Dusty plasma experiment to confirm an expression for the decay of autocorrelation functions

Statistical physicists recently proposed an expression for an autocorrelation function (ACF) [Belousov and Cohen, Phys. Rev. E 94, 062124 (2016)] that has, until now, not been tested experimentally. The expression captures the early behavior of the ACF decay, when the ACF is flattened. Using experimental data from a nonequilibrium steady-state dusty plasma, we confirm that the expression's use extends to liquidlike strongly coupled plasmas. A transition in the shape of the ACF is identified, and we suggest that it corresponds to the onset of collisional scattering.

Figure 1

Experimentally measured microsphere trajectories, under liquidlike conditions. The data points are the positions of microspheres in 15 successive video frames. The shading indicates the passage of time. A significant fraction of the microspheres are seen to be deflected after only four video frames, and a few are already deflected by the third frame. Data points shown here (for a run at $T=96800\mathrm{K}$) were recorded at intervals of $0.014\mathrm{s}$. Microsphere positions and velocities from trajectories like these were used to calculate shear stress autocorrelation functions. The region analyzed in the experiment was $15\times 21\mathrm{mm}$, larger than the representative portion shown here.

Figure 2

Shear stress autocorrelation function (ACF). An experimental ACF, obtained from Eq. (3), is presented as a series of data points. At short times, $t\lesssim 0.02\mathrm{s}$, the ACF is flattened, and not exponential; this shape is captured well by the theoretical Eq. (1). Time is indicated in both experimental and normalized units. The lower panel is for the same experimental run as in Fig. 1, while the upper panel is for a different run. Fit parameters for Eq. (1) are (a) $a=82{\mathrm{s}}^{-1}$ and $d=53{\mathrm{s}}^{-1}$ and (b) $a=174{\mathrm{s}}^{-1}$ and $d=150{\mathrm{s}}^{-1}$.