A Consistent Description of Scaling Law for Flux Pinning in$rm Nb_3rm Sn$Strands Based on the Kramer Model

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
_c2

^5/2
, whereas the strain dependence of F
_m
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
_s
for the flux line lattice shearing pinning force F
_s
. It is found that the strain dependence of F
_m
at 4.2K 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 4.2K is proportional to B
_c2

^5/2
kappa
^-2
, consistent with the temperature dependence of F
_m
. Moreover, this model agrees reasonably well even with the data in a high compressive strain region (< -0.8%)