The Influence of Electron Beam Divergence on the CXR in a Periodic Layered Medium With Three Layers Per Period
DOI:
https://doi.org/10.52575/2687-0959-2025-57-4-279-289Keywords:
periodic layered structure, three-layer structure, dynamic diffraction, angular divergence of the electron beam, coherent X-ray radiationAbstract
A dynamic theory of coherent X-ray radiation of relativistic electron beams in a periodic layered medium with three layers per period has been developed. Coherent X-ray radiation is considered in the Bragg scattering geometry within the framework of the two-wave approximation of the dynamic diffraction theory as a sum of contributions from parametric X-ray radiation and diffracted transition radiation, taking into account their interference. Expressions are obtained that describe the spectral-angular and angular densities of parametric X-ray radiation, diffracted transition radiation and their interference, taking into account the angular divergence of the electron beam. Based on the expressions obtained, numerical calculations are performed for specific parameters of the radiation process.
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References
Nasonov NN., Kaplin VV., Uglov SR., Piestrup MA. and Gary CK. X rays from relativistic electrons in a multilayer structure. Physical Review E. 2023;68(3):036504.
Garibian GM. and Yang C. Quantum microscopic theory of radiation by a charged particle moving uniformly in a crystal. Sov. Phys. JETP. 1972;34:495.
Baryshevsky VG., Feranchuk ID. Transition radiation of y-rays in a crystal. Sov. Phys. JETP. 1972;34:502.
Caticha A. Transition-diffracted radiation and the Cerenkov emission of x-rays. Physical Review A. 1989; 40(8):4322.
Nasonov NN. Influence of the density effect upon the parametric x-rays of high energy particles. Phys. Lett. A. 1998;246:148.
Kaplin VV. et al. Observation of bright monochromatic x rays generated by relativistic electrons passing through a multilayer mirror Appl. Phys. Lett. 76. 2000;24:3647-3649.
Blazhevich SV., Kolosova IV. and Noskov AV. Coherent x-ray radiation generated by a relativistic electron in an artificial periodic structure. J. Exp. Theor. Phys. 2012;114:547-554.
Blazhevich SV., Noskov AV. Dynamic theory of coherent X-radiation of relativistic electron within a periodic layered medium in Bragg scattering geometry. Nucl. Instrum. Meth. B. 2013;309:70-75.
Potylitsyn A. Electromagnetic Radiation of Electrons in Periodic Structures. Springer. 2011.216 p.
Uglov SR., Kaplin VV., Kubankin AS. et.al. Cr/Sc multilayer radiator for parametric EUV radiation in “water-window” spectral range. Journal of Physics: Conference Series. 2016;732(1):012017.
Shevelev MV., Uglov SR., Vukolov AV. Spectrum of coherent VUV radiation generated by 5.7 MeV electrons in a multilayer X-ray mirror. Journal of Instrumentation. 2024;19(4):C04049.
Huang S., Duan R., Pramanik N., Herrin JS., Boothroyd C., Liu Z. &Wong LJ. Quantum recoil in free-electron interactions with atomic lattices. Nature Photonics. 2023;17(3):224-230.
Huang S., Duan R., Pramanik N., Boothroyd C., Liu Z., Wong LJ. Enhanced Versatility of Table-Top X-Rays from Van der Waals Structures. Advanced Science. 2022;9(16):2105401.
Shi X., Kurman Y., Shentcis M., Wong LJ., Javier Garcia de Abajo F. and Kaminer I. Free-electron interactions with van der Waals heterostructures: a source of focused X-ray radiation. Light Sci Appl. 2023;12(1):148.
Blazhevich SV., Noskov AV. Coherent X-ray Radiation Generated by a Relativistic Electron Beam in a Periodic Layered Medium in the Bragg Scattering Geometry. Journal of Experimental and Theoretical Physics. 2017;125(2):223–234.
Blazhevich SV., Drygina YuA., Shevchuk OYu., Noskov AV. Coherent X-Ray Radiation Generated Near the Axis of the Beam of Relativistic Electrons in an Artificial Periodic Structure. Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques. 2020;14(3):586-595.
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Noskov AV., Kipersha VK., Blazhevich SV., Pleskanev AA., Ilyinsky RYu., Voloshkina EV. Spectral-angular densities of transition radiation and diffracted transition radiation of relativistic electrons in a periodic layered medium. Applied Mathematics & Physics. 2024;56(1):66-74 (In Russ.).
Noskov AV., Blazhevich SV. Coherent X-ray radiation excited by a relativistic electron in a periodic layered medium. Journal of Instrumentation. 2024;19(7):P07007 (In Russ.).
Noskov A.V., Blazhevich S.V. Effects of dynamic diffraction in coherent X-ray radiation from a beam of relativistic electrons in a periodic layered medium with three layers in a period. Physics Letters A. 2024;525:129835.
Noskov A.V., Blazhevich S.V., Chueva A.I., Machukaev D.D., Kipersha V.K. The influence of asymmetric diffraction on the spectral-angular density of the CRI of a relativistic electron in a three-layer structure. Applied Mathematics & Physics. 2025;57(1):59-67 (In Russ.).
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