The Impedance of Dipoles in a Circular Tunnel with an Axial Conductor

The electromagnetic fields of dipole emitters located inside an empty tunnel or cylindrical cavity are first formulated. Both electric and magnetic types are considered. The results are used to deduce an expression for the change of self-impedance due to the presence of the tunnel walls. The input resistance R of the electric dipole is approximately a constant for frequencies less than about 25 MHz for a typical tunnel radius of 2 m. In contrast, for the same conditions, R for the magnetic dipole or small loop varies approximately as the square of the frequency. The theory is extended to allow for the presence of an axial conductor or cable within the tunnel. The presence of the cable increases R for both a transversely oriented electric dipole and a circumferentially oriented magnetic dipole but decreases R for an axial electric dipole. Not surprisingly, the axial magnetic dipole is only weakly influenced by the presence of the cable.