Background: Deep-inelastic scattering (DIS) on the deuteron with spectator nucleon tagging represents a unique method for extracting the free neutron structure functions and exploring the nuclear modifications of bound protons and neutrons. The detection of the spectator (with typical momenta $lesssim$ 100 MeV/c in the deuteron rest frame) controls the nuclear configuration during the DIS process and enables a differential analysis of nuclear effects. At the future electron-ion collider (EIC) such measurements will be performed using far-forward detectors. Purpose: Simulate deuteron DIS with proton or neutron tagging with the baseline EIC far-forward detector design. Quantify detector acceptance and resolution effects. Study feasibility of free nucleon structure extraction using pole extrapolation in the spectator momentum. Methods: DIS events with proton and neutron spectators are generated using the BeAGLE Monte Carlo generator. The spectator nucleon momentum is reconstructed including effects of detector acceptance and resolution. Pole extrapolation is performed under realistic conditions. The free nucleon structure extraction is validated by comparing with the input model. Results: Proton and neutron spectator detection is possible over the full transverse momentum range $0 < p_T < 100$ MeV/c needed for pole extrapolation. Resolution effects on the distributions before corrections are ~10% for proton and ~30 for neutron spectators. The overall accuracy of nucleon structure extraction is expected to be at the few-percent level. Conclusions: Free neutron structure extraction through proton tagging and pole extrapolation is feasible with the baseline EIC far-forward detector design. The corresponding extraction of free proton structure through neutron tagging provides a reference point for future studies of nuclear modifications.
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