A Consistent Description of Scaling Law for Flux Pinning in ${\hbox {Nb}}_{3}{\hbox {Sn}}$ Strands Based on the Kramer Model (Corrected)*

There are a lot of experimental reports on the scaling of flux pinning in the form of F = F_mb^1/2(1 - b)², with b = B/B_c2.The temperature dependence of F_m is approximately proportional to B´.2 , whereas the strain dependence of Fm is reported to be proportional to the upper critical field Bc2. In this work, we re-analyze our previous data with the Kramer model including the pin-breaking dynamic pinning force (F_p) for a low field region. It is shown that the extrapolated upper critical field B_c2*, strongly depend on the ratio between the mean of the parameter K_p for F_p (<K_p>) and the parameter K, for the flux line lattice shearing pinning force F_s. It is found that the strain dependence of F_m at 4.2 K is approximately proportional to (B_c2*)^1.5. We further compare the data with the prediction of our recent scaling theory based on Eliashberg theory of strongly coupled superconductors. It is shown that the strain dependence of F_m at 4.2 K is proportional to BC₂ ^5/2 kappa^-2, consistent with the temperature dependence of Fm. Moreover, this model agrees reasonably well even with the data in a high compressive strain region (<-0.8%).