Spectral-angular Densities of Parametric X-ray Radiation and Diffraction Transition Radiation from Relativistic Electrons in a Periodic Layered Medium
DOI:
https://doi.org/10.52575/2687-0959-2026-58-3-307-317Keywords:
Periodic Layered Medium, Dynamic Diffraction, Coherent X-ray RadiationAbstract
A dynamic theory of coherent X-ray radiation from relativistic electrons traversing a finite-thickness target made of a periodic layered medium with three layers per period in Laue scattering geometry is developed. Expressions describing the spectral-angular densities of parametric X-ray radiation and diffracted transition radiation are derived. It is shown that changing the ratio of the real parts of the dielectric susceptibilities of the layer materials and changing the ratio of the layer thicknesses significantly affects the spectral-angular characteristics of the coherent X-ray emission. It is established that,
under certain conditions, weakening of photoabsorption within the second layer of the multilayer medium period leads to a noticeable increase in the radiation densities differentiated by frequencies and propagation directions.
Downloads
References
Список литературы
Nasonov N.N., Kaplin V.V., Uglov S.R., Piestrup M.A. and Gary C.K. X rays from relativistic electrons in a multilayer structure. Physical Review E. 2023;68:036504. DOI:10.1103/PhysRevE.68.036504
Garibian G.M. and Yang C. Quantum microscopic theory of radiation by a charged particle moving uniformly in a crystal. Soviet Physics JETP. 1972;34:495.
Baryshevsky V.G., Feranchuk I.D. Transition radiation of y-rays in a crystal. Soviet Physics JETP. 1972;34:502.
Caticha A. Transition-diffracted radiation and the Cerenkov emission of X-rays. Physical Review A. 1989;40:4322.
DOI:10.1103/PhysRevA.40.4322
Nasonov N.N. Influence of the density effect upon the parametric x-rays of high energy particles. Physics Letters A.
;246:148. DOI:10.1016/S0375-9601(98)00544-8
Kaplin V.V. et al. Observation of bright monochromatic x rays generated by relativistic electrons passing through a
multilayer mirror. Appl. Phys. Lett. 2000;76(24):3647-3649. DOI:10.1063/1.126735
Blazhevich S.V., Kolosova I.V. and Noskov A.V. Coherent x-ray radiation generated by a relativistic electron in an artificial
periodic structure. Journal of Experimental and Theoretical Physics. 2012;114:547-554. DOI:10.1134/S1063776112030187
Blazhevich S.V., Noskov A.V. Dynamic theory of coherent X-radiation of relativistic electron within a periodic layered
medium in Bragg scattering geometry. Nuclear Instruments and Methods in Physics Research Section B. 2013;309:70-75.
DOI:10.1016/j.nimb.2013.01.074
Blazhevich S., Noskov A., Shevchuk O. Coherent X-ray radiation excited by a beam of relativistic electrons in a layered
periodic structure. Journal of Instrumentation. 2020;15:C05075. DOI:10.1088/1748-0221/15/05/C05075
Uglov S.R., Kaplin V.V., Kubankin A.S. et.al. 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/s41566-022-01131-z
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., Javier Garcia de Abajo F. and Kaminer I. Free-electron interactions with
van der Waals heterostructures: a source of focused X-ray radiation. Light: Science & Applications. 2023;12(1):148.
DOI:10.1038/s41377-023-01189-0
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:P07007. DOI:10.1088/1748-0221/19/07/P07007
Noskov A.V., Blazhevich S.V., Pronina E.D. Influence of the divergence of relativistic electron beam on spectral-angular
densities of PXR and DTR in a periodic layered medium with three layers on a period. Journal of Instrumentation.
;20:P06014. DOI:10.1088/1748-0221/20/06/P06014
NoskovA.V.,BlazhevichS.V.EffectsofdynamicdiffractionincoherentX-rayradiationfromabeamofrelativisticelectrons
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.
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.
;57(4):279-289.
Носков А.В., Пирматова М.Д., Мачукаев Д.Д., Бардакова И.Н., Блажевич С.В. Угловаяплотность ПРИ впериодической слоистой среде с тремя слоями в периоде в геометрии рассеяния Лауэ. Прикладная математика & Физика.
;58(1):78–87. DOI:10.52575/2687-0959-2026-58-1-78-87
Borrmann G. Uber Extinktionsdiagramme der Rontgenstrahlen von Quarz. Zeitschrift f"ur Physik. 1941;42:157.
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;68:036504.
Garibian GM. and Yang C. Quantum microscopic theory of radiation by a charged particle moving uniformly in a
crystal. Soviet Physics JETP. 1972;34:495.
Baryshevsky VG., Feranchuk ID. Transition radiation of y-rays in a crystal. Soviet Physics JETP. 1972;34:502.
Caticha A. Transition-diffracted radiation and the Cerenkov emission of X-rays. Physical Review A. 1989;40:4322.
Nasonov NN. Influence of the density effect upon the parametric x-rays of high energy particles. Physics Letters 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. 2000;76(24):3647-3649.
Blazhevich SV., Kolosova IV. and Noskov AV. Coherent x-ray radiation generated by a relativistic electron in an artificial
periodic structure. Journal of Experimental and Theoretical Physics. 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. Nuclear Instruments and Methods in Physics Research Section B. 2013;309:70-75.
Blazhevich S., Noskov A., Shevchuk O. Coherent X-ray radiation excited by a beam of relativistic electrons in a layered
periodic structure. Journal of Instrumentation. 2020;15:C05075.
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 J.S., Boothroyd C., Liu Z. and Wong L.J. 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 L.J. 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: Science & Applications. 2023;12(1):148.
Noskov AV., Blazhevich SV. Coherent X-ray radiation excited by a relativistic electron in a periodic layered medium.
Journal of Instrumentation. 2024;19:P07007.
Noskov AV., Blazhevich SV., Pronina ED. Influence of the divergence of relativistic electron beam on spectral-angular
densities of PXR and DTR in a periodic layered medium with three layers on a period. Journal of Instrumentation.
;20:P06014.
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.
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. Applied Mathematics & Physics. 2025;57(1):59-67. (In Russ.)
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.AppliedMathematics &Physics. 2025;57(4):279–289. (In Russ.)
Noskov AV., Pirmatov MD., Machukaev DD., Bardakova IN., Blazhevich SV. Angular Density of the PXR in a Periodic Layered Medium with Three Layers in a Period in Laue Scattering Geometry. Applied Mathematics & Physics. 2026;58(1):78–87. (In Russ.)
Borrmann G. Uber Extinktionsdiagramme der Rontgenstrahlen von Quarz. Zeitschrift f"ur Physik. 1941;42:157.
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.
