Fields in a rough-walled circular tunnel excited by a ring source: surface-impedance formulation

The subject of electromagnetic wave propagation in regions such as caves and tunnels, for application to wireless communications in these environments, is of interest from both theoretical and practical points of view. We present an approach for determining the electromagnetic field in a circular tunnel with a rough wall when the field is excited by an electric or magnetic ring source. An equivalent surface-impedance boundary condition has been used to represent the actual rough interface between the tunnel and the surrounding medium. The field is found to comprise a deterministic or coherent component, identical to that which would be found in a tunnel with a smooth wall, and a random or incoherent component whose expected value is zero and whose covariance functions can be expressed in terms of integrals over the power spectral density of the surface roughness. Representations of the field in the tunnel can now be developed in terms of modal or ray expansions; these can be obtained from different methods for evaluating the integral representations in certain integral equations.