Characteristic Length for Pinning Force Density in Nb(3)Sn

The pinning force density, [Formula: see text] , 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: see text] , 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: see text] on the average grain size, [Formula: see text] , in Nb(3)Sn-based conductors. [Formula: see text] datasets were analyzed and a scaling law for the dependence [Formula: see text] was proposed. Despite the fact that this scaling law is widely accepted, it has several problems; for instance, according to this law, at [Formula: see text] and [Formula: see text] , Nb(3)Sn should lose its superconductivity, which is in striking contrast to experiments. Here, we reanalyzed the full inventory of publicly available [Formula: see text] data for Nb(3)Sn conductors and found that the dependence can be described by the exponential law, in which the characteristic length, [Formula: see text] , varies within a remarkably narrow range of [Formula: see text] 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: see text]) 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: see text] , and the surface is a superconductor–vacuum surface). An alternative interpretation is that [Formula: see text] represents the characteristic length of the exponential decay flux pinning potential from the dominant defects in Nb(3)Sn superconductors, which are grain boundaries.