Hybrid Optimal Design of Biplanar Coils With Uniform Magnetic Field or Field Gradient

This article presents a hybrid optimal design of biplanar coils, which produce uniform fields and field gradients. It treats the coil design issue as a nonlinear programming problem, and seeks the best performance via the optimal algorithm. The target field method is first utilized to obtain the initial coefficients and ranges of searching areas in stream functions. Then, the magnetic field relative error is defined as the fitness function for minimization, and the particle swarm optimization algorithm is adopted to optimize the aforementioned coefficients. It not only overcomes the dependence on the position distribution of target field points, but also reduces the required computational dimensions without affecting the pursuit of the ultimate performance. Comparing this work with the traditional target field method, the field inhomogeneity error in the region of interest is reduced from 6.55% to 0.95% (B _x coil), 12.02% to 0.35% (B _z coil), 16.54% to 0.57% (dB _x /dz coil), and 11.8% to 0.28% (dB _z /dz coil). Numerical simulation and experimental results show the validity and significance of the proposed method. It has great improvements in both uniform fields and field gradients, which is beneficial to the perfect realization of nulling undesired magnetic fields.