Scaling law for voltage-current curve of a superconductor tape with a power-law dependence of electric field on a magnetic-field-dependent sheet current density

Systematic theoretical study on the voltage (V) vs. current (I) curves of high-Tc superconductor (HTS) thin tapes has not been done till now, although their measurements are frequently used for determining critical current Ic at electric field E≡V/lv=Ec=10−4 V/m, lv being the voltage tap distance. On the other hand, it is well recognized that such tapes obey a power-law dependence of local electric field on local sheet current density with a Kim-model critical sheet current density, from which the V vs. I curve may be calculated as a function of current ramp rate R. Such calculations are carried out in the present work with a scaling law deduced, which states that if E/Ec vs. I/Ic is a solution at given apparent power-law exponent na and R/Ec, then this R/Ec multiplied by a constant C leads to another solution with E/Ec and I/Ic multiplied by C and C1/na, respectively. In the help of the scaling law, condition-dependent V vs. I may be studied systematically and completely based on a limited amount of numerical computations and V−I curve measurements may be performed under properly controlled conditions to become a more powerful tool for HTS research.