A new formula for calculating the magnetic force between two coaxial thick circular coils with rectangular cross-section

References

• Grover FW. Inductance calculations. New York (NY): Dover; 1964.
   Google Scholar
• Dwight HB. Electrical coils and conductors. New York (NY): McGraw-Hill Book; 1945.
   Google Scholar
• Snow C. Formulas for Computing Capacitance and Inductance. National bureau of standards circular 544. Washington (DC): GPO; 1954.
   Google Scholar
• Coulomb JL, Meunier G. Finite element implementation of virtual work principle for magnetic or electric force and torque computation. IEEE Trans. Magn. 1984;5:1894–1896.10.1109/TMAG.1984.1063232
   Web of Science ®Google Scholar
• Benhama A, Williamson AC, Reece ABJ. Force and torque computation from 2-D and 3-D finite element field solutions. IEE Proc. Electr. Power Appl. 1999;146:25–31.10.1049/ip-epa:19990219
   Google Scholar
• Demenko A, Stachowiak D. Electromagnetic torque calculation using magnetic network methods. COMPEL. 2008;27:17–26.
   Web of Science ®Google Scholar
• Tarnhuvud T, Reichert K. Accuracy problems of force and torque calculation in FE-systems. IEEE Trans. Magn. 1988;24:443–446.10.1109/20.43952
   Web of Science ®Google Scholar
• Coulomb JL. A methodology for the determination of global electromechanical quantities from a finite element analysis and its application to the evaluation of magnetic forces, torques and stiffness. IEEE Trans. Magn. 1983;19:2514–2519.10.1109/TMAG.1983.1062812
   Web of Science ®Google Scholar
• McFee S, Webb J, Lowther DA. A tunable volume integration formulation for force calculation in finite-element based computational magnetostatics. IEEE Trans. Magn. 1988; 24:439–442.10.1109/20.43951
   Web of Science ®Google Scholar
• Conway JT. Inductance calculations for noncoaxial coils using Bessel functions. IEEE Trans. Magn. 2007;43:1023–1034.10.1109/TMAG.2006.888565
   Web of Science ®Google Scholar
• Conway JT. Inductance calculations for circular coils of rectangular cross section and parallel axes using Bessel and Struve functions. IEEE Trans. Magn. 2010;46:75–81.10.1109/TMAG.2009.2026574
   Web of Science ®Google Scholar
• Ravaud R, Lemarquand G, Lemarquand V, Babic S, Akyel C. Mutual inductance and force exerted between thick coils. PIER. 2010;102:367–380.10.2528/PIER10012806
   Web of Science ®Google Scholar
• Babic SI, Akyel C. New analytic-numerical solutions for the mutual inductance of two coaxial circular coils with rectangular cross section in air. IEEE Trans. Magn. 2006;42:1661–1669.10.1109/TMAG.2006.872626
   Web of Science ®Google Scholar
• Babic S I, Akyel C. Magnetic force calculation between thin coaxial circular coils in air. IEEE Trans. Magn. 2008;44:445–452.
   Google Scholar
• Akyel C, Babic SI, Kincic S, Lagacé JP. Magnetic force calculation of some circular coaxial coils in air. JEMWA. 2007;21:1273–1283.
   Google Scholar
• Babic S, Sirois F, Akyel C, Lemarquand G, Lemarquand V, Ravaud R. New formulas for mutual inductance and axial magnetic force between a thin wall solenoid and a thick circular coil of rectangular cross-section. IEEE Trans. Magn. 2011;47:2034–2044.10.1109/TMAG.2011.2125796
   Web of Science ®Google Scholar
• Babic S, Akyel C. New Formulas for Mutual Inductance and axial magnetic force between magnetically coupled coils: thick circular coil of the rectangular cross-section-thin disk coil (pancake). IEEE Trans. Magn. 2013;49:860–868.10.1109/TMAG.2012.2212909
   Web of Science ®Google Scholar
• Ravaud R, Lemarquand G, Babic S, Lemarquand V, Akyel C. Cylindrical magnets and coils: fields, forces, and inductances. IEEE Trans. Magn. 2010;46:3585–3590.10.1109/TMAG.2010.2049026
   Web of Science ®Google Scholar
• Furlani EP. A formula for the levitation force between magnetic disks. IEEE Trans. Magn. 1993;29:4165–4169.10.1109/20.280867
   Web of Science ®Google Scholar
• Furlani EP. Formulas for the force and torque of axial couplings. IEEE Trans. Magn. 1993;29:2295–2301.10.1109/20.231636
   Web of Science ®Google Scholar
• Ren Y, Wang F, Kuang G, Chen W, Tan Y, Zhu J, He P. Mutual inductance and force calculations between coaxial bitter coils and superconducting coils with rectangular cross section. J. Supercond. Nov. Magn. 2010;24:1687–1691.
   Web of Science ®Google Scholar
• Župan T, Štih Ž, Trkulja B. Fast and precise method for inductance calculation of coaxial circular coils with rectangular cross section using the one dimensional integration of elementary functions applicable to superconducting magnets. IEEE Trans. Appl. Supercond. 2014;24:4901309.
   Web of Science ®Google Scholar
• Babic S, Akyel C, Ren VY, Chen W. Magnetic force calculation between circular coils of rectangular cross section with parallel axes for superconducting magnet. Prog. Electromagnet. Res. B. 2012;37:275–288.10.2528/PIERB11110508
   Google Scholar
• Martinez JM, Babic S, Akyel C. On evaluation of inductance, dc- resistance and capacitance of coaxial inductors at low frequencies. IEEE Trans. Magn. 2014;50:8401012.
   Web of Science ®Google Scholar
• Abramowitz M, Stegun IA. Handbook of mathematical functions. Washington (DC): National Bureau of Standards Applied Mathematics; 1972 (Series 55: 595).
   Google Scholar
• Gradshteyn IS, Ryzhik IM. Table of integrals, series and products. New York (NY): Academic Press; 1965.
   Google Scholar