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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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https://hal.inria.fr/hal-02968889
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Submitted on : Friday, October 16, 2020 - 10:55:09 AM
Last modification on : Tuesday, October 19, 2021 - 11:06:03 PM

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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, Springer Verlag, In press. ⟨hal-02968889⟩

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