Smooth plasma-sheath transition in a hydrodynamic model

In the hydrodynamic plasma and sheath models, when the two models are treated separately, the use of Bohm´s (1949) criterion to obtain boundary conditions at the plasma-sheath interface leads to singularities and discontinuities in some physical quantities. This problem can be overcome by using an appropriate boundary condition; namely, by specifying a particular finite value of the electric field at the plasma-sheath interface. Using such a boundary condition and arbitrary collision parameters, sheath characteristics are then calculated continuously from the collisionless to the collisional sheath. When applied to the plasma model, this new boundary condition takes into account the space-charge effect on the behavior of the plasma at its boundary