Exact solution for the generalized Bohm criterion in a two-ion-species plasma

For a weakly collisional two-ion species plasma, it is shown that the minimum phase velocity of ion acoustic waves (IAWs) at the sheath-presheath boundary is equal to twice the phase velocity in the bulk plasma. This condition provides a theoretical basis for the experimental results that each ion species leaves the plasma with a drift velocity equal to the IAW phase velocity in the bulk plasma [D. Lee et al., Appl. Phys. Lett. 91, 041505 (2007)]. It is shown that this result is a consequence of the generalized Bohm criterion and fluid expressions for the IAW phase velocities.