Design of Highly Uniform Axial Magnetic Field Coils Within Magnetic Shielding Box for Miniature NMRG Sensors

The uniform magnetic field coils within the magnetic shielding layer find numerous applications, particularly in miniature nuclear magnetic resonance gyroscope (NMRG) sensors. However, the target magnetic field generated by the designed coils is inevitably distorted due to the adjacent ferromagnetic material that attracts the magnetic field. To address this issue, a novel image method based on uniqueness principle is proposed, which takes into account the coupling effect between the magnetic shielding box (MSB) and the coils. The particle swarm optimization (PSO) algorithm is employed to assist the novel image method in designing highly uniform axial magnetic field coils within a compact MSB. The validity and uniformity of the designed coils are verified by the finite element method (FEM), demonstrating that the maximum relative uniformity error of magnetic flux density ${B}_{z}$ is $2.6\times 10^{-4}$ compared to the original point. Moreover, two classic configurations of uniform magnetic field coils, the Helmholtz coils and the 9449 coils, are introduced to compare the uniformity with the designed coils. Finally, the designed scheme was measured both within and without MSB, and the experimental results indicated that the relative uniformity error of ${B}_{z}$ was in good agreement with the reference values. These findings further substantiate the applicability of the proposed method to miniature atomic sensors that require generating a highly uniform magnetic field within the MSB.