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

Abstract

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 $1.4\! \times\! 10^{21} \text{m}^{-2}$ ) and neutrons (> 0.1 MeV, up to $1.8 \!\times\! 10^{22} \text{m}^{-2}$ ). 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 ∼0.3 K. The variation of $J_{c}$ versus $dpa$ shows some similarities between proton and neutron irradiation, too, but the analysis is more complex, the observed enhancement of $J_{c}$ with irradiation being due to enhanced point pinning caused by the radiation-induced defect clusters.