A Modular Toroidal Coil (MTC) is composed of several solenoidal coils (SCs), which are connected in a series and distributed in the toroidal and symmetrical form. This paper presents analytical equations of mutual inductance and electromagnetic torque of the MTC applicable to Tokomak reactors. These equations are based on those formulated by Neumann. The numerical analysis of the integrations resulting from these equations is solved using the extended three-point Gaussian algorithm. The results obtained from the numerical simulation agree with the empirical results, the experimental results, and the virtual work theorem, which indicates the reliability of the presented equations. The behavior of the mutual inductance of the coil shows that the maximum stored energy is obtained when the electromagnetic torque is zero, and vise versa.
1. Babic, S. I. and C. Akyel, "New mutual inductance calculation of the magnetically coupled coils: Thin disk coil-thin wall solenoid," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 10, 1661-1669, 2006. doi:10.1163/156939306779276794
2. Akyel, C., S. I. Babic, and M.-M. Mahmoudi, "Mutual inductance calculation for noncoaxial circular air coils with parallel axes," Progress In Electromagnetics Research, Vol. 91, 287-301, 2009. doi:10.2528/PIER09021907
3. Zhao, P. and H. G. Wang, "Resistances and inductances extraction using surface integral equation with the acceleration of multilevel green function interpolation method," Progress In Electromagnetics Research, Vol. 83, 43-54, 2008. doi:10.2528/PIER08032001
4. Babic, S. I. and C. Akyel, "Calculating mutual inductance between ircular coils with inclined axes in air," IEEE Trans. on Magnetics, Vol. 4, No. 7, 1743-1750, Jul. 2008.
5. Babic, S., C. Akyel, and S. J. Salon, "New procedures for calculating the mutual inductance of the system: Filamentary circular coil-massive circular solenoid," EEE Trans. Magn., Vol. 39, No. 3, 1131-1134, May 2003. doi:10.1109/TMAG.2003.810550
6. Pennington, R. H., Introductory Computer Methods and Numerical Analysis, 4th Ed., Macmillan, New York, 1970.
7. Grover, F. W., Inductance Calculation Working Formulas and Tables, 77-87, Dover Publications, Inc., New York, 1946.