LAUSR

The coupling between the coil and the cylindrical magnetic shield (CMS) in atomic sensors not only results in the inconsistency of the coil constant with the theory but also deteriorates the uniformity, which affects the sensor performance. To solve the abovementioned deficiencies, a design method of highly uniform field coils inside the CMS based on the coupling model with finite permeability and thickness and particle swarm optimization (PSO) with dynamic inertia weights is proposed for the first time. The coupling model of the coil inside the CMS is established by Green’s function method (GFM). Then, it is combined with the nonlinear optimization method, and the coil configuration is optimized by the dynamic inertia weight PSO (DW-PSO) to obtain the optimal parameters. It not only reduces the calculation error of the model, but also improves the uniformity. Comparing this work with the Lee-Whiting coil inside a CMS, the theoretical uniformity is further improved by two orders of magnitude, and measured uniformity errors in the target region reach $1.404\times {10^{-4}}$ , and $2.317\times {10^{-4}}$ , respectively. The correctness and effectiveness are proved by finite-element simulation and experimental results. The accuracy and uniformity of coils can be considerably improved, which is beneficial to further improve the measurement sensitivity of instruments related to magnetic field uniformity.