Numerical solutions to the weakly collisional plasma and sheath in the fluid approach and the reduction of the ion current to the wall

The plasma-sheath problem is solved numerically for the transition regime from collisionless to strongly collisional in both planar and cylindrical geometry. An improved frequency for ion-neutral momentum transfer collisions is introduced as a combination of the constant collision frequency and constant mean free path models. The model is correct in the limiting cases of collisionless and strongly collisional plasmas. The current density at the wall is calculated for a wide range of parameters and an analytic form J=J₀/(1+kappaL/lambda) ^1/2 is found to describe the reduction of the flux, where J ₀ is the ion flux for the collisionless case, L is the dimension of the plasma, lambda is the ion-neutral mean free path, and kappa is a fitting parameter