Моделирование градиентных гипомагнитных полей на базе квадратных катушек Гельмгольца

M S Emelyanova; S A Murashov

doi:10.22213/2413-1172-2025-2-22-37

Authors

M. S. Emelyanova Kalashnikov ISTU
S. A. Murashov Kalashnikov ISTU

DOI:

https://doi.org/10.22213/2413-1172-2025-2-22-37

Keywords:

modeling, magnetic field strength gradient, Square Helmholtz coils, magnetic field

Abstract

Helmholtz coils are widely used to generate controlled magnetic fields in magnetometer calibration, electromagnetic system testing, material property research experiments, and biotesting. Existing limitations in the homogeneity region of magnetic fields create difficulties in implementing experimental studies. Using multilevel generators with adjustable currents in coils allows generating gradient fields, which speeds up biotesting and increases its accuracy. This work is devoted to modeling gradient hypomagnetic fields using square Helmholtz coils. In COMSOL Multiphysics 6.1, a finite element model has been developed for analyzing magnetic fields generated by DC coils interacting with the Earth’s external magnetic field. The patterns of field formation for different coil orientations relative to the declination and inclination angles of the magnetic field vector have been studied. The study of the formation patterns of gradient hypomagnetic fields in the space between square Helmholtz coils placed in the external magnetic field of the Earth was carried out using finite element modeling in the COMSOL Multiphysics software environment. The effect of currents in the coils on the distribution of the hypomagnetic field intensity in space and along the axis was investigated. Dependences of the informative parameters of the gradient curve of the hypomagnetic field intensity on the value of currents in the coils were obtained, allowing one to construct control functions for currents in square Helmholtz coils to form multi-level fields with an adjustable attenuation coefficient. The results of numerical modeling performed for cases of uniform and gradient distribution of magnetic fields were experimentally confirmed. The conducted full-scale experiments made it possible to compare the calculated data with actual measurements, which indicates a high reliability of the developed model.

Author Biographies

M. S. Emelyanova, Kalashnikov ISTU

Senior Lecturer

S. A. Murashov, Kalashnikov ISTU

PhD in Engineering, Associate Professor

References

Емельянова М. С., Муравьев В. В. Многоуровневый градиентный генератор для исследования влияния гипомагнитных полей на биообъекты // Контроль. Диагностика. 2024. Т. 27. № 8(314). С. 17-27. DOI: 10.14489/td.2024.08.pp.017-027. EDN IVOJLF.

Емельянова М. С., Ломаев Г. В. К вопросу об онтогенезе пчел в гипомагнитном поле Земли // Интеллектуальные системы в производстве. 2014. № 2 (24). С. 157-159. EDN TCUJOZ.

Ломаев Г. В., Емельянова М. С. Влияние вариаций магнитного поля Земли на эмбриональное развитие G. Gallus // Интеллектуальные системы в производстве. 2014. № 1(23). С. 127-131. EDN SNHTRZ.

Álvarez A.F., Mejia É.F., Ramírez H.C., Jaramillo C.R. (2016) Analysis of the Magnetic Field Homogeneity for an Equilateral Triangular Helmholtz Coil. Progress in Electromagnetics Research M. Vol. 50, pp. 75-83. DOI: 10.2528/PIERM16062309

Nismayanti A., Jannah H., Rugayya S. (2021) Helmholtz coils model as pulsed electromagnetic field therapy devices for fracture healing using comsol multiphysics. Journal of Physics: Conference Series. Vol. 1763, no 1, pp. 012060. DOI: 10.1088/1742-6596/1763/1/012060

Huang Y., Jiang L., Lei H. (2022) Optimal coil configuration analysis for the high-uniformity and large-caliber magnetic field immunity testing system. Journal of Industrial Information Integration. Vol. 30, pp. 100384. DOI: 10.1016/j.jii.2022.100384

Zhao F., Zhou X., Xie X., Wang K. (2021) Design of Gradient Magnetic Field Coil Based on an Improved Particle Swarm Optimization Algorithm for Magnetocardiography Systems: IEEE Transactions on Instrumentation and Measurement. Vol. 70, pp. 1-9. DOI: 10.1109/TIM.2021.3106677

Schill R.A., Karin H. (2001) Characterizing and calibrating a large Helmholtz coil at low ac magnetic field levels with peak magnitudes below the earth's magnetic field. Review of Scientific Instruments. Vol. 72, no. 6, p. 2769-2776. DOI: 10.1063/1.1368853

Feng Y., Li Y., Feng H., Yuan H. (2021) Method for generating variable magnetic field based on Helmholtz coil and its simulation research: 7th International Symposium on Mechatronics and Industrial Informatics (ISMII), Zhuhai, China, 22-24 January 2021. Zhuhai, pp. 61-64. DOI: 10.1109/ISMII52409.2021.00020

Baranova V.E., Baranov P.F. (2014) The Helmholtz coils simulating and improved in COMSOL. Dynamics of Systems, Mechanisms and Machines (Dynamics): Proceedings, Omsk, November 11-13, 2014. Omsk: Institute of Electrical and Electronics Engineers Inc., pp. 1-4. DOI: 10.1109/Dynamics.2014.7005634

Ke W., Qingwen F., Hongliang P. (2020) Research on Magnetic Field Uniformity of Compensated Helmholtz Coi: 5th International Conference on Mechanical, Control and Computer Engineering (ICMCCE), Harbin, pp. 175-179. DOI: 10.1109/ICMCCE51767.2020.00046

Zhu X., Xing M., Liu Ch. (2023) Optimization of composite Helmholtz coils towards high magnetic uniformity. Engineering Science and Technology, an International Journal. Vol. 47, p. 101539. DOI: 10.1016/j.jestch.2023.101539

Chen X., Luo J., Lin D. (2021) Analysis and Visualization of Magnetic Field for Multi-dimensional Helmholtz Coils Based on PEEC: IEEE 1st International Power Electronics and Application Symposium (PEAS), Shanghai, China, pp. 1-7. DOI: 10.1109/PEAS53589.2021.9628580

Фишбейн Л. А. О магнитном поле системы колец Гельмгольца // Международный журнал гуманитарных и естественных наук. 2023. № 9-1 (84). С. 289-293. DOI: 10.24412/2500-1000-2023-9-1-289-293. EDN MIJCIQ.

