Bohm criterion for collisionless sheaths in two-ion-species plasmas

The sheaths of a plasma containing two species of positive ion produced in a low pressure discharge ($\sim$ mTorr) are studied using a fluid model. It is shown analytically that for the weakly collisional presheath, as long as the ion-ion streaming instability is absent, each ion species enters the sheath satisfying each individual Bohm criterion. The fluid equations of electrons and ions including the time derivative terms are solved numerically to follow the temporal evolution of the plasma and sheath. Our numerical results show that in the parameter range explored, the ion-ion streaming instability is not observed, and each ion species has its own Bohm criterion independent of the relative concentrations of the two ion species. In addition, the rf sheath is studied numerically and the similar conclusion is drawn.