Evaluation of the Critical Current Density of Multifilamentary ${\rm Nb}_{3}{\rm Sn}$ Wires From Magnetization Measurements

Abstract

A simple model for evaluating the critical current density of multifilamentary <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm Nb}_{3}{\rm Sn}$</tex></formula> wires from magnetization measurements was examined. This model assumes that each sub-element is in good approximation a superconducting hollow cylinder, which limits its validity to powder-in-tube wires and wires whose filaments are completely merged within the sub-elements. The magnetic moment of short samples of four wire types was measured in a SQUID magnetometer at applied fields of up to 7 T in the temperature range from 4.2 to 15 K. The <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$J_{\rm c}$</tex></formula> evaluation model discussed in this work was used to obtain critical current densities from the results of these measurements. The calculated <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$J_{\rm c}$</tex></formula> values were compared to transport measurement results, and satisfactory agreement was found between the two data sets. Furthermore, it was shown by means of magnetization measurements of individual sub-elements that the coupling between the sub-elements in the wire samples has a negligible effect on such measurements.