Design of high uniformity magnetic field three-axis coil based on simulated annealing-particle swarm hybrid optimization algorithm

Abstract A uniform magnetic field offers numerous advantages in fluxgate calibration and human magnetic field detection. By employing three-axis coils, interference from the geomagnetic field and other magnetic fields can be minimized within a confined space, thereby providing optimal environmental conditions. The traditional Helmholtz coil design has been improved by adopting an octagonal coil as the primary design element. The position of each coil group in the optimized design is determined using a simulated annealing-particle swarm hybrid optimization algorithm. The proposed optimized structures include the post-octagonal Garrett coil and the octagonal Merritt coil, along with the introduction of a non-moment coil concept to further enhance the uniformity of the magnetic field distribution. According to finite element simulations and experimental results, the average error in the target area for the optimized coil is 0.043%, and the space utilization rate reaches 88%, which is approximately half that of the Lee-Whiting coil and cos θ coils system (44.84%). These results demonstrate the superior performance of the proposed coil in terms of uniform region size, providing a more homogeneous magnetic field.