PHYSICAL REVIEW E 87, 013101 (2013) Dust particle radial conﬁnement in a dc glow discharge G. I. Sukhinin, 1,2,* A. V. Fedoseev, 1 S. N. Antipov, 3 O. F. Petrov, 3 and V. E. Fortov 3 1 Institute of Thermophysics SB RAS, Lavrentyev Ave., 1, 630090 Novosibirsk, Russia 2 Novosibirsk State University, Pirogova St. 2, 630090 Novosibirsk, Russia 3 Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya St. 13 bld.2, 125412 Moscow, Russia (Received 9 October 2012; published 3 January 2013) A self-consistent nonlocal model of the positive column of a dc glow discharge with dust particles is presented. Radial distributions of plasma parameters and the dust component in an axially homogeneous glow discharge are considered. The model is based on the solution of a nonlocal Boltzmann equation for the electron energy distribution function, drift-diffusion equations for ions, and the Poisson equation for a self-consistent electric ﬁeld. The radial distribution of dust particle density in a dust cloud was ﬁxed as a given steplike function or was chosen according to an equilibrium Boltzmann distribution. The balance of electron and ion production in argon ionization by an electron impact and their losses on the dust particle surface and on the discharge tube walls is taken into account. The interrelation of discharge plasma and the dust cloud is studied in a self-consistent way, and the radial distributions of the discharge plasma and dust particle parameters are obtained. It is shown that the inﬂuence of the dust cloud on the discharge plasma has a nonlocal behavior, e.g., density and charge distributions in the dust cloud substantially depend on the plasma parameters outside the dust cloud. As a result of a self-consistent evolution of plasma parameters to equilibrium steady-state conditions, ionization and recombination rates become equal to each other, electron and ion radial ﬂuxes become equal to zero, and the radial component of electric ﬁeld is expelled from the dust cloud. DOI: 10.1103/PhysRevE.87.013101 PACS number(s): 52.27.Lw, 52.25.Fi, 52.35.We I. INTRODUCTION Dusty or complex plasma is a partly ionized gas containing dispersed micro-sized particles with large negative charge, Q d = e 0 Z d ∼ 10 3 − 10 5 e 0 . Dusty plasma is observed in space (interstellar clouds, tails of comets, planet rings), in atmo- spheres of planets, in ﬂames, in technological installations (plasma-chemical reactors, thermonuclear reactors), in labo- ratory conditions in a rf discharge, or in a dc glow discharge at low pressures [1–8]. A number of spectacular physical phenomena (such as the formation of dusty structures, phase transitions, and different wave and convective processes) can be observed in dusty plasma. The charge of dust particles plays a paramount role for the understanding of all phenomena in dusty plasma [1–8]. Many papers are devoted to the determination of dust charge [9–11]. However, it is usually assumed that electrons in plasma have the Maxwellian energy distribution, which is an obvious idealization for the laboratory conditions of low density rf or dc glow discharge plasmas. The high-energy tail of the electron energy distribution function (EEDF) in low-pressure plasma is depleted due to nonelastic electron-atom collisions. In a stratiﬁed glow discharge in cylindrical tubes, EEDF even becomes nonmonotonous and depends on axial and radial coordinates. Only electrons with energy higher than the potential of the dust particle surface can reach it. To solve this problem, a hybrid nonlocal kinetic model of positive column (PC) of glow discharge plasma with dust particles was created that was based on the solution of the Boltzmann equation for EEDF, drift-diffusion equations for ions, and the Poisson equation for a self-consistent electric ﬁeld [12,13]. In these papers, axial distributions of the electric ﬁeld and EEDF * Corresponding authors: sukhinin@itp.nsc.ru on the axis of the discharge tube were calculated and radial distributions were obtained in the approximation of ambipolar diffusion. The 2D plasma parameters and charge distribution of a probe dust particle placed in different points of striations in PC of the glow discharge were calculated. It was shown that the dust particle spatial distribution strongly depends on the nonequilibrium EEDF and on the inhomogeneous distribution of the electric ﬁeld in a stratiﬁed glow discharge. However, the inﬂuence of dust particles on gas discharge plasma was not taken into account; it is true only for low dust particle concentration. When the density of dust particles is small, i.e., Havnes number P H = N d Z d /n e ≪ 1[14] (where N d is the density of the dust particle, Z d is the average charge number of the dust particle, n i and n e are the ion and electron densities in ambient plasma far from the dust particle, and n i ≈ n e + N d Z d ), the charge of the dust particles can be obtained with the help of local plasma parameters. In this case, the dust particles can be used as a small probe to obtain plasma parameters [15–17]. With the increase of P H , the local parameters in the plasma region containing dust particles change, which in turn leads to a change of the average charge of dust particles and all properties of dusty plasma. For low-density discharge plasma with n i ∼ 10 9 cm −3 , we can expect that the inﬂuence of dust particles with the charge number Z d ∼ 10 4 should be taken into account at dust concentration N d ∼ n i /Z d  10 5 cm −3 . For the conditions of rf discharge used for thin ﬁlms preparation in the semiconductor industry, the inﬂuence of dust particles on discharge properties was investigated in 1992 with the help of particle-in-cell Monte Carlo simulations by Boeuf [18]. Recently, the dusty plasma of rf discharge was investigated by Denysenko et al. [19,20] with the help of the Boltzmann equation for EEDF. Different models for reactive dusty plasma of rf discharge were also presented by Goedheer et al. [21] and Schweigert et al. [22]. For the conditions of dc 013101-1 1539-3755/2013/87(1)/013101(10) ©2013 American Physical Society