S.V. Blazhevich 1 ) , I.V. Kolosova 2) , A.V. Noskov 2)

1. DIFRACTED TRANSITION RADIATION OF A RELATIVISTIC ELECTRON IN THE ARTIFICIAL PERIODIC MULTILAYER MEDIUM S.V. Blazhevich1), I.V. Kolosova2), A.V. Noskov2) 1) National Research University Belgorod State University, Belgorod, Russia2) Belgorod University of Cooperation, Economics and Low, Belgorod, RussiaE-mail: blazh@bsu.edu.ru

2. INTRODUCTION • When a charged particle crosses the entrance surface of the crystal plate the transition radiation arises (TR) [1], • 1. G. M. Garibian, C. Yang, X- ray Transition Radiation, Erevan, USSR, 1983 (in Russian). • which then is diffracted by a system of parallel atomic planes of the crystal, forming the diffracted transition radiation DTR [2-4]. • 2. CatichaA. //Phys. Rev. A. 1989. V. 40. P. 4322. • 3. NasonovN.N. //Phys. Lett. A. 1998. V. 246. P. 148. • 4. ArtruX. Rullhusen P.// Nucl. Instr. Meth. В. 1998. V.145. P. 1. • At the same time a charged particle Coulomb field is scattered by a system of parallel atomic planes of the crystal, creating a parametric X-ray radiation (PXR) [5-7]. • 5. М.Л. Тер-Микаэлян, Влияние среды на электромагнитные процессы при высоких энергиях, АН АрмССР, Ереван (1969), с. 459. • 6. Г.М. Гарибян, Ян Ши// ЖЭТФ.1971.T. 61.P. 930. • 7. В.Г. Барышевский, И. Д. Феранчук// ЖЭТФ. 1971. T. 61. P. 944. • In the scheme of a symmetric reflection when the system of diffracting atomic planes perpendicular (in the case of Laue scattering geometry) or parallel (in the case of Bragg scattering) to the surface of the crystal plate, the radiation mechanisms in the two-wave approximation of dynamic diffraction theory were considered in [8-11]. • 8. NasonovN., Noskov A.// Nucl. Instr. Meth. B. 2003. V. 201. P.67. • 9. Kubankin A.S., Nasonov N.N., Sergienko V.I., Vnukov I.E.//Nucl. Instr. Meth. В. 2003. V. 201.P. 97. • 10. AdischevY.N., Arishev S.N., Vnukov A.V., et al. //Nucl. Instr. Meth. В. 2003. V.201. P. 114. • 11. NasonovN.N., Kaplin V.V., Uglov S.R., et al. // Nucl. Instr. Meth. В. 2005. V. 227. P.41. • In the general case of asymmetric reflection of radiation from the plate when the diffracted atomic planes make an arbitrary angle with the surface of the plate, the dynamic effects of PXR and DTR are considered in [12-15], • 12. S. Blazhevich, A. Noskov // Nucl. Instr. Meth. B. 2006. V. 252. P. 69. • 13. C.В. Блажевич, А.В. Носков // Поверхность. Рентгеновские, синхротронные и нейтронные исследования. 2009. №6. C.71. • 14. C.В. Блажевич, А.В. Носков// ЖЭТФ. 2009. Т.136. Вып.6. С.1043. • 15. Blazhevich S.V., Noskov A.V.// Nucl. Instr. Meth. В. 2008. V. 266. P.3770. • which shown that by changing the asymmetry of reflection, we can significantly increase the radiation yield. Traditionally, the radiation of a relativistic particle in a periodically layered structure was considered in the Bragg scattering geometry for the case where the reflecting layers are parallel to the entrance surface, i.e. for the case of symmetric reflection. Theradiationin a periodiclayeredstructureisusuallyviewedasresonanttransitionradiation [5.16]. • 5. М.Л. Тер-Микаэлян, Влияние среды на электромагнитные процессы при высоких энергиях, АН АрмССР, Ереван (1969), с. 459. • 16. M.A. Piestrup, D.G. Boyers, C.I. Pincus et al.// Phys.Rev. A. 1992. V. 45. P. 1183. • In the works [17], • 17. N.N. Nasonov, V.V. Kaplin, S.R. Uglov, M.A. Piestrup, C.K. Gary //Phys. Rev. E. 2003. V 68. P. 3604. • the radiation from an artificial periodic structure was represented as the sum of diffracted transition radiation (DTR) and parametric X-ray radiation (PXR). • In the cited works the radiation of relativistic particles in an artificial periodic structure was considered only in the Bragg scattering geometry for the special case of symmetric reflection of the particle field with respect to the target surface, when the diffracted layers are parallel to the target surface. • In the present paper we consider the relativistic electron coherent X-ray radiation scattering in the direction of Bragg crossing the artificial periodic structure in the Laue scattering geometry. By analogy with the crystalline environment the coherent radiation is considered as the sum of PXR and DTR contributions. On the basis of two-wave approximation of dynamic diffraction theory [18] • 18. Пинскер З.Г. Динамическое рассеяние рентгеновских лучей в идеальных кристаллах. М.: Наука, 1974, 369 c. • the expressions describing the spectral and angular characteristics of radiation are derived.

