On the magnetization of a superconducting ball

As it is well known at present, the consistent theory of superconductivity should be the quantum one, whereas phenomenological electrodynamics of superconductors can be built on the basis of classical ideas. Furthermore, despite the major advances in explaining the phenomenon of superconductivity, the elementary classical theory requires significant refinements and improvements. Consequently, it is important to reexamine the basic laws of electrodynamics as an example of the current distribution on the surface of a superconducting sphere, as well as the magnitude of the magnetic induction. For this purpose, the field outside the sphere is calculated in a standard way with the help of Maxwell's equations, and the filed inside is calculated by Londons' equations. The main physical conclusion of the result is as follows: in a superconductor in an external magnetic field there occur surface currents distributed in a thin layer of finite thickness, previously interpreted as the penetration depth of the magnetic field with the appropriate volume currents. In the previous work it was shown that the direct current in a conductor of any type is displaced to the surface together with the magnetic field, which leads to the so-called surface current. This current is proposed as a volume current, but flowing in a thin layer of finite thickness. As this thickness does not depend on the material and the nature of the conductor, according to Londons' theory, it can be assumed that the latter is equal to the characteristic penetration depth of the magnetic field into the superconductor.

References

[1] Green G. Mathematical papers. London, Macmillan a Co., 1871. 325 p.

[2] Thomson K.W. Reprint of papers on electrostatics a magnetism. Macmillan a Co., 1872. 628 p.

[3] Aliev I.N., Kopylov I.S. Use of Dirac monopoles formalism in some magnetism problems. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], 2015, no. 6, pp. 2539 (in Russ.). DOI: 10.18698/1812-3368-2015-6-25-39

[4] Meissner W., Ochsenfeld R. Ein neurer effekt bei eintritt der supraleitfahigkeit. Natuvwissenschaften, 1933, vol. 21, iss. 44, pp. 787-788.

[5] London F., London H. The electromagnetic equations of the supracondactor. Proc. Roy. Soc, 1935, vol. 149, pp. 71-88.

[6] London H. Phase-equilibrium of supracondactors in a magnetic field. Proc. Roy. Soc, 1935, vol. 152, pp. 650-663.

[7] Lynton E.A., Mc Lean W.L. Type II Superconductors. Advances Electronics and Electron Phys., 1967, vol. 23, no. 1.

[8] Aliev I.N., Kopylov I.S. Applying the Lagrange multipliers method to the calculation of DC magnetic field. Dinamika slozhnykh system [Dynamics of Complex Systems], 2015, no. 4, pp. 3-10 (in Russ.).

[9] Kamke E. Differentialgleichungen: Losungsmethoden und Losungen, I, Gewohnliche Differentialgleichungen [Handbook of ordinary differential equations]. Leipzig, B.G. Teubner, 1977.

[10] De Llano M., Tolmachev V.V. Multiple phases in a new statistical boson-fermion model of superconductivity. Physica A, 2003, vol. 317, pp. 546-564.

[11] Yurchenko S., Komarov K., Pustovoit V. Multilayer-graphene-based amplifier of surface acoustic waves. AIP advances, 2015, vol. 5, p. 057144.

[12] Mitrokhin V.N. Elektrodinamicheskie svoystva material’nykh sred [The Electrodynamic Properties of Material Media]. Moscow, MGTu im. N.E. Baumana Publ., 2006. 120 p.

[13] Kravchenko V.F. Elektrodinamika sverkhprovodyashchikh struktur. Teoriya, algoritmy i metody vychisleniy [Electrodynamics of Superconducting Structures. Theory, Algorithms and Computational Methods]. Moscow, Fizmatlit Publ., 2006. 280 p.