Asymptotically matched sheath and presheath in a dense plasma

Abstract

Asymptotically matched solutions for electron and ion density, electron and ion velocity, and electric potential are obtained in the boundary region of a dense low-temperature plasma adjacent to perfectly absorbing walls – walls that absorb, without reflection, incident electrons and ions. Leading-order composite solutions, valid throughout the boundary region, are constructed from solutions in three subdomains distinguished by different physical length scales: the geometric length, the ion mean free path and the Debye length. The composite solutions are used to assess the impact of electron–ion recombination in the ionization nonequilibrium region on sheath and presheath profiles, and on quantities evaluated at the wall. While, at leading order, the velocity profiles throughout the boundary region are not influenced by recombination, the density and potential profiles are significantly altered when recombination is included. These results show that the region of rapid change in these profiles lies closer to the wall when recombination is explicitly included in the model. The influence of recombination on the presheath potential, and consequently the wall potential, is found to scale as the natural logarithm of the recombination length. The broadening of the density profile results in a larger flux of ions accelerating through the sheath and impacting on the wall. The influence of recombination on the ion power flux to the wall is found to scale with the inverse recombination length. This scaling influences the prediction of surface erosion rates in technological applications that utilize these plasmas.