Radiation of a charged particle in the ideally conducting metal waveguide filled with a spatially periodic layered dielectric

The parametric Cherenkov radiation of a uniformly moving particle in an ideally conducting metal waveguide filled with a spatially periodic layered dielectric is investigated analytically and numerically for the case of wavelengths comparable with the inhomogeneity period. Fields and spectra of par...

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Дата:	2018
Автори:	Tkachenko, V.I., Tkachenko, I.V., Tolstoluzhsky, A.P., Khizhnyak, S.N.
Формат:	Стаття
Мова:	English
Опубліковано:	Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2018
Назва видання:	Вопросы атомной науки и техники
Теми:	Нерелятивистская электроника
Онлайн доступ:	http://dspace.nbuv.gov.ua/handle/123456789/147321
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Цитувати:	Radiation of a charged particle in the ideally conducting metal waveguide filled with a spatially periodic layered dielectric / V.I. Tkachenko, I.V. Tkachenko, A.P. Tolstoluzhsky, S.N. Khizhnyak // Вопросы атомной науки и техники. — 2018. — № 4. — С. 13-16. — Бібліогр.: 3 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine

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spelling	irk-123456789-1473212019-02-15T01:24:18Z Radiation of a charged particle in the ideally conducting metal waveguide filled with a spatially periodic layered dielectric Tkachenko, V.I. Tkachenko, I.V. Tolstoluzhsky, A.P. Khizhnyak, S.N. Нерелятивистская электроника The parametric Cherenkov radiation of a uniformly moving particle in an ideally conducting metal waveguide filled with a spatially periodic layered dielectric is investigated analytically and numerically for the case of wavelengths comparable with the inhomogeneity period. Fields and spectra of parametric Cherenkov radiation are described. The particle's average energy losses on the period of the structure and energy fluxes of the fields are determined Аналітично та чисельно проведено дослідження параметричного черенковського випромінювання частинки, що рівномірно рухається в ідеально провідному металевому хвилеводі, заповненому просторово періодичним шаруватим діелектриком для випадку довжин хвиль, які можна порівняти з періодом неоднорідності. Описано поля і спектри параметричного черенковського випромінювання. Знайдено середні по періоду структури втрати енергії частинки і визначені потоки енергії полів. Аналитически и численно проведено исследование параметрического черенковского излучения равномерно движущейся частицы в идеально проводящем металлическом волноводе, заполненном пространственно периодическим слоистым диэлектриком для случая длин волн, сравнимых с периодом неоднородности. Описаны поля и спектры параметрического черенковского излучения. Найдены средние по периоду структуры потери энергии частицы и определены потоки энергии полей. 2018 Article Radiation of a charged particle in the ideally conducting metal waveguide filled with a spatially periodic layered dielectric / V.I. Tkachenko, I.V. Tkachenko, A.P. Tolstoluzhsky, S.N. Khizhnyak // Вопросы атомной науки и техники. — 2018. — № 4. — С. 13-16. — Бібліогр.: 3 назв. — англ. 1562-6016 PACS: 41.60.-m http://dspace.nbuv.gov.ua/handle/123456789/147321 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Нерелятивистская электроника Нерелятивистская электроника
spellingShingle	Нерелятивистская электроника Нерелятивистская электроника Tkachenko, V.I. Tkachenko, I.V. Tolstoluzhsky, A.P. Khizhnyak, S.N. Radiation of a charged particle in the ideally conducting metal waveguide filled with a spatially periodic layered dielectric Вопросы атомной науки и техники
description	The parametric Cherenkov radiation of a uniformly moving particle in an ideally conducting metal waveguide filled with a spatially periodic layered dielectric is investigated analytically and numerically for the case of wavelengths comparable with the inhomogeneity period. Fields and spectra of parametric Cherenkov radiation are described. The particle's average energy losses on the period of the structure and energy fluxes of the fields are determined
format	Article
author	Tkachenko, V.I. Tkachenko, I.V. Tolstoluzhsky, A.P. Khizhnyak, S.N.
author_facet	Tkachenko, V.I. Tkachenko, I.V. Tolstoluzhsky, A.P. Khizhnyak, S.N.
author_sort	Tkachenko, V.I.
