Experimental Determination of Dust-Particle Charge in a Discharge Plasma at Elevated Pressures S. Ratynskaia, 1 S. Khrapak, 1 A. Zobnin, 2 M. H. Thoma, 1 M. Kretschmer, 1 A. Usachev, 2 V. Yaroshenko, 1 R. A. Quinn, 1 G. E. Morfill, 1 O. Petrov, 2 and V. Fortov 2 1 Centre for Interdisciplinary Plasma Science, Max-Planck-Institut fu ¨r extraterrestrische Physik, D-85741 Garching, Germany 2 Institute for High Energy Densities, Russian Academy of Sciences, Izhorskaya 13/19, 125412, Moscow, Russia (Received 12 March 2004; published 17 August 2004) The charge of dust particles is determined experimentally in a bulk dc discharge plasma in the pressure range 20–100 Pa. The charge is obtained by two independent methods: one based on an analysis of the particle motion in a stable particle flow and another on an analysis of the transition of the flow to an unstable regime. Molecular-dynamics simulations of the particle charging for conditions similar to those of the experiment are also performed. The results of both experimental methods and the simulations demonstrate good agreement. The charge obtained is several times smaller than predicted by the collisionless orbital motion theory, and thus the results serve as an experimental indication that ion-neutral collisions significantly affect particle charging. DOI: 10.1103/PhysRevLett.93.085001 PACS numbers: 52.27.Lw, 52.20.–j, 52.35.–g There is currently considerable interest in understand- ing the properties of dusty (complex) plasmas—plasmas containing charged micron-size particles (grains). This interest was originally driven by astrophysical topics [1] and industrial plasma applications [2]. It is also recog- nized that complex plasmas open up the possibility to study a variety of phenomena (e.g., phase transitions, transport, waves, etc.) at the most elementary kinetic level [3,4]. The particle charge is one of the most important pa- rameters of complex plasmas. In gas discharges the (nega- tive) charge on a particle is determined by the balance of electron and ion fluxes to its surface. To calculate these fluxes the collisionless orbital motion limited (OML) theory [5] is typically used on the basis that the electron and ion mean free paths l ei are long compared to the plasma screening length  D . However, theory has shown that ion-neutral charge exchange collisions in the vicinity of a small probe or dust grain can lead to a substantial increase in the ion current to their surfaces [5–9]. It has been demonstrated that the ion collisions can suppress the particle charge even when l i is considerably greater than  D . Another effect for charge reduction is that of ‘‘closely packed’’ grains [10]. So far most of the experimental particle charge deter- minations were performed in sheath or striation regions of discharges [11–15]. The comparison with theory is complicated here due to the strong plasmas anisotropy and non-neutrality, the presence of ‘‘suprathermal’’ ions and electrons, etc. In addition to the charging model one needs to choose an appropriate model for the sheath, which is itself a sophisticated task. Hence, there is clearly a lack of direct measurements of particle charge in bulk plasmas. In this Letter, we present experimental results on the dust-particle charge in a plasma at elevated neutral gas pressures. The experiment is performed with particles of radius a  0:6 m in a horizontal dc discharge tube. For these particles the weak ambipolar radial electric field is sufficient to compensate gravity allowing us to study dust charging in the quasineutral plasma. Highly space and time-resolved measurements of the particle flow and comprehensive probe measurements of plasma parame- ters make it possible to use theoretical models where the only unknown parameter is the particle charge. This enables us to determine the charge experimentally by two independent methods. The results are then compared with those of molecular-dynamics (MD) simulations. The experiment is performed in a dc discharge gener- ated in an U-shaped glass tube, the PK-4 facility (see sketch in Fig. 1), and operated in neon at pressures 20–100 Pa and current of 1 mA (voltage of 1 kV). The plasma parameters are measured in the absence of dust Camera Dust Dispenser Anode Cathode 3cm 35cm Vacuum Glass Tube Gas v d Dust Particles E FIG. 1. Sketch of the experimental setup. VOLUME 93, NUMBER 8 PHYSICAL REVIEW LETTERS week ending 20 AUGUST 2004 085001-1 0031-9007= 04=93(8)=085001(4)$22.50  2004 The American Physical Society 085001-1