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A new design method is proposed for a triaxial magnetic field gradient compensation system based on ferromagnetic boundary for atomic sensors. The target field method and the whale optimization algorithm are combined to design magnetic field coils thus transforming the complex analytical solution process into an intelligent optimization problem, while the boundary mirror method is introduced to decouple the coil from the magnetic shield. Magnetic field gradient coils are designed according to the coil design method and combined with the divergence and rotation theorems to form the triaxial gradients compensation system to suppress the magnetic field inhomogeneity in nine directions. The simulation and experimental results are compared with the results before and after compensation by using the box line diagram representing the statistics of the magnetic field deviation, in which the median value is reduced by 65.87% and 85.16%, the minimum by 99.66% and 77.76%, the 25 th quantile by 97.89% and 79.94%, and the 75th quantile by 91.52% and 85.17%, respectively.
Wu et al. (Wed,) studied this question.