Design of Highly Uniform Magnetic Field Coils Based on a Particle Swarm Optimization Algorithm

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.