Design Method for Planner Coils under Magnetic Shielding Cylinder

A novel strategy using the target field method (TFM) to design uniform and gradient magnetic field coils is proposed thereby addressing the coupling effect of magnetic field coils with high permeability materials. By combining the mirror method and Green’s function to solve the coupling effect between the magnetic field generated by the coil of the cylindrical structure and the externally enclosed high permeability material, the magnetic field generated on the inner surface of the magnetic shield and on the boundary of the magnetic field coil is finally calculated accurately. Compared with the design method that does not consider the magnetic field coupling effect, the field deviation is reduced from 3.3 × 10 ⁻¹ to 3.9 × 10 ⁻² (B x coil), and 9.0×10 ⁻² to 1.20×10 ⁻² (B z coil), the maximum |δ 2 | were reduced from 1.30 × 10 ⁻¹ to 4.0 × 10 ⁻² (dB x /dz coil), and 2.0 × 10 ⁻² to 1.5 × 10 ⁻² (dB z /dz coil). The proposed design strategy is validated by simulation analysis, and the research methodology of this strategy can be further applied to the development of core apparatus for magnetic field regulation and compensation of atomic sensors.