Analytical model and precise evaluation of multi-layer magnetic shielding performances considering ultra-weak magnetic properties

Regarding the vast difference between the design index and the actual performance of magnetic shielding devices, this paper proposes a novel method of using precise permeability under a specific weak magnetic field, aiming to improve the design accuracy of shielding performance. Firstly, the relative permeability of the permalloy is measured under the applied magnetic field from the geomagnetic field down to 1 nT. Next, the precise shielding coefficient formulas of the single- and double-layer spherical shells are derived. For the double-layer spherical shell, the deviation of remanence between considering the ultra-weak magnetic properties and using the constant permeability is 24.3%. This clarifies the necessity of considering the ultra-weak magnetic properties in multi-layer structures. Then, a new accurate method of the shielding coefficient for the finite-length magnetic shielding cylinder is proposed, with a deviation of less than 5%. Finally, this method has been validated again by remanence measurement of the three-layer magnetic shielding cylinders. The deviation between simulation and experiment is 4.03% when considering the ultra-weak magnetic properties. While using the constant permeability, the deviation is as high as 19.31%. Therefore, considering the ultra weak magnetic properties in multi-layer structures can-significantly improve the accuracy of the performance evaluation.