Ion temperature profiles in front of a negative planar electrode studied by a one-dimensional two-fluid model

Abstract

Plasma-wall transition is studied by a one-dimensional steady state two-fluid model. Continuity and momentum exchange equations are used for the electrons, while the continuity, momentum exchange, and energy transport equation are used for the ions. Electrons are assumed to be isothermal. The closure of ion equations is made by the assumption that the heat flux is zero. The model equations are solved for potential, ion and electron density, and velocity and ion temperature as independent variables. The model includes coulomb collisions between ions and electrons and charge exchange collisions between ions and neutral atoms of the same species and same mass. The neutral atoms are assumed to be essentially at rest. The model is solved for finite ratio ε=λDL between the Debye length and λD and ionization length L in the pre-sheath and in the sheath at the same time. Charge exchange collisions heat the ions in the sheath and the pre-sheath. Even a small increase of the frequency of charge exchange collisions causes a substantial increase of ion temperature. Coulomb collisions have negligible effect on ion temperature in the pre-sheath, while in the sheath they cause a small cooling of ions. The increase of ε causes the increase of ion temperature. From the ion density and temperature profiles, the polytropic function κ is calculated according to its definition given by Kuhn et al. [Phys. Plasmas 13, 013503 (2006)]. The obtained profiles of κ indicate that the ion flow is isothermal only in a relatively narrow region in the pre-sheath, while close to the sheath edge and in the sheath it is closer to adiabatic. The ion sound velocity is space dependent and exhibits a maximum. This maximum indicates the location of the sheath edge only in the limit ε→0.