Evaluation of Surface Impedance Models for Axisymmetric Eddy-Current Fields

We have investigated the range of validity of the perfect electric conductor and of the standard Rytov-Leontovich impedance boundary condition models for the analysis of axisymmetric eddy-current problems. Using these models, we derived approximate expressions for the magnetic vector potential, field quantities, Joule losses, and forces for conducting spheroids placed in external nonuniform magnetic fields produced by coaxial circular turns carrying currents varying sinusoidally with time. We compared our numerical results for the magnetic field intensity at the conductor surface, power losses, and forces (for both prolate and oblate spheroidally shaped conducting objects) with the results from analytical expressions obtained by applying the exact boundary conditions. While the simpler perfect conductor model can be employed only when the electromagnetic depth of penetration is much smaller than the smallest local radius of curvature, the results obtained by using the standard surface impedance model for conducting prolate and oblate spheroids of various axial ratios are in good agreement with the exact results for skin depths of about 1/5 of the semi-minor axis for electromagnetic forces and for skin depths less than 1/20 of the semi-minor axis for Joule losses