A new generation of 3D silicon pixel detectors with a small pixel size of 50$times$50 and 25$times$100 $mu$m$^{2}$ is being developed for the HL-LHC tracker upgrades. The radiation hardness of such detectors was studied in beam tests after irradiation to HL-LHC fluences up to $1.4times10^{16}$ n$_{mathrm{eq}}$/cm$^2$. At this fluence, an operation voltage of only 100 V is needed to achieve 97% hit efficiency, with a power dissipation of 13 mW/cm$^2$ at -25$^{circ}$C, considerably lower than for previous 3D sensor generations and planar sensors.
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