Long periodically modulated Josephson contact in a magnetic field and correctness of the bean model

The distribution of vortices and the profile of a magnetic field penetrating into a long contact are calculated on the basis of analysis of a continuous modification of the configuration in the direction of a decrease in its Gibbs potential. The computer calculations based on the proposed method have shown that critical value I (C) exists in the interval 0.95-1.00, which separates two possible regimes of penetration of the external magnetic field into the contact. For I > I (C) , the calculation for any value of external field H (e) leads to a finite-length near-boundary current configuration, which completely compensates the external field in the bulk of the contact. If, however, I < I (C) , such a situation takes place only up to certain value H (max) of the external magnetic field. For high values of the field, it penetrates into the contact to an infinite depth. If the magnetic field is zero in the bulk of the contact, near the boundary it decreases with increasing depth almost linearly. The values of the slope are rational fractions and remain constant in finite intervals of I. If the value of I exceeds the upper boundary of such interval, the slope increases jumpwise and assumes the value of another rational fraction. These results lead to the conclusion that the Bean assumptions are violated and that the Bean model is inapplicable for the analysis of the processes considered here.