Single-Conductor Transmission Line Model Incorporating Radiation Reaction

Abstract

Increasing attention has been paid to the study of electromagnetic (EM) phenomena in complicated wire networks [e.g., metamaterials and EM compatibility (EMC)]. However, their lack of physical insights usually prevents systematic analysis of the phenomena. To address this, this article describes a transmission line (TL) model of a finite-length single conductor without a return current path to be applied as a fundamental physical model. The model includes radiation effects in a self-consistent way (i.e., its radiation reaction is included in an explicit way), and it is based on Sommerfeld principal wave propagation (strictly speaking, its behavior is asymptotic as the wire's conductivity approaches infinity). This formulation naturally leads to the consequence that the current flowing along a single conductor illuminated by an incident EM field is classified into three components, which are dominated by physically distinct principles, the principal wave itself (I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tr</sub> , the traveling wave), the one reinduced by the traveling wave radiation (I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">re</sub> , the radiation reaction), and the one that directly scatters the incident field (I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sc</sub> , the scattering wave). The EM energies of the traveling wave and radiation reaction components are stored in the TL and propagate, while the scattering component indicates an instantaneous scattering process. These components reveal the dynamical characteristics of a single-conductor TL model that includes radiation phenomena.