The magnetic field, temperature, strain and angular dependence of the critical current density for Nb-Ti

Abstract A scaling law for J c in commercial Nb-Ti wire is proposed that describes its magnetic field, temperature and strain dependence. The scaling law is used to fit extensive measurements of the total strand critical current density, J c,TS ( B, T, ε ), with the applied field orthogonal to the axis of the wire. We present critical current density, heat capacity and resistivity measurements to obtain <?CDATA ${B}_{{\rm{c}}2}^{* }(\theta )$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> <mml:mn>2</mml:mn> </mml:mrow> <mml:mo>*</mml:mo> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>θ</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> , which shows clear angular anisotropy. At 4.2 K, the resistivity data show <?CDATA ${B}_{{\rm{c}}2}^{* }(B\parallel J)-{B}_{{\rm{c}}2}^{* }(B\perp J)\approx 1\,{\rm{T}}$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> <mml:mn>2</mml:mn> </mml:mrow> <mml:mo>*</mml:mo> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>B</mml:mi> <mml:mo>∥</mml:mo> <mml:mi>J</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>−</mml:mo> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> <mml:mn>2</mml:mn> </mml:mrow> <mml:mo>*</mml:mo> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>B</mml:mi> <mml:mo>⊥</mml:mo> <mml:mi>J</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>≈</mml:mo> <mml:mn>1</mml:mn> <mml:mspace width="0.25em" /> <mml:mi mathvariant="normal">T</mml:mi> </mml:mrow> </mml:math> . We also discuss whether the fusion community should consider re-optimising standard commercial Nb-Ti wires that were developed for MRI applications at ~ 5 T, to produce higher J c at say 10T, and higher upper critical fields, perhaps using quaternary Nb-Ti alloys with artificial pinning centres.