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
_m
b
^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
(_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 BC
₂

^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%).