Electron motion in the cathode sheath region of a glow discharge in helium has been simulated using a one-dimensional computer model. Distribution functions for the electron flux across the cathode sheath have been calculated for fourteen values of the cathode fall between 150 and 1700 V. Macroscopic variables including the Townsend ionisation coefficient, multiplication coefficient and mean electron energy have been determined for the cathode fall range 150-1000 V. It is shown that the proportion of electron flux crossing the cathode sheath without collisions increases as the cathode fall is raised. For a cathode fall between 400 and 1400 V, the electron flux at the cathode sheath/negative glow boundary possesses beam-like characteristics. Beyond 1400 V, the largest component, in the electron flux distribution, to reach the sheath boundary is the collision-free group. These electrons enter the negative glow with energies corresponding to the cathode fall potential, and are practically mono-energetic. The authors propose that this is a suitable criterion to refer to the entire cathode sheath/negative glow region as an 'electron-beam' glow discharge.