Electron motion in the cathode sheath region of a glow discharge in argon has been simulated for a linearly decreasing electric field using a one-dimensional computer model. Distribution functions for the electron flux crossing the sheath have been calculated for 12 values of the cathode fall between 180 and 1400 V encompassing the normal and abnormal regimes. Macroscopic variables including the Townsend ionisation coefficient, the electron multiplication factor and the mean electron energy have been determined for cathode fall values between 180 and 1000 V. It is shown that the proportion of electron flux crossing the sheath without collisions increases as the cathode fall is raised. When the cathode fall is in the range 300-900 V, the electron flux at the sheath/negative-glow boundary is found to be highly directional with distinct beam-like characteristics. Beyond 900 V, the largest component in the distribution of electron flux to reach the boundary region is the collision-free group. These electrons enter the negative glow with energies corresponding to the cathode fall potential and are nearly mono-energetic. In this case, the entire cathode sheath/negative-glow region can be referred to as an ‘electron-beam’ glow discharge.