An integral equation approach to electromagnetic diffraction by a cylinder
type: Item
instance of: scholarly article
title: An integral equation approach to electromagnetic diffraction by a cylinder
zbMATH Open document ID: 0977.78011
author: R. Cade
published in: IMA Journal of Applied Mathematics
publication date: 2001-04-04T00:00:00Z
Mathematics Subject Classification ID: 78A45
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 45E99
zbMATH DE Number: 1584444
zbMATH Keywords: Robin type integral equations
zbMATH Keywords: diffraction
zbMATH Keywords: electromagnetic plane wave
zbMATH Keywords: surface charge density
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1093/imamat/66.1.33
OpenAlex ID: W2056577620
DOI: 10.1093/IMAMAT/66.1.33
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review text: The author considers the diffraction of an electromagnetic plane wave by a non-perfectly conducting circular cylinder of radius \(a\). He shows that the surface charge density satisfies two integral equations, one being of the first type and the second being of Robin type. He looks for a series solution for the surface charge density of the form NEWLINE\[NEWLINE\sigma (P,t)= \sigma_0 (P,t)+ \sum^\infty_{n=1} \sigma_n(P,t)NEWLINE\]NEWLINE where \(\sigma_n (P,t)= \alpha^n \sum^n_{m=0} \log^m \alpha\tau_{mn} (P,t)\) and \(\alpha= (\omega a)/c\). NEWLINENEWLINENEWLINESimilar expansions are given for the scalar and vector potentials. The solution for \(\sigma\) is obtained by a perturbation process, it being shown that in the first approximation there is no body current. It is pointed out that the theory is only valid for near fields and low frequencies, but not for optical frequencies nor for great distances from the cylinder.
reviewed by: Ll. G. Chambers
description: scientific article