X-ray Cherenkov radiation under conditions of grazing incidence of relativistic electrons onto a target surface
Introduction
The Cherenkov effect allows to produce soft X-rays in the vicinity of atomic absorption edges, where the medium refractive index may exceed unity (Bazylev et al., 1976). This theoretical prediction has been confirmed experimentally (Bazylev et al., 1981, Moran et al., 1990, Knulst et al., 2001, Knulst et al., 2003, Knulst et al., 2004). The obtained experimental results (Knulst et al., 2001, Knulst et al., 2003, Knulst et al., 2004) demonstrate a possibility to create an effective quasi-monochromatic X-ray source with intensity of the order of . On the other hand, the average angular density of emission from a possible X-ray Cherenkov source is not high because of both a large value of the Cherenkov emission angle and an angular spread of the Cherenkov photon flux close to the hollow cone. The above-mentioned circumstances lead to the following question: how to increase the angular density for the discussed X-ray source?
Some possible ways to solve this problem are considered in our work theoretically. In Section 2, we discuss a possibility to increase the emission angular density by using grazing incidence of emitting electrons onto the target. The next section is devoted to a study of X-ray Cherenkov radiation from a multilayer nanostructure. A possibility to focus the Cherenkov photon flux is considered in Section 4 on the basis of grazing-angle optics. Our conclusions are presented in the last section.
Section snippets
Grazing-incidence Cherenkov radiation
Let us consider emission from relativistic electrons crossing a foil of an amorphous medium. This theoretical task is well known (see, for example, Garibian and Yang (1983)), so we can use general results presented in the cited work. We assume that the photoabsorption length is less than the electron path in the target. Here is imaginary part of the dielectric susceptibility of the target material, L is the thickness of the target, and is the grazing incidence
Cherenkov X-rays from relativistic electrons crossing a multilayer nanostructure
Let us consider X-ray emission from relativistic electrons moving in a medium with a periodic dielectric susceptibility . Under conditions of Bragg scattering of a fast electron by the Coulomb field of periodic heterogeneities of the medium, the angle between electron velocity and direction of emitted photons can be large. This feature allows to arrange an irradiated sample in the immediate vicinity of the source and consequently increase the photon density at
On focusing Cherenkov X-rays with grazing-angle optics
Let us consider the next possibility to increase the angular density of Cherenkov radiation using the grazing-angle optics. Returning to the scheme described in Section 2, one should estimate a possible growth of the Cherenkov angular density which can be achieved using a simple cylindrical mirror placed on the in-vacuum side of the target so that the axis of the mirror coincides with the axis of the emitting electron beam. It is clear that, in the considered case, primary Cherenkov photons
Conclusions
The performed studies of the process of Cherenkov X-ray radiation from relativistic electrons moving through a dense medium showed some possibilities to increase the angular density of emitted photons.
The emission angular density can be increased substantially under conditions of grazing incidence of emitting electrons on a target surface, when the structure of radiation in the Cherenkov cone is strongly modified. According to performed calculations, such an approach allows to achieve an
Acknowledgements
This work was supported by the United States National Institute for Health under Small Business Innovation Research (SBIR) program (grant 2-R33CA086545-02), by the United States National Science Foundation under the SBIR program (grant DMI-0214819), by the Russian Foundation of Basic Research (grant 04-02-16583), by Programs DOPFIN, University of Russia (grant 02.01.002), and by Ministry of Education and Science of Russia. One of the authors (AK) is grateful to Ministry of Education RF and
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