Analysis of Induced Currents on a Thin Wire Located Symmetrically Inside a Cylinder

This paper deals with the electromagnetic interaction of a straight thin wire located inside a cylinder with the cylinder walls. The wire runs parallel to the cylinder axis and connects its two opposite caps. A lumped source is chosen, which feeds the terminated conductor. For this configuration, an exact analytical solution for the induced current on the conductor is presented. On the basis of a two-sum Green's function expressed in cylindrical coordinates, the current is derived from the boundary conditions for the total electrical field on the surface of the conductor and the Fourier expansion series for the unknown current and the (known) exciting electrical field. The obtained analytical results are compared to those obtained from a full-wave method and show excellent agreement. They clearly document that the electromagnetic interaction between the cylinder and wire can strongly influence the shape of the transmitted signal. In particular, at higher frequencies, more and more resonance frequencies of the cylinder occur in the current spectrum. Therefore, the application of classical transmission-line theory on conductors, which are housed in resonators, is not allowed in general.