Linear source in a circular tunnel

We study models for propagation in circular tunnels. The excitation is a fundamental electric current source. We produce expressions for the fields in terms of a Fourier transform over the axial variable. We perform an asymptotic analysis of the complex wavenumbers; for use as initial estimates in a complex root finder. We then produce the modes in the lossy structure by contour integration techniques. We include numerical results for the field intensity as a function of axial distance for several frequencies and constitutive parameters of interest. We comment in particular concerning the modal content and the specific form of the field both near to and far from the antenna source.