Effects of inhomogeneities on pinning force scaling in Nb$_3$Sn wires

We analyzed the effects of A-15 phase inhomogeneities, in particular Sn concentration gradients, on the pinning force scaling behavior of Nb$_3$Sn wires. This was accomplished using a software code capable of simulating both magnetization and transport measurements on wires containing sub-elements with an arbitrary (e.g. modeled after EDX data) Sn concentration profile. We demonstrate that certain experimentally observed deviations from the ideal scaling behavior, in particular large values of the high-field scaling exponent $q$ and the zero-temperature scaling field $B^*_{c2}(0)$ are caused by gradients in stoichiometry. In the presence of such gradients the scaling analysis results depend on the field and temperature ranges covered by the input data, and we discuss the stronger influence of inhomogeneities on magnetometry-based results. Our simulation code was benchmarked by attempting to mimic the scaling behavior of a Ti-alloyed Restack Rod Process wire observed in magnetometry experiments with a field limit of 7 T. By comparison to transport data obtained in fields of up to 15 T, we found that the simulations provide a significantly better high-field $J_c(B)$ prediction compared to an extrapolation based on conventional scaling.