On the polytropic coefficient of negative ions for modeling the sheath and presheath of electronegative plasmas

Abstract

The fluid description is widely used for the multi-dimensional modeling of low temperature plasmas with complex chemistries due to their relative low computational cost. It relies, however, on a series of simplifying assumptions and some truncation of the moment equations for describing the non-equilibrium between the electrons, positive ions, negative ions, and the neutrals. In this paper, the classical assumption of isothermal negative ions is revisited for electronegative plasmas and, more particularly, for the fluid modeling of the transition between the plasma and its sheath. To do so, and in contrast to previous studies, the energy balance equation for the negative ions is also computed, and it allows us to derive the polytropic coefficient γ of the negative ions in addition to one of the positive ions. Strong variations in the sheath and presheath of the negative ions temperature and their polytropic coefficient are observed. The polytropic coefficient is shown to be a strongly varying function of space having for consequence that the negative ions are isothermal only in a very narrow extension of the presheath. For the case considered in this paper, both positive and negative ion flows are nearly adiabatic at the sheath-edge and become adiabatic inside the sheath. This paper shows that classical fluid modeling assumptions need to be verified for each system under consideration, most particularly while modeling the transition from plasma to a wall.