Modelling electronegative discharges at low pressure

In a previous study, a macroscopic analytical model was developed for a plasma discharge with a three-component (electronegative) core and an electropositive edge region. Both regions were treated in the high-pressure approximation of constant mobility for the positive ions. We extend the treatment to low pressures, for which the ion thermal velocity within the electropositive region is much less than the ion flow velocity, by using a variable mobility model with constant mean free path for the positive ions. The density at the interface between the electropositive region and the sheath is determined by generalizing a low-pressure electropositive solution to a finite-flow boundary condition at the interface with the electronegative plasma. The results are also extended to include an additional transition region in which the flow within the electronegative region is not allowed to exceed the local ion sound speed, which can result in an abrupt decrease in negative ion density. The approximation of a parabolic negative ion profile results in algebraic equations which are solved numerically over a range of parameters. Typical cases are compared with particle-in-cell (PIC) Monte Carlo simulations.