title	Radiation of a charged particle in the ideally conducting metal waveguide filled with a spatially periodic layered dielectric
title_short	Radiation of a charged particle in the ideally conducting metal waveguide filled with a spatially periodic layered dielectric
title_full	Radiation of a charged particle in the ideally conducting metal waveguide filled with a spatially periodic layered dielectric
title_fullStr	Radiation of a charged particle in the ideally conducting metal waveguide filled with a spatially periodic layered dielectric
title_full_unstemmed	Radiation of a charged particle in the ideally conducting metal waveguide filled with a spatially periodic layered dielectric
title_sort	radiation of a charged particle in the ideally conducting metal waveguide filled with a spatially periodic layered dielectric
publisher	Національний науковий центр «Харківський фізико-технічний інститут» НАН України
publishDate	2018
topic_facet	Нерелятивистская электроника
url	http://dspace.nbuv.gov.ua/handle/123456789/147321
citation_txt	Radiation of a charged particle in the ideally conducting metal waveguide filled with a spatially periodic layered dielectric / V.I. Tkachenko, I.V. Tkachenko, A.P. Tolstoluzhsky, S.N. Khizhnyak // Вопросы атомной науки и техники. — 2018. — № 4. — С. 13-16. — Бібліогр.: 3 назв. — англ.
series	Вопросы атомной науки и техники
work_keys_str_mv	AT tkachenkovi radiationofachargedparticleintheideallyconductingmetalwaveguidefilledwithaspatiallyperiodiclayereddielectric AT tkachenkoiv radiationofachargedparticleintheideallyconductingmetalwaveguidefilledwithaspatiallyperiodiclayereddielectric AT tolstoluzhskyap radiationofachargedparticleintheideallyconductingmetalwaveguidefilledwithaspatiallyperiodiclayereddielectric AT khizhnyaksn radiationofachargedparticleintheideallyconductingmetalwaveguidefilledwithaspatiallyperiodiclayereddielectric
first_indexed	2025-07-11T01:52:19Z
last_indexed	2025-07-11T01:52:19Z
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fulltext	ISSN 1562-6016. ВАНТ. 2018. №4(116) 13 RADIATION OF A CHARGED PARTICLE IN THE IDEALLY CONDUCTING METAL WAVEGUIDE FILLED WITH A SPATIALLY PERIODIC LAYERED DIELECTRIC V.I. Tkachenko1,2, I.V. Tkachenko1, A.P. Tolstoluzhsky1, S.N. Khizhnyak1 1National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine; 2V.N. Karazin Kharkiv National University, Kharkov, Ukraine The parametric Cherenkov radiation of a uniformly moving particle in an ideally conducting metal waveguide filled with a spatially periodic layered dielectric is investigated analytically and numerically for the case of wave- lengths comparable with the inhomogeneity period. Fields and spectra of parametric Cherenkov radiation are de- scribed. The particle's average energy losses on the period of the structure and energy fluxes of the fields are deter- mined. PACS: 41.60.-m INTRODUCTION In [1], for the first time, a general expression was obtained for the energy losses of a uniformly moving charged particle in an unbounded layered medium and in a waveguide filled with a layered dielectric. The main attention was paid to the energy losses of the charged particle for the case of wavelengths exceeding the peri- od of the dielectric structure. Here the spectral distribu- tion of the polarization losses as well as the losses to the parametric Cherenkov radiation due to the specificity of the interaction of waves in a layered dielectric is studied in detail. For the case of wavelengths comparable with the in- homogeneity period, the energy losses of an oscillating charge moving with a nonrelativistic velocity in a peri- odically changing medium are considered in [2, 3]. In the present paper we continue the investigation of the parametric Cherenkov radiation of a uniformly moving particle in a layered dielectric for the case of wave- lengths comparable to the inhomogeneity period. The fields of the parametric Cerenkov radiation and the spectra of this