Fractal geometry of normal phase clusters and magnetic flux trapping in high-Tc superconductors

Magnetic-flux creep at the initial stage of resistive transition in superconductors with fractal clusters of normal phase

“…Different variants of distribu tion of critical currents for clusters with fractal bound aries are considered in [8,9]. Further description will be confined to the practically most important case of exponential-hyperbolic distribution of critical depin ning currents, (1) which is realized in YBCO based film structures with exponential distribution of cluster areas [5,6]. In for mula (1), the following designations are used: i ≡ I/I c is a dimensionless electric current normalized with respect to critical transition current to resistive state,…”

“…Pinning centers with lower critical cur rents are almost absent, which explains the negligibly small creep induced voltage in this range of currents. The critical current of transition to the resistive state found by the function of accumulated probability [5] is i = 1. Since, at low transport currents, vortex jumps are relatively rare, the creep induced electric field is small and does not have a disrupting effect on the supercon ducting state.…”

“…Since any mag netic flux motion causes energy scattering in a super conductor, the problem of prevention or partial sup pression of this phenomenon is of great practical importance. New possibilities to increase critical cur rent are opened by normal phase clusters with fractal boundaries used as pinning centers [5,6]. In this work, the effect of fractal clusters on an electric field induced by magnetic flux creep is considered for the first time.…”

“…The statement of the problem is described in detail in [5,6,8]. The superconductor is considered, which contains isolated clusters of normal phase.…”

“…In [5], it was found for the first time that clusters of normal phase can have fractal boundaries, this prop erty having a considerable effect on the vortex dynam ics. For fractal clusters, the scaling relation between perimeter P and area A is fulfilled: P 1/D ∝ A 1/2 (where D is fractal dimensionality of a cluster boundary), Abstract-The effect of magnetic flux creep on an electric field induced in a percolating superconductor containing fractal clusters of normal phase is considered.…”