Superadaptive magnetic-field profile design based on stream-function active random selection

Magnetic-field coils are devices utilized to generate high-precision magnetic fields across various physical research and application domains. They typically require specific profile characteristics to effectively fulfill their intended purposes. Among these characteristics, a stream-function-based method has emerged as a crucial approach for designing magnetic-field coils in complex scenarios by constructing the inverse solution according to desired magnetic-field profiles. Its feasibility and accuracy are limited by deviations from the original problem contingent upon the singularities and condition numbers of the coefficient matrix. Moreover, the limited applicability complicates the acquisition of a consistent magnetic field. To construct a fundamentally general approach, this study introduces a superadaptive stream-function design method based on active random selection. The novel method integrates the inverse solution with the Kaczmarz iterative process and incorporates nonuniform grabbing based on matrix row information. These enhancements enable a direct approximation of complex problems and circumvent the challenges encountered with a coefficient matrix. Through the application of designs for shimming planar coils, it is demonstrated that the method can converge to obtain high-precision stream-function parameters that meet the specified profile requirements, even when faced with an unprecedented sharp reduction in the number of target-field points. The method proves to be a promising avenue for expanding design and application scenarios, subverting the limitations of traditional stream-function methods.