Double Layers in a Modestly Collisional Electronegative Discharge

Abstract

The effect of ion-neutral collisions on the structure and ion flux emanating from a steady-state, planar discharge with two negative components is investigated. The positive ion component is modelled as a cold fluid subject to constant-mobility collisions, while the electrons and negative ions obey Boltzmann relations. The model includes the collisionless limit. When the negative ions are sufficiently cold three types of discharge structures are found. For small negative ion concentrations or high collisionality, the discharge is 'stratified', with an electronegative core and an electropositive edge. For the opposite conditions, the discharge is 'uniform' with the negative ion density remaining significant at the edge of the plasma. Between these cases lies the special case of a double-layer-stratified discharge, where quasi-neutrality is violated at the edge of the electronegative core. Double-layer-stratified solutions are robust in that they persist for moderate collisionality. Numerical solutions for finite non-neutrality verify that the plasma flux varies continuously with collisionality, although the derivative of the flux with respect to collisionality is discontinuous when the discharge structure changes from uniform to stratified. Double-layer solutions are found when the flux predicted for the plasma approximation is double-valued and the flux associated with the smaller plasma edge potential is less than that associated with the larger edge potential. A comparison with numerical non-neutral solutions confirms that the flux is correctly predicted using the plasma approximation when the larger value of the flux is taken in the two-solution regime.