An innovative design method is proposed for highly uniform magnetic field coils using a particle swarm optimization (PSO) algorithm. We use an optimization approach instead of the conventional method of solving closed-form equations to obtain the coil geometric parameters. We apply a PSO algorithm to the optimization of the coil structure and set an appropriate penalty function and boundary conditions. A discrete optimization is employed to avoid obtaining parameters with a large number of decimal places. Compared with the conventional design method, our method solves the problem of how to design a coil set to produce a highly uniform magnetic field under various structural and process constraints. The coil designed by this method can produce a highly uniform magnetic field for a larger effective space. This is significant for miniaturized applications, especially for miniature atomic sensors. The calculations show that the magnetic field deviations of the triaxial cylindrical coils designed by this innovative method are decreased by more than two orders of magnitude in the volume of interest (VOI) compared to conventional triaxial cylindrical coils. Our experimental measurements are consistent with theoretical values. Measurements show that relative magnetic field uniformities of the axial and radial coils reache 1.2×10–4 and 3.9×10–3 along the magnetic field axis in the range of ±0.5R. In addition, this method can also be used to design gradient field coils or other shaped coils.

In this paper, an optimization method that uses the derivatives and the target field information of the magnetic field simultaneously is proposed to suppress the coupling between the coil and the magnetic shielding in miniature atomic sensors. The coupling between the coil and the magnetic shielding varies with the material magnetic permeability, which causes the magnetic field to fluctuate with the temperature as the material permeability. The magnetic field fluctuations will cause the measurement errors and drifts of the sensors. The proposed method can effectively suppress the magnetization of the magnetic shielding caused by the coil magnetic field. A shielded coil outside the main coil is used to efficiently attenuate the magnetic field outside the main coil to suppress the coupling between the coil and the magnetic shielding. A coil system consisting of pairs of circular coils distributed on two coaxial cylinder surfaces is proposed in this paper. The Taylor expansion is used to ensure the uniformity of the internal magnetic field, while the target field information is used to ensure the attenuation of the external magnetic field. A particle swarm optimization (PSO) algorithm is used to optimize the parameters of the main and shielded coils. The theoretical calculations and the finite element analysis prove that the proposed approach is an effective design method for the self-shielded coils.

Heating the vapor cell without introducing magnetic field is a requirement for magnetically sensitive atomic instruments. But, the magnetic field is inevitable in the electrical heating mode. Therefore, how to realize the optimal design of electric heating film becomes an important issue in practice. To solve this problem, a quantitative analysis of magnetic field cancellation is conducted, and a quadra-layered multipole moment heating film is proposed with optimized conduction pattern. First, considering that the wire number and current directions may influence the magnetic field, a different conduction pattern in a single-layer heating film is analyzed. Second, the electromagnetic multipole moment of multilayer heating film is further analyzed. Based on the study of self-cancellation effect of magnetic field, the configuration of the designed heating film is optimized with minimal magnetic field. Finally, sufficient simulations and experiments are developed to verify the superiority of the designed quadra-layered multipole moment heating film on magnetic field minimization.