radiation are obtained, the energy loss of the particle are averaged over the period of the struc- ture and the energy fluxes of the fields are determined. However, it should be noted that the conclusions of [1] are based not on calculating the radiation obtained for the spectral distribution, but on the basis of the tran- sition to an equivalent anisotropic dielectric. Such tran- sition is possible in the case when the wavelength of the radiation considerably exceeds the period of the struc- ture. However, such limitation on the wavelength of the radiation is not always justified. Therefore, it is of interest to consider the parametric Cherenkov radiation of a uniformly moving particle in an ideally conducting metal waveguide filled with a spatially periodic layered dielectric for the case of the wavelengths comparable with the period of inhomoge- neity. Let’s consider the radiation of a charged particle moving along the axis of an ideally conducting metal waveguide filled with a spatially periodic layered die- lectric. Let us determine the spectrum of its parametric Cherenkov radiation. 1. OBTAINING EQUATIONS DESCRIBING PARTICLE RADIATION IN A SPATIALLY PERIODIC LAYERED DIELECTRIC To solve the stated problem let's start from the sys- tem of Maxwell equations describing the interaction of a uniformly moving particle with the electromagnetic waves of a given medium [1]: ˆ ( ) rH Ez z c t φ ε∂ ∂ − = ⋅ ∂ ∂ , (1) ˆ ( )r z HE E z z r c t φµ ∂∂ ∂ − = − ⋅ ∂ ∂ ∂ , (2) ˆ1 ( ) 4 ( )( ) 2 zEz rrH qv vt z r r c t c rφ ε π δδ π ∂∂ ⋅ = ⋅ + ⋅ − ⋅ ∂ ∂ . (3) Here the operators ˆ ˆ, ,ε µ are defined as ˆ ( ) ( , )i t i tz e z eω ωε ε ω⋅ = ⋅ , ˆ ( ) ( , )i t i tz e z eω ωµ µ ω⋅ = ⋅ , (4) q is the charge and v is the velocity of the particle. In the considered case of a charged particle's motion along the axis of a waveguide filled with a dielectric, the equation for determining the Fourier component of the longitudinal component of the electric induction , ( )z nD zω can be represented as: 2 , 2 , 2 , ( )1( , ) ( ) ( , ) ( , )z n n z n z D z z D z k z z z z R ω ω ω λ ε ω µ ω ε ω ε  ∂  ∂ + − =    ∂ ∂    ( ) ( , ) ( , ) , i z i z v vq q ez ik z e c v z z ω ω ε ω µ ω π π ε ω − −    ∂  = + ⋅  ∂      . (5) Here the component of , ( )z nD zω is obtained from the expression for the electric induction , , 0 ,2 2 1 1 2( , ) ( , ) ( ) ( )z z n z n n n rD r z z E J D z RR Jω ω ωε ω λ α ∞ =  = ⋅ =     ∑ using the orthogonality condition of Bessel functions, R is the radius of the waveguide, and nλ the n-th root of the zero-order Bessel function ( )0 0nJ λ = . In what fol- lows we omit the ω , n indices. The layered medium is represented by layers of two homogeneous and isotropic dielectrics alternating along the axis of the waveguide: the layer 0a z− ≤ ≤ has die- lectric and magnetic permeabilities 1 1,ε µ , respectively, the layer has 0 z b≤ ≤ permeabilities 2 2,ε µ . Thus, in ISSN 1562-6016. ВАНТ. 2018. №4(116) 14 each layer, equation (5) is an equation with constant coefficients, the solutions of which in each layer will have the form: 1 1 2 2 1 2 1 1 2 2 1̀ 2 2 2 2 2 2 2 `2 2 1 1 , 1 1 , i z ip z ip z v z i z ip z ip z v z iqkE A e B e e c p v iqkE C e D e e c p v ω ω µ εβ π ω µ εβ π ω −− −−   − ⋅     = ⋅ + ⋅ + ⋅ ⋅   −       − ⋅   = ⋅ + ⋅ + ⋅ ⋅   −    (6) where 2 2 2 1 1 1p k kε µ ⊥= ⋅ − , 2 2 2 2 2 2p k kε µ ⊥= ⋅ − , k c ω = , nk R λ ⊥ = . From equations (1) we find expressions for the com- ponents of the electric and magnetic field strength in each of the regions: 1 2 1 2 2 1 , , i z v z i z v z i kH k k i k qE e c qEH k e kc ω ϕ ϕ ωε π ε π ⊥ ⊥ ⊥ ⊥ − − = + = +       (7) 1 1 1 2 2 1 1 1 , . ikz i r z z z r k dE q e c E k dz dE E k d q e cz β β π π βε βε − − ⊥ ⊥  − = −      − =  −           (8) From the boundary conditions on the surface of die- lectrics and the conditions for the periodicity of the fields ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 01 2 0 01 2 1 2 1 2 ( ) ( ) , ( ) ( ) , ( ) ( ) , ( ) ( ) , z