Structure of the plasma sheath in collisional to weakly collisional plasmas

Recently, a set of two fluid equations has been derived that describes the transport of plasmas with anisotropic pressure along the lines of force and is valid for collisional to weakly collisional regimes [Phys. Fluids 29, 463 (1986); 31, 3280 (1988)]. These transport equations coupled with Poisson’s equation are used to study the structure of the nonquasineutral transition region between the plasma and the material wall. This transition region is defined as the electric sheath region. The Bohm sheath criteria has been derived by various authors by examining behavior of the solution to the plasma-sheath equation. These investigations have shown that only for a supersonic flow would an increasing electric potential (in magnitude) exist in the sheath region to accelerate the ions further toward the wall. For subsonic flows, the behavior of the electric potential is purely oscillatory, which is not physical (electrons would trap in these potential wells and wipe them out). This work shows that when a more accurate set of equations is used, the solution is purely oscillatory when the flow speed is below the ion ‘‘thermal speed.’’ For flow velocities in the range between the thermal and sound speed, there exist solutions where the electric field is positive definite and oscillatory but the potential is monotonic. Therefore, solutions to the sheath problem exist for subsonic flow and Bohm’s sheath criteria can be violated.