Skin Effect in Inhomogeneous Euler-Cauchy Tubular Conductors

Abstract

Abstract-This paper presents a novel contribution to the analysis of skin effect phenomena in inhomogeneous tubular conductors. For homogeneous tubular geometries the skin effect diffusion equation has an analytical solution described by a combination of Bessel functions, but, when the conductivity and magnetic permeability of the tubular conductor arbitrarily depend on the radial coordinate an analytical solution cannot be found. However, this work shows that simple closed form solutions for the electromagnetic field and conductor internal impedance do exist, provided that a specific type of radial variation of medium parameters is properly chosen -these novel structures are coined here Euler-Cauchy Structures. Analytic and computation results concerning general and particular Euler-Cauchy Structures are presented, validated, and discussed. Future research on this seminal topic may lead to new engineering applications.

Research on the transmission of electric power via the increased frequency coaxial line to a remote low-power load (consumer)

“…Thus the distribution of the current over the cross-section area of the conductor occurs peripherally according to the surface effect fig. 2 [10]. The inductive resistance of the coaxial cable is much smaller than of other conductor configurations, this is due to the minimum distance between the conductors and the surface effect.…”

Surface Wave, Skin Effect, and Per Unit Length Parameters of the Single-Wire Transmission Line at Low Frequency, for Nonmagnetic and Magnetic Wires

“…That is not the purpose of the present article, where the skin effect is a tool, not a target. Nonetheless, with respect to recent advances (2010's) regarding solid and tubular circular geometries, we may cite: [32], [33] for contributions to full time-domain skin-effect theory in homogeneous solid wires; [34], [35] for contributions to accurate numerical computations of skin-effect impedance in homogeneous cylindrical conductors; [36], [37], [38] for contributions to frequency-domain skin-effect impedance and field calculations in inhomogeneous cylindrical structures; and, also, [39], [40] for contributions to the problematics of the solitary conductor.…”

“…Int ′ (∞) = 0, the contribution W z for the electric energy in(37) takes the form: the Hankel functions from(17), and making a 0 b 0 = αβ, we findW z = Re g…”

A Circuit Approach for the Electromagnetic Analysis of Inhomogeneous Cylindrical Structures

“…Considering that the radial variations of ε(r), σ(r), and µ(r) are such that (A1) can be transformed into an Euler-Cauchy equation [15], a general closed-form analytical solution for the magnetic vector potential in the form of a sum of two complex powers of r was obtained in [15]. Here, however, we offer a new, simpler, particular solution for (A1), which can be expressed in terms of two exponential functions.…”