XENON is a dark matter direct detection project, consisting of a time projection chamber (TPC) filled with liquid xenon as detection medium. The construction of the next generation detector, XENON1T, is presently taking place at the Laboratori Nazionali del Gran Sasso (LNGS) in Italy. It aims at a sensitivity to spin-independent cross sections of $2 cdot 10^{-47} ~ mathrm{cm}^{mathrm{2}}$ for WIMP masses around 50 GeV/c$^{2}$, which requires a background reduction by two orders of magnitude compared to XENON100, the current generation detector. An active system that is able to tag muons and muon-induced backgrounds is critical for this goal. A water Cherenkov detector of $sim$10 m height and diameter has been therefore developed, equipped with 8 inch photomultipliers and cladded by a reflective foil. We present the design and optimization study for this detector, which has been carried out with a series of Monte Carlo simulations. The muon veto will reach very high detection efficiencies for muons ($>99.5%$) and showers of secondary particles from muon interactions in the rock ($>70%$). Similar efficiencies will be obtained for XENONnT, the upgrade of XENON1T, which will later improve the WIMP sensitivity by another order of magnitude. With the Cherenkov water shield studied here, the background from muon-induced neutrons in XENON1T is negligible.
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