Uniform Magnetic Field Coils Decoupling Under Ferromagnetic Boundary

The high-performance weak magnetic field system consisting of active and passive components is urgently required in fields, such as industrial electronics, biomedicine, frontier scientific research, and quantum metrology. However, the accuracy of the system will be inevitably affected by the coupling effect between active magnetic field coils and the magnetic shield materials with high permeability. In this study, we proposed a design method of uniform magnetic field coils decoupling under ferromagnetic boundary, which can essentially eliminate the influence of coupling effect on magnetic field profiles. Based on Green's function and the mirror image method (IM), the magnetic field profile is formulated, in which the coupled and uncoupled terms are separated. Correspondingly, the coupling ratio determined by the coupling term and the relative magnetic field error are taken as two objectives. Combined with the multipole expansion of magnetic vector potential, the constraints between the coil parameters are constructed, and the optimal coil structural parameters are achieved by using multiobjective particle swarm optimization (MOPSO) algorithm. Compared with the conventional structure, the designed coil set can significantly reduce the coupling ratio from 27% to 0.34%, almost three orders of magnitude, meanwhile improve the uniformity by about 46%. We further apply the designed coil set to the closed-loop control in the zero-field environment, and it shows excellent dynamic performance under ferromagnetic boundary comprehensively. The proposed method can quantitatively evaluate the coupling effect on magnetic field, with universal applicability to various magnetic shielding scenarios. It can pave the way for applications that require extremely high-precision magnetic fields.