Dynamics of the magnetic flux trapped in fractal clusters of a normal phase in percolative superconductors

The effect of the fractal clusters of a normal phase, which act as pinning centers, on the dynamics of magnetic flux in percolative type-II superconductor is considered. The main features of these clusters are studied in detail: the cluster statistics is analyzed; the fractal dimension of their boundary is estimated; the distribution of critical currents is obtained, and its peculiarities are explored. It is found that there is the range of fractal dimension where this distribution has anomalous statistical properties, specifically, its dispersion becomes infinite. It is examined how the finite resolution capacity of the cluster geometric size measurement affects the estimated value of fractal dimension. The effect of fractal properties of the normal phase clusters on the electric field arisen from magnetic flux motion is investigated for the cluster area distribution of different kinds. The voltage-current characteristics of fractal superconducting structures in the resistive state are obtained for an arbitrary fractal dimension. It is revealed that the fractality of the boundaries of the normal phase clusters intensifies the magnetic flux trapping and thereby raises the critical current of a superconductor.