volume | PIER Journals

2011-12-14

A Semi-Analytical Method for the Design of Coil-Systems for Homogeneous Magnetostatic Field Generation

Marco A. Azpurua

Dr. Marco A. Azpurua

ENINSEL

Instituto de Ingeniería

Venezuela

Homepage

Progress In Electromagnetics Research B, Vol. 37, 171-189, 2012

doi:10.2528/PIERB11102606

Abstract

This paper proposes a simple semi-analytical method for designing coil-systems for homogeneous magnetostatic field generation. The homogeneity of the magnetic field and the average magnitude of the magnetic flux density inside of the volume of interest are the objective functions chosen for the selection of the coil-system geometry (size and location), number of coils and the number of turns of each winding. The spatial distribution of the magnetostatic field is estimated superposing the magnetic induction numerically computed from the analytical expression of the magnetic field generated by each coil, obtained using the Biot-Savart's law and the current filament method. The homogeneous magnetic field is synthesized using an iterative algorithm based on TABU search with geometric constraints, which varies the design parameters of the windings to meet the requirements. The number of turns of each coil and gauge of wire used for the windings is adjusted automatically in order to achieve the target average magnitude of the magnetic induction under the constraints imposed by power consumption. This method was used to design a coil arrangement that can generate up to 10 mT within a volume (0.5 × 0.5 × 1) m with 99% of spatial homogeneity, with square loops of length less than or equal to 1.5 m, and with a power dissipated by Joule effect less than or equal to 1 W per coil. The synthesized magnetic field distribution was validated using Finite Element Method simulation, showing a good correspondence between the objective values and the simulated fields. This method is an alternative to design magnetic field exposure systems over large volumes such as those used in bioelectromagnetics applications.

Citation

Copy Export

Marco A. Azpurua, "A Semi-Analytical Method for the Design of Coil-Systems for Homogeneous Magnetostatic Field Generation," Progress In Electromagnetics Research B, Vol. 37, 171-189, 2012.
doi:10.2528/PIERB11102606

References

1. Di Barba, P., F. Dughiero, and E. Sieni, "Magnetic field synthesis in the design of inductors for magnetic fluid hyperthermia," IEEE Transactions on Magnetics, Vol. 46, No. 8, 2931-2934, 2010.
doi:10.1109/TMAG.2010.2044769

2. Brooks, N. and T. Baldwin, "Methodology for universal synthesis of magnetic designs based on field specifications," Proceedings of the Thirty-Fourth Southeastern Symposium on System Theory, 113-117, 2002.

3. Pittman, M. E. and D. L. Waidelich, Three and four coil systems for homogeneous magnetic fileds, NASA Technical Note, National Aeronautics and Space Administration, Washington, 1964.

4. Pulyer, Y. M. and M. I. Hrovat, "Generation of remote homogeneous magnetic fields," IEEE Transactions on Magnetics, Vol. 38, No. 3, 1553-1563, 2002.
doi:10.1109/20.999131

5. Bongiraud, J. P., G. Cauffet, and C. Jeandey, "An optimization method for magnetic field generator," 2nd International Conference on Marine Electromagnetic, Francia, 1999.

6. Anderson, T., "Design of a helmholtz coil for susceptibility testing using variational calculus and experimental verification," IEEE International Symposium on Electromagnetic Compatibility, Vol. 2, 601-604, 1999.

7. Cvetkovic, D. and I. Cosic, "Modelling and design of extremely low frequency uniform magnetic field exposure apparatus for in vivo bioelectromagnetic studies," 29th Annual International Conference of the IEEE on Engineering in Medicine and Biology Society, 1675-1678, 2007.
doi:10.1109/IEMBS.2007.4352630

8. Lugansky, L. B., "Field synthesis in solenoidal magnetic systems (review)," Instruments and Experimental Techniques, No. 4, 9-36, 1992.

9. Kirschvink, J., "Uniform magneticfields and double-warpped coil systems: Improved techniques for the design of bioelectromagnetic experiments," Bioelectromagnetics, Vol. 13, No. 5, 401-411, 1992.
doi:10.1002/bem.2250130507

10. Wang, J., S. She, and S. Zhang, "An improved helmholtz coil and analysis of its magnetic field homogeneity," Review of Scientific Instruments, Vol. 76, No. 5, 2175-2179, 2002.
doi:10.1063/1.1471352

11. Borghi, C. A. and M. Fabbri, "A global optimization method for the solution of a magnetic field synthesis problem," IEEE Transactions on Magnetics, Vol. 32, No. 3, 1897-1904, 1996.
doi:10.1109/20.492884

12. Sato, S., S. Sakaguichi, K. Futamata, and K. Katou, "Coil optimization for homogeneous magnetic field with small leakage field," IEEE Transactions on Magnetics, Vol. 36, No. 4, 649-653, 2000.
doi:10.1109/20.877533

13. Kuns, K., "Calculation of magnetic field inside plasma chamber," UCLA Tech. Rep., 2007, http://plasmalab.pbworks.com/f/bfield.pdf .

14. Glover, F. and M. Laguna, Tabu Search, Kluwer Academic, Boston, 1997.

15. Turkmen, I. and K. Guney, "Tabu search tracker with adaptive neuro-fuzzy infeernce system fro multiple target tracking," Progress In Electromagnetics Research, Vol. 65, No. 10, 169-185, 2006.
doi:10.2528/PIER06090601

16. Meyrath, T., Electromagnet design basics for cold atom experiments, University of Texas, Austin, 2004, Availeable at: http://george.ph.utexas.edu/ meyrath/informal/.

17. Moore, J., C. Davis, M. Coplan, and S. Greer, Building Scientific Apparatus, Cambridge University Press, New York, 2009.

18. Garcia, F. and L. Arza, "Influence of a stationary magnetic field on water relations in lettuce seeds. Part I: Theoretical considerations," Bioelectromagnetics, Vol. 22, No. 8, 589-595, 2001.
doi:10.1002/bem.88

19. Garcia, F., L. Arza, and I. Almanza, "Influence of a stationary magnetic field on water relations in lettuce seeds. Part II: Experimental results," Bioelectromagnetics, Vol. 22, No. 8, 596-602, 2001.
doi:10.1002/bem.89