We combined a simple plasma convection model with an ionospheric-atmospheric composition model in order to study the high-latitude winter F region at solar minimum for low magnetic activity. Our numerical study produced time dependent, three-dimensional ion density distributions for the ions NO+, O2+, N2+, O+, N+, and He+. We covered the high-latitude ionosphere above 54¿N magnetic latitude and at altitudes between 160 and 800 km for a time period of one complete day. The main result we obtained was that high-latitude ionospheric features, such as the 'main trough,' the 'ionization hole,' the 'tongue of ionization,' the 'aurorally produced ionization peaks,' and the 'universal time effects,' are a natural consequence of the competition between the various chemical and transport processes known to be operating in the high-latitude ionosphere. In addition, we found that (1) the F region peak electron density at a given location and local time can vary by more than an order of magnitude, owing to the UT effect that results from the displacement between the geomagnetic and geographic poles; (2) a wide range of ion compositions can occur in the polar F region at different locations and times; (3) the minimum value for the electron density in the main trough is sensitive to nocturnal maintenance processes; (4) the depth and longitudinal extent of the main trough exhibit a significant UT dependence; (5) the way the auroral oval is positioned relative to the plasma convection pattern has an appreciable effect on the magnetic local time extent of the main trough; (6) the spatial extent, depth, and location of the polar ionization hole are UT dependent; (7) the level of ion production in the morning sector of the auroral oval has an appreciable effect on the location and spatial extent of the polar ionization hole; and (8) in the polar hole the F region peak electron density is below 300 km, and at 300 km, diffusion is a very important process for both O+ and NO+. Contrary to the suggestion based on an analysis of AE-C satellite data obtained in the polar hole that the concentration of NO+ ions is chemically controlled, we find diffusion to be the dominant process at 300 km.