Evidence of Kramer extrapolation inaccuracy for predicting high field Nb$_3$Sn properties

Future applications requiring high magnetic fields, such as the proposed Future Circular Collider, demand a substantially higher critical current density, $J_c$, at fields ≥16 T than is presently available in any commercial strand, so there is a strong effort to develop new routes to higher $J_c$ Nb$_3$Sn. As a consequence, evaluating the irreversibility field ($H_{irr}$) of any new conductor to ensure reliable performance at these higher magnetic fields becomes essential. To predict the irreversibility field for Nb$_3$Sn wires, critical current measurements, $I_c$, are commonly performed in the 12-15 T range and the Kramer extrapolation is used to predict higher field properties. The Kramer extrapolation typically models the contribution only for sparse grain boundary pinning, yet Nb3Sn wires rely on a high density of grain boundaries to provide the flux pinning that enables their high critical current density. However, whole-field range VSM measurements up to 30 T recently showed for Nb$_3$Sn RRP® wires that the field dependence of the pinning force curve significantly deviates from the typical grain boundary shape, leading to a 1-2 T overestimation of $H_{irr}$ when extrapolated from the typical mid-field data taken only up to about 15 T. In this work we characterized a variety of both RRP® and PIT Nb3Sn wires by transport measurements up to 29 T at the Laboratoire National des Champs Magnétiques Intenses (LNCMI), part of the European Magnetic Field Laboratory in Grenoble, to verify whether or not such overestimation is related to the measurement technique and whether or not it is a common feature across different designs. Indeed we also found that when measured in transport the 12-15 T Kramer extrapolation overestimates the actual $H_{irr}$ in both types of conductor with an inaccuracy of up to 1.6 T, confirming that high field characterization is a necessary tool to evaluate the actual high field performance of each Nb3Sn wire.