On a magnetic skin effect in eddy current problems: the magnetic potential in magnetically soft materials. (English) Zbl 1480.35371
The authors study the time-harmonic eddy current problem in \(\mathbb{R}^2\) and derive an asymptotic expansion for the magnetic potential with high relative permeability. The main result is a description of the magnetic skin effect for the magnetic potential with a multiscale expansion. The power series expansion is done in terms of a small parameter \(\varepsilon\) which is the inverse of the square root of the relative permeability. First order asymptotics up to order \(\varepsilon^3\) are obtained explicitly. The skin effect is measured with a characteristic length which depends on the scalar curvature of the boundary of the conductor. Asymptotic behavior of this characteristic length function is obtained when \(\varepsilon \to 0\).
Reviewer: Eric Stachura (Marietta)
MSC:
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 35C20 | Asymptotic expansions of solutions to PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35B35 | Stability in context of PDEs |
| 35R05 | PDEs with low regular coefficients and/or low regular data |
| 41A60 | Asymptotic approximations, asymptotic expansions (steepest descent, etc.) |
| 78A30 | Electro- and magnetostatics |
Keywords:
asymptotic expansions; impedance conditions; eddy current problems; magnetic potential; ferromagnetic materialReferences:
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