AbstractFor a thermally non-equilibrium system that consists of a monoenergetic ion beam propagating through a partially ionized plasma at a density up to solid state, an approximate equilibrium formula is obtained following entropy considerations that relate to ion beam charge states, including the dependence on the beam velocity and substance, and on the medium substance, temperature and density. At low temperatures, as a consequence the Bohr-Lamb criterion, an ‘average ion’ approximation is derived (in the Lamb version). Also, if the beam substances and that of the medium are the same, and the beam velocity equals zero, then Saha's formula for the ionization equilibrium is obtained.