Improved Square-Coil Configurations for Homogeneous Magnetic Field Generation

Homogeneous magnetic field is widely used in various applications, and Helmholtz and Merritt coils are the most commonly used homogeneous field generators. However, only the field homogeneity at the center point is concerned in their design, which leads to restriction for most applications, where a certain volume of homogeneous field is required. This indicates that traditional coil configurations can be further optimized. Based upon a comprehensive definition of homogeneous field, improved three-s and four-coil configurations are proposed in this article. Practical formulae with normalized coil parameters are given to provide a convenient tool for designers. These formulae establish relationships between coil parameters and the required homogeneous field. The accuracy of the formulae is verified by the finite-element analysis. Comparisons with Merritt coils show that, when getting the same homogeneous field, the improved coils can reduce both power loss and conductor mass by up to 24.8%. Through a comparison among main coil configurations, the improved four-coil configuration is recommended for homogeneous magnetic field generation. For high-intensity magnetic field applications, the winding cross-section effect is analyzed. At last, experiments are performed to verify the theoretical analysis, and the reason why the improved coils have better performance than traditional ones is revealed.