Correlation Between the Number of Displacements Per Atom and Tc After High-Energy Irradiations of Nb3Sn Wires for the HL-LHC

In order to predict the irradiation effects in the quadrupoles of the High-Luminosity Large Hadron Collider accelerator at the European Organization for Nuclear Research (CERN) during operation up to a luminosity of 4000 fb(-1), an irradiation program was carried out on industrial Ta- and Ti-added Nb3Sn wires. Wire samples from the same batch were irradiated with high-energy protons (65 MeV and 24 GeV, up to 1.4x10(21) m(-2)) and neutrons (> 0.1MeV, up to 1.8x10(22) m(-2)). The values of T-c and J(c) were reported as a function of particle fluence. After replacing the fluence by the number of displacements per atom (dpa), which is determined using the FLUKA code, it was found that the variation of T-c in Nb3Sn wires as a function of the dpa value for both proton and neutron irradiation falls on the same curve, reflecting a universal behavior. This result reflects the fact that the variation of T-c is uniquely governed by the change in atomic ordering S. Both the measured value T-c and the calculated one dpa essentially depend on the number of Frenkel defects. With the new relationship between T-c and dpa for both protons and neutrons, the decrease of T-c in the quadrupoles at the maximum luminosity can be estimated to similar to 0.3 K. The variation of Jc versus dpa shows some similarities between proton and neutron irradiation, too, but the analysis is more complex, the observed enhancement of Jc with irradiation being due to enhanced point pinning caused by the radiation-induced defect clusters.