We review the scaling relations for the critical current density
(Jc)
in Nb3Sn
wires and include recent findings on the variation of the upper critical field
(Hc2) with temperature
(T) and A15 composition.
Measurements of Hc2(T)
in inevitably inhomogeneous wires, as well as analysis of literature results, have shown that all available
Hc2(T)
data can be accurately described by a single relation from the microscopic
theory. This relation also holds for inhomogeneity averaged, effective,
Hc2*(T)
results and can be approximated by
, with t = T/Tc.
Knowing Hc2*(T)
implies that Jc(T)
is also known. We highlight deficiencies in the Summers/Ekin
relations, which are not able to account for the correct
Jc(T) dependence.
Available Jc(H)
results indicate that the magnetic field dependence for all wires from
T up to about 80% of the maximum
Hc2 can
be described with Kramer's flux shear model, if nonlinearities in Kramer plots when approaching the
maximum Hc2
are attributed to A15 inhomogeneities. The strain
(
) dependence is introduced through a temperature and strain dependent
Hc2*(T,
) and Ginzburg–Landau
(GL) parameter κ1(T,
)
and a strain dependent critical temperature
Tc(
). This is more consistent than the usual Ekin unification of strain and
temperature dependence, which uses two separate and different dependences on
Hc2*(T)
and Hc2*(
). Using a correct temperature dependence and accounting for the A15 inhomogeneities
leads to the remarkably simple relation
, where C is
a constant, s(
)
represents the normalized strain dependence of
Hc2*(0) and
h = H/Hc2*(T,
). Finally, a
new relation for s(
)
is proposed, which is an asymmetric version of our earlier deviatoric strain
model and based on the first, second and third strain invariants. The new
scaling relation solves a number of much debated issues with respect to
Jc scaling
in Nb3Sn
and is therefore of importance to the applied community, who use scaling relations to
analyse magnet performance from wire results.