Angular density of the PXR in a periodic layered medium with three layers in a period in Laue scattering geometry
DOI:
https://doi.org/10.52575/2687-0959-2026-58-1-78-87Keywords:
periodic layered structure, three-layer structure, dynamic diffraction, parametric X-ray radiationAbstract
A theory of parametric X-ray radiation from a relativistic electron traversing a periodic layered medium with three layers per period in Laue scattering geometry has been developed. Within the two-wave approximation of dynamic diffraction theory, an expression describing the angular density of parametric X-ray emission has been derived. Using this expression, numerical calculations of the PXR angular density have been performed. A significant dependence of the PXR angular density on the ratio of the real parts of the dielectric susceptibilities of the layer materials and the ratio of the layer thicknesses has been demonstrated.
Downloads
References
Список литературы
Nasonov N.N., Kaplin V.V., Uglov S.R., Piestrup M.A., Gary C.K. X rays from relativistic electrons in a multilayer structure. Physical Review E. 2023;68(3):036504. DOI: 10.1103/PhysRevE.68.036504
Garibian G.M., Yang C. Quantum microscopic theory of radiation by a charged particle moving uniformly in a crystal. Sov. Phys. JETP. 1972;34:495.
Baryshevsky V.G., Feranchuk I.D. Transition radiation of γ-rays in a crystal. Sov. Phys. JETP. 1972;34:502.
Kaplin V.V., Uglov S.R, Zabaev V.N., Piestrup M.A. Observation of bright monochromatic x rays generated by relativistic electrons passing through a multilayer mirror Appl. Phys. Lett. 76. 2000;24:3647-3649. DOI: 10.1063/1.126735
Blazhevich S.V., Kolosova I.V., Noskov A.V. Coherent x-ray radiation generated by a relativistic electron in an artificial periodic structure. J. Exp. Theor. Phys. 2012;114:547-554. DOI: 10.1134/S1063776112020021
Blazhevich S.V., Noskov A.V. 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. DOI: 10.1016/j.nimb.2013.02.035
Potylitsyn A. Electromagnetic Radiation of Electrons in Periodic Structures. Springer. 2011.216 p. DOI: 10.1007/978-3-642-19248-7
Uglov S.R., Kaplin V.V., Kubankin A.S., Andre J.M., Le Guen K., Jonnard Ph., De Rossi S., Meltchakov E., Delmotte F. Cr/Sc multilayer radiator for parametric EUV radiation in “water-window” spectral range. Journal of Physics:Conference Series. 2016;732(1):012017. DOI: 10.1088/1742-6596/732/1/012017
Shevelev M.V., Uglov S.R., Vukolov A.V. Spectrum of coherent VUV radiation generated by 5.7 MeV electrons in a multilayer X-ray mirror. Journal of Instrumentation. 2024;19(4):C04049. DOI: 10.1088/1748-0221/19/04/C04049
Huang S., Duan R., Pramanik N., Herrin J.S., Boothroyd C., Liu Z.,Wong L.J. Quantum recoil in free-electron interactions with atomic lattices. Nature Photonics. 2023;17(3):224-230. DOI: 10.1038/s41566-022-01132-6
Huang S., Duan R., Pramanik N., Boothroyd C., Liu Z., Wong L.J. Enhanced Versatility of Table-Top X-Rays from Van der Waals Structures. Advanced Science. 2022;9(16):2105401. DOI: 10.1002/advs.202105401
Shi X., Kurman Y., Shentcis M., Wong L.J., Garcia J.F., Kaminer I. Free-electron interactions with van der Waals heterostructures: a source of focused X-ray radiation. Light Sci Appl. 2023;12(1):148. DOI: 10.1038/s41377-023-01141-2
Blazhevich S.V., Noskov A.V. 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. DOI: 10.1134/S1063776117070172
Blazhevich S.V., Drygina Yu.A., Shevchuk O.Yu., Noskov A.V. 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. DOI: 10.1134/S1027451020030222
Носков А.В., Бондаренко В.А., Блажевич С.В., Юрьева А.А., Федосеев А.Э. О влиянии многократного рассеяния на переходное излучение в монокристалле. Прикладная математика & Физика. 2023;55(2): 183–192. DOI 10.52575/2687-0959-2023-55-2-183-192
Носков А.В., Киперша В.К., Блажевич С.В., Плесканев А.А., Ильинский Р.Ю., Волошкина Е.В. Спектрально-угловые плотности переходного излучения и дифрагированного переходного излучения релятивистских электронов в периодической слоистой среде. Прикладная математика & Физика. 2024;56(1):66-74. DOI 10.52575/2687-0959-2024-56-1-66-74
Noskov A.V., Blazhevich S.V. Coherent X-ray radiation excited by a relativistic electron in a periodic layered medium. Journal of Instrumentation. 2024;19(7):P07007. DOI: 10.1088/1748-0221/19/07/P07007
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. DOI: 10.1016/j.physleta.2024.129835
Носков А.В., Блажевич С.В., Чуева А.И., Мачукаев Д.Д., Киперша В.К. Влияние асимметрической дифракции на спектрально-угловую плотность КРИ релятивистского электрона в трехслойной структуре. Прикладная математика & Физика. 2025;57(1):59-67. DOI 10.52575/2687-0959-2025-57-1-59-67
Носков А.В., Мачукаев Д.Д., Киперша В.К., Пугина П.Д., Пирматова М.Д. Влияние расходимости электронного пучка на КРИ в периодической слоистой среде с тремя слоями на периоде. Прикладная математика & Физика. 2025;57(4):279-289. DOI 10.52575/2687-0959-2025-57-4-279-289
References
Nasonov NN., Kaplin VV., Uglov SR., Piestrup MA., Gary CK. X rays from relativistic electrons in a multilayer structure. Physical Review E. 2023;68(3):036504. DOI: 10.1103/PhysRevE.68.036504
Garibian GM., Yang C. Quantum microscopic theory of radiation by a charged particle moving uniformly in a crystal. ZHurnal Eksperimental’noj i Teoreticheskoj Fiziki [Journal of Experimental and Theoretical Physics]. JETP. 1972;34(3):495.
