AbstractThe theoretical description of the positive column at low gas pressure is improved by taking into account both the space charge sheath at the wall and the radial variation of the radial ion temperature. Assuming the ion temperature being zero on the axis only, simplified moment equations up to the third order are used. Under free‐fall conditions and by taking into account the charge exchange between ions and atoms the spatial distributions of the number densities and of the drift velocities of the ions and of the electrons, of the radial ion temperature, and of the electric potential are calculated. Moreover, the electron temperature is given. It has been found out that at low gas density the charge exchange causes a high ion temperature and not only an increase of the neutral gas temperature, where the electron collisions do not remarkably contribute to the heating of the ion ga