Observation of particle pairing in a two-dimensional plasma crystal

The observation is presented of naturally occurring pairing of particles and their cooperative drift in a two-dimensional plasma crystal. A single layer of plastic microspheres was suspended in the plasma sheath of a capacitively coupled radio-frequency discharge in argon at a low pressure of 1 Pa. The particle dynamics were studied by combining the top-view and side-view imaging of the suspension. Cross-analysis of the particle trajectories allowed us to identify naturally occurring metastable pairs of particles. The lifetime of pairs was long enough for their reliable identification.

Figure 1

Sketch of the experimental setup. Plastic microspheres are confined in a stable single layer above the lower rf electrode in a capacitively coupled rf discharge in argon (the top ring-shaped grounded electrode is not shown here). The particle illumination system consists of two orthogonal laser sheets with different wavelengths. The particles are imaged from the top and from the side by two digital cameras equipped with narrow-band interference filters to admit only the respective wavelengths. This setup enables simultaneous recording of the in-plane and out-of-plane particle motion.

Figure 2

Fluctuation spectra of the out-of-plane particle velocity in a 2D plasma crystal. The spectra were calculated from the top-view experimental movies (using the image intensity-sensitive analysis technique [13, 24, 46], left panel) or directly from the side-view movies (right panel). The intensities of the spectra are in arbitrary units (the logarithmic scale spans over two decades). The theoretical dispersion relations [41] for the two main crystallographic directions (solid and dashed lines) are very close to each other. A reasonably good agreement of the theoretical and experimental results is evident. The intercept of the out-of-plane phonon spectrum with the frequency axis gives the vertical confinement parameter $f_v$; see Table 1. An unrelated excitation at about 29 Hz is separated from the spectrum by a gap of about 3–5 Hz.

Figure 3

Fluctuation spectra of the in-plane particle velocity in a 2D plasma crystal. The spectra are for the two principal orientations of the lattice, $\theta =0^{\circ }$ (left panel) and $\theta ={30}^{\circ }$ (right panel). $\theta$ is defined as in Ref. [24]. The intensities of the spectra are in arbitrary units. The black solid (dash-dotted) lines are the theoretical dispersion relations of the longitudinal (transverse) waves computed with the parameters from Table 1 (last column). The white dashed (dotted) lines indicate the sound speeds of the longitudinal (transverse) waves; see Table 1.

Figure 4

Traces of the fast-moving upstream particles recorded by the side-view camera (a movie is available in the Supplemental Material [49]). Each panel was obtained by blending a sequence of snapshots; the recording timing is indicated [50]. The white arrows indicate the direction of motion of upstream particle. The apparent variation of the particle density across the image is due to the domain structure of the crystalline layer and its slow rotation. The illuminating laser light is coming from the left. Notice a small left grade ($\approx 1\%$) of the main layer.

Figure 5

Pairing of an upstream particle with intralayer particles. The left panel shows a space-time diagram assembled from 20 consecutive side-view images (each approximately $4.3\times 0.8{\text{mm}}^2$ in size). Time advances from top to bottom (in the range of $16.38$–$16.57$ s; see Fig. 4), the time step is $0.009646$ s. The cyan and red circles indicate the positions of, respectively, upstream and intralayer particles. The arrows indicate pairing events. The track of a long-living pair of particles (with a lifetime $\tau \simeq 0.05$ s) is highlighted by two parallel dashed lines. The inset shows the dragging geometry. The right panel shows the top view of a different dragging event (assembled from 15 blended images; here, the illuminating laser sheet was shifted upward, which allowed us to simultaneously record the upstream and intralayer particles). The filled circles indicate the positions of the upstream (cyan) and intralayer (red) particles in the beginning of a pairing event. The empty circles indicate the particle positions $0.06$ s later. The arrows indicate the resultant directions of particle motion.

Figure 6

Series of short-term coupling events (left panel) and a long-term coupling event (right panel) initiated by two different upstream particles in the course of the same experiment. Each panel is assembled from 14 consecutive side-view images (each approximately $3.9\times 0.9{\text{mm}}^2$ in size). Time advances from top to bottom; the time step is $0.009646$ s. The upstream particles are clearly seen somewhat above the main layer. The white arrows indicate the starting points of pairing events.

Figure 7

Caged upstream particle. In the upper row, four configurations are shown from left to right: stable configuration, the onset of instability, and two pairing events. In all images, the field of view is $1.2\times 1.2{\text{mm}}^2$. Panel (a) shows the horizontal $x$ projection of the particle positions as a function of time. The instability sets in at $t\simeq 11.6$–$11.8$ s. Panel (b) shows the fluctuation spectrum of the longitudinal oscillations of upstream particle.