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

Victor Péron 1 Clair Poignard 2
1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
2 MONC - Modélisation Mathématique pour l'Oncologie
IMB - Institut de Mathématiques de Bordeaux, Institut Bergonié [Bordeaux], Inria Bordeaux - Sud-Ouest
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
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Victor Péron, Clair Poignard. On a magnetic skin effect in eddy current problems: the magnetic potential in magnetically soft materials. 2020. ⟨hal-02968889⟩

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