Magnetic Field Coil Design Based on Distributed Taylor Expansion: Toward Large Uniform Area with High Orthogonality and Self-Shielding Feature

The uniform magnetic field coils have typically served as important devices for concern in various scientific research and application fields. However, due to the insufficient proportion of uniform areas and the presence of stray magnetic fields, conventional coil systems fail to meet the high-precision magnetic field distribution requirements of various applications. Therefore, this study proposes a distributed Taylor expansion method based on Taylor series convergence analysis within intervals, to solve the divergence problem associated with the conventional coil design and increase the effective magnetic field working area. In addition, through the creation and screening of characteristic functions, the orthogonality and attenuation of the generated magnetic field are comprehensively improved without changing the basic structure, which is beneficial to solving the common crosstalk and coupling problems caused by stray magnetic fields. The relevant magnetic field characteristics were verified through simulations and experiments, demonstrating that the designed square-coil system can achieve significantly increased large uniform area with high orthogonality and self-shielding features evaluated by suitable characteristic functions established. Thus, the proposed method comprehensively improves coil performance and has strong application advantages and potential.