Electromagnetic excitation of a thin wire: a traveling-wave approach

An approximate representation for the current along a perfectly conducting straight thin wire is presented. The current is approximated in terms of pulsed waves that travel along the wire with the velocity of the exterior medium. At the ends of the wire, these pulses are partially reflected, with a constant reflection coefficient and delay time. Subsequently, the traveling-wave representation for the current is used to derive an approximate expression for the electric field outside the wire that is caused by this current. For voltage excitation, this expression contains only closed-form contributions. For plane-wave excitation, the expression contains a single integral over the initial pulse that must be computed numerically. Although the expression obtained is essentially a far-field approximation, it turns out to be valid from distances of the order of a single wire length. Results for a representative choice of wire dimensions and pulse lengths are presented and discussed.