New Scaling Laws for Pinning Force Density in Superconductors

Abstract

Since the report by Fietz and Webb (Phys. Rev.1968, 178, 657–667), who considered the pinning force density, Fp→=Jc→×B→ (where Jc is the critical current density and B is applied magnetic flux density), in isotropic superconductors as a unique function of reduced magnetic field, BBc2 (where Bc2 is the upper critical field), Fp→ has been scaled based on the BBc2 ratio, for which there is a widely used Kramer–Dew–Hughes scaling law of Fp→B=Fp,maxBBc2p1−BBc2q, where Fp,max, Bc2, p, and q are free-fitting parameters. To describe Fp→B in high-temperature superconductors, the Kramer–Dew–Hughes scaling law has been modified by (a) an assumption of the angular dependence of all parameters and (b) by the replacement of the upper critical field, Bc2, by the irreversibility field, Birr. Here, we note that Fp→ is also a function of critical current density, and thus, the Fp→Jc scaling law should exist. In an attempt to reveal this law, we considered the full Fp→B,Jc function and reported that there are three distinctive characteristic ranges of BBc2,JcJcsf (where Jcsf is the self-field critical current density) on which Fp→B,Jc can be splatted. Several new scaling laws for Fp→Jc were proposed and applied to MgB2, NdFeAs(O,F), REBCO, (La,Y)H10, and YH6. The proposed scaling laws describe the in-field performance of superconductors at low and moderate magnetic fields, and thus, the primary niche for these laws is superconducting wires and tapes for cables, fault current limiters, and transformers.