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Abstract The demand for spatial nonlinear magnetic fields (SNMF) spans diverse domains, encompassing medical applications like drug transportation and aerospace applications such as attitude control. Existing designs of magnetic field coils predominantly focus on uniform and gradient fields as the complexity of nonlinear magnetic field distribution often leads to intricate solution processes. This paper presents a novel approach to coil design, addressing the challenge of SNMF distribution by reconstructing the characteristic matrix within the traditional target field method (TFM). To solve the overdetermined equations involved, we incorporate an improved particle swarm optimization algorithm into the TFM framework. A pair of symmetrical and asymmetrical coils are designed and the effectiveness of this method is verified by comparing the simulated and experimental results.
Yuan et al. (Mon,) studied this question.