Hybrid Optimal Design of Square Highly Uniform Magnetic Field Coils

Square coils with a high magnetic field uniformity have a wide range of applications. This study innovatively proposes a hybrid design optimization method for uniform magnetic field coils. The Taylor series expansions of the three components (3-TE) are applied to the design of multiple pairs of square coils for the first time, and on this basis, field relative errors of the target field points are further combined to improve the uniformity of the target area. Through this hybrid optimization method, the design of the coils is transformed into a constrained nonlinear optimization problem, and the structural parameters are obtained through the particle swarm optimization algorithm. Simulation and experimental results establish that in comparison with the conventional square Helmholtz coil, the uniformity of the coils designed by the 3-TE method has been optimized by 52.83%, and the introduction of target field points further improved the uniformity by 86.61% in the target area. Simultaneously, the proportion of areas with a field relative error of less than $10^{-4}$ increased from 5.71 to 21.43% as a consequence of this method.