Design of Uniform Magnetic Field Coil by Quasi-Elliptic Function Fitting Method With Multiple Optimizations in Miniature Atomic Sensors

This article presents a design method of cylindrical uniform field coil based on quasi-elliptic function fitting (EFF) method with multiple optimizations. The EFF method is a type of discrete wire techniques aiming at simplifying the coil structure. Combing with particle swarm optimization (PSO) algorithm, the optimized parameters of EFF coil are obtained for highly uniform magnetic field. To further improve the uniformity of magnetic field in the central space, a new regional points selection optimization method is proposed. The calculation results show that after PSO optimization, the absolute maximum relative error in the target region is optimized to 0.098% by EFF coil comparing with modified single saddle coil (3.08%), nest coil (2.4%), and target field method (TFM) coil (0.11%). After regional points selection optimization, the volume proportion of absolute magnetic field relative error less than
$1\times 10^{-4}$
increases from 35.24% to 54.38% by EFF coil comparing with TFM coil. In addition, the simple EFF coil structure is verified to be easy to process and keep high performance through experiments. As the EFF coil’s high uniformity and simple structure, the new method has important significance for the miniaturization of atomic sensors.