MSC2010 97-04; 90C99; 82D55
Mathematical modeling of the magnetic properties of spheroids of hard second kind superconductors in the Bean model
N. D. Kuzmichev1, A. A. Shushpanov2, M. A. Vasyutin3
| Annotation | 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. |
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| Keywords | hard II-type superconductors, critical state, Bean model, Fredholm integral equations of the 1st and 2nd kind, magnetic properties, spheroid |
1Nikolay D. Kuzmichev, Professor, Department of Design and Technology Informatics, National Research Mordovia State University (68/1 Bolshevistskaya St., Saransk 430005, Russia), ORCID: http://orcid.org/0000-0001-6707-4950, kuzmichevnd@yandex.ru
2Aleksey A. Shushpanov, Post-Graduate student, Department of Applied Mathematics, Differential Equations and Theoretical Mechanics, National Research Mordovia State University (68/1 Bolshevistskaya St., Saransk 430005, Russia), ORCID: http://orcid.org/0000-0002-5005-9831, aashushpanov@gmail.com
3Mihail A. Vasyutin, Associate Professor, Department of Design and Technology Informatics, National Research Mordovia tate University (68/1 Bolshevistskaya St., Saransk 430005, Russia), ORCID: http://orcid.org/0000-0002-4856-7407, vasyutinm@mail.ru
Citation: 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]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,21:3 (2019) 353–362 (In Russian)
DOI 10.15507/2079-6900.21.201903.353-362
