Topological transformation of eddy currents in anisotropic electrically conductive structures

Abstract

This paper presents numerical modeling and a comprehensive topological analysis of the eddy current density component jz distribution in homogeneous anisotropic electrically conductive plates. The analysis is performed using a spectral-domain solver based on the Fourier transform of the Poisson equation and covers a wide range of anisotropy coefficients (0.05 ≤ K ≤ 150) at a crystallographic axis orientation angle γ = 45°. The results demonstrate that the classical interpretation of eddy current structure 'destruction' at extreme K values is actually a qualitative topological transformation—specifically, a transition from closed elliptical trajectories to quasi-linear directed flows. We prove the invariance of this transformation mechanism with respect to the reciprocal transformation K → 1/K accompanied by a 90° coordinate system rotation. Furthermore, by analyzing the curvature radius of eddy current lines at the ellipse vertices, we propose a physically justified criterion for determining critical operating regimes. This criterion directly links the plate's geometric parameters (thickness dlayer, major and minor semi-axes l and m) to the critical anisotropy coefficient K_cr. Practically, these findings allow for deliberate control over the eddy current field topology in anisotropic electrically conductive transducers. Transitioning to the quasi-linear regime enables significant adjustments in device impedance, control of the transformation ratio and inductance, and the realization of directed energy flows. This opens up new avenues for developing efficient matching elements, directed electromagnetic radiation sources, antenna systems, and optimized wideband infocommunication devices with enhanced energy efficiency.