A self-consistent method for solving ion diffusion and mobility coefficients

Abstract

A self-consistent method for computation and testing of transport coefficients in low pressure radio frequency plasma discharges is detailed by comparing the experimental fitting formula and previous results gained from the Langevin expression. In this paper, for the first time, we apply the Chapman–Enskog method for calculating transport coefficients of ions to a weakly ionized plasma which is laid in a thermodynamic non-equilibrium and chemical non-equilibrium state. The ion diffusion coefficient is obtained by using the Chapman–Enskog method expanded to the second order approximation. The corresponding ion mobility coefficient is deduced from Einstein's relation. A two-dimensional axisymmetric fluid model of capacitively coupled plasmas is employed to determine the plasma composition. Moreover, the comparison of plasma physical characteristics using ion transport coefficients calculated by the Chapman–Enskog method with those derived from theoretical and experimental methods is also investigated. The results show that the ion transport coefficients obtained by the Chapman–Enskog method and their effect on plasma physical quantities are in good agreement with the experimental measurement and theoretical expression. Furthermore, the results indicate that the set of exponential and Morse potentials is more reasonable for the ion–neutral particles' interaction.