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To enable the realization of ultra-low magnetic fields for scientific and technological research, magnetic shielding is required to create a space with low residual magnetic field and high shielding factors. The shielding factors of magnetic shields are due to nonlinear material properties, the geometry and structure of the shields, and the external magnetic fields. Magnetic shielding is used in environments full of random realistic disturbances, resulting in an arbitrary and random external magnetic field, and in this case, the shielding effect is hard to define simply by the shielding factors. A new method to simulate and predict a dynamic internal space magnetic field wave is proposed based on the Finite Element method (FEM) combined with the Jiles-Atherton (JA) model. By simulating the hysteresis behavior of the magnetic shields and establishing a dynamic model, the new method can simulate dynamic magnetic field changes inside magnetic shields as long as the external disturbances are known. The shielding factors under an AC external field with a sine wave and certain frequencies are calculated to validate the feasibility of the new method. A real-time wave of internal magnetic flux density under an AC triangular wave external field is simulated directly with the new method versus a method that splits the triangular wave into several sine waves by a Fourier transform, divides the shielding factors, and then adds the quotients together. Moreover, real-time internal waves under some arbitrary fields are measured. Experimental internal magnetic flux density waves of a 4-layer magnetically shielded room (MSR) at the Harbin Institute of Technology (HIT) fit the simulated results well, taking experimental errors into account.

Ultra-low magnetic fields have drawn lots of attention due to their important role in scientific and technological research. The combination of a magnetic shield and an active compensation coil is adopted in most high performance magnetically shielded rooms. Special consideration needs to be taken in the coil design since the magnetic shield significantly affects the uniformity of the magnetic field that is generated by the coil. An analytical model for the magnetic field calculation of the coil inside a cubic magnetic shield is proposed based on the generalized image method, which is validated by finite element analysis. A novel design method of the coil used in a cubic magnetic shield with a large homogeneous volume is proposed. The coil parameters are optimized to obtain a large cubic uniform volume with desired total deviation rate by discretizing the central volume in the coil. In the desired total deviation rate, the normalized usable volume of the new coil increases by 70% when compared with the Merritt coil. A coil system is developed according to the parameters obtained based on this method. The magnetic flux density and practical deviation rate of the coil are measured to validate the accuracy of this model and the feasibility of the design method. The experimental magnetic flux density agrees well with the analytical value. The maximum practical deviation rate of uniform volume of 0.8 × 0.8 × 0.8 m is in good agreement with the theoretical design value, taking into account the experiment errors.