  In powder-in-tube (PIT) Nb3Sn composites, the A15 phase forms between a
central tin-rich core and a coaxial Nb tube, thus causing the tin content and
superconducting properties to vary with radius across the A15 layer. Since this
geometry is also ideal for magnetic characterization of the superconducting
properties with the field parallel to the tube axis, a system of concentric
shells with varying tin content was used to simulate the superconducting
properties, the overall severity of the Sn composition gradient being defined
by an index N. Using well-known scaling relationships and property trends
developed in an earlier experimental study, the critical current density for
each shell was calculated, and from this the magnetic moment of each shell was
found. By summing these moments, experimentally measured properties such as
pinning-force curves and Kramer plots could be simulated. We found that
different tin profiles have only a minor effect on the shape of Kramer plots,
but a pronounced effect on the irreversibility fields defined by the
extrapolation of Kramer plots. In fact, these extrapolated values H_K are very
close to a weighted average of the superconducting properties across the layer
for all N. The difference between H_K and the upper critical field commonly
seen in experiments is a direct consequence of the different ways measurements
probe the simulated Sn gradients. Sn gradients were found to be significantly
deleterious to the critical current density Jc, since reductions to both the
elementary pinning force and the flux pinning scaling field H_K compound the
reduction in Jc. The simulations show that significant gains in Jc of Nb3Sn
strands might be realized by circumventing strong compositional gradients of
tin.
