Coupling-Free Magnetic Field Coils at Identical Surface Inside Magnetic Shielding Systems

In precision magnetic field measurement, the combination system of magnetic shielding devices and coils is essential to provide a stable and controllable magnetic field environment. However, close proximity between coils and shielding introduces severe coupling effects that degrade performance of the system. Self-shielded coil is conventionally used to reduce this effect, but its suppression effect is limited, and its nested configuration causes a large volume waste. To address the problem, we propose a novel design method for coupling-free magnetic field coil set, including main coils and shielded coils, at identical surface inside magnetic shielding systems, which can achieve ultra-high coupling-resistance and uniformity with maximum space saving. Based on the Fourier-Bessel function and magnetic field boundary condition, analytical models for magnetic field of the designed coils set under free and ferromagnetic boundaries are established, respectively. Through comparative analysis, the additional term caused by the coupling effect is separated, which enables the complete suppression of the coupling effect at the source. In addition, the quantum-inspired genetic algorithm is employed to solve the complex problem with strong constraints of higher performance and identical surface configuration efficiently. Taking the most commonly used circular coils in the shielding cylinder as the optimization object, we carry out the optimization. Experimental results demonstrate that our optimized coils reduce coupling factor to 0.28%, and improve uniformity to the order of 10⁻⁴ without any volume loss. The method can also be extended to other types of coils and magnetic shielding configurations to improve the accuracy of magnetic field measurement.