On potentials in Londons’ electrodynamics

The study tested the model of a multiply connected superconductor, for which we introduce the concept of fluxoids and present the classification of fluxoids. The findings of the research show that for simply connected circuits of the first type fluxoids equal to zero, but for the circuits of the second type, surrounding one and the same hole, fluxoid is even. By taking the quantization condition of Bohr-Sommerfeld into consideration, we established quantization of the magnetic flux in superconductors. For this condition, we examined the structure of the canonical momentum and introduced the concept of overpotential. Moreover, we clarified the problem of calibration of the introduced potential. As a result, we established that the relation binding at each point the density of the superconducting current and the vector potential of a constant magnetic field, taken in the selected calibration in the case of a simply connected superconductor, is a simple account of both material Londons’ equations.

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