Figure 1

Configuration for the experiment [8]. (a) This diagram of the vacuum chamber is shown in an exploded view to better show the lower electrode, which in the experiment was located inside the chamber. A low-pressure gas of neutral argon atoms filled the chamber. A radiofrequency voltage was applied between two electrodes, separated by an insulator. One electrode was the powered lower electrode, and the other consisted of the grounded vacuum chamber and shield. The gas was partially ionized, yielding a plasma with three components: electrons, positive argon ions, and neutral argon atoms. The $x$ and $y$ axes correspond to the two orthogonal directions used in measuring the positions and velocities of dust particles. The side ports were used to admit laser beams, not shown here. For heating, a pair of 532 nm laser beams were directed into the chamber by scanning mirrors as in [28], while for illumination a 577 nm laser sheet was used with a configuration as in [47]. (b) This sketch shows a side view of the lower electrode. Polymer microspheres were introduced by shaking them into the plasma from above, and they moved downward due to gravity $g$. They gained a negative electric charge $Q$ and were levitated upward due to a vertical dc electric field $E$ so that they remained in a single horizontal layer above the lower electrode. There was also a smaller radial dc electric field, not shown, which provided horizontal confinement. Images of the dust particles were recorded by a video camera viewing through the top port. Shown here are $5\mathrm{mm}\times 5\mathrm{mm}$ portions of two images: (c) a Wigner lattice without laser heating (lines have been drawn to indicate the lattice structure) and (d) a liquid maintained by laser heating.Reuse & Permissions

Figure 2

Sketch of the division of the camera FOV into inner and outer regions for the experiment [8]. In Eq. (5), the subscripts $i$ and $j$ refer to particles located in the inner region and both the inner and outer regions, respectively. The circle indicates the cutoff distance $5b$ for the potential. The unused portion of the camera FOV on the right is not included in the analysis.Reuse & Permissions

Figure 3

Stress autocorrelation function (SACF), i.e., $C_{\eta }\left(t\right)$, and its time integration. Results are shown for four runs of the experiment [8]. All quantities shown are normalized. The SACF is normalized as $\mathbb{C}\equiv C_{\eta }/\left(A{k}_{B}T\rho a^2{\omega }_{pd}^2\right)$ and is drawn here at $10\times$ magnification. Time is given in units of ${\omega }_{pd}^{-1}$, that is, $\tau =t{\omega }_{pd}$. The integral shown by the smooth curve is used in the Green-Kubo relation, Eq. (7), to calculate the viscosity. Choosing the integration limit $t_I$ as the time when $\mathbb{C}\left(\tau \right)$ crosses zero as described in Sec. IV D, the integral yields the dimensionless viscosity, as indicated by the solid circle for each run.Reuse & Permissions

Figure 4

Test of the Green-Kubo relation for viscosity. We compare our value of the kinematic viscosity, calculated from the Green-Kubo relation, using input from the experiment [8], to results from a hydrodynamical analysis of a previous experiment [31]. Values are made dimensionless by normalizing by $a^2{\omega }_{pd}$. The $x$ axis, which has a logarithmic scale, is the Coulomb coupling parameter $\Gamma$ as defined in Sec. III. Our result, shown as a solid diamond, is the mean for four experimental runs in Fig. 3, and the vertical error bar indicates only the run-to-run variation, calculated as the standard deviation of the mean. The horizontal error bar (for the result from the Green-Kubo relation) reflects a $10\%$ uncertainty in $Q$.Reuse & Permissions

Figure 5

Comparison of our result using the Green-Kubo relation for viscosity with the input of data from the experiment [8], shown as a diamond as in Fig. 4, to values from previously reported 2D Debye-Hückel simulations [24, 34, 35]. The simulation results shown for [24] are also listed in Table . Both axes are logarithmic.Reuse & Permissions