Magnetic field amplification by slender cuboid-shaped magnetic concentrators with a single gap

This paper proposes a compact model for the magnetic field amplification by long cuboid-shaped magnetic concentrators with a single perpendicular gap. The amplification factor Am is defined as the ratio of the magnetic flux density Bgap within the gap and the external flux density Bext far from the concentrator. A compact expression for Am makes it possible to evaluate the concentrator performance as a function of the relative magnetic permeability μr of the concentrator, of its overall length l  , width ww, and thickness t  , and of the gap width wgwg. Using finite elements, Bgap was modelled for 1050 combinations of concentrator geometries and magnetic permeabilities covering a large range of values. From this systematic numerical study, a phenomenological model for Am as a function of the normalized dimensions wg/lwg/l, w/lw/l, and t/l and of μr was extracted. The model applies to both cases of concentrators limited in their amplification capability by geometry or by permeability. For the common case of geometry-limited concentrators, the model expression for Am is Am≈[(wg/l)+0.421]/[(wg/l)+0.421D]Am≈[(wg/l)+0.421]/[(wg/l)+0.421D], where D denotes the demagnetization factor of the gap-free ellipsoid with the same length, width, and height as the concentrator. The accuracy of the model is highest for such geometry-limited concentrators.