Distribution functions of positive ions and electrons in a plasma near a surface

In this study, the velocity distribution functions of the ions and electron s in a collisional presheath and collisionless sheath of a plasma near a wa ll emitting and reflecting ions and electrons are systematically determined . The collisions in the presheath are modeled by a relaxation time approxim ation (namely, Bhatnagar-Gross-Krook model, or simply BGK model), To find t he variation in electrostatic potential with position, the model and analys is from Emmert et al. are used. Distribution functions of the ions and elec trons in a collisionless presheath and sheath on a wall partially reflectin g ions and electrons, therefore, ran be exactly obtained, The reflections o f the ions and electrons hy a wall play important roles in studying heat tr ansfer from a plasma sheath to a workpiece surface, and sputter etching and deposition, ion implantation, and ion scattering spectroscopy. Irrespectiv e of ion and electron reflectivities, velocities of the ions in the preshea th and sheath are of highly non-Maxwell-Boltzmann distributions, The electr ons in the presheath are close to Maxwell-Boltzmann distributions, whereas those in the sheath are non-Maxwell-Boltzmann distributions, Even though th e wall partially reflects ions and electrons, the Bohm's criterion is margi nally satisfied at the sheath edge, The computed distribution functions for a completely absorbing surface agree with theoretical results provided in the literature. Good comparison of the resulted transport variables with av ailable analytical work is presented in the companion paper.