Propagation Along Thin Conductors Parallel to Interfacing Homogeneous Half-Spaces

• Published in: IEEE transactions on electromagnetic compatibility Vol. 60; no. 1; pp. 266 - 275
• Main Authors: Pawlik, Brent, Woodhouse, Darren, Summers, Terrence J.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Boundary conditions; Buried pipes; Conductors; Derivation; Earth return impedance; Electric potential; electromagnetic wave propagation; Fourier transforms; full spectrum; grounding; Half spaces; Impedance; impedance boundary condition; Media; modal equation; mutual impedance; Permeability; Pipelines; Power lines; Resistance; Wave propagation; Wires
• ISSN: 0018-9375; 1558-187X
• DOI: 10.1109/TEMC.2017.2689793

This paper provides a detailed derivation of the complete solution to an electromagnetic wave propagating along a thin wire parallel to the interface between two homogeneous half-spaces, and by extension for multiple parallel wires. The final solution presented in this paper extends the existing theory to include the effects of half-spaces with different magnetic permeabilities, the effects of wire/s with finite conductance, and in the multiconductor case the cross boundary mutual impedances. The latter is of particular importance when considering the coupling between power lines and buried continuously earthed systems, such as counterpoise conductors or buried metallic pipelines. Drawing on the numerous existing methodologies used to solve this problem, the derivation herein utilizes only a partial Fourier transform in combination with continuity conditions to achieve a general solution, which is novel. The solution is shown to agree with earlier works after appropriate restrictions are applied. The approach also serves as a review of some of the more fundamental works on the subject, contributes to understanding the limitations of existing theory, and establishes an alternate process for further extensions in the field.