Dynamics of spinning particle pairs in a single-layer complex plasma crystal

Spontaneous formation of spinning pairs of particles, or torsions, is studied in a single-layer complex plasma crystal by reducing the discharge power at constant neutral gas pressure. At higher gas pressures, torsions spontaneously form below a certain power threshold. Further reduction of the discharge power leads to the formation of multiple torsions. However, at lower gas pressures the torsion formation is preceded by mode-coupling instability (MCI). The crystal dynamics are studied with the help of the fluctuation spectra of crystal particles' in-plane velocities. Surprisingly, the spectra of the crystal with torsions and MCI are rather similar and contain hot spots at similar locations on the $(k,\omega )$ plane, despite very different appearances of the respective particle trajectories. The torsion rotation speed is close (slightly below) to the maximum frequency of the in-plane compressional mode. When multiple torsions form, their rotation speeds are distributed in a narrow range slightly below the maximum frequency.

Figure 1

Spinning pair of particles in a single-layer plasma crystal. The left panel shows the top view and the right panel the side view. The particles spin around the vertical axis shown by the dashed line. Notice that the lattice cell containing the pair is enlarged by $\approx 10\%$. Ninety frames from the video are superimposed; the resulting image is inverted and its brightness and contrast are adjusted. The experimental parameters are the following: argon pressure $p_{\mathrm{Ar}}=17.4$ Pa and discharge power $P_{\mathrm{rf}}=7$ W.

Figure 2

Mode-coupling instability in a single-layer plasma crystal. The left panel shows the top view and the right panel the side view. Ninety frames from the video are superimposed; the resulting image is inverted and its brightness and contrast are adjusted. The experimental parameters are the following: argon pressure $p_{\mathrm{Ar}}=12$ Pa and discharge power $P_{\mathrm{rf}}=15$ W.

Figure 3

Fluctuation spectra of the particles' in-plane velocities within a crystal (longitudinal mode). The spectral intensity is color coded as indicated, except for panels (d) and (f), where the scale is from $-6.2$ to $-3.6$ and from $-5.4$ to $-2.8$, respectively. The wave propagation direction is $\theta =0^{\circ }$ (see the text for more details). The wave number $k$ is normalized by the inverse interparticle spacing ${\mathrm{\Delta }}^{-1}$. The neutral gas pressure is (a) and (b) 19.3 Pa, (c) and (d) 17.4 Pa, and (e) and (f) 12 Pa. The left column is for the undisturbed crystal and the right column is for the crystal with (b),(d) a single torsion or (f) MCI. The discharge power $P_{\mathrm{rf}}$ is as follows: (a) 7 W, (b) 4 W, (c) 20 W, (d) 7 W, (e) 20 W, and (f) 15 W.

Figure 4

Fluctuation spectrum of the particle velocity (compressional in-plane mode) integrated over the hot-spot frequency in the range of $20.6\le \left|f\right|\le 23.6$ Hz and shown as a function of $(k_x,k_y)$. The wave number is normalized by the inverse interparticle spacing ${\mathrm{\Delta }}^{-1}$. The experimental parameters are as in Figs. 2 and 3.

Figure 5

Hot-spot frequency $f_{\mathrm{HS}}$ as a function of the discharge power $P_{\mathrm{rf}}$ for two different pressures of argon (up triangles are for $p_{\mathrm{Ar}}=17.4$ Pa and down triangles are for 19.3 Pa). The theoretically calculated (for $p_{\mathrm{Ar}}=17.4$ Pa) maximum frequency of the in-plane compressional mode $f_{\max }$ is shown by open squares and the lattice Einstein frequency ${\left(2\pi \right)}^{-1}{\omega }_{\mathrm{E}}$ by solid squares. Where a single torsion is present, its rotation speed is shown by an open circle.

Figure 6

(a) Mean interparticle spacing $\mathrm{\Delta }$, (b) screening parameter $\kappa =\mathrm{\Delta }/\lambda$, and (c) particle charge number $Z$ as functions of the discharge power $P_{\mathrm{rf}}$. Open symbols indicate undisturbed crystal and closed symbols indicate crystal with torsions. The pressure of argon is $p_{\mathrm{Ar}}=17.4$ Pa, except for down triangles in (a), which correspond to $p_{\mathrm{Ar}}=19.3$ Pa.