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We discuss an experiment to investigate neutrino physics at the LHC in Run 3, with emphasis on tau flavour. As described in our previous paper [arXiv:1903.06564v1], the detector can be installed in the decommissioned TI18 tunnel, about 480 m downstream the ATLAS cavern, after the first bending dipoles of the LHC arc. In that location, the prolongation of the beam Line-of-Sight from Interaction Point IP1 to TI18 traverses about 100 m of rock. The detector intercepts the intense neutrino flux, generated by the LHC beams colliding in IP1, at large pseudorapidity eta, where neutrino energies can exceed a TeV. This paper focuses on optimizing global features of the experiment, like detector mass and acceptance. Since the neutrino-nucleon interaction cross section grows almost linearly with energy, the detector can be light and still collect a considerable sample of neutrino events; in the present study it weighs less than 3 tons. The detector is positioned off the beam axis, slightly above the ideal prolongation of the LHC beam from the straight section, covering 7.4 < eta < 9.2. In this configuration, the flux at high energies (0.5-1.5 TeV and beyond) is found to be dominated by neutrinos originating directly from IP1, mostly from charm decays, of which about 50% are electron neutrinos and about 5% are tau neutrinos. The contribution of pion and kaon decays to the muon neutrino flux is studied by means of simulations that embed the LHC optics and found small at high energies. The above studies indicate that with 150 /fb of delivered LHC luminosity in Run 3 the experiment can record a few thousand very high energy neutrino charged current interactions and over 50 tau neutrino charged current events.