1. Low – frequency electromagnetic scattering by a perfectly conducting torus. The Rayleigh approximations.
- Author
-
Venkov, George
- Subjects
- *
ELECTROMAGNETIC waves , *TORUS , *HELMHOLTZ equation , *RIEMANNIAN manifolds , *LINEAR algebra - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2006
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