**AUTHORS:**S. Babic, C. Akyel

**Download as PDF**

**ABSTRACT:**
In this paper we calculate the mutual inductance and the magnetic force between the thick Bitter coil of
rectangular cross section with the inverse radial current and the thin wall superconducting solenoid with the constant
azimuthal current. The semi-analytical and the analytical expressions of these magnetic quantities are obtained over
complete elliptic integrals of the first and second kind as well as Heuman's Lambda function. There is a simple
integral which has to be solved numerically by some of numerical integrations. The results of this method are
compared by those obtained by the modified filament method for the presented configuration. All results are in an
excellent agreement.

**KEYWORDS:**
Pmagnetic field, mutual inductance, magnetic force, Bitter coils, inverse radial current, azimuthal
current.

**REFERENCES:**

[1] F. Bitter, “The Design of Powerful Electromagnets Part II. The Magnetizing Coil, ” Rev. Sci. Instrum., 1936, 7, (12), pp.482-489.

[2] Y. Sakai, K. Inoue, H. Maeda, “High-strength and high-conductivity Cu-Ag alloy sheets: new promising conductor for high-field Bitter coils, ” IEEE Trans. Mag.,1994, 30, (4), pp. 2114-2117.

[3] Y. Nakagawa, K. Noto, A. Hoshi, K. Watanabe, S. Miura, G. Kido, Y. Muto, “High field laboratory for superconducting materials, Institute for Materials Research, Tohoku University,” Physica B: Condensed Matter, Vol. 155, No. 1–3, pp. 69-73, 1989.

[4] Y. Sakai, K. Inoue,H. Maeda, “High-strength and high-conductivity Cu-Ag alloy sheets: new promising conductor for high-field Bitter coils,” IEEE Trans. Mag., Vol. 30, No.4, pp. 2114-2117, 1994.

[5] S. Babic, C. Akyel, V. Y. Ren and W. 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.

[6] S. Babic, C. Akyel, S. J. Salon, S. Kincic, “New expressions for calculating the magnetic field created by radial current in massive disks, ” IEEE Trans. Mag., Vol. 38, No. 2, pp. 497-500, Mars, 2002.

[7] B. Azzerboni, G.A. Saraceno and E. Cardelli, “Three-dimensional calculation of the magnetic field created by current-carrying massive disks, ” IEEE Trans. on Mag., Vol. 34, No 5, pp. 2601 – 2604, Sept. 1998.

[8] Babic, S., Milojkovic, S., Andjelic, Z., Krstajic, B, Salon, J.S., “Analytical calculation of the 3D magnetostatic field of a toroidal conductor with rectangular cross section,” IEEE Trans. Mag., 24, (2), 1988, pp 3162-3164.

[9] C. Akyel, S. I. Babic, S. Kincic and J. P. Lagacé, “ Magnetic Force Calculation of Some Circular Coaxial Coils in Air, ” Journal of Electromagnetic Waves and Applications, Vol. 21, No.9, 1273-1283, 2007.

[10] K.-B. Kim E. Levi Z. Zabar L. Birenbaum, “Restoring force between two non-coaxial circular coils, ” IEEE Trans. Magn., Vol. 32, No. 2, pp. 478- 484, Nov. 1997.

[11] E.P. Furlani, “A formula for the levitation force between magnetic disks, ” IEEE Trans. Magn., Vol. 29, No. 6, pp. 4165 – 4169, Mar. 1993.

[12]J.T.Conway, “ Non coaxial force and inductance calculations for bitter coils and coils with uniform radial current distributions, ” Applied Superconductivity and Electromagnetic devices (ASEMD) International Conference, Melbourne, Australia, pp. 61-64.

[13] Lang, M., “Fast calculation method for the forces and stiffness’s of permanent-magnet bearings,” 8th International Symposium on Magnetic Bearing, 533–537, 2002.

[14] Selvaggi, J. P., et al., “Computation of the external magnetic field, near-field or far-field from a circular cylindrical magnetic source using toroidal functions” IEEE Trans. Magn., Vol. 43, No. 4, 1153–1156, 2007.

[15] A. Shiri A. Shoulaie, “A new methodology for magnetic force calculations between planar spiral coils,” PIER, vol. 95 pp. 39-57, 2009.

[16] Y. Ren, F. Wang, G.Kuang, W. Chen, Y. Tan, J. Zhu and P. He, “Mutual Inductance and Force Calculations between Coaxial Bitter Coils and Superconducting Coils with Rectangular Cross Section, ” Jou. Supercond. Nov. Magn., 2010, DOI 10.1007/s10948-010-1086-0.

[17] Y. Ren, G.Kuang, and W. Chen, “Inductance of Bitter Coil with Rectangular Cross-Section, “ Jou. Supercond. Nov. Magn., 2013, 26:2159–2163, DOI 10.1007/s10948-012-1816-6.

[18]J. T. Conway, “Inductance Calculations for Noncoaxial Coils using Bessel Functions, ” IEEE Trans. Magn., vol 43, n 3, pp 1023-1034, 2007.

[19]Babic S. and Akyel C., “Mutual Inductance and Magnetic Force Calculations for Bitter Disk Coils (Pancakes)” IET Science, Measurement & Technology, Vol.10, Issue 8, 2016, pp. 972-976.

[20] S. Babic S. and C. Akyel, “Mutual Inductance and Magnetic Force Calculations for Bitter Disk Coil (Pancake) with Nonlinear Radial Current and Filamentary Circular Coil with Azimuthal Current, ”Hindawi Publishing Corporation Advances in Electrical Engineering Volume 2016, Article ID 3654021, 6 pages http://dx.doi.org/10.1155/2016/3654021.

[21]Babic S. and Akyel C., “Mutual Inductance and Magnetic Force Calculations between two Thick Coaxial Bitter Coils of Rectangular Cross Section, ” IET Electric Power Applications, Vol. 11, Issue 3, 2017, pp. 441-446.

[22]Babic S. and Akyel C.,“ Mutual Inductance and Magnetic Force Calculations between Thick Coaxial Bitter Coil of Rectangular Cross Section with Inverse Radial Current and Filamentary Circular Coil with Constan Azimuthal Current, ”IET Electric Power Applications, Vol. 11, Issue 9, 2017, pp. 1596 – 1600.

[23] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards Applied Mathematics, Washington DC, December 1972, Series 55, p. 595.

[24]I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, New York and London, Academic Press Inc., 1965.