On the theory of plasma-wall transition layers

Abstract

The problem of the plasma-wall transition (PWT) layer in an unmagnetized plasma is considered, without the usual splitting into a sheath and presheath region. The electrons are assumed to be Boltzmann distributed, while the ion dynamics is described by a kinetic theory which includes ionization, recombination, and charge exchange. A condition is derived, which must be fulfilled by the ion velocity throughout the whole PWT in order to exclude oscillatory behavior of the electrostatic potential. The resulting system of equations is solved numerically for various physical situations. The Harrison–Thomson solution for the Tonks–Langmuir model is extended to the case where the quasineutrality is violated, and it is shown that the parabolic shape of the potential profile is retrieved also in this case. For a complete PWT layer, good agreement with recent experimental observations is demonstrated, whereas marked disagreement is found with results based on theories where no recombination is included and/or the ratio of Debye length to characteristic presheath length is assumed to be infinitesimally small. A comparison between recent experimental results with a numerical solution of the model presented here reveals that the model accurately describes the transition from the bulk plasma to the electron-free plasma sheath.