7 M ay 2 00 9 Experimental and computational characterization of a modified GEC cell for dusty plasma experiments

A self-consistent fluid model developed for simulations of microgravity dusty plasma experiments has for the first time been used to model asymmetric dusty plasma experiments in a modified GEC reference cell with gravity. The numerical results are directly compared with experimental data and the experimentally determined dependence of global discharge parameters on the applied driving potential and neutral gas pressure is found to be well matched by the model. The local profiles important for dust particle transport are studied and compared with experimentally determined profiles. The radial forces in the midplane are presented for the different discharge settings. The differences between the results obtained in the modified GEC cell and the results first reported for the original GEC reference cell are pointed out. PACS numbers: 52.25.Fi, 52.27.Lw, 52.50.-b, 52.65.-y, 52.70.Ds, 52.80.Pi Experimental and computational characterization of a modified GEC cell. 2 1. Motivation for this study The GEC reference cell was originally designed to allow fair comparison between plasma processing studies performed in different laboratories [1, 2]. A large experimental and numerical effort was undertaken to understand both the proper operation of the cell from a technical viewpoint, as well as the physics of chemically active plasmas with different gas mixtures [3, 4, 5]. In the early nineties, it was realized that the GEC cell could also play the role of a standard experimental platform for dusty plasma experiments [6]. Several modifications to the original design were required in order to suspend dust particles in the discharge and to use different optical systems to visualize them. This in a way led to a loss of standardization, since different solutions were to deal with the additional challenge of conducting dusty plasma experiments [7]. Despite numerous experimental and numerical efforts to describe these experiments, a study employing a self-consistent numerical model, which can selfconsistently calculate the dust forces from the plasma parameters, is missing. Furthermore, the changes in discharge characteristics with respect to the original GEC reference cell, due to the necessary modifications for dusty plasma experiments, are usually ignored. We have developed such a code in the past and applied it to micro-gravity dusty plasma experiments in symmetrically driven discharges as well as to devices including the effects of gravity and additional thermophoretic forces, due to heated surfaces [8, 9, 10, 11]. The results have always shown excellent agreement with results reported in the literature, but the model has never been directly compared to measurements in a GEC reference cell. The motivation for this study is therefore to examine dusty plasma environments in a modified GEC cell with a self-consistent dusty plasma model for the first time, to compare results from the model to measurements of plasma properties in the experiment, rather than from the literature alone, and determine the effect of the modifications to the GEC cell on the local and global discharge characteristics. The latter depend on the global particle and power balance of the discharge, which can be observed through the DC bias on the powered electrode and the power absorbed in the plasma. The local parameters include the dust charge, the plasma densities, and the plasma potential, which directly determine the forces that would act on dust particles present in the discharge. Section 2 describes the geometry of the modified GEC cell used at CASPER, and clarifies the Langmuir probe measurements, section 3 discusses the numerical model, section 4 shows the results for the global parameters studied, i.e. the DC bias and the absorbed power and section 5 shows the results for the local plasma profiles, i.e. the plasma potential, the particle densities, and the derived dust charge number. In section 6 the forces obtained from the measured plasma parameters are presented and compared to the outcome of the model. Section 7 discusses the results and briefly mentions the outlook for future work. Experimental and computational characterization of a modified GEC cell. 3 2. Description of the experimental setup 2.1. The modified GEC cell. The GEC reference cell used by CASPER, shown schematically in figure 1, is modified to allow dusty plasma experiments to be performed. The upper electrode is a grounded hollow cylinder rather than a solid electrode, so that a top-mounted camera can be used to take pictures of dust crystals from above. In total, two camera/dye laser systems have been added, to capture side-view and top-view pictures of dust clouds suspended in the plasma volume. The lasers are equipped with cylindrical lenses, to creat thin laser sheets that illuminate selected areas within the dust clouds. The cameras can also be equipped with filters that allow only light at the laser frequency to pass through. This helps to select light scattered by the dust particles, and not from the plasma glow. The dust clouds suspended in the modified GEC cell are confined in the radial direction by a parabolically shaped electric potential, created by a circular cutout milled in a cover plate set on top of the powered electrode. The different cutouts used in the experiments have radii of 0.63, 1.25, and 2.5 cm. To introduce particles into the plasma, two dust shakers have been added to the top flange near the upper grounded electrode. Tapping these shakers forces dust particles to enter the plasma under the force of gravity. The bottom of each dust shakers is covered by a calibrated mesh to prevent