Surface wave, skin effect, and per unit length parameters of the single-wire transmission line at low frequency, for nonmagnetic and magnetic wires

Surface wave technology for high-speed communications is a current research topic aimed to respond to increasing data rate demands on existing copper infrastructures. Also, the topic of surface waves has recently gained importance in the modeling of transmission line towers hit by lightning strikes with spectral content in the megahertz band. The single-wire transmission line structure (return conductor absent) cannot support TEM waves; it supports a TM Sommerfeld wave fully described by two propagation constants and two characteristic impedances. Nonetheless, the literature on single-wire transmission-line structures has been employing quasi-static per unit length constitutive parameters, inductance and capacitance, borrowed from ordinary two-conductor transmission line TEM analysis. This work develops, discusses, and compares various possible definitions of these constitutive parameters using different physical approaches: TEM-approach, circuit-approach, and energy-approach. Numerical results for nonmagnetic and magnetic wires, copper and steel wires, respectively, are obtained in the range 1 Hz to 1 GHz. Our analysis shows that in some circumstances the TEM and circuit approaches may lead to nonphysical results, but, remarkably, all the approaches seem to converge to a common dominant term either in the per unit length capacitance or in the per unit length inductance, whose product is frequency-invariant. Considering the different approaches under discussion, the differences among the observed results for the per unit length constitutive parameters are negligibly small, of second-order importance.