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) =1t1.52, 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 nonlinearities 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 GinzburgLandau 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):
 LBNL60142
R&D Project: Z5M711; BnR: KA1502010; TRN: US0801838
 DOE Contract Number:
 DEAC0205CH11231
 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:10.1088/09532048/19/10/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:10.1088/09532048/19/10/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:10.1088/09532048/19/10/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) =1t1.52, 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 nonlinearities 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 GinzburgLandau 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)(1t1.52)(1t2)h0.5(1h)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 = {10.1088/09532048/19/10/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}
}

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) =1t1.52, 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 themore »

Scaling properties of the anisotropic critical current density in bulk textured YBaCuO. Evidence toward a 3D flux line lattice
The dc transport critical current densities of melt texture grown and magnetically melt textured bulk YBaCuO have been measured at 77 K and in magnetic fields. A maximum value of over 31,000 A/cm[sup 2] is obtained with a field of 7 teslas applied parallel to the (a,b) planes. Over the rest of the angular range the critical current is shown to be determined mainly by the caxis component of the applied field. Although this dependency is expected in the presence of twodimensional vortices, in fact the data are shown to correspond better to the behavior expected of an anisotropic threedimensionalmore » 
Scaling of critical current density in fieldaligned grains of (Tl/sub 0. 75/Bi/sub 0. 25/)/sub 1. 33/Sr/sub 1. 33/Ca/sub 1. 33/Cu/sub 2/ O/sub 6. 67+//sub delta/, the ''1212'' phase
We have measured intragrain critical currents in fieldoriented samples of a rareearthfree highT/sub c/ superconductor (Tl/sub 0.75/Bi/sub 0.25/)/sub 1.33/Sr/sub 1.33/Ca/sub 1.33/Cu/sub 2/ O/sub 6.67+//sub delta/, the ''1212'' phase. The critical current J/sub c/ is anisotropic. For fields oriented along the conducting planes, a simple scaling of J/sub c/ with field is found. The critical current scales to zero at a field H/sup B//sub c//sub 2/ (T) which is in good agreement with the form predicted by the flux creep theory.