Impact of the Number of dpa on the Superconducting Properties in HiLumi-LHC and FCC Accelerators

The aim of this paper is to estimate the change of the superconducting properties T c, J c, and B c2 in the quadrupoles of the future accelerators HiLumi-LHC and FCC, submitted to irradiation by multiple high-energy sources. The estimations are performed based on the number of displacements per atom ( dpa ), calculated by means of the FLUKA code. It is found that the dpa can be used as a single parameter for describing the radiation induced change of T c, the degree of atomic order parameter S , and the lattice parameter a in the case of multiple energy sources. The mechanism leading to the enhancement of $J_{\text{c}}$ after proton and neutron irradiation is analyzed based on a possible correlation with the concentration of Frenkel defects produced by the irradiation. Experimental data on J c/ J co versus dpa at 4.2 K allow estimating J c in the quadrupoles of HiLumi-LHC and FCC/Run1, where the values of dpa for lifetime are 2.5 × 10−4 and 5 × 10−4, respectively. The dpa in FCC/Run2 is much higher, 3 × 10 −3, thus reaching well beyond the maximum of J c versus dpa. An accurate estimation of the variation of T c, J c, and B c2 is performed based on earlier irradiation data with 14-MeV neutrons.