Design of improved four-coil structure with high uniformity and effective coverage rate

Helmholtz coils have extensive applications in biological medicine, aerospace, and other industries depending on the simple structure and miraculous magnetic field characteristics. However, the uniform zone generated by them is not appropriate for scientific experiments with large devices. Due to the limitations of Helmholtz coils in application, a novel design technique is proposed to improve the homogeneity and region of magnetic field. The main approach is to add an auxiliary coil on each side of Helmholtz coils to compensate for the magnetic field that exists farther out from the center point. To analyze the size relationship between the auxiliary coil and the main coil to obtain the best magnetic field distribution, the traditional Maclaurin expansion method and particle swarm optimization (PSO) algorithm are used to research and discuss. The magnetic field distribution and the corresponding effective coverage rate (ECR) of the improved schemes with different structural parameters are calculated under the relative deviations of 0.1%, 0.5% and 1%, respectively. The results obtained by the above optimization methods are verified by the finite element software COMSOL and specific experiments. Both optimization methods manifest that the maximum effective coverage rate can be achieved when the size of the auxiliary coil is consistent with that of the main coil. In addition, we compare the improved four-coil structure proposed in this paper with the existing four-coil square structure under the same volume. The data show that the improved structure has certain advantages in the spatial magnetic field distribution. The corresponding tri-axial coil system is established by adopting the parameters on the single axis, which can achieve a constant magnetic field in arbitrary directions by controlling the magnitude and direction of current on each axis. This provides a theoretical basis for the application of magnetic navigation technology.