Correlation Between the Number of Displacements Per Atom and $T_{c}$ 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 Taand Ti-added Nb3Sn wires. Wire samples from the same batch were irradiated with high-energy protons (65 MeV and 24 GeV, up to 1.4×10
²¹
m
^-2
) and neutrons (> 0.1 MeV, up to 1.8×10
²²
m
^-2
). The values of T' and Jc 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 Nb
₃
Sn 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.