Boundary Value Problems of Shielding Magnetic Fields by Cylindrical Multilayered Film Screens with Nonlinear Properties of the Layers

A mathematical model is proposed for shielding permanent magnetic fields by a cylindrical thin-walled multilayered film screen made of materials with permeability depending nonlinearly on the magnetic field intensity. Boundary value problems with Robin boundary conditions and integral boundary conditions on the screen surface are stated for the magnetostatic equations. Efficient numerical methods are developed for solving these problems with allowance for the matching of contact layers with different magnetic properties. A new form of the nonlinear permeability factor is derived from experimental data. The magnetic field potential and intensity in the multilayered screen, as well as the shielding efficiency factor, which characterizes the attenuation of an external magnetic field when penetrating into the cylindrical screen, are studied numerically.