Impact of the Residual Resistivity Ratio on the Stability of Nb$_{3}$Sn Magnets

The CERN Large Hadron Collider (LHC) is envisioned to be upgraded in 2020 to increase the luminosity of the machine. The major upgrade will consist in replacing the NbTi quadrupole magnets of the interaction regions with larger aperture magnets. The Nb$_{3}$Sn technology is the preferred option for this upgrade. The critical current density Jc of Nb$_{3}$Sn strands have reached sufficiently high values (in excess of 3000 A/mm2 at 12 T and 4.2 K) allowing larger aperture/stronger field magnets. Nevertheless, such large Jc values may cause magneto-thermal instabilities that can drastically reduce the conductor performance by quenching the superconductor prematurely. In Nb$_{3}$Sn magnets, a relevant parameter for preventing premature quenches induced by magneto-thermal instabilities is the Residual Resistivity Ratio (RRR) of the conductor stabilizing copper. An experimental and theoretical study was carried out to investigate how much the value of the RRR affects the magnet stability and to identify the proper conductor specifications. In this paper the main results are presented and discussed