3. Fig. 1Geometry of the radiation process and the system of the using parameters notations, and are the radiation angles, is Bragg angle, and are wave vectors of incident and diffracted photons.

4. Fig.2. Schema of the radiation reflection off the crystal plate. The case ( ) corresponds to the symmetric reflection.

5. Fig.2a. L=Le*cos(d-qb)

8. Since two X-ray waves determine the DTR yield, so for the analysis of their contributions to the radiation spectral density it is convenient to write the expression for R(s)DTR in such a form: (*) is the path of the electron in the target

9. Next we write the expression (*) in a more demonstrable form: • Where • is the path of a photon in a crystal • is the length of the X-waves extinction in a periodic medium.

10. We have carried out a numerical analysis for each of the waves and for their interference term separately:

11. Fig.3. The contributions of two the fields, and and of their interference term to the total spectral density of DTR:

12. Fig. 4. The same as Fig.3 for a bigger target thickness

13. Fig.5. The same as in Fig.4 for bigger target thickness

14. Fig.6. The spectral density of the relativistic electron DTR for different values of the target thickness L= b* (Lext/2) .

15. Comparison of DTR from crystal … • Fig.7. Angular density of DTR of a relativistic electron crossing a plate of tungsten single crystal (W)

16. …and multilayered target • Fig.8. The DTR angular density of the relativistic electron crossing the artificial periodic structure (BE-W) under the conditions similar to the ones which presented in Fig.7.

17. Fig.9. The spectra of the PXR at different observation angles q^.

18. Fig.10. The spectra of DTR at different observation angles q^

19. Fig.11. Same as fig.8 but for another value of asymmetry parameter .

20. Fig.12. Same as fig.10 but for other value of asymmetry parameter .

21. Fig.13. The dependence of the DTR angular density on the target thickness for a fixed observation angle q^ .

22. Fig.14. The comparison of the DTR and PXR densities for the target thickness optimal for DTR.

23. CONCLUSION • A theory for the coherent radiation of the relativistic electron crossing an artificial periodic structure is constructed for case of Laue scattering geometry. The expressions for spectral-angular characteristics of the radiation in Bragg direction are derived and investigated. • The contributions to the DTR yield of two X-ray waves, which are responsible for DTR formation, are studied. It is shown that with increasing of the target thickness, one of these waves is absorbed anomalously strongly and the other wave abnormally weakly, i.e. the Borrmann effect is manifested in DTR in an artificial periodic structure in the Laue geometry • Based on these expression it is shown that the angular density of diffracted transition radiation in layered target are more than one order higher than the density in single crystal radiator under similar conditions. • It was found, that DTR in artificial periodic structure is more monochromatic than parametric X-radiation (PXR). In this connection, DTR mechanism may be more promising in terms of the building of a new intense tunable X-ray source on basis of the relativistic electron interaction with artificial multilayer structure. It is shown, that DTR yield in an artificial periodic structure in the direction of maximum angular density increases as a function of target thickness up to some optimal value of thickness and then decreases because of the photoabsorption in the target substance.

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