Baryshevsky VG., Feranchuk ID. Transition radiation of γ-rays in a crystal. ZHurnal Eksperimental’noj i Teoreticheskoj Fiziki [Journal of Experimental and Theoretical Physics]. 1972;34(3):502.
Kaplin VV., Uglov SR, Zabaev VN., Piestrup MA. Observation of bright monochromatic x rays generated by relativistic electrons passing through a multilayer mirror Appl. Phys. Lett. 76. 2000;24:3647-3649. DOI: 10.1063/1.126735
Blazhevich SV., Kolosova IV., Noskov AV. Coherent x-ray radiation generated by a relativistic electron in an artificial periodic structure. ZHurnal Eksperimental’noj i Teoreticheskoj Fiziki [Journal of Experimental and Theoretical Physics]. 2012;141(4):547-554 (In Russian). DOI: 10.1134/S1063776112020021
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. DOI: 10.1016/j.nimb.2013.02.035
Potylitsyn A. Electromagnetic Radiation of Electrons in Periodic Structures. Springer. 2011.216 p. DOI: 10.1007/978-3-642-19248-7
Uglov SR., Kaplin VV., Kubankin AS., Andre JM., Le Guen K., Jonnard Ph., De Rossi S., Meltchakov E., Delmotte F. Cr/Sc multilayer radiator for parametric EUV radiation in “water-window” spectral range. Journal of Physics: Conference Series. 2016;732(1):012017. DOI: 10.1088/1742-6596/732/1/012017
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. DOI: 10.1088/1748-0221/19/04/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. DOI: 10.1038/s41566-022-01132-6
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. DOI: 10.1002/advs.202105401
Shi X., Kurman Y., Shentcis M., Wong LJ., Garcia JF., Kaminer I. Free-electron interactions with van der Waals heterostructures: a source of focused X-ray radiation. Light Sci Appl. 2023;12(1):148. DOI: 10.1038/s41377-023-01141-2
Blazhevich SV., Noskov AV. Coherent X-ray Radiation Generated by a Relativistic Electron Beam in a Periodic Layered Medium in the Bragg Scattering Geometry. ZHurnal Eksperimental’noj i Teoreticheskoj Fiziki [Journal of Experimental and Theoretical Physics]. 2017;152(2):223–234 (In Russian). DOI: 10.1134/S1063776117070172
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. Poverhnost’. Rentgenovskie, sinhrotronnye i nejtronnye issledovaniya [Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques]. 2020;14(3):586-595 (In Russian). DOI: 10.1134/S1027451020030222
Noskov AV., Bondarenko VA., Blazhevich SV., Yuryeva AA., Fedoseev AE. On the influence of multiple scattering on transition radiation in a single crystal. Prikladnaya matematika & Fizika [Applied Mathematics & Physics]. 2023;55(2):183–192 (In Russ.). DOI 10.52575/2687-0959-2023-55-2-183-192
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. Prikladnaya matematika & Fizika [Applied Mathematics & Physics]. 2024;56(1):66-74 (In Russ.). DOI 10.52575/2687-0959-2024-56-1-66-74
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. DOI: 10.1088/1748-0221/19/07/P07007
Noskov AV., Blazhevich SV. 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. DOI: 10.1016/j.physleta.2024.129835
Noskov AV., Blazhevich SV., Chueva AI., Machukaev DD., Kipersha VK. The influence of asymmetric diffraction on the spectral-angular density of the CRI of a relativistic electron in a three-layer structure. Prikladnaya matematika & Fizika [Applied Mathematics & Physics]. 2025;57(1):59-67 (In Russ.). DOI 10.52575/2687-0959-2025-57-1-59-67
Noskov AV., Machukaev DD., Kipersha VK., Pugina PD., Pirmatova MD. The influence of electron beam divergence on the CXR in a periodic layered medium with three layers per period. Prikladnaya matematika & Fizika [Applied Mathematics & Physics]. 2025;57(4):279–289 (In Russ.). DOI 10.52575/2687-0959-2025-57-4-279-289
Abstract views: 0
##submission.share##
Published
How to Cite
Issue
Section
Copyright (c) 2026 Applied Mathematics & Physics

This work is licensed under a Creative Commons Attribution 4.0 International License.