larger clumps from entering the plasma. Figure 1. Sketch of the interior of the modified GEC cell. The lower electrode is powered, the upper electrode is grounded, as are the outer walls and the groundshield surrounding the lower electrode. The inter-electrode spacing is 3 cm, the radius of the cell is 13 cm, the height is 21 cm, and the electrode radius is 5.4 cm. The cutouts used for this experiment were 0.63, 1.25, or 2.5 cm in radius and 1 mm deep. The discharge parameters under external control include the neutral gas pressure, which can be adjusted using a butterfly valve controlling the input gas flow, the input power, which is adjusted by changing the driving potential of the RF source, and the DC bias on the powered electrode. For the current study, the DC bias was allowed to float. Experimental and computational characterization of a modified GEC cell. 4 2.2. Langmuir probe. The plasma parameters in the modified GEC cell described above were measured with a SmartProbe produced by Scientific Instruments LTD [12]. The SmartProbe is a RF-compensated Langmuir probe, with a 10 mm long, 0.38 mm diameter tungsten probe tip attached to a 470 mm long shaft. By moving the shaft toward or away from the center of the powered lower electrode, radial profiles of the plasma parameters were obtained at the midplane between the two electrodes. The probe was inserted into the system through a sideport in an attempt to ensure that the profiles were obtained exactly in this plane; however, bending of the probeshaft by gravity can not be excluded. The deviation from this plane was estimated to be less than 10% of the inter-electrode spacing, after inspection of side-view pictures. The radial probe position with respect to the electrode center was determined through examination of still-frame images from the top-mounted camera. Using imaging software [13], the midpoint of the 10 mm long probe tip and the center of the electrode were determined. The line connecting these two points was taken to be the true radial direction and any small angle the tip made with this line was measured. The projection of the probe tip onto this line was then taken as the error in the radial direction, assuming that the probe measurements represent the plasma parameters averaged over the length of the tip. For each radial position, the bias voltage on the probe tip was swept from -95 V to +95 V in steps of 0.1 V. For every voltage step, the current collected by the probe tip was measured ten times, and the average was then computed by the probe software and stored. This measurement was repeated several times, for each radial position. Employing the IV-characteristic data, the probe software computed several plasma parameters using standard Laframboise theory for cylindrical probes [14]. Parameters computed include the electron and ion density, ne, n+, the plasma potential, VP , the floating potential Vfl, and the electron temperature Te. 3. Description of the numerical model A two-dimensional hydrodynamic model is used to solve the equations for the electronand ion-fluid (in an argon discharge), coupled to the dust fluid. In this study, we are concerned with the effect of changing discharge settings on the dust transport, and the effect of the modifications in the modified GEC cell on the plasma parameters. We therefore only consider situations where small numbers of dust particles are present in the discharge, so that the plasma parameters, and the forces acting on the dust, are not altered by the dust itself. However, the forces are still self-consistenly computed from the plasma parameters. We now proceed with a description of the solution for the plasma parameters. 3.1. Solution scheme for the plasma. The continuity equation for the density nj for the electrons and ions (j = e, ions) is solved using a drift-diffusion approximation for the flux, Γj : ∂nj ∂t +∇ · Γj = Sj , Γj = njμjE −Dj∇nj , (1) with μj the mobility and Dj the diffusion coefficient. The sinks and sources Sj include electron-impact ionization and electron-impact excitation. The electric field is found Experimental and computational characterization of a modified GEC cell. 5 from the Poisson equation, ∇V = − e ǫ0 (n+ − ne) , E = −∇V, (2) with n+, ne the ion and electron density, ǫ0 the permittivity of vacuum, and e the electron charge. Since the argon ions are too massive to follow the instantaneous electric field, an effective electric field is calculated to include the effect of ion inertia by solving dEeff/dt = νm,+(E − Eeff ), with νm,+ the momentum transfer frequency for ionneutral collisions. A similar set of equations is solved for the average electron energy density, w = neǫ, with ǫ the average electron energy. ∂w ∂t +∇ · Γw = −eΓe · E + Sw, Γw = 5 3 (μewE −De∇w) . (3) In the above, −eΓe · E is the Ohmic electron heating, which is the power input. The sinks, Sw, include electron impact ionization and excitation. The ions are assumed to locally dissipate their energy, so that it is not necessary to solve a similar equation for the ions. Equations (1, 2, 3) are progressed in time on sub-RF timescales until the solution set U(t) becomes periodic over a RF cycle to within a very small user-defined parameter; (U(t) = U(t+ τRF )). 3.2. Solution scheme for the dust fluid. 3.2.1. Dust particle charging A spherical dust particle with radius a immersed in plasma absorbs electrons and ions (with mass me and m+ respectively) until in equilibrium the electron and ion currents balance. Due to the high electron mobility compared to ion mobility, the equilibrium dust charge becomes negative, V (a) < 0. Using energy and angular momentum conservation, the ion and electron current can be calculated from OML theory [15] through