Anomalous statistical properties of the critical current distribution in superconductor containing fractal clusters of a normal phase

Statistical properties of the critical current distribution in superconductor with fractal clusters of a normal phase are considered. It is found that there is the range of fractal dimensions in which the variance and expectation for this distribution increases infinitely. Simple technique of avoiding such a divergence by the use of truncated distributions is proposed. It is suggested that the most current-carrying capability of a superconductor can be achieved by modifying the cluster area distribution in such a way that the regime of giant variance of critical currents will be realized.