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The Target Absorbers for Neutrals (TANs) are located in a high-intensityradiation environment inside the tunnel of the Large Hadron Collider (LHC).TANs are positioned about $140$ m downstream from the beam interaction points.Seven $40$ cm long fused silica rods with different dopant specifications wereirradiated in the TAN by the Beam RAte of Neutrals (BRAN) detector group during$p$+$p$ data taking from 2016 to 2018 at the LHC. The peak dose delivered tothe fused silica rods was $18$ MGy. We report measurements of the $^{22}$Naactivation of the fused silica rods carried out at the University of Illinoisat Urbana-Champaign and Argonne National Laboratory. At the end of theirradiation campaign, the maximum $^{22}$Na activity observed was $A=21$kBq$/{\rm cm^3}$ corresponding to a density, $\rho= 2.5\times 10^{12} /{\rmcm^3}$, of $^{22}$Na nuclei. FLUKA Monte Carlo simulations have been performedby the CERN FLUKA team to estimate $^{22}$Na activities for the irradiated BRANrod samples. The simulations reproduce the $^{22}$Na activity profile measuredalong the rods, with a 35% underestimation of the experimental measurementresults.

$^{22}$Na Activation Level Measurements of Fused Silica Rods in the LHC Target Absorber for Neutrals (TAN) Compared to FLUKA Simulations