In a coil magnetometer, the size and uniformity of the bias magnetic field generated by the Helmholtz coil directly determine the accuracy of the solution of the geomagnetic direction. The design of traditional spherical coils relies heavily on the manual experience or mathematical derivation, making it difficult to obtain optimal parameters or requiring larger spherical coils. To address the problem, first, a coaxial symmetrical spherical coil model that improves space utilization was established. Second, an optimal design method for the spherical magnetic field generation coil based on a differential evolution algorithm was proposed. Third, the optimal bias magnetic field was obtained without increasing the volume of the coil. The verification results showed that the magnetic non-uniformity and magnetic gradient of the bias field generated by the optimized coil were reduced by 63.2% and 82.8%, respectively.

1. [1] M. Mandea and M. Korte (Eds.), “Geomagnetic Observations and Models,” Springer, 2011. https://doi.org/10.1007/978-90-481-9858-0
2. [2] N. P. Dharmadhikari et al., “Vein Width Measurement of Groundwater on Earth’s Surface Using Semiconductor Laser Light and Proton Precession Magnetometer,” J. of Applied Geophysics, Vol.171, Article No.103864, 2019. https://doi.org/10.1016/j.jappgeo.2019.103864
3. [3] X.-C. Song, “Comparison of Magnetic Field Distribution and Homogeneity Between Helmholtz Coil and Maxwell Coil,” J. of Magnetic Materials and Devices, Vol.47, No.5, pp. 16-18+77, 2016 (in Chinese).
4. [4] J. J. Abbott, “Parametric Design of Tri-Axial Nested Helmholtz Coils,” Review of Scientific Instruments, Vol.86, No.5, Article No.054701, 2015. https://doi.org/10.1063/1.4919400
5. [5] J. Jankowski and C. Sucksdorff, “Guide for Magnetic Measurements and Observatory Practice,” International Association of Geomagnetism and Academy (IAGA), 1996.
6. [6] J. E. Everett and J. E. Osemeikhian, “Spherical Coils for Uniform Magnetic Fields,” J. of Scientific Instruments, Vol.43, No.7, pp. 470-474, 1966. https://doi.org/10.1088/0950-7671/43/7/311
7. [7] Z. Hu et al., “Design Method for Cylindrical Coil Systems for Generating Uniform Magnetic Field,” J. of Beijing University of Aeronautics and Astronautics, Vol.44, No.3, pp. 454-461, 2018 (in Chinese). https://doi.org/10.13700/j.bh.1001-5965.2017.0152
8. [8] X. Song, “Analysis of Barker Magnetic Field Coils with High Homogeneity,” Ship Electronic Engineering, Vol.36, No.6, pp. 141-145, 2016 (in Chinese).
9. [9] P. Baranov et al., “Creating a Uniform Magnetic Field Using Axial Coils System for Calibration of Magnetometers,” 2016 Dynamics of Systems, Mechanisms and Machines (Dynamics), 2016. https://doi.org/10.1109/Dynamics.2016.7818973
10. [10] R. Beiranvand, “Effects of the Winding Cross-Section Shape on the Magnetic Field Uniformity of the High Field Circular Helmholtz Coil Systems,” IEEE Trans. on Industrial Electronics, Vol.64, No.9, pp. 7120-7131, 2017. https://doi.org/10.1109/TIE.2017.2686302
11. [11] Y. Yang et al., “An Improved Two-Coil Configuration for Low Frequency Magnetic Field Immunity Test and its Field Inhomogeneity Analysis,” IEEE Trans. on Industrial Electronics, Vol.65, No.10, pp. 8204-8214, 2018. https://doi.org/10.1109/TIE.2018.2807420
12. [12] P. Mahavarkar et al., “Tri-Axial Square Helmholtz Coil System at the Alibag Magnetic Observatory: Upgraded to a Magnetic Sensor Calibration Facility,” Geoscientific Instrumentation, Methods and Data Systems, Vol.7, No.2, pp. 143-149, 2018. https://doi.org/10.5194/gi-7-143-2018
13. [13] R. Beiranvand, “Analyzing the Uniformity of the Generated Magnetic Field by a Practical One-Dimensional Helmholtz Coils System,” Review of Scientific Instruments, Vol.84, No.7, Article No.075109, 2013. https://doi.org/10.1063/1.4813275
14. [14] G. Zhang, Y. Li, and Y. Shi, “Distributed Learning Particle Swarm Optimizer for Global Optimization of Multimodal Problems,” Frontiers of Computer Science, Vol.12, No.1, pp. 122-134, 2018. https://doi.org/10.1007/s11704-016-5373-1
15. [15] G. Feng, N. Cao, and X. Zhang, “A Novel Self-Learning Differential Evolution Algorithm in Two-State Dynamic Optimization,” Int. J. of Hybrid Information Technology, Vol.9, No.12, pp. 209-220, 2016. https://doi.org/10.14257/ijhit.2016.9.12.19
16. [16] N. S. Nguyen and D. K. Nguyen, “Parameter Estimation of Pendubot Model Using Modified Differential Evolution Algorithm,” Int. J. of Modelling and Simulation, Vol.39, No.3, pp. 157-165, 2019. https://doi.org/10.1080/02286203.2018.1525938
17. [17] N. K. Das et al., “Design of Miniature Coil to Generate Uniform Magnetic Field,” Progress in Electromagnetics Research M, Vol.34, pp. 99-105, 2014. https://doi.org/10.2528/PIERM13112602