2011-12-27
Magnetic Force Calculation Between Circular Coils of Rectangular Cross Section with Parallel Axes for Superconducting Magnet
By
Progress In Electromagnetics Research B, Vol. 37, 275-288, 2012
Abstract
The electromagnetic force between two misaligned coils (coils with parallel axes) with uniform current density distribution and rectangular cross section based on the derived semi-analytical expressions was presented. Using the semi-analytical expressions for magnetic force between filamentary misalignment circular coils we calculate the propulsive and the transverse magnetic force. In order to verify the validity of the expressions, we use the filament method with Grover's formula to calculate the magnetic force for two coils with parallel axes. The results obtained by two methods are in a very good agreement. In this paper, the derivation of the semi-analytical expressions and the calculation results of the magnetic force are introduced.
Citation
Slobodan Babic, Cevdet Akyel, Yong Ren, and Wenge Chen, "Magnetic Force Calculation Between Circular Coils of Rectangular Cross Section with Parallel Axes for Superconducting Magnet," Progress In Electromagnetics Research B, Vol. 37, 275-288, 2012.
doi:10.2528/PIERB11110508
References

1. Kim, K. B., E. Levi, Z. Zabar, and L. Birenbaum, "Restoring force between two noncoaxial circular coils," IEEE. Trans. Magn., Vol. 32, No. 2, 478-484, Mar. 1997.        Google Scholar

2. Gao, B. J., "Calculation of the forces between coils in 20T hybrid magnetic system," Chin. J. Low. Temp. Phys., Vol. 7, No. 4, 331-335, Dec. 1985.        Google Scholar

3. Iwasa, Y., Case Studies in Superconducting Magnets-design and Operational Issues, 95-97, Plenum Press, New York, 1994.

4. Iwasa, Y., Case Studies in Superconducting Magnets-design and Operational Issues , 2nd Ed., 82-205, Plenum Press, New York, 2009.

5. Ren, Y., F.Wang, Z. Chen, and W. Chen, "Mechanical stability of superconducting magnet with epoxy impregnated," J. Supercond. Novel Magn., Vol. 23, 1589-1593, 2010.
doi:10.1007/s10948-010-0816-7        Google Scholar

6. Ren, Y., "Magnetic force calculation between misaligned coils for a superconducting magnet," IEEE Trans. Appl. Supercond., Vol. 20, No. 6, 2350-2353, Dec. 2010.
doi:10.1109/TASC.2010.2068297        Google Scholar

7. Ravaud, R., G. Lemarquand, V. Lemarquand, S. I. Babic, and C. Akyel, "Mutual inductance and force exerted between thick coils," Progress In Electromagnetics Research, Vol. 102, 367-380, 2010.
doi:10.2528/PIER10012806        Google Scholar

8. Babic, S. and C. Akyel, "Magnetic force calculation between thin coaxial circular coils in air," IEEE. Trans. Magn., Vol. 44, No. 4, 445-452, Apr. 2008.
doi:10.1109/TMAG.2007.915292        Google Scholar

9. Cheremnykh, P. A., et al. "The KS-250 combined magnetic system with 25 T induction," Cryogenics, Vol. 17, No. 6, 366-368, 1977.
doi:10.1016/0011-2275(77)90136-9        Google Scholar

10. Watanabe, K., et al. "Construction of the cryogen-free 23T hybrid magnet," IEEE Trans. Appl. Supercond., Vol. 12, No. 1, 678-681, Mar. 2010.
doi:10.1109/TASC.2002.1018492        Google Scholar

11. Grover, F. W., Inductance Calculations, Dover, New York, 1964.

12. Akyel, C., S. I. Babic, and M.-M. Mahmoudi, "Mutual inductance calculation for non-coaxial circular coils with parallel axes," Progress In Electromagnetics Research, Vol. 91, 287-301, 2009.
doi:10.2528/PIER09021907        Google Scholar

13. Babic, S. I., F. Sirois, and C. Akyel, "Validity check of mutual inductance formulas for circular filaments with lateral and angular misalignments ," Progress In Electromagnetics Research M, Vol. 8, 15-26, 2009.
doi:10.2528/PIERM09060105        Google Scholar

14. Conway, J. T., "Noncoaxial inductance calculations without the vector potential for axisymmetric coils and planar coils ," IEEE Trans. Magn., Vol. 44, No. 4, 453-462, Apr. 2010.
doi:10.1109/TMAG.2008.917128        Google Scholar

15. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards Applied Mathematics, Series 55, 595, Washington DC, Dec. 1972.

16. Gradshteyn, I. S. and I. M. Rhyzik, Tables of Integrals, Series and Products, Dover, New York, 1972.

17. Conway, J. T., Forces between thin coils with parallel axes using bessel functions, Private Communication, Jun. 2011.

18. Babic, S. and C. Akyel, "Magnetic force between inclined circular filaments placed in any desired position," IEEE Trans. Magn., Vol. 48, No. 1, Jan. 2012.
doi:10.1109/TMAG.2011.2165077        Google Scholar