Low – frequency electromagnetic scattering by a perfectly conducting torus. The Rayleigh approximations

Article type: Research Article

Authors: Venkov, George^a

Affiliations: [a] Faculty of Applied Mathematics, Department of Differential Equations, Technical University of Sofia, 8 'Kl. Ohridski' Str., 1756 Sofia, Bulgaria. Tel.: +359 2 968 1841; E-mail: [email protected]

Abstract: The paper investigates the propagation of a plane electromagnetic wave in the exterior of a perfectly conducting torus. Using the fact that in toroidal coordinates the vector Helmholtz equation does not admit separation of variables we apply the low-frequency method and the electromagnetic scattering problem reduces to a sequence of potential problems. The incomplete R-separation leads to infinite system of three-diagonal form. More precisely, the boundary conditions for the magnetic field produce a third-order recurrence relations, due to the Riemannian radical and the non-orthogonality of the toroidal harmonics in the angular variable. The three-diagonal infinite systems of linear algebraic equations are solved analytically via the appropriate use of finite continuous fractions.

Keywords: Electromagnetic scattering, low-frequency approximation method, toroidal harmonics, infinite algebraic systems; The author is partially supported by the NATO–CNR Advanced fellowships no. 215.36 S

DOI: 10.3233/JAE-2006-779

Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 24, no. 1-2, pp. 91-103, 2006