Computation of the Magnetic Field around Long Nonconducting Magnetic Shields

A numerical method for computation of the quasi-static magnetic field in the vicinity of long nonconducting magnetic shields placed parallel with straight conductors is presented. The primary magnetic-field source are time-harmonic currents in conductors. The purpose of the shields is to reduce the magnetic-flux density in a particular region. The shielding efficiency can be determined by a comparison of the primary and total field. The method assumes the magnetic shields to be electrically nonconducting, ferrite, laminated, or weakly conducting, so that the impact of the induced eddy currents is negligible. The calculation of the field in the vicinity of the shield structure is based on a preceding determination of the magnetization current distribution on the shield surfaces. This distribution results from the solution of the appropriate integral equation which we solve by using the moment method. If the flat magnetic and/or conducting shield is exceedingly wide (Fig. 2), the analytical solution (5) for the infinite planar shield can be applied. This enables verification of the method and the numerical procedure. As seen from the comparison given in Fig. 3, the proposed method is suitable for weakly conducting and also in some cases for conducting magnetic shields thus enabling the analysis of a wider spectrum of the shield structures. The proposed method offers an excellent insight in the shielding effect and is found to be a very useful tool in designing shielding structures. This is demonstrated in the case of shileding the magnetic field from a pair of conductors by a U-shaped shield (Fig. 4). We compare four types of shields: a) weakly conducting magnetic, b) conducting nonmagnetic, and two shileds that consist of two layers, c) the first one has its inner layer magnetic and the outer conducting and d) the second one has its inner layer conducting and the outer magnetic. The first of the four types of shileds is analysed with the proposed method, the second one with the multiconductor method [1], and the last two with a concept reasonably combining both methods. Figs. 5 and 6 show the magnetic-flux lines and distribution of the shielding factor, respectively, in the vicinity of the shield.