Analysis and improvement of the uniformity of magnetic field coil based on the cylindrical magnetic shield in atomic magnetometers

The magnetic field performance of the uniform coils will be affected by magnetic shields and produce errors in the atomic magnetometer. It is necessary to analyze the influencing factors and guide the coil design. Aiming at the above shortcomings, this paper analyzes the coupling effect of magnetic shield and coil and proposed a Lee-Whiting coil design method based on the linearly decreasing inertia weight particle swarm optimization (LDW-PSO) algorithm. Firstly, the magnetic field model under the ferromagnetic boundary is established, and the effects of the size, thickness and permeability of the magnetic shield on the magnitude and uniformity of the Lee-Whiting coil magnetic field are analyzed. The results show that the coupling coefficient of the coil changes monotonically with the change of the size of the magnetic shield, while the uniformity error has a minimum value with the change of the size of the shield. In addition, an improved Lee-Whiting coil is designed by combining the LDW-PSO algorithm, which improves the uniformity of the coil. Compared with the original coil, the measured uniformity error of the improved coil is reduced from 8.39×10⁻⁴ to 2.81×10⁻⁴. The accuracy of the theoretical analysis is verified by experiments. This paper is of great significance to study the coupling and optimization design of the coil based on the magnetic shields in atomic magnetometers.