In several experiments on a magnetically confined plasma and under certain conditions of a fusion reactor in stationary operation, neutral gas will be present in the regions surrounding the plasma. The inflow of neutrals and the outflow of plasma by diffusion or free streaming is studied in this paper, both for closed and open-ended systems: In a closed bottle neutral gas will not be able to penetrate through the cool boundary layers into the hot core of a high-density plasma. At plasma densities above 1021 m−3 the energy losses from interaction with the neutrals become negligible compared to the thermonuclear power production, but not at densities below 1019 m−3. This is due to the fact that the penetration depth of the neutrals depends on the ionization rate and becomes about 10−3 and 0.1 m at the densities 1021and 1019 m−3. Further, the neutral gas inflow will be delayed by diffusion through a cool boundary region of sufficiently high density. In stationary operation the plasma density will be determined by the magnetic field strength and the density of the surrounding neutral gas. A condition for stable heat balance in a boundary region of finite thickness is deduced in this paper. As an alternative to a fusion device where the plasma is surrounded by an ultra-high vacuum region, it is therefore possible to surround a high-density plasma by a neutral gas blanket. The latter should be dense enough for released wall impurities to diffuse only slowly towards the plasma boundary. With a superimposed stream of neutral gas along the plasma boundary, the impurities can then be removed before reaching the plasma. In an open-ended system, thin layers of neutral gas are formed by plasma particles which escape along the magnetic field and recombine at the end walls. The theory agrees with measurements of the density of a fully ionized plasma as a function of the applied magnetic field and the density of the surrounding neutral gas. It also suggests that Bohm diffusion has not been present in earlier experiments with rotating plasmas where the density was found to decay at a very slow rate during free-wheeling.