Mehdi Tabrizi | Searcharxiv

arXiv2016

On the relation between Airy integral and Bessel functions revisited

The Airy integral and Bessel functions are of significant in mathematical description of spectral distribution of different types of radiation produced by relativistic charged particles moving in synchrotron and in periodical macro- and micro-structures. A simple proof of the relation between Airy integral and modified Bessel function is of most important for radiation physicists, who are not expert in pure mathematics. In this paper we discuss an old proof proposed by Nicholson, and suggest another simple one based on the Bowman transformation of Bessel differential equation with a complex constant.

math-ph↗

arXiv2015

Influence of the multiple scattering of relativistic electrons on the line width of the backward Parametric X-ray Radiation in the absence of photo absorption

The multiple scattering effect on the line width of the backward Parametric X-ray Radiation (PXR) in the extremely Bragg geometry, produced by low energy relativistic electrons traversing a single crystal, is discussed. It is shown that there exist conditions, when the influence of photo absorption on the line width can be neglected, and the only multiple scattering process of relativistic electrons in crystal leads to the PXR lines' broadening. Based on the obtained theoretical and numerical results for the line width broadening, caused by the multiple scattering of $30$ and $50$ MeV relativistic electrons in a Si crystal of varying thicknesses, an experiment could be performed to help to reveal the scattering effect on the PXR lines in the absence of photo absorption. This leads to a more accurate understanding of the influence of scattering phenomenon on the line width of the backward PXR and helps to a better construction of a table-top narrow bandwidth X-ray source for scientific and industrial applications.

physics.acc-ph↗