Empirical approximation for the ion current to the surface of a dust grain in a weakly ionized gas-discharge plasma
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Y PLASMA
Empirical Approximation for the Ion Current to the Surface of a Dust Grain in a Weakly Ionized Gas-Discharge Plasma O. S. Vaulina, A. Yu. Repin, and O. F. Petrov Institute for High Energy Densities, Russian Academy of Sciences, Izhorskaya ul. 13/19, Moscow, 125412 Russia Received September 19, 2005
Abstract—The results from numerical simulation of the dust grain charging process in a weakly ionized gasdischarge plasma are analyzed. An empirical approximate formula for the ion current to the grain surface under conditions close to those in laboratory experiments with dusty plasmas is derived. Investigations show that the approximation proposed greatly simplifies determination of the grain charge by avoiding laborious calculations for different grain sizes and different parameters of the surrounding plasma. PACS numbers: 52.25.Ub, 52.25.Zb, 82.70.Db DOI: 10.1134/S1063780X06060055
1. INTRODUCTION A dusty plasma is an ionized gas containing macroscopic (micron-size) charged particles (dust grains). Such plasmas are widely encountered in nature (e.g., in space and in the upper atmospheric layers of the Earth) and are produced in some technological processes (e.g., during fuel burning, in etching and spraying, in manufacturing nanoparticles, etc.). A dusty plasma is a good model for studying various physical processes in systems of interacting particles, which are of great interest for nonideal plasma physics and for other branches of natural sciences such as chemistry, atmospheric physics, astronomy, and so on. The properties of dusty plasma are investigated mostly in experiments with weakly ionized plasmas of gas discharges, which are usually initiated in noble gases at pressures P of 0.03– 3 Torr and in which the dissipation due to collisions with gas atoms and/or molecules plays a significant role and the electron temperature Te (~1–7 eV) is much greater than the ion temperature Ti, close to the room temperature [1–4]. Terrestrial laboratory experiments are usually carried out with dust grains of size ~1– 40 µm [1–4]. The transport properties of dusty plasmas containing larger grains (of size 100–200 µm) are studied under microgravity conditions [5, 6]. The kinetic temperature Td of the dust grains, which characterizes the energy of their chaotic (thermal) motion, may be substantially higher than both their surface temperature (determined by the neutral particles of the surrounding gas) and the temperature of the electron plasma component [5–12]. In a gas-discharge plasma, nonemitting dust grains are charged by electron and ion fluxes and can acquire a substantial negative charge, about 102–104 e [13–21]. The grain charge Z is an important parameter that governs the physical properties of the dusty plasma, in par-
ticular, the energy Td the grain can gain by various mechanisms [5–12]. The grain charge Z is most often estimated by using the orbit motion limited (OML) approximation [18, 19], which is, however, valid only for a weakly collisional plasma such that lni(ne) /R 1 and, accordingly, λ/R 1 and l
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