Time domain generalized telegrapher's equations for the electromagnetic field coupling to finite-length wires buried in a lossy half-space

The paper deals with a derivation of a time domain variant of the generalized telegrapher's equations for transient electromagnetic field coupling to buried wires. The formulation is based on the thin wire antenna theory in the time domain. The influence of a lossy half-space is taken into account by means of the time dependent reflection coefficient approximation arising from the modified image theory (MIT), while the per-unit-length surface impedance accounts for the conductor losses. The obtained space-time integral expressions are handled analytically. The concept of the scattered voltage is naturally included in the full model formulation. Computational examples are given for the induced currents along the buried wire and compared to the results obtained by using the transmission line (TL) approximation.