Design of uniform field coils with ferrite shielding considering coupling effects: An EDM approach

Uniform field coils are indispensable components in the field of quantum precision measurement, especially in ultra-weak magnetic measurements, where the enhancement of field uniformity and the size of the uniform region are crucial. In achieving customized weak magnetic environments, the coupling effect between ferrite magnetic shielding and the coil's magnetic field is a major challenge in the high-precision design of uniform field coils. This paper analyzes the relationships between the coil-to-ferrite radius ratio, the number of coil pairs, the length-to-diameter ratio, and the uniformity of the coil's magnetic field. A design for uniform field coils using the equal division method (EDM) and the SNOPT algorithm is proposed, enabling the identification of optimal coil configurations tailored to specific geometric constraints. This method is verified through finite element simulation and experimental validation and applied to design axial uniform field coils for ferrite magnetic shielding barrels with radii of 90 mm and 110 mm. Experimental validation shows that coils designed using this method exhibit larger uniform regions and higher uniformity compared to traditional Lee-Whiting coils. Specifically, the uniformity in the target uniform region is improved by factors of 70 and 22.5 for the two coil sizes, respectively. The proposed design significantly reduces the complexity of the design process, minimizes reliance on approximate conditions, and takes into account the influence of ferrite magnetic shielding barrels on the coil's magnetic field uniformity. This advancement supports the construction of zero-magnetic-field environments and provides a practical foundation for balancing performance, noise minimization, and engineering feasibility in ultra-sensitive magnetic measurement applications.