An expression for the $h_l$ factor 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 $\Gamma_{\rm wall}=h_ln_{\rm i0}u_B$, where $n_{\rm i0}$ 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 electronegative discharges valid in a large parameter space of practical interest. We use the numerical solution of fluid equations including Poisson's equation as a guide to derive an analytical expression that can easily be incorporated in global models.