Self-organization of the critical state in Josephson lattices and granulated superconductors

A number of models of a Josephson medium and granulated superconductors are studied. It is shown that an important parameter is the quantity V∼jca3/Φ0, where jc is the Josephson-current density, a is the granule size, and Φ0 is the quantum of flux. In the limit V>>1 the continuum approximation is inapplicable. In this case the Josephson medium is transformed into a system in which pinning is realized on elementary loops that incorporate Josephson junctions. Here, nonlinear properties of these junctions obtain. The equations obtained for the currents of the Josephson lattice are identical to the standard formulation in the problem of self-organized criticality, while in granulated superconductors a problem of self-organized criticality with a different symmetry arises-a problem not of sites, but of loop. From the point of view of the critical state in granulated superconductors the concept of self-organized criticality radically changes the entire customary picture. The usual equations of the critical state describe only the average values of the magnetic field in the hydrodynamic approximation. However, it follows from the concept of self-organized criticality that the critical state has an extremely complicated structure, much more complicated than that which follows from the equation of the critical state. In particular, the fluctuations of various quantities in the critical state are much stronger than the ordinary statistical fluctuations, since there are large-scale fluctuations of the currents and fields, with a power-law (scaling) behavior that extends up to scales of the order of the size of the system, as in a turbulent medium. On the other hand, the basic equations in it reflect all the features of pinning - hysteresis and threshold behavior. Therefore, the self-organization of the critical state of a superconductor is a natural realization of this extremely general problem. 15 refs., 4 figs