Asymptotic expansion for the magnetic potential in the eddy current problem : the ferromagnetic case

We derive rigorously a multiscale expansion at any order for the solution of an eddy current problem which is addressed in a bidimensional setting where the conducting medium is magnetic. We make explicit the first terms of the expansion up to the fifth order of approximation with respect to the skin depth parameter. As an application of this expansion we derive impedance conditions up to the fifth order for the magnetic potential. This approach leads to solve only equations in the dielectric medium.