Radiation of a point charge moving uniformly along the axis of a narrow cylindrical ring

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

“…The aim of this appendix is to investigate the asymptotic behaviour of the expansion functions Equation (5). By recalling the well-known asymptotic behaviour of Bessel functions, it is easy to show that…”

“…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). As demonstrated in [34], such a procedure leads to a matrix operator which can be recast as the sum of an invertible matrix, corresponding to the static part of the operator as shown below and a completely continuous operator.…”

“…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.…”

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

“…Today this effect is considered to be a particular case of more broadly defined phenomenon: the radiation that occurs if the charged particles or their beams excite nearby material objects without touching them, in various frequency regions. Such an effect is called diffraction radiation (DR) [5][6][7][8][9][10][11][12][13][14], in order to distinguish it from the transient radiation appearing when a particle crosses a boundary between different materials. Physically, the sources of DR are the surface and polarization currents induced on the scatterers placed in proximity to the beam trajectory.…”

“…In our case, we have the surface wave (2) as the incident field. Still, a similar expression can be derived using the complex angles of incidence y 1,2 above and below the beam trajectory, as defined in (6), and substituting them into the complex Poynting theorem. Extracting the real part, we find that…”