Diffraction Radiation Generated by a Density-Modulated Electron Beam Flying Over the Periodic Boundary of the Medium Section. I. Analytical Basis

Abstract

The paper is focused on reliable modeling of the effects associated with the resonant transformation of the field of a plane, density modulated electron beam, flying over the periodically uneven boundary of a natural or artificial medium, in the field of volume outgoing waves. Here, the general information (analytical basis) is presented on the peculiarities and principal characteristics of electromagnetic fields arising in the situations under consideration, on the procedures for regularization of model boundary value problems describing these situations, and on possible eigen modes of periodic structures. Without relying on this information, it is impossible to advance considerably effectively in solving numerous urgent physical problems (establishing the conditions providing anomalously high levels of Vavilov-Cherenkov and/or Smith-Purcell radiation; diagnostics of beams of charged particles, artificial materials and media) and in practical implementation of new knowledge about the effects of diffraction radiation and their wave analogues in new devices and instruments of optoelectronics, high-power electronics, antenna, and accelerator technology.

Diffraction Radiation Generated by a Density-Modulated Electron Beam Flying Over the Periodic Boundary of the Medium Section. Iv. Structures of Finite Thickness

“…As we wrote in the first of three papers [1][2][3] of this series, Vavilov-Cherenkov radiation (VChR) [4] and Smith-Purcell radiation (SPR) [5] are among the most significant physical phenomena discovered in the 20th century. Classic works [6][7][8][9] are devoted to the theory of these phenomena and questions of their practical use.…”

“…It is not enough to simply record such results, and they also need to be convincingly explained in order to make them interesting, to disclose their potential for prospective consumers working in the field of diffraction electronics, diagnostics of charged particle beams, and monitoring of natural or artificial materials and environments of practical interest. The works [1][2][3] are just devoted to this problem, and there are the main components that are solved: (i) a mathematical model has been constructed and implemented in software that allows obtaining reliable numerical data on all the features of the processes of coherent diffraction radiation during the flight of a plane density-modulated electron beam over a periodic boundary of a half-space occupied by a dispersion medium [1]; (ii) the conditions for the excitation of the so-called eigen modes of the corresponding periodic structure were studied, and those of them which could provoke the effects with an anomalously high level of VChR and SPR were determined [2]; (iii) problem-oriented computational experiments confirming the conclusions based on an analytical consideration of model problems were carried out; they once again demonstrated the possibility of implementing regimes of spatial-frequency transformations of the electron beam field having undoubted practical interest [3].…”

“…All the results of works [1][2][3] concerned the system 'flat density-modulated electron beam -the periodic boundary of the half-space occupied by the dispersion medium'. Obviously, with necessity they had to be 'extended' to more realistic systems in which the dispersion half-space would give way to periodic structures with the same material parameters, but limited in thickness, or the geometric variety of multilayer structures arising due to their wide application in various areas of science and technology.…”

“…This is the provenance and background of the problem considered in this paper. We start it with a brief presentation of the model problem, which is the key for all situations of interest here and was considered in detail in [1].…”

“…form a complete (in space L 2 (0, l)) orthonormal system in the cross-section of the Floquet channel R; Φ n = (n + ζ)2π/l, ζ : Imζ = 0 is a numeric parameter, characterizing the phase shift of the field of spatial harmonics U + n (g, k) and U − n (g, k) along one period of the structure; k = 2π/λ is a frequency parameter; λ is a wavelength in free space. The choice of the branches of the square roots Γ ± n is due to the so-called partial radiation conditions [1,[11][12][13][14], according to which the fields U ± (g, k) should not contain harmonics arriving (transferring energy) from y = ±∞ to the boundary Σ ε,μ…”