A numerical study is done of a plasma in contact with a solid surface that reemits some fraction of the incident plasma as neutral gas. The calculation uses a steady‐state, kinetic treatment of the transport equations in one space dimension and one or two velocity dimensions to determine self‐consistently the distribution functions of the interacting species and the electrostatic potential. The dominant phenomena are the ionization of the neutral gas and the acceleration of the resulting ions away from a potential maximum that is predicted to form in the ionization region. Other effects involved are a Debye sheath structure between the solid surface and the potential maximum, and collisional trapping and untrapping of electrons in the well represented by the potential maximum. Results are presented from a nondimensional model with a monatomic returning neutral species, and for diatomic molecular deuterium returning from the surface. For each set of physical parameters chosen, a one parameter family of solutions is obtained. A hypothesis is presented for the choice from this family of solutions that would be found experimentally.