A study of IECC design and low frequency magnetic field noise suppression in sMSC by random Kaczmarz algorithm

To address the degradation of magnetic field (MF) uniformity caused by the coupling between active compensation coils and the ferromagnetic boundaries of spindle-shaped magnetic shielding cylinder (sMSC), this study proposes an internal and external compact coil (IECC) design and optimization method. The IECC integrates coils placed near the inner and outer surfaces of the sMSC to improve space utilization. The method transforms the complex sMSC cross-section into a rectangular MSC cross-section by conformal mapping. The active-passive coupling model of the IECC and the sMSC shield is then established using the Green’s function method. To overcome overfitting issues in conventional target field methods, the random Kaczmarz (RK) algorithm is introduced for optimization, reducing the required target field points while establishing a large homogeneous region. Simulation results demonstrate the superiority of the RK-optimized IECC: within a target region (R_t = 0.5 R_o), the maximum MF deviation f₁ and the average MF deviation f₂ are 4.24% and 0.97%, representing reductions of 47.52% and 63.26% compared to Tikhonov regularization. Experimental validation confirms significant low-frequency MF noise suppression (50.42%–97.99% amplitude reduction within 50 Hz), notably reducing 0.01 Hz noise from 1439.911 pT/Hz¹/²–46.507