Coupling impedance of a PEC angular strip in a vacuum pipe

Abstract

This study deals with the evaluation of the longitudinal and transverse coupling impedance of a charge travelling in a drift tube with a perfectly electric conductive angular strip. The problem is formulated in the particle frame as dual series equations, and efficiently solved through the representation of the unknown in terms of Neumann series. Then, the electric parameters are obtained in the pipe frame through the Lorentz transforms. The presented solution can be adopted as the general methodology in case of angular discontinuities in particle accelerators.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

General approach to the line source electromagnetic scattering by a circular strip: Both E‐ and H‐polarisation cases

“…The results show that less than 5% deviation occurs. The reason for the deviation is that MAS does not take into account the edges of the structures [21]. As provided in the figure, the proposed method is validated by different methods.…”

“…Note that, Φ E ðφÞ stands for the RP of the electric field. Explicitly, Φ E is provided in Equation (21):…”

“…Then, the scattered field is expressed by using Fourier series properties and the addition theorem. Before satisfying the boundary condition, the Fourier series expansion of the current density on the arc is utilised due to periodicity in the radial direction [21]. Here, first, the current density is expressed in terms of Gegenbauer polynomials with respect to both the nature of the geometry and the edge condition [8, 19].…”

Guest Editorial: Method of analytical regularisation for new frontiers of applied electromagnetics

“…The paper ‘Coupling impedance of a PEC angular strip in a vacuum pipe’ by Assante et al. [18], presents a general methodology which can be applied in the case of the angular discontinuities in particle accelerators. The evaluation of the longitudinal and transverse coupling impedance of a charge travelling in a drift tube with an angular strip is formulated in terms of the dual series equation solved by means of the method of analytical preconditioning selecting the expansion functions reconstructing the behaviour of the unknown at the edges.…”

Analysis of the Scattering from a Two Stacked Thin Resistive Disks Resonator by Means of the Helmholtz–Galerkin Regularizing Technique

“…This is what happens when: (1) the Galerkin scheme is adopted, and (2) the selected expansion functions are orthonormal eigenfunctions of a suitable operator containing the most singular part of the integral operator at hand. Such an approach, appropriately called method of analytical preconditioning, is very effective, as clearly shown in the literature devoted to the study of the scattering, propagation, and radiation problems [23][24][25][26][27][28][29][30][31][32][33]. Another way to obtain a guaranteed-convergence consists in solving numerically the singular integral equation by means of a Nyström-type discretization scheme taking into account the singularity of the integral equation and the behavior of the unknowns at the edges [34][35][36][37][38].…”