z r rz z i L v z a z b i L v r rz a z b H z H z E z E z e H z H z e E z E z ϕ ϕ ω ϕ ϕ ω = = = = − =− = − =− =  =   =  =   = L a b= + , (9) we obtain a system of linear algebraic equations for finding the coefficients A, B, C and D: ( ) ( ) 1 1 2 2 1 1 2 2 1 2 1 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 i Z , i Z , i Z , i Z , k ki L i b ip a ip a ip b ip b k ki L i b ip a ip a ip b ip b A B C D p A p B p C p D e e A e B e C e D e e p e A p e B p e C p e D k k e β β β β η η ε ε ε ε β ε ε β ηε ε η − − − − − − − − + − − =   − − + = −    + − − =   − − + = −        (10) or in the matrix form M̂ a b⋅ =   . Here 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 ˆ k ki L i L ip a ip a ip b ip b k ki L i L ip a ip a ip b ip b p p p p M e e e e e e p e e p e e p e p e β β β β ε ε ε ε ε ε ε ε − − − − − − − − −   − −   =  − −     − −  , a C A B D      =        , 1 2 1 2 i Z i Z i Z i Z ki b ki b k b ek e β β η η β η η β − −             −   =            −      , 2kq ck η π ⊥= , 1 2 2 1 2 1 1Z P P = − , 2 2 2 1 1 2 2 1 1Z P Pε ε = − , 2 2 2 2m mP p v ω = − , 1, 2m = . From (10) we find the expression for the coefficients A, B, C and D: , , ,A B C DA B C DD D D D = = = = D D D D , (11) where 1 2 1 2 ˆdet( ) 8 cos cosM p p L v ωε ε ψ  D = = −      is a matrix determinant M̂ , 1 2 2 1 1 2 1 2 2 1 1 2 1cos cos( )cos( ) sin( )sin( ) 2 p pp a p b p a p b p p ε ε ψ ε ε   = − −    . It should be noted that the field , ( )r nÅ zω contains the derivative with respect to the longitudinal coordinate from the longitudinal field , ( )z ndЕ z dzω , so that the right-hand sides of equations (10) have the terms pro- portional to v kω β= . Thus, the equalities (11) allow us to determine the coefficients , , ,A B C D . All the singularities in the expressions for the coeffi- cients , , ,A B C D are determined by the conditions of [1]: 2 2 2 1 / 0,p vω− = (12) 2 2 2 2 / 0,p vω− = (13) cos( / ) cos( ) 0.L vω ψ− = (14) We are interested in the radiation of a particle in a medium due to the interference of fields in a layered dielectric, which is determined by the roots of equation (14). Since the equation cos( / ) cos( ) 0L vω ψ− = is the dispersion equation of a layered dielectric, the frequen- cies determined by the roots of this equation correspond to waves propagating in such a layered medium. We note that the values of the coefficients , , ,A B C D are expressed in terms of 1Z and 2Z . Hence it follows that for small differences in the param- eters of the medium for each of the regions, for exam- ple, for 1 2 1ε ε− << , the values of the coefficients , , ,A B C D will also be small. Physically it is ex- plained by the fact that when the media parameters dif- ference in two regions decrease we turn to the case of a homogeneous medium in which interference effects are absent. Therefore, to increase the interference efficiency of fields excited in layered media, it seems necessary to use dielectric layers with substantially different dielec- tric permittivities. ISSN 1562-6016. ВАНТ. 2018. №4(116) 15 2. NUMERICAL SOLUTION OF EQUATIONS DESCRIBED OF PARTICLE RADIATION IN SPATIALLY PERIODIC LAYER DIELECTRIC Since the expressions for the fields (6) - (8), and the dispersion equation (14) in the general case can not be analytically investigated, let us analyze them numerical- ly. To do this, we choose the following values of the media parameters: 1 2 1µ µ= = , 1 2.1ε = , 2 3.5ε = , 210 0.1a b −= = m, 23 10R −= ⋅ m, / 0.65, 0.95v cβ = = . In following calculations the particle charge was chosen equal to 9 106 10 , 9.613 10q e C−= ⋅ = ⋅ . Graphs of the dependence of the function ( / ) cos( / ) cos( )D c L cω ω β ψ= − , and its spectrum, shown in Figs. 1 and 3 show that the dependence of ( / )D cω is determined mainly by the beating of two cosines with a period /L L βL = equal to the characteristic length of the change cos( / )L cω β and with a period ψL equal to the characteristic length of the change cos( )ψ . In addition, as follows from the form of the normal- ized spectral power SpD , there is a weakly expressed branch of cos( )ψ with a small period of variation ψλ . Fig. 1. Dependence ( / ) cos( / ) cos( )D c L cω ω β ψ= − on / cω and its spectrum SpD for / 0.65v cβ = = . Where in 0.973LL = , 1.0528ψL = , 0.1353ψλ = Fig. 2. Dependences of the difference 1( ) /i i ik cω ω π−D = − of the neighboring roots of the dispersion equation ( / ) 0iD cω = of layered dielectric on the values / cω of these roots for / 0.65v cβ = = and 1k Rλ⊥ = Fig. 3. Dependence ( / ) cos( / ) cos( )D c L cω ω β ψ= − on / cω and its spectrum SpD for / 0.95v cβ = = , 1k Rλ⊥ = . Where in 0.6657LL = , 1.0528ψL = , 0.1353ψλ = Fig. 4. Dependences of the difference 1( ) /i i ik cω ω π−D = − of the neighboring roots of the dispersion equation ( / ) 0iD cω = of layered dielectric on the values / cω of these roots for / 0.95v cβ = = and 1k Rλ⊥ = On the graphs of the difference in the wavenumbers of the neighboring zeros of the dispersion equation (Figs. 2 and 4), it is clearly seen that in addition to the main two wavenumbers, which make the maximum contribution to the change in the dispersion equation (14), there is one more wavenumber indicating the roots of the dispersion equation with close values of wave- numbers. Thus, we see that there are different periods of succession of the roots of the dispersion equation (14). To determine the averages over the period of energy losses of particles, the expressions for the average field structures of the field have the form [1]: , 1 b i t z za z vt E E e dz L ω ω − = = ∫ , , 1 b i t r ra z vt E E e dz L ω ω − = = ∫ , , 1 b i t a z vt H H e dz L ω ϕ ω ϕ− = = ∫ . (15) Summarizing the obtained fields for various trans- verse wavenumbers with allowance for their radial dis- tribution, we find the dependences of the mean fields , ,z rE E Hϕ of the parametric Cherenkov radiation on the radius (shown in the figures below), as well as the dependence of the energy losses averages on the period of the structure on the radius: 1 0 2 2 1 11 ( , ) 2 ( ) 2 ( ( , ) ( , )), ( ) res j j Nbess z n NNbess n z res z res n jn z W q E r d z J rk iq E E r E r R J q ω ω π ω ω λ ∞ = −∞ ⊥ = = ∂ − = = ∂ + − = ∑ ∫ ∑ ∑ (16) where n nk Rλ⊥ = , Nbess is the number of radial har- monics, jresω are the roots of the dispersion equation (14) for each nk⊥ , Nres is equal to the number of roots of the dispersion equation (14) in a given frequency interval. The values for the fields ( ) jz resE ω are deter- mined from equations (6) in each region. It follows from (16) that the particle's average ener- gy loss is determined by the average field on the period of the structure zE . Let us find the dependence of the fields averages on the structure period , ,z rE E Hϕ on the radius for the case when the thicknesses of the dielectric layers are the same. To represent the radial dependence, the number of steps along the radius is chosen equal to 70, 24Nbess = . ISSN 1562-6016. ВАНТ. 2018. №4(116) 16 The graphs of the average fields dependence , ,z rE E Hϕ on radius averaged on the structure period are shown in Figs. 5, 6 а b а b Fig. 5. Dependence of the fields on the radius averaged on the structure period: а) zE ; b) ,rE Hϕ for the parameters / 0.65v cβ = = Fig. 6. Dependence of the fields on the radius averaged on the structure period: а) zE ; b) ,rE Hϕ for the parameters / 0.95v cβ = = Analysis of (15) shows that the mean values of the field zE are real, and the mean values of the fields rE and Hϕ are, as expected, purely imaginary. This indi- cates on the transfer of radiation energy along the axis of the waveguide. The energy flux for the average over the period struc- ture of the fields excited by the particle is determined by the Umov-Poynting vector: Re mid midS E H = ×     . Hence, it is not difficult to determine the values of the energy fluxes from the projections on the coordinate axes: ( )Re zr HS E ϕ= − , 0Sϕ = , ( )*Re rz ES H ϕ= . Fig. 7. The average energy fluxes over a structure period zS for / 0.65v cβ = = Fig. 8. The average energy fluxes over a structure period zS for / 0.95v cβ = = CONCLUSIONS Thus, as a result of the carried out investigation of the radiation of a charged particle moving along the axis of an ideally conducting metal waveguide filled with a spatially periodic layered dielectric, the following con- clusions can be drawn. 