Design of Compact Self-Shielded Uniform Magnetic Field Coils Based on Multipole Moment Optimization

Uniform magnetic field coils (UMFCs) are essential for generating accurate magnetic fields that meet a variety of application requirements. However, the magnetic fields generated by such coils lose their original distribution characteristics due to various interference factors, such as the coupling effect between the coil and magnetic material and crosstalk between adjacent coils. Herein, we propose a novel method for designing self-shielded UMFCs (S-UMFCs) to fundamentally solve the magnetic field distortion problem by preadjusting the field distribution characteristics, which particularly enable compact applications. Taylor series expansions were used to ensure field uniformity inside the coil, and multipole moment cancellation was applied to promote the attenuation of the external magnetic field. Furthermore, a function balancing uniformity and attenuation was introduced into the optimization model. The performance of the proposed method did not depend on the selection of characteristic points, which solved the problem of universality and was superior to that of the conventional method. Moreover, the method could significantly reduce the volume of the resulting coils. Simulation and experimental results indicated that the maximum magnetic field error generated in the central region of the designed coil was on the order of 10-4 regardless of the boundary condition (free or ferromagnetic) and that the field attenuation ratio at the same external position was lower by an order of magnitude compared with that of the commonly used Lee-Whiting coil.