A multiscale approach to the analysis of magnetic grid shields and its validation

This paper illustrates the application of the multiple scale expansion theory to the analysis of heterogeneous thin structures employed for the magnetic field shielding and, in particular, the attention is focused on grid shields. These structures are conveniently employed in the mitigation of magnetic fields when the thermal dissipation is a severe restriction. The problem modelling is faced by applying the thin-shell approximation to the Maxwell equations, introducing appropriate interface conditions between the shield surfaces. Starting from this formulation, a homogenisation technique, based on the multiple scale expansion theory, is developed in order to replace the heterogeneous structure with an equivalent homogenous one. The proposed method enables an efficient analysis of magnetic and pure conductive heterogeneous shields with a significant decrease of the computational burden. The results are validated by comparison with a standard modelling approach, when possible, and with experiments developed on specific laboratory set-ups for frequencies up to 2 kHz.