Figure 1

Sketch of apparatus. (a) Oblique view. Spherical particles charge negatively and form a monolayer levitating in the plasma sheath above the lower electrode. They are illuminated with a horizontal sheet of a doubled Nd:YAG laser (532 nm) and viewed from the top with a video camera. (b) Side view. The heating of the particle cloud was provided by an instability caused by a “perturbation layer” of heavier particles levitated below the main layer. Increasing the number of particles in the perturbation layer produced a higher kinetic temperature in the main layer.Reuse & Permissions

Figure 2

Results of experiments and a molecular dynamics (MD) simulation for different kinetic temperatures $T$ and coupling parameter ${\Gamma }^{*}$. (a)–(d) Particle orbits. (e)–(h) Pair correlation function. (i)–(l) Spectra of the longitudinal (compressional) waves averaged over all directions. (m)–(p) Spectra of the transverse (shear) waves. The figures are arranged in rows corresponding to different conditions: (a),(e),(i),(m) experiment at $T=0.037\mathrm{e}\mathrm{V}$, ${\Gamma }^{*}=4000$, $a=1.07\mathrm{m}\mathrm{m}$ (particle separation). The lattice is in a highly ordered crystalline state; the phonon spectra are periodic and have a cutoff frequency. (b),(f),(j),(n) Experiment at $T=14.5\mathrm{e}\mathrm{V}$, ${\Gamma }^{*}=10.6$, $a=1.05\mathrm{m}\mathrm{m}$. The particle cloud is in a partly melted state, the longitudinal mode has no cutoff, and the width of both modes increases. (c),(g),(k),(o) Experiment at $T=54.9\mathrm{e}\mathrm{V}$, ${\Gamma }^{*}=2.7$, $a=1.01\mathrm{m}\mathrm{m}$, and the lattice is melted. The overlayed dotted line (k) indicates a fit to the well-known dust-acoustic mode ($C_{\mathrm{D}\mathrm{A}}=26.9\mathrm{m}\mathrm{m}/\mathrm{s}$), the dashed line is a fit to the thermal mode ($v_{\mathrm{D}\mathrm{T}}=5.98\mathrm{m}\mathrm{m}/\mathrm{s}$), and the frequency of longitudinal waves grows linearly with $ka$ at high wave numbers. The transverse wave mode (o) almost disappears in the fluid state. (d),(h),(l),(p) Finally, we show a MD simulation at $T=37.2\mathrm{e}\mathrm{V}$, ${\Gamma }^{*}=4.3$, $a=0.8\mathrm{m}\mathrm{m}$. The cloud is melted; the result closely reproduces that of the experiment.Reuse & Permissions

Figure 3

Experimentally measured phonon spectrum of both longitudinal and transverse waves averaged over all directions of propagation in the crystalline state for the conditions of Figs. 2i, 2m. The dashed lines show the theoretically calculated spectra at every $5°$ for the directions between the main crystal axes. This illustrates the observed fine structure of the spectrum in the crystalline phase.Reuse & Permissions

Figure 4

Velocity of the dust-thermal wave mode vs dust kinetic temperature. The least square fit (straight line) gives us the adiabatic index $\gamma =2.2\pm 0.4$. Filled circles (●) are data from an experiment at a gas pressure of 1.0 Pa, triangles (△) denote a simulation at 1.0 Pa, whereas filled squares (■) are experimental data for a denser particle suspension ($a\simeq 0.75\mathrm{m}\mathrm{m}$) at higher gas pressures, 4.0, 3.4, 2.2, and 1.5 Pa.Reuse & Permissions