Nonasymptotic Homogenization of Laminated Magnetic Cores

We consider the homogenization of laminated magnetic cores in the non-asymptotic case when the spatial period of the structure is not vanishingly small relative to the penetration depth. In contrast to the well-established numerical multiscale methods, the objective of this article is to construct an analytical homogenized model, which can then be solved using any available numerical technique. We discuss two alternative definitions of effective magnetic permeability, its dependence on the penetration depth, and a corresponding peculiar resonance of its imaginary part.