Geodesic
Mathematical modeling of the magnetic properties of spheroids of hard second kind superconductors in the Bean model
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 21 (2019) no. 3, pp. 353-362.

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Authors have modelled magnetic field in hard II-type superconductor bodies with cylindric symmetry by means of Bean model. Using the equations of electrodynamics and the Poisson equation for the vector potential, the Fredholm equation of the first kind is derived for the screening supercurrent density. By introducing the explicit form of the current-voltage characteristic and the law of electromagnetic induction, the equation for the supercurrent density is reduced to an integral equation of the 2nd kind, which is solved numerically in matrix form on a non-uniform grid with compaction to the edges of the sample. Density distribution of the screened superconductive current, sample-self magnetic field and hysteresis loops of magnetization in the cases of cylinders and spheroids are obtained.
Keywords: hard II-type superconductors, critical state, Bean model, Fredholm integral equations of the 1st and 2nd kind, magnetic properties, spheroid. 
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N. D. Kuzmichev; A. A. Shushpanov; M. A. Vasyutin. Mathematical modeling of the magnetic properties of spheroids of hard second kind superconductors in the Bean model. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 21 (2019) no. 3, pp. 353-362. http://geodesic.mathdoc.fr/item/SVMO_2019_21_3_a4/

[1] E. H. Brandt, “Superconductor disks and cylinders in an axial magnetic field. I. Flux penetration and magnetization curves”, Phys. rev. B, 58:10 (1998), 6506–6522 | DOI

[2] N. D. Kuzmichev, A. A. Fedchenko, “Mathematical modeling of the magnetization process of a cylindrical superconductor in the Bean model”, Proceedings of Higher Educational Institutions. Volga Region. Physics and Mathematics, 21:1 (2012), 139-148 (In Russ.)

[3] N. D. Kuzmichev, A. A. Fedchenko, “Mathematical modeling of the distribution of the screening current and the hysteresis of the magnetization of short cylinders of rigid superconductors of the 2nd kind in the Bean approximation”, Zhurnal Srednevolzhskogo matematicheskogo obshchestva, 13:4 (2011), 25–34 (In Russ.)

[4] D. Frankel, “Critical-state model for the determination of critical currents in disk-shaped superconductors”, Appl. Phys., 50:8 (1979), 5402–5407 | DOI

[5] P. N.Ṁikheenko, Yu. E Kuzovlev, Physica C., 204 (1993), 229–236 | DOI

[6] J. Zhu, J. Mester, J. Lockhart, J. Turneaure, “Critical states in 2D disk-shaped type-II superconductors in periodic external magnetic field”, Physica C., 212:1-2 (1993), 216–222 | DOI

[7] C. P. Been, “Magnetization of hard superconductors”, Phys. Rev., 8:6 (1962), 250–253

[8] U. M. Tsipenyuk, Physical basis of superconductivity, MPhTI, Moscow, 1996, 90 pp. (In Russ.)

[9] V. Bukkel, Superconductivity, foundation and application, Mir, M., 1975, 370 pp. (In Russ.)