Dark Matter experiments are recently focusing their detection techniques in low-mass WIMPs, which requires the use of light elements and low energy threshold. In this context, we describe the TREX-DM experiment, a low background Micromegas-based Time Projection Chamber for low-mass WIMP detection. Its main goal is the operation of an active detection mass $sim$0.3 kg, with an energy threshold below 0.4~keVee and fully built with previously selected radiopure materials. This work focuses on the commissioning of the actual setup situated in a laboratory on surface. A preliminary background model of the experiment is also presented, based on Geant4 simulations and two discrimination methods: a conservative muon/electron and one based on a $^{252}$Cf source. Based on this model, TREX-DM could be competitive in the search for low mass WIMPs and, in particular, it could be sensitive to the WIMP interpretation of the DAMA/LIBRA hint.
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