In the aperture limiter shadow of the T-10 tokamak, the temporal evolution of plasma density and electron temperature during single discharges is studied by using a Langmuir double probe. It is observed that the plasma of the scrape-off layer (SOL) passes through a stationary phase when the Ohmic heat input Uloop Ip also does, suggesting that the stationarity of the SOL is correlated with the stationarity of the discharge power balance. During this stationary phase the plasma density at the aperture limiter edge was found to be approximately proportional to the square of the line averaged core plasma density. – It is shown in the paper that this quadratic density scaling can be easily understood within the framework of a stationary particle balance model of the recycling process, i.e. the interaction of plasma and neutral particles of the working gas in the edge region. Quadratic density scaling is expected to hold generally if the plasma density is high enough to prevent the neutrals from reaching the centre. For high densities, on the other hand, there is a density limit defined by the requirement that the discharge should supply enough power to sustain recycling.