Field and earth‐return impedance for conductors inside an elliptic tunnel

Abstract

An electrodynamic boundary value problem is solved in the elliptic cylindrical coordinates to give the earth-return impedance of conductors inside an elliptic tunnel. The authors commence the analysis with the eigenfunction expansion of the source in the elliptic cylindrical coordinates, and the series solutions are obtained from the field ansatzes consisting of the modified Mathieu functions Ke m (ξ, q) and Ko m (ξ, q) with imaginary q, for which the detailed descriptions of the numerical implementations are provided, especially for the sign determination rule of Fourier coefficients of the expressions of modified Bessel function products. The proposed method is verified by the numerical results compared with those of finite-element method and good agreement is achieved in all cases. In addition, the presented method is further compared with those developed for the special cases in the literature, from which it is confirmed that proposed method is a valid generalisation of existing ones.