Characteristic Length for Pinning Force Density in Nb3Sn

Abstract

The pinning force density, (Formula presented.), is one of the main parameters that characterize the resilience of a superconductor to carrying a dissipative-free transport current in an applied magnetic field. Kramer (1973) and Dew-Hughes (1974) proposed a widely used scaling law for this quantity, where one of the parameters is the pinning force density maximum, (Formula presented.), which represents the maximal performance of a given superconductor in an applied magnetic field at a given temperature. Since the late 1970s to the present, several research groups have reported experimental data on the dependence of (Formula presented.) on the average grain size, (Formula presented.), in Nb3Sn-based conductors. (Formula presented.) datasets were analyzed and a scaling law for the dependence (Formula presented.) was proposed. Despite the fact that this scaling law is widely accepted, it has several problems; for instance, according to this law, at (Formula presented.) and (Formula presented.), Nb3Sn should lose its superconductivity, which is in striking contrast to experiments. Here, we reanalyzed the full inventory of publicly available (Formula presented.) data for Nb3Sn conductors and found that the dependence can be described by the exponential law, in which the characteristic length, (Formula presented.), varies within a remarkably narrow range of (Formula presented.) for samples fabricated using different technologies. The interpretation of this result is based on the idea that the in-field supercurrent flows within a thin surface layer (thickness of (Formula presented.)) near grain boundary surfaces (similar to London’s law, where the self-field supercurrent flows within a thin surface layer with a thickness of the London penetration depth, (Formula presented.), and the surface is a superconductor–vacuum surface). An alternative interpretation is that (Formula presented.) represents the characteristic length of the exponential decay flux pinning potential from the dominant defects in Nb3Sn superconductors, which are grain boundaries. © 2023 by the authors.