Ambipolar Diffusion and Electric Field Reversal in Electronegative Plasma with Charged Nanoparticles

An analytical model of ambipolar diffusion in plasma consisting of electrons, positive ions, negative ions, and negatively charged nanoparticles is proposed. Analytical expressions are derived for the ambipolar diffusion coefficients of all charged species, as well as for the ambipolar electric field strength. In plasma containing only electrons, positive ions, and negative ions, high concentrations of negative ions lead to a transition from ambipolar to free diffusion, where the ambipolar diffusion coefficients approach the corresponding free diffusion coefficients. In plasma consisting of electrons, positive ions, and negatively charged nanoparticles, high nanoparticle concentrations result in qualitatively different behavior: the ambipolar diffusion coefficient of electrons approaches twice the free electron diffusion coefficient, while the ambipolar diffusion coefficient of positive ions approaches twice the free diffusion coefficient of nanoparticles. For the general four-component plasma, the ambipolar diffusion regime is governed by the dominant electron-loss mechanism, namely, electron attachment to either electronegative gas molecules or nanoparticles. If electron attachment to gas molecules dominates, the ambipolar diffusion coefficients of electrons, negative ions, and nanoparticles remain close to their free diffusion coefficients. In contrast, when electron attachment to nanoparticles dominates, these coefficients approach twice the corresponding free diffusion coefficients. The ambipolar diffusion coefficient of positive ions was found to depend strongly on the dominant negatively charged species in plasma. Under intensive negative-ion formation, it approaches the free diffusion coefficient of negative ions, whereas in plasma dominated by electron attachment to nanoparticles it asymptotically approaches twice the free diffusion coefficient of nanoparticles. It is shown that sufficiently high concentrations of negative ions and/or charged nanoparticles substantially reduce the ambipolar electric field strength and may even reverse its sign. A weakly negative ambipolar electric field can remove excess negative ions and nanoparticles from plasma, thereby stabilizing the discharge. Experiments with acetylene plasma demonstrated intense transport of small nanoparticles toward the tube walls, which may serve as indirect evidence of an ambipolar electric-field reversal.