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Journal Articles Zeitschrift für Angewandte Mathematik und Physik Year : 2021

On a magnetic skin effect in eddy current problems: the magnetic potential in magnetically soft materials

Abstract

This work is concerned with the time-harmonic eddy current problem in a bidimen-sional setting with a high contrast of magnetic permeabilities between a conducting medium and a dielectric medium. We describe a magnetic skin effect by deriving rigorously a multiscale expansion for the magnetic potential in power series of a small parameter ε which represents the inverse of the square root of a relative permeability. We make explicit the first asymptotics up to the order ε^3. As an application we obtain impedance conditions up to the fourth order of approximation for the magnetic potential. Finally we measure this skin effect with a characteristic length that depends on the scalar curvature of the boundary of the conductor.
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Dates and versions

hal-02968889 , version 1 (16-10-2020)

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Victor Péron, Clair Poignard. On a magnetic skin effect in eddy current problems: the magnetic potential in magnetically soft materials. Zeitschrift für Angewandte Mathematik und Physik, 2021, ⟨10.1007/s00033-021-01596-6⟩. ⟨hal-02968889⟩
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