XSEN (Cross Section of Energetic Neutrinos) is a small experiment designed to study, for the first time, neutrino-nucleon interactions (including the tau flavour) in the 0.5-1 TeV neutrino energy range. The detector will be installed in the decommissioned TI18 tunnel and uses nuclear emulsions. Its simplicity allows construction and installation before the LHC Run 3, 2021-2023; with 150/fb in Run3, the experiment can record up to two thousand neutrino interactions, and up to a hundred tau neutrino events. The XSEN detector intercepts the intense neutrino flux, generated by the LHC beams colliding in IP1, at large pseudo-rapidities, where neutrino energies can exceed the TeV. Since the neutrino-N interaction cross section grows almost linearly with energy, the detector can be light and still collect a considerable sample of neutrino interactions. In our proposal, the detector weighs less than 3 tons. It is lying slightly above the ideal prolongation of the LHC beam from the straight section; this configuration, off the beam axis, although very close to it, enhances the contribution of neutrinos from c and b decays, and consequently of tau neutrinos. The detector fits in the TI18 tunnel without modifications. We plan for a demonstrator experiment in 2021 with a small detector of about 0.5 tons; with 25/fb, nearly a hundred interactions of neutrinos of about 1 TeV can be recorded. The aim of this pilot run is a good in-situ characterisation of the machine-generated backgrounds, an experimental verification of the systematic uncertainties and efficiencies, and a tuning of the emulsion analysis infrastructure and efficiency. This Letter provides an overview of the experiment motivations, location, design constraints, technology choice, and operation