Hybrid optimal design method for magnetic field coils under magnetic shielding boundary

A novel strategy for designing uniform magnetic field and gradient magnetic field coils considering the boundary effect of magnetic shielding is proposed in this study. This strategy uses intelligent optimization algorithm to skillfully transform the complex coil design problem into the spatial optimization problem of individual population. The mirror method is combined with Green’s function to accurately calculate the magnetic field, and the target field method (TFM) is combined with the whale optimization algorithm to optimize the stream functions using adaptive ridge regression. The minimum fitness function is defined as the real-time magnetic field relative error, and the optimal ridge coefficient is continuously obtained by determining the current density coefficient. The proposed method significantly reduces the magnetic field deviation in the target area compared to the conventional TFM, with reductions ranging from 12.2% to 0.11% (Bx coil), 0.3% to 0.02% (Bz coil), 20% to 10% (dBx/dz coil) and 2.9% to 2.4% (dBz/dz coil). The strategy has been effectively validated by analytical simulations and experimental results, and is expected to be applied to the design of uniform field coils and gradient coils for ultra-high precision atomic sensors.