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The upgrade of the LHC collimation system foresees installation of additional collimators around the LHC ring. The longitudinal space for the collimators could be provided by replacing some 8.33 T NbTi LHC main dipoles with shorter 11 T Nb3Sn dipoles compatible with the LHC lattice and main systems. To demonstrate this possibility, FNAL and CERN have started a joint program with the goal of building a 5.5 m long twin-aperture dipole prototype suitable for installation in the LHC. The first step of this program is the development of a 2 m long single-aperture demonstrator dipole with a nominal field of 11 T at the LHC nominal current of 11.85 kA and ~ 20% margin. This paper describes the design, construction, and test results of the first single-aperture Nb3Sn demonstrator dipole model.