One of the most promising types of thermal radiation detectors are superconducting mesoscopic rings. The principle of such detectors operation is based on a discreteness of current states of the superconductor. During detection experiments the asymmetric rings are frequently used with asymmetric current-voltage characteristic, which provides them additional benefits. Theoretical and numerical analysis of the current states of such rings is far from complete, which reason justifies the urgency of this task. In this paper the theoretical and numerical analysis of the currents distribution in the superconducting asymmetric ring bounded by two circles of different radii which centers do not coincide, is performed. For the analysis of the distribution of the superconducting current in the ring, placed in an external uniform magnetic field, a system of Ginzburg-Landau-Maxwell equations were used supplemented with specially selected calibration of the vector potential of the magnetic field. The essence of the proposed method is that a scalar function of gradient is added to the vector potential, with gradient is chosen in a way that the superconducting current density at the boundaries of a superconducting ring has only a tangential component. In this approach, the Ginzburg-Landau-Maxwell equations are supplemented by the gauge calibration-fixing equation. Application of the proposed method, which allows to calculate the distribution of currents in the rings of any geometry, let us come to the conclusion that in such rings when the external magnetic field changes, there is an alternation between the superconducting and normal state because of the spatial quantization of Landau orbits of the Cooper electrons pairs. Unlike the symmetrical superconducting rings containing one vortex or two oppositely directed vortices, in the asymmetric rings the additional current states arise, in a narrow part of which there is one vortex contained, and in wide part - there are two vortices. On the other hand, the average characteristics of the integral (the averaged current density in the ring area, etc.) slightly depend on the degree of the ring asymmetry.

Предложен метод расчета распределения тока в асимметричных мезоскопических сверхпроводящих кольцах, использующий неоднозначность выбора вектор-потенциала магнитного поля. С помощью предложенного метода произведен расчет и классификация токовых состояний асимметричных сверхпроводящих мезоскопических колец.