Numerical investigations of electromagnetic processes in a solid cylindrical shield

Abstract

A mathematical model is suggested to describe the processes in a solid cylindrical shield in protection against an alternating magnetic field. The model is constructed with respect to the complex amplitude of magnetic vector potential. Since magnetic field lines are in a plane perpendicular to the axis of a cylindrical shield, the problem becomes two-dimensional. The electromagnetic parameters of the considered media are constant and isotropic. The plates at which the magnetic potential is set are the source of the magnetic field. A distribution of real and imaginary components of the complex amplitude of magnetic potential is described by four differential equations in the conducting medium and by two equations in the dielectric one. An equality of magnetic potential at both sides of the interface is predetermined at the interfaces. The Robin boundary condition provides equality of the magnetic vector potential to zero at an infinite distance from the shield. The obtained differential equation system supplemented with the boundary conditions can be numerically solved by the finite elements method using the Galerkin method. As a result, distributions of magnetic potential and magnetic field intensity in the absence and presence of a shield are determined; shielding attenuation is then calculated. It is found that, with increasing shield thickness and noise frequency, the efficiency of electromagnetic shielding is increased. The adequacy of the suggested model and technique of determination of the shielding efficiency is corroborated by comparison with the results of an analytical model for a copper cylindrical shield.