Design of Cylindrical Coils Within Spindle-Shaped Magnetic Shielding Cylinders Using Conformal Mapping

The coupling effect between the active magnetic compensation coil and the ferromagnetic material in the spindle-shaped magnetic shielding cylinder (sMSC) normally leads to distortion of the target magnetic field. The existing methods for designing coils within ferromagnetic boundaries are mainly for regular magnetic shielding cylinder (MSC) and cubic magnetic shielding room (MSR); there is currently no analytical method available for designing coils within ferromagnetic boundaries for sMSC. In this article, a new method based on conformal mapping and target field method (CM-TFM) for designing high uniformity cylindrical coils within a closed sMSC is introduced. It addresses the issue of degradation in magnetic field uniformity due to the coupling of the axial uniform field coil with the magnetic shielding ferromagnetic material inside the sMSC. The simulations indicate that the maximum magnetic field deviation in the target area is reduced from 4.04% to 1.38% in the CM-TFM compared to the coil designed using the conventional target field method (TFM) without considering the coupling effect of the magnetically shielded ferromagnetic material and the coil. The overall percentage of the target area with the magnetic field deviation less than 1% is 92.59% in CM-TFM coils, compared to only 40.74% in TFM coils. The experimental results confirm the effectiveness and practicality of this design method in compensating for the residual magnetic field of sMSC. The proposed approach is essential for the implementation of near-zero magnetic field environments.