Математическое моделирование магнитных полей постоянных магнитов цилиндрической формы и эквивалентных им соленоидов / Ю. Н. Слесарев, Б. В. Малышев, А. А. Борисова, А. А. Воронцов // Модели, системы, сети в экономике, технике, природе и обществе. 2016. № 4 (20). С. 150-157. EDN XKOMCN.

Свидетельство о государственной регистрации программы для ЭВМ № 2023689378 Российская Федерация. Экспресс-калькулятор магнитной индукции десятикатушечных систем / П. Ф. Баранов, И. А. Затонов. EDN ZDXNGS.

Li J., Zhu X., Sun Y. (2024) Optimal design of thick-walled circular coils for uniform magnetic field generation. Journal of Physics D: Applied Physics. Vol. 57, p. 455001. DOI: 10.1088/1361-6463/ad6672

Erzhanova N. (2024) Determining magnetic field strength as a function of current in Helmholtz coils. Technobius Physics. Vol. 2, p. 0016. DOI: 10.54355/tbusphys/2.3.2024.0016

Adil M., Rakisheva Z. (2018) Design and Simulation of Uniform Magnetic Field. Balkan Journal of Electrical and Computer Engineering. Vol. 6, pp. 232-236. DOI: 10.17694/bajece.475537

Фишбейн Л. А., Бушманов В. И. Сравнение пространственной неоднородности магнитных полей колец Гельмгольца и цилиндрических соленоидов // Инновации в науке. 2015. № 44. С. 7-12. EDN TQSWAT.

Гормаков А. Н., Ульянов И. А. Расчет и моделирование магнитных полей, создаваемых системой "кольца Гельмгольца - соленоид" // Фундаментальные исследования. 2015. № 3. С. 40-45. EDN TNIQLR.

Контрольно-измерительное устройство для управления магнитным полем катушек Гельмгольца / Е. Н. Блажкова, В. В. Бадашев, П. В. Кременской [и др.] // Инженерный вестник Дона. 2022. № 1 (85). С. 161-167. EDN RLDBIY.

Brewer M.R. (2012) CubeSat Attitude Determination and Helmholtz Cage Design: thesis. Ohio: Air force institute of technology, 92 p.

Baranov P., Baranova V. (2016) Modeling axial 8-coil system for generating uniform magnetic field in COMSOL. MATEC Web of Conferences: 4th Russian Forum for Young Scientists with International Participation "Space Engineering", Tomsk. Vol. 48, p. 03001. DOI: 10.1051/confmatec/20164803001. EDN WWFYXD.

Trevino T., Rector T., Lutz K. (2022) Design and Build of Electromagnetic HelmHoltz Coil: 51st International Conference Environmental Systems, Minessota.

Компьютерная система генерации и регистрации низкочастотных магнитных полей в магнитобиологических экспериментах / В. С. Мартынюк, Н. А. Темурьянц, А. В. Яценко [и др.] // Ученые записки Крымского федерального университета имени В. И. Вернадского. Биология. Химия. 2003. Т. 16, № 1 (55). С. 71-73.

Гипомагнитные условия: способы моделирования и оценка воздействия / А. А. Артамонов, М. К. Карташова, Е. В. Плотников, Н. А. Константинова // Медицина экстремальных ситуаций. 2019. Т. 21, № 3. С. 357-370. EDN YGPTPH.

Saqib M., Francis N.S., Francis N.J. (2020) Design and Development of Helmholtz Coils for Magnetic Field: 2020 International Youth Conference on Radio Electronics, Electrical and Power Engineering (REEPE), Moscow, pp. 1-5. DOI: 10.1109/REEPE49198.2020.9059109

Nieves F.J., Bayón A., Gascón F. (2019) Optimization of the magnetic field homogeneity of circular and conical coil pairs: Review of Scientific Instruments. Vol. 90, no. 4, pp. 045120. DOI: 10.1063/1.5079476

Beiranvand R. (2017) Effects of the Winding Cross-Section Shape on the Magnetic Field Uniformity of the High Field Circular Helmholtz Coil Systems: IEEE Transactions on Industrial Electronics. Vol. 64, no. 9, pp. 7120-7131. DOI: 10.1109/TIE.2017.2686302.

Batista D., Granziera F., Tosin M., Melo L. (2018) Three-Axial Helmholtz Coil Design and Validation for Aerospace Applications: IEEE Transactions on Aerospace and Electronic Systems. Vol. 54, no. 1, pp. 392-403. DOI: 10.1109/TAES.2017.2760560

Создание однородного магнитного поля с помощью системы аксиальных катушек для калибровки магнитометров / В. Е. Баранова, П. Ф. Баранова, С. В. Муравьев, С. В Учайкин // Измерительная техника. 2015. № 5. С. 52-56. EDN TUDZAH.