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Principle of minimum energy of surface superconducting currents

Keywords:

I.N. Aliev – Dr. Sc. (Phys.-Math.), Professor, Department «Physics», Bauman Moscow State Technical University E-mail: alievprof@yandex.ru Z.A. Samedova – Undergraduate, Bauman Moscow State Technical University E-mail: samezara@bk.ru


Applied thermodynamic hypothesis of Gibbs for finding the equilibrium distribution of surface and volume currents in a stationary solid body, allows to solve the problem using the magnetic principle of virtual work. The calculated variation of magnetic energy with additional conditions, two of which, determine the constancy of the currents and being of a differential character, are necessary and sufficient to solve the problem in the case of a single body, and for dvuhsvetnoe body (top, thick ring) it turns out you need one more condition. It is shown that this additional condition, at the same time ensure the uniqueness of the solution can be chosen value of the magnetic dipole moment of the equilibrium distribution of the currents. The problem is solved using the method of Lagrange multipliers. Shows as expected that the three-dimensional currents together with the magnetic field pushed out into the surface layer. The calculated magnetic energy of the equilibrium distribution of superconducting currents for dvuhsvetnoe body placed in an external homogeneous magnetic field.
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