Truncated Conical Helmholtz Coils for Improved Homogeneity in Strong Magnetic Fields

Year 2025, Volume: 8 Issue: 2, 114 - 120, 26.12.2025

Muzaffer Erdoğan

https://doi.org/10.70030/sjmakeu.1817000

Abstract

This study introduces a new winding method for Helmholtz coils that solves two key problems: it maintains magnetic field uniformity even when the number of turns is increased, and it optimizes coil design under size constraints. Traditional coils lose uniformity as turns increase due to the radius-to-separation ratio. Our method employs a truncated conical winding approach to keep this ratio optimal, allowing for more turns without sacrificing field quality. We also optimize coil thickness to maximize usable space while maintaining high field strength. Simulations show our technique significantly improves field uniformity and intensity compared to traditional coils, making it ideal for applications requiring compact, high-performance magnetic fields, such as medical imaging and particle accelerators operating under spatial limitations.

Keywords

Helmholtz coils , truncated cone , magnetic field uniformity

References

• Beiranvand, R. (2013). Optimizing the magnetic field uniformity of a periodic solenoid with infinite length. Review of Scientific Instruments, 84(6), 063903.
• Wang, J., She, S., & Zhang, S. (2002). An improved Helmholtz coil and analysis of its magnetic field homogeneity. Review of Scientific Instruments, 73(5), 2175-2179.
• Beiranvand, R. (2014). Effects of the winding cross-section shape on the magnetic field uniformity of the high field circular Helmholtz coil systems. Review of Scientific Instruments, 85(7), 075116.
• Juhas, A., Nad, N. P., & Toepfer, H. (2018). Analysis of magnetic field uniformity for circular, square and equilateral triangular Helmholtz coils. Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska, 8(4), 30-33.
• Tang, Y., Ding, Y., Jin, T., & Flesch, R. C. C. (2023). Improvement for magnetic field uniformity of Helmholtz coils and its influence on magnetic hyperthermia. IEEE Transactions on Instrumentation and Measurement, 72, 1-9.
• Nayak, P. K., Prasad, U., Sharma, A. N., Patel, D., Kedia, S., & Pradhan, S. (2009). Helmholtz coils based magnetic field generation system for magnetic hyperthermia therapy. Physica C: Superconductivity and its Applications, 469(5), 211-214.
• Uher, M., Fialka, J., & Vagner, M. (2011). Modeling of magnetic field deviations in Helmholtz coils caused by production inaccuracies. Proceedings of the 22nd International DAAAM Symposium, 22(1), 1269-1270.
• Baranova, V. E., Baranov, P. F., Muravyov, S. V., & Uchaikin, S. V. (2015). Calculation and design of Helmholtz coil intended for magnetostatic testing. Measurement Techniques, 58(5), 550-554.
• Haghnegahdar, A., Khosrovpanah, H., Andisheh-Tadbir, A., Mortazavi, G., Moghadam, M. S., Mortazavi, S., Zamani, A., Haghani, M., Fard, M. S., Parsaei, H., & Koohi, O. (2014). Assessment of the extremely low frequency magnetic fields in Helmholtz coils for in vitro studies. Journal of Biomedical Physics & Engineering, 4(3), 83-88.
• Alldred, J. C., & Scollar, I. (1967). Uniformity of magnetic fields generated by Helmholtz coils. Journal of Scientific Instruments, 44(9), 755-760.
• Zhu, X., Meng, X., Liu, C., Ye, J., & Cheng, H. (2023). Optimization of composite Helmholtz coils towards high magnetic uniformity. Engineering Science and Technology, an International Journal, 47, 101539.
• Gao, J., Tian, S., Yuan, C., Ma, Z., & Gao, C. (2024). Design and optimization of a novel double-layer Helmholtz coil for wirelessly powering a capsule robot. IEEE Transactions on Power Electronics, 39(2), 2678-2690.
• Li, Y., Xu, J., Kang, X., Fan, Z., & Dong, X. (2021). Design of highly uniform three-dimensional square magnetic field coils for external magnetic shielding of magnetometers. Sensors and Actuators A: Physical, 331, 113037.
• Wang, K., Ma, D., Gao, Y., Dou, Y., & Li, S. (2024). Design and measurement of three-dimensional uniform-field coils based on swarm intelligence algorithms under ferromagnetic boundaries. IEEE Transactions on Instrumentation and Measurement, 73, 1-11.
• Yang, K., Zhang, Y., Zhao, A., Zhang, H. W., & Zhang, Q. (2024). Design of uniform magnetic field coil with off-center target region based on slime mould algorithm for atomic magnetometers. IEEE Transactions on Instrumentation and Measurement, 73, 1-9.
• Sun, J., Shang, S. P., Wang, H., & Gong, X. (2025). Design of high uniformity magnetic field three-axis coil based on simulated annealing-particle swarm hybrid optimization algorithm. Measurement, 239, 115424.
• Li, J. T., Zhu, X., Sun, Y., Cao, Q., & Li, L. (2024). Optimal design of thick-walled circular coils for uniform magnetic field generation. Journal of Physics D: Applied Physics, 57(42), 425001.
• Mendl, H. (2023). Design and modeling of Helmholtz coil based on winding method optimization. Measurement: Sensors, 27, 100746.
• Li, Y., Dou, S., Liu, X., Cui, P., & Yang, Z. (2024). Low noise magnetic field compensation based on differential biplanar coils with small coil constant. IEEE Transactions on Instrumentation and Measurement, 73, 1-10.