Radon mitigation during the installation of the CUORE $0\nu\beta\beta$ decay detector

CUORE - the Cryogenic Underground Observatory for Rare Events - is an experiment searching for the neutrinoless double-beta ($0\nu\beta\beta$) decay of $^{130}$Te with an array of 988 TeO$_2$ crystals operated as bolometers at $\sim$10 mK in a large dilution refrigerator. With this detector, we aim for a $^{130}$Te $0\nu\beta\beta$ decay half-life sensitivity of $9\times10^{25}$ y with 5 y of live time, and a background index of $\lesssim 10^{-2}$ counts/keV/kg/y. Making an effort to maintain radiopurity by minimizing the bolometers' exposure to radon gas during their installation in the cryostat, we perform all operations inside a dedicated cleanroom environment with a controlled radon-reduced atmosphere. In this paper, we discuss the design and performance of the CUORE Radon Abatement System and cleanroom, as well as a system to monitor the radon level in real time.