The COSINUS (Cryogenic Observatory for SIgnatures seen in Next-generation Underground Searches) experiment aims at the detection of dark matter-induced recoils in sodium iodide (NaI) crystals operated as scintillating cryogenic calorimeters. The detection of both scintillation light and phonons allows performing an event-by-event signal to background discrimination, thus enhancing the sensitivity of the experiment. The construction of the experimental facility is foreseen to start by 2021 at the INFN Gran Sasso National Laboratory (LNGS) in Italy. It consists of a cryostat housing the target crystals shielded from the external radioactivity by a water tank acting, at the same time, as an active veto against cosmic ray-induced events. Taking into account both environmental radioactivity and intrinsic contamination of materials used for cryostat, shielding and infrastructure, we performed a careful background budget estimation. The goal is to evaluate the number of events that could mimic or interfere with signal detection while optimising the geometry of the experimental setup. In this paper we present the results of the detailed Monte Carlo simulations we performed, together with the final design of the setup that minimises the residual amount of background particles reaching the detector volume.
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