Nonlinear Modeling Research on External Magnetic Field and Remanent Magnetism in Magnetic Shielding Shell

In magnetoencephalography (MEG) and cold atom clocks systems, measurement of target signals requires a near-zero magnetic environment. To achieve this, it is critical to apply external magnetic field to minimize the internal field. However, external magnetic compensation remains challenging due to the nonlinear relationship between the external magnetic field and remnant magnetism. Precise and parsimonious modeling for this nonlinear characteristic is important to enhance the magnetic compensation performance. Currently, two methods are employed for modeling the nonlinear behavior: analytical methods involve complex computational procedures and are easily subject to geometric constraints of the shell; direct fitting methods are unsuitable for high-precision tasks. In this paper, a three-dimensional modeling method for the nonlinear relationship is proposed. The remanent magnetism is divided into the sum of the linearly attenuated magnetic field from the external environment and the induced magnetic field from the material. The nonlinear magnetisation behaviour of the material is then described by Bouc-Wen (BW) model. Thus, the remanent magnetisation nonlinear model is obtained based on attenuated field, induced field and BW model (AIF-BW model). The results show that AIF-BW model is superior to existing methods in terms of calculation accuracy and computational simplicity. And it is applicable to shielding layers with different geometries. On the other hand, the model is in the form of a first-order derivative equation, which allows to establish a close connection between the magnetic shielding problem and control theory. Therefore, this study has important application significance for active magnetic compensation technology.