the effective length L d . Since for an ultrarelativistic particle L d / " [11][12][13], it seems natural that to increase the effective length one can consider higher energies.…”