Design of Biplane Coils Based on Funnel Algorithm for Generating a Near-Zero Magnetic Environment in MSR

The biplane coils (BCs) based on the inverse design method are crucial for creating the near-zero magnetic environment in magnetic shielding room (MSR), but multiparameter optimization remains a key factor that limits the performance of the BCs. This study proposes a funnel algorithm (FA) to solve the issue of multiparameter optimization in the design. The upper and lower limits of the parameters are dynamically adjusted based on the previous calculating step. By gradually reducing the upper and lower limits, we achieve the BCs with optimal performance. This method has been verified by both the theoretical analysis and experimental test. Compared with other methods, the designed coils show a higher space utilization ratio (SUR) and smaller relative errors, with the SUR improved from 1.6% to 3.75% and the relative errors all less than 2%. Based on the designed BCs, the total residual magnetic field is stabilized below 40.4 pT at the central point of the MSR, with the noise reaching the intrinsic noise of the flux-gate magnetometer in the frequency range of interest. The proposed method can significantly improve the performance of the BCs, thus reducing the space and construct cost of the MSR and promoting the magnetoencephalogram (MEG) measurement based on the quantum technology.