Effects of Size of the Largest Crack and Size Difference among Cracks on Critical Current of Superconducting Tape with Multiple Cracks in Superconducting Layer

抄録

The effects of the size of the largest crack and size difference among cracks on critical current of superconducting tape with multiple cracks of different sizes in the superconducting layer were investigated by a model analysis and a Monte Carlo simulation, using the specimens consisting of a series circuit of local sections where each section has one crack of different size from each other. It was revealed that, with increasing distribution-width of crack size, the increase in the size of the largest crack acts to reduce the critical current and the increase in the crack size-difference among the sections acts to raise the critical current, and these conflicting two effects are summed up and determine the critical current value. To describe this feature quantitatively, we expressed the statistics of the size of the largest crack in specimens with the Gumbel’s extreme value distribution function. Also we monitored the effect of the difference in crack size among the sections on specimen’s critical current, using the number of the sections equivalent to the largest crack-section at the critical voltage for determination of specimen’s critical current. In this monitoring, small number of the sections equivalent to the largest crack-section corresponds to large difference in crack size among the sections. With the present approach, the effect of the increase in size of the largest crack, which acts to reduce critical current, and the effect of the increase in difference in crack size among the sections, which acts to raise critical current, with increase in distribution-width of crack size, could be estimated separately.

With model analysis and Monte Carlo simulation, it was clarified and quantified that the critical current I_c of a superconducting tape with multiple cracks of different sizes is given by the sum of the lower bound of the critical current I_c,lower determined by the size of the largest crack and the increment of the critical current ΔI_c resulting from the size difference among the cracks.