Fluid model of an electronegative discharge with magnetized electrons and unmagnetized ions

A fluid model is developed to determine the cross-field equilibrium densities and fluxes in a finite-size electronegative discharge with magnetized electrons and unmagnetized positive and negative ions. A two-dimensional rectangular geometry with a uniform axial magnetic field is considered. After averaging over the axial losses, the fluid equations, including ion inertia terms, are integrated numerically along the transverse direction to determine the equilibrium quantities, for the boundary condition of vanishing electron density and flux at a transverse insulating wall. This yields equilibrium solutions with equal flows of positive and negative ions to the transverse wall, and with equal positive ion and electron flows to the axial walls. An analytical model is developed for this case, neglecting ion inertia, and is used to determine the scaling of the discharge equilibrium with discharge parameters and to optimize the ion fluxes. The model and the numerical integrations are in reasonable agreement.