Development of general expressions for the temperature and magnetic field dependence of the critical current density in coated conductors with variable properties

REBa2Cu3Oy coated conductors have recently become viable for high field superconducting magnets and this use may be the principal present driver of coated conductor development. Driving the transport critical current density (J(c)) as high as possible has become one of the principal goals of CC manufacturers but this can only be done by developing highly engineered nanostructures that may not be easy to control in quantity production of long lengths. Protection of high field (B) magnets operating in the temperature (T) of 4-20K range is challenging and one key data set needed for accurate quench modeling is a wide-ranging J(c)(B, T) data set. At the National High Magnetic Field Laboratory (NHMFL), 12 km of REBCO tapes were purchased for the all-superconducting 32 T user magnet that successfully reached field recently. They were characterized at 4.2 K with field orientation B perpendicular to tape and at 18 degrees off the tape-plane axis. Of the tapes selected for 32 T, three were chosen for additional J(c)(B, T) characterization from 4.2 to 75K in the B perpendicular to tape orientation in fields from 1 to 15 T. Although all tape lengths were bought to the same advanced pinning specification, in fact there was substantial variation of more than 2 in the low temperature, high field J(c). Here we probe the reasons for this variability in the context of measurements of the transport J(c)(B, T) dependence of 3 representative samples from this distribution with Ginzburg-Landau models of vortex pinning using a power law for J(c)(B) and an exponential temperature dependence for T < 45K and 3 T < B < 15 T. A fourth tape from the 32 T magnet procurement with J(c) outside this range was then selected to test the validity of our modelling. Using this extensive data set, the correlation between J(c)(B, 4.2 K) and J(c)(B, T) enabled us to predict J(c)(B, T) for tapes procured for the 32 T magnet with an expected accuracy of 10% or less for T < 40 K and B up to 15 T. Transmission electron microscopy made clear that the BaZrO3 (BZO) size, volume fraction and density varied significantly across the range of conductors studied, suggesting that nano-structural control is difficult during coated conductor manufacture and that the resulting J(c) variations may have to be accepted in procurement practice.