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

Abstract

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. [

Analysis of Critical Current Dependence on Specimen Length and Crack Size Distribution in Cracked Superconductor

“…Critical current I c (estimated by application of the electrical field criterion E c = 1 µV/cm to the voltage V—current I curve) and n -value (estimated as the index n of the approximated I ∝ I n curve in the electrical field range of E = 0.1~10 µV/cm) are reduced under high electromagnetic and mechanic stresses, as have been reported for the superconducting oxide (such as RE(Y, Sm, Dy, Gd,···)Ba 2 Cu 3 O 7-δ : REBCCO) layer-coated tape [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 ], and Bi2223 [ 15 , 16 , 17 , 18 , 19 , 20 ]-, MgB 2 [ 21 , 22 , 23 , 24 , 25 ]- and Nb 3 Sn [ 26 , 27 , 28 , 29 , 30 , 31 ]-filamentary types. In this work, we conduct a fundamental study on the influences of cracks in superconducting layer-coated tape on I c .…”

“…The following technical terms were used. “ f and 1 − f : ratios of cross-sectional area of the cracked- and ligament-parts to the total cross-sectional area of the superconducting layer, respectively”, “ I RE : current transported by the superconducting layer in the ligament part”, “ I s : crack-induced shunting current”, “ R t : electrical resistance of the shunting circuit”, “ V RE : voltage developed at the ligament part that transports current I RE , being equal to the voltage vs. (= I s R t ) developed at the cracked part by shunting current I s , since the cracked part and the ligament part constitute a parallel electrical circuit”, “ I c0 and n 0 : critical current and n -value of the sections in the non-cracked state, respectively”, “ E c (=1 μV/cm): critical electrical field for determination of the critical current value”, “ s (<< L 0 ): current transfer length”, “ L p : ligament parameter of section, given by L p = (1 − f )( L 0 / s ) 1/ n 0 , which was derived by the authors [ 13 , 14 ] through a modification of the formulations of Fang et al [ 17 ]”, and “Δ L p : standard deviation of the ligament parameter L p ”.…”

“…In this work, we conduct a fundamental study on the influences of cracks in superconducting layer-coated tape on I c . Usually, the cracking takes place non-uniformly, and hence, the I c / n -values vary by specimen [ 3 , 7 , 13 , 18 ] and along the length of the specimen [ 7 , 13 , 14 ]. Not limited to the stress-induced cracks, the non-uniformly distributed defects introduced during the fabrication process also cause a reduction in I c and n -values [ 11 , 13 ].…”

“…In studying the effect of crack size distribution and specimen length on I c and n -values, the authors used a Monte Carlo simulation method [ 13 , 14 ] combined with a current shunting model of cracks [ 17 ]. From the simulation results using the model specimens consisting of multiple short sections with cracks of different sizes, the following results have been obtained: (i) The section with the largest crack contributes most significantly to the synthesis of the V – I curve of the specimen.…”

“…Factor 2 is the difference in size among cracks at the critical voltage of the critical current of the specimen. As the research tools, we used the monitoring method for numerical estimation of the effect of Factor 1 and Factor 2, together with the Monte Carlo simulation method [ 13 , 14 ] and Gumbel’s extreme value distribution function [ 33 ].…”