Radio frequency transmission via a trolley wire in a tunnel with a rail return

An analysis is given for the transmission of electromagnetic waves along a circular tunnel in the presence of axial conductors. One of these conductors is an idealization of a trolley wire with its bonded feeder line that may be located anywhere in the tunnel. The other is a metal rail that is located within the homogeneous rock medium at a finite distance from the tunnel wall. A mode equation for the propagation modes is obtained that is used to obtain numerical results for the attenuation rate in the frequency range 50 to 800 kHz. It is shown that the attenuation rate is only weakly dependent on the burial depth of the rail conductor, at least in the range up to 50 cm. Also, it is found that the rail conductor for the model adopted carries an appreciable fraction of the total return current when typical rock conductivities are assumed. A thin layer of insulation on the rail appears to have a negligible effect. In fact, there is little change even if the rail is within the tunnel and just above the tunnel floor.