A computational methodology and results for quasistatic multilayered magnetic shielding

A methodology for accurate calculations of shielding factors for quasistatic multilayered magnetic shields is described. "Transfer relations" for individual layers with specified magnetic permeabilities and electrical conductivities are spliced together. Specific transfer relations for four layer geometries (planar, cylindrical with transverse fields, cylindrical with axial fields, and spherical) and constraints at source and shielded surfaces for six source-shield configurations involving both externally applied fields and enclosed sources are developed. Limiting cases are extracted for magnetically permeable, nonconducting layers, and for thin, magnetically nonpermeable, conducting layers. Reciprocity conditions are identified for interchanged source and shielded regions in planar, transverse field cylindrical, and spherical geometries. Variations of magnetic field and flux density with position are shown for a specific planar example involving alternating layers of aluminum and steel, with the same total shield thickness occupied by either one or five layer pairs. Simulations with alternating layers of aluminum and steel for the four layer geometries are used to study the effects of material composition, number of layer pairs, and air gaps. An optimal number of layer pairs for a given total shield thickness is identified. Results from simulations where induced currents in the steel layers are neglected are compared with those for simulations with a realistic conductivity value for steel to assess the relative effects of flux shunting and induced current shielding.