An integral equation approach to electromagnetic diffraction by a cylinder (Q2707970)

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.