An expression for the hlfactor in low-pressure electronegative plasma discharges

The positive ion flux exiting a low-pressure plasma discharge is a crucial quantity in global (volume-averaged) models. In discharges containing only electrons and positive ions (electropositive discharges), it is common to write this flux Gamma wall = h(l)n(i0)u(B), where n(i0) is the central positive ion density, u(B) is the positive ion fluid speed at the sheath edge (the Bohm speed), and h(l) is the positive ion edge-to-centre density ratio. There are well established formulae for h(l) in electropositive discharges, but for discharges containing negative ions (electronegative discharges), the analysis is more complicated. The purpose of this paper is to propose a formula for the h(l) factor in low-pressure electronegative discharges. We use the numerical solution of fluid equations with Boltzmann negative ions, including Poisson's equation, as a guide to derive an analytical expression that can easily be incorporated in global models. The parameter space in which the derived expression is valid is discussed at the end of the paper.