1. The problem of radiation of charged particle in an ideally conducting metal waveguide filles with a spatial- ly periodic layered dielectric is solved without a transi- tion to an equivalent anisotropic dielectric. 2. The dependencies of electric and magnetic radia- tion fields averaged on the structure period on the waveguide's radius are determined numerically under conditions when the period of the structure is of the same order as the wavelength of the radiation and the width of the dielectrics is the same. 3. It is shown that for equal thicknesses of the dielec- trics the mean values of the field zE are real, and the mean values of the fields ,rE Hϕ are purely imaginary. 4. The average over the structure period radiation flux for equal thicknesses of dielectrics is positive, di- rected along the waveguide axis, has a maximum at small distances from the waveguide axis, and decreases with approach to the waveguide wall. 5. The carried out investigation makes it possible to determine both the average fields generated by the charged particle and the energy fluxes of these fields for arbitrary values of the thicknesses and dielectric permit- tivities of the layers, the velocity of the charged particle, and the waveguide's radius. REFERENCES 1. Ia.B. Fainberg and N.A. Khizhniak. Energy Loss of a Charged Particle Passing Through a Laminar Dielectric // Soviet Physics JETP. 1957, v. 32, № 4, p. 720-729. 2. B.V. Borts, V.I. Tkachenko, I.V. Tkachenko. Multi- layer bimetallic media as protection method from radi- oactive radiation // Problems of Atomic Science and Technology. Series “Physics of Radiation Effects and Radiation Materials Science”. 2010, № 1, p. 123-130. 3. V.I. Tkachenko, I.V. Tkachenko Radiation of the oscillating charge moving with a non-relativistic ve- losity in a periodically non-uniform media // Prob- lems of Atomic Science and Technology. Series “Plasma Electronics and New Methods of Accelera- tion”. 2008, № 4, p. 242-244. Article received 16.05.2018 ИЗЛУЧЕНИЕ ЗАРЯЖЕННОЙ ЧАСТИЦЫ В ИДЕАЛЬНО ПРОВОДЯЩЕМ МЕТАЛЛИЧЕСКОМ ВОЛНОВОДЕ, ЗАПОЛНЕННОМ ПРОСТРАНСТВЕННО ПЕРИОДИЧЕСКИМ СЛОИСТЫМ ДИЭЛЕКТРИКОМ В.И. Ткаченко, И.В. Ткаченко, А.П. Толстолужский, С.Н. Хижняк Аналитически и численно проведено исследование параметрического черенковского излучения равномерно движу- щейся частицы в идеально проводящем металлическом волноводе, заполненном пространственно периодическим слои- стым диэлектриком для случая длин волн, сравнимых с периодом неоднородности. Описаны поля и спектры параметри- ческого черенковского излучения. Найдены средние по периоду структуры потери энергии частицы и определены пото- ки энергии полей. ВИПРОМІНЮВАННЯ ЗАРЯДЖЕНОЇ ЧАСТИНКИ У ІДЕАЛЬНО ПРОВІДНОМУ МЕТАЛЕВОМУ ХВИЛЕВОДІ, ЗАПОВНЕНОМУ ПРОСТОРОВО ПЕРІОДИЧНИМ ШАРУВАТИМ ДІЕЛЕКТРИКОМ В.І. Ткаченко, І.В. Ткаченко, О.П. Толстолужський, С.М. Хижняк Аналітично та чисельно проведено дослідження параметричного черенковського випромінювання частинки, що рівно- мірно рухається в ідеально провідному металевому хвилеводі, заповненому просторово періодичним шаруватим діелектри- ком для випадку довжин хвиль, які можна порівняти з періодом неоднорідності. Описано поля і спектри параметричного черенковського випромінювання. Знайдено середні по періоду структури втрати енергії частинки і визначені потоки енергії полів.

Radiation of a charged particle in the ideally conducting metal waveguide filled with a spatially periodic layered dielectric

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