In experiments in which an intense relativistic electron beam is injected into an evacuated drift tube with a localized gas cloud located near the anode, ions with energies several times the electron beam energy have been observed. These experiments have been simulated using a particle‐in‐cell code which realistically models ionization of the gas. It was found that when the injected electron beam current exceeds the space‐charge limiting current, ions are accelerated to energies several times the electron beam energy by coherent motion of the ions and the intense virtual cathode electric fields. The dependence of the peak ion energy on the system parameters as observed in the simulations is also discussed. For the parameter regimes investigated with beam energies up to 3 MV, beam currents up to 35 kA, gas pressures up to 600 mTorr, and gas cloud widths up to 6 cm, peak ion energies of 5–6 times the electron beam energy have been observed.