Effects of Crack Size Distribution and Specimen Length on the Correlation between n-Value and Critical Current in Heterogeneously Cracked Superconducting Tape

A Monte Carlo simulation study was carried out to reveal the effects of crack size distribution and specimen length on the correlation between n-value and critical current in heterogeneously cracked superconducting tapes. First, it was shown that, with increasing distribution width of crack size, the distribution widths of critical current and n-values increase, and, the average critical current-value and average n-value of specimens decrease. Also, it was shown that the decrease in average n-value with increase in distribution width of crack size is more intense than the decrease in average critical current-value and this feature is more pronounced in longer specimens. Then it was revealed that plural n-values can exist for one critical current value since the n-value of specimen was dependent on the positional relation among the voltage-current curves of the sections, of which specimen is constituted. This phenomenon could be described by the difference in the resistance value in the current shunting circuit by application of a single equivalent crack-current shunting model in which the cracks within a specimen are replaced by a single equivalent crack. Based on this result, an approach, in which the resistance value in the current shunting circuit is used to describe the upper-lower bounds and the center of n-value in the correlation diagram between n-value and critical current, was presented. It was shown that the correlation diagrams at various distribution widths of crack size and specimen lengths, obtained by simulation and experiments, are described well by this approach.