Diffraction radiation of a point charge moving along the axis of a segment of a circular waveguide

Pazynin, V. L.; Sologub, V. G.

doi:10.1007/bf01039457

Cited by 11 publications

(6 citation statements)

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“…1320which can be substituted into the right hand side of Equation (8). We can now multiply both sides of the resulting equation by functions (6) and integrate it in rdr from 0 to ∞. At both sides, upon inversion of the order of integrations, the spatial integrals are the inverse Hankel transform of Equation ( 6), thus giving back Equation (5).…”

Section: Single Ringmentioning

confidence: 99%

“…which can be reduced to an algebraic system of equations, according to the Galerkin method, by means of the projection onto the same functions defined by Equation (6). In order to analytically perform the projection, it is useful to recall that [52].…”

Section: Single Ringmentioning

confidence: 99%

“…This appendix is devoted to the demonstration of Equation (6). The starting point is the definition of the Dirac Delta function via Bessel functions.…”

Section: Appendix Amentioning

confidence: 99%

“…It was considered for the first time likely by Bobrinev and Braginskii [1] in 1958 for non-relativistic particles and in 1959 by Dnestrovskii and Kostomarov for the ultra-relativistic case [2]. Since then, many other articles have dealt with the diffraction by axially symmetric structures [3][4][5][6][7][8][9][10][11][12][13] as well as perfectly conducting semi-planes [14,15] and wedges [16,17]. In particular, in [10] a paradox rose when calculating the wake potential, which happened to be a not-causal function in the ultra-relativistic case.…”

Section: Introductionmentioning

confidence: 99%

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Longitudinal coupling impedance of a particle traveling in PEC rings: A regularised analysis

Assante

Panariello

Schettino

et al. 2021

IET Microwaves Antenna & Prop

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The analysis of a charged particle traveling through one, two, or infinite conducting rings is presented. The problem is formulated in the spectral domain as integral equations of Fredholm type, solved by Galerkin's method employing entire domain functions factorising the correct edge behaviour of the unknown induced current. As a result, high accuracy and numerical stability are achieved. Numerical results are presented, proving the effectiveness of the method, and the parameters relevant to accelerator physics are calculated.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Section: Single Ringmentioning

confidence: 99%

Section: Single Ringmentioning

confidence: 99%

“…This appendix is devoted to the demonstration of Equation (6). The starting point is the definition of the Dirac Delta function via Bessel functions.…”

Section: Appendix Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Longitudinal coupling impedance of a particle traveling in PEC rings: A regularised analysis

Assante

Panariello

Schettino

et al. 2021

IET Microwaves Antenna & Prop

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show abstract

“…As for the 3-D MAR-based algorithms, they have been developed so far only for a few rotationally symmetric zero-thickness PEC screens of simple shapes: flat disk [24], finite circular cylinder [25], spherical disk [26], and finite cone [27]. The corresponding numerical results can be considered as reference ones; however, they relate only to the near and far fields of on-axis dipoles and, for flat and spherical disks, to the broadside incidence of plane wave.…”

Section: Introductionmentioning

confidence: 99%

Nystrom-Type Method in Three-Dimensional Electromagnetic Diffraction by a Finite PEC Rotationally Symmetric Surface

Bulygin

Nosich

Gandel³

2012

IEEE Trans. Antennas Propagat.

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Time-harmonic electromagnetic wave diffraction by a perfectly electrically conducting (PEC) finite rotationally symmetric surface located in free space is investigated. The problem is split to independent azimuth orders and reduced to the sets of coupled hypersingular and singular integral equations (IEs) for the surface current components. These IEs are discretized by the Nystrom-type method of discrete singularities using the interpolation type quadrature formulas. From the solutions of corresponding matrix equations the near-and the far-field patterns are obtained. The presented method has guaranteed convergence for arbitrary not axially symmetric primary field.Index Terms-Body of revolution (BOR), focusing, interpolation type quadrature formulas, radar cross-section, scattering, singular and hypersingular integral equations.

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Visible light from modulated electron beam moving between twin circular silver nanowires forming plasmonic photonic molecule

Yevtushenko¹,

Dukhopelnykov²

2020

J. Opt.

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The visible-range diffraction radiation of harmonically modulated electron beam, which moves between twin circular silver nanowires, is considered. The electromagnetic field of such a two-dimensional beam is a surface wave propagating along its trajectory with the phase velocity equal to the beam velocity. This wave induces currents on the nanowires and hence radiation occurs even if the beam does not touch the wires. If the wires are tuned to a resonance, the radiated power displays a peak proportional to the resonant mode Q-factor. Sub-wavelength in radius silver nanowires are famous as nanoresonators due to the localized surface-plasmon modes. In our analysis, we use the field expansions in the azimuthal Fourier series and the addition theorems for the cylindrical functions. This enables us to reduce the wave scattering problem to a Fredholm second kind infinite-matrix equation that guarantees convergence of numerical solutions. Truncating this matrix, we compute the near and far field patterns of the wires as optically coupled plasmonic resonators and analyze dependence of the far-field spectral characteristics on the wavelength and electron beam parameters.

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Diffraction radiation of a point charge moving along the axis of a segment of a circular waveguide

Cited by 11 publications

References 0 publications

Longitudinal coupling impedance of a particle traveling in PEC rings: A regularised analysis

Longitudinal coupling impedance of a particle traveling in PEC rings: A regularised analysis

Nystrom-Type Method in Three-Dimensional Electromagnetic Diffraction by a Finite PEC Rotationally Symmetric Surface

Visible light from modulated electron beam moving between twin circular silver nanowires forming plasmonic photonic molecule

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