Moment Fluid Equations For Ions In Weakly Ionized Plasma

A one-dimensional fluid model for ions in weakly ionized plasma is proposed. The model differs from the existing ones in two aspects. First, a more accurate approximation of the collision terms in the fluid equations is suggested. For this purpose, the results obtained using the Monte Carlo kinetic model of the ion swarm experiments are considered. Second, the ion energy equation is taken into account. The fluid equations are closed using a simple model of the ion velocity distribution function. The accuracy of the fluid model is examined by comparing with the results of particle-in-cell Monte Carlo simulations. In particular, several test problems are considered using a parallel plate model of the capacitively coupled radio-frequency discharge. It is shown that the results obtained using the proposed fluid model are in good agreement with those obtained from the simulations over a wide range of discharge conditions. An approximation of the ion velocity distribution function for the problem under consideration is also discussed.