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 A m is defined as the ratio of the magnetic flux density B gap within the gap and the external flux density B ext far from the concentrator. A compact expression for A m makes it possible to evaluate the concentrator performance as a function of the relative magnetic permeability μ r of the concentrator, of its overall length l, width w , and thickness t, and of the gap width w g . Using finite elements, B gap 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 A m as a function of the normalized dimensions w g / l , w / l , and t/ l and of μ r 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 A m is A m ≈ [ ( w g / l ) + 0.421 ] / [ ( w g / l ) + 0.421 D ] , 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.