Critical Current and Magnetization Scaling of Nb3Sn Wires: Measurements and Simulations from Exact Wire Geometries

Abstract

In the context of the High Field Magnet (HFM) program, 14 T dipole magnets are under development towards requirements for a proposed Future Circular Collider (FCC-hh). For evaluation of operating margins, a reliable critical current density scaling, J_c(B,T), is required up to 18 T and for 1.9–10 K; whilst AC loss calculations for designing cooling and quench protection schemes require this to be extended down to an injection field of ∼1 T or below at the operating temperature. Scaling laws for Nb₃Sn wires have been extensively studied in the literature. However, for practical high I_c wires, it is rarely possible to access this full temperature and field range in measurements with a transport current, and a variety of procedural methodologies have been proposed to address divergences between transport and magnetization measurements. In this study, a recently-developed Coupled Axial and Transverse Currents (CATI) finite element method is applied for modeling the electrical and magnetic behavior of the RRP Nb₃Sn wire used for HL-LHC MQXF magnets, incorporating its exact twisted composite geometry as parameterized by image analysis. Fitting parameters for the J_c(B,T) of the superconductor are found to simultaneously match transport I_c (6–15 T, 1.9 K and 4.3 K) and magnetization (0–10 T, 1.9–16 K), and the assumptions required are discussed. The model is then used to explore the validity of common procedures applied to experimental data, including self-field correction and procedural fitting approaches.