# A general scaling relation for the critical current density inNb3Sn

## Abstract

We review the scaling relations for the critical currentdensity (Jc) in Nb3Sn wires and include recent findings on the variationof the upper critical field (Hc2) with temperature (T) and A15composition. Measurements of Hc2(T) in inevitably inhomogeneous wires, aswell as analysis of literature results, have shown that all availableHc2(T) data can be accurately described by a single relation from themicroscopic theory. This relation also holds for inhomogeneity averaged,effective, Hc2*(T) results and can be approximated by Hc2(t)=Hc2(0) =1-t1.52, with t = T=Tc.Knowing Hc2*(T) implies that also Jc(T) is known.We highlight deficiencies in the Summers/Ekin relations, which are notable to account for the correct Jc(T) dependence. Available Jc(H) resultsindicate that the magnetic field dependence for all wires from mu0H = 1 Tup to about 80 percent of the maximum Hc2 can be described with Kramer'sflux shear model, if non-linearities in Kramer plots when approaching themaximum Hc2 are attributed to A15 inhomogeneities. The strain (e)dependence is introduced through a temperature and strain dependentHc2*(T,e) and Ginzburg-Landau parameter kappa1(T,e) and a straindependent critical temperature Tc(e). This is more consistent than theusual Ekin unification of strain and temperature dependence, which usestwo separate and different dependencies on Hc2*(T) and Hc2*(e). Using acorrect temperature dependence and accounting for themore »

- Authors:

- Publication Date:

- Research Org.:
- Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)

- Sponsoring Org.:
- USDOE Director. Office of Science. Office of High EnergyPhysics; University of Twente

- OSTI Identifier:
- 923445

- Report Number(s):
- LBNL-60142

R&D Project: Z5M711; BnR: KA1502010; TRN: US0801838

- DOE Contract Number:
- DE-AC02-05CH11231

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Superconductor, Science and Technology; Journal Volume: 19; Related Information: Journal Publication Date: 2006

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75; CRITICAL CURRENT; CRITICAL FIELD; CRITICAL TEMPERATURE; MAGNETIC FIELDS; MAGNETS; PERFORMANCE; SHEAR; STRAINS; TEMPERATURE DEPENDENCE; Critical Current Scaling Nb3Sn

### Citation Formats

```
Godeke, A., Haken, B. ten, Kate, H.H.J. ten, and Larbalestier, D.C..
```*A general scaling relation for the critical current density inNb3Sn*. United States: N. p., 2006.
Web. doi:10.1088/0953-2048/19/10/R02.

```
Godeke, A., Haken, B. ten, Kate, H.H.J. ten, & Larbalestier, D.C..
```*A general scaling relation for the critical current density inNb3Sn*. United States. doi:10.1088/0953-2048/19/10/R02.

```
Godeke, A., Haken, B. ten, Kate, H.H.J. ten, and Larbalestier, D.C.. Mon .
"A general scaling relation for the critical current density inNb3Sn". United States.
doi:10.1088/0953-2048/19/10/R02. https://www.osti.gov/servlets/purl/923445.
```

```
@article{osti_923445,
```

title = {A general scaling relation for the critical current density inNb3Sn},

author = {Godeke, A. and Haken, B. ten and Kate, H.H.J. ten and Larbalestier, D.C.},

abstractNote = {We review the scaling relations for the critical currentdensity (Jc) in Nb3Sn wires and include recent findings on the variationof the upper critical field (Hc2) with temperature (T) and A15composition. Measurements of Hc2(T) in inevitably inhomogeneous wires, aswell as analysis of literature results, have shown that all availableHc2(T) data can be accurately described by a single relation from themicroscopic theory. This relation also holds for inhomogeneity averaged,effective, Hc2*(T) results and can be approximated by Hc2(t)=Hc2(0) =1-t1.52, with t = T=Tc.Knowing Hc2*(T) implies that also Jc(T) is known.We highlight deficiencies in the Summers/Ekin relations, which are notable to account for the correct Jc(T) dependence. Available Jc(H) resultsindicate that the magnetic field dependence for all wires from mu0H = 1 Tup to about 80 percent of the maximum Hc2 can be described with Kramer'sflux shear model, if non-linearities in Kramer plots when approaching themaximum Hc2 are attributed to A15 inhomogeneities. The strain (e)dependence is introduced through a temperature and strain dependentHc2*(T,e) and Ginzburg-Landau parameter kappa1(T,e) and a straindependent critical temperature Tc(e). This is more consistent than theusual Ekin unification of strain and temperature dependence, which usestwo separate and different dependencies on Hc2*(T) and Hc2*(e). Using acorrect temperature dependence and accounting for the A15 inhomogeneitiesleads to the remarkable simple relation Jc(H,T,e)=(C/mu0H)s(e)(1-t1.52)(1-t2)h0.5(1-h)2, where C is a constant, s(e)represents the normalized strain dependence of Hc2*(0) andh =H/Hc2*(T,e). Finally, a new relation for s(e) is proposed, which is anasymmetric version of our earlier deviatoric strain model and based onthe first, second and third strain invariants. The new scaling relationsolves a number of much debated issues withrespect to Jc scaling in Nb3Snand is therefore of importance to the applied community, who use scalingrelations to analyze magnet performance from wire results.},

doi = {10.1088/0953-2048/19/10/R02},

journal = {Superconductor, Science and Technology},

number = ,

volume = 19,

place = {United States},

year = {Mon May 08 00:00:00 EDT 2006},

month = {Mon May 08 00:00:00 EDT 2006}

}