Hysteresis Losses and Effective $J_{c}(B)$ Scaling Law for ITER Nb$_{3}$Sn Strands

Hysteresis losses of five Nb$_{3}$Sn International Thermonuclear Experimental Reactor reference strands were investigated by means of magnetization loop measurements in a vibrating sample magnetometer in a perpendicularly applied magnetic field. The magnetization loops were recorded while continuously sweeping the applied field between the extreme values $±B_m$, covering a wide range of maximum applied fields (0.2-10 T). In this paper, we compare the directly determined hysteresis losses based on the area of the smaller measured loops and the losses calculated by the integration of the width ΔM of the $B_m$ = 10 T magnetization loop. A suitable fitting function is proposed to describe the ΔM(B) dependence, which leads, for each strand, to an excellent agreement with the experimentally determined hysteresis losses, magnetization, and pinning force. Transport critical current measurements in a perpendicularly applied magnetic field were also performed for all the strands, and on the basis of the comparison with the transport measurements, the critical current densities were determined from the magnetization data.