The polygon construction method of Glaser and Clark is used to characterize melting and crystallization in a two-dimensional (2D) strongly coupled dusty plasma. Using particle positions measured by video microscopy, bonds are identified by triangulation, and unusually long bonds are deleted. The resulting polygons have three or more sides. Geometrical defects, which are polygons with more than three sides, are found to proliferate during melting. Pentagons are found in liquids, where they tend to cluster with other pentagons. Quadrilaterals are a less severe defect, so that disorder can be characterized by the ratio of quadrilaterals to pentagons. This ratio is found to be less in a liquid than in a solid or a superheated solid. Another measure of disorder is the abundance of different kinds of vertices, according to the type of polygons that adjoin there. Unexpectedly, spikes are observed in the abundance of certain vertex types during rapid temperature changes. Hysteresis, revealed by a plot of a disorder parameter vs temperature, is examined to study sudden heating. The hysteresis diagram also reveals features suggesting a possibility of latent heat in the melting and rapid cooling processes.

The nonlinear phenomenon of synchronization is characterized experimentally for dust density waves, i.e., dust acoustic waves, which are self-excited due to an ion streaming instability. The waves propagate in a dust cloud with a natural frequency of 22 Hz. We synchronize these waves to a different frequency using a driving electrode that sinusoidally modulates the ion density. We study four synchronized states, with frequencies that are multiples of 1, 2, 3, and 1/2 of the driving frequency. Comparing to phenomena that are typical of the van der Pol paradigm, we find that synchronization of our waves exhibit the signature of the suppression mechanism but not that of the phaselocking mechanism. Additionally, synchronization of our waves exhibits three characteristics that differ from the van der Pol paradigm: a threshold amplitude that can be seen in the Arnold tongue diagram, a branching of the 1:1 harmonic tongue at its lower extremity, and a nonharmonic state. The latter state appears to be a nonlinear oscillation; it is neither at the natural frequency nor a synchronized state.

The dust acoustic wave dispersion relation is tested to quantify its sensitivity to many physical processes that are important in laboratory dusty plasmas. It is found that inverse Landau damping and ion-neutral collisions contribute about equally to the growth rate ωi, pointing to the advantage of using a kinetic model for the instability. The growth rate ωi increases the most with an increase of dust number density, followed by an increase in ion-drift speed. The quantities that cause ωi to decrease the most when they are increased are the dust-neutral collision rate followed by the ion-neutral collision rate, ion collection current onto dust particles, and the ion thermal speed. In general, ωi is affected more than ωr by the choice of processes that are included. Strong Coulomb-coupling effects can be included in a compressibility term. The susceptibilities derived here can be combined in various ways in a dispersion relation to account for different combinations of physical processes.

The pair correlation function g(r) and the number density n for particles in a three-dimensional (3D) sample can be determined from a single two-dimensional (2D) image. The 2D image is obtained experimentally with a simple setup: a cross-sectional slab of particles is illuminated with a laser sheet and imaged with a single camera. After image analysis, to find positions of particles in two dimensions, along with their brightness, one obtains g(r), also known as the radial distribution function. The key for attaining high accuracy is to use only the particles that are brighter than a filter level, which we refine to achieve greater accuracy. The density n is obtained from g(r). This method is demonstrated in a dusty plasma experiment. Accuracy is quantified using simulation data; errors of 2% for both the pair correlation function and the number density are achievable. The method is useful for dusty plasmas and colloids.

Abstract-A self-excited dust acoustic wave is synchronized by sinusoidal modulation of the ion density, and the wave is imaged by planar laser-light scattering. Space-time diagrams based on the images reveal how the nonlinearity of the plasma's response causes the wave's frequency to be synchronized to a multiple of 0.5, 1, 2, or 3 of the modulation frequency. Space-time diagrams also reveal wave front merging as is observed for a wide range of modulation frequencies.Index Terms-Dusty plasmas, plasma waves. T HE dust acoustic wave (DAW) is a plasma wave that an experimenter can observe with the naked eye. This wave is analogous to an ion acoustic wave and propagates in a dusty plasma containing highly charged particles of solid matter (dust) in addition to electrons, ions, and neutral gas atoms. Compressions and rarefactions of the dust particles have such a high amplitude, and they propagate so slowly, that they are easy to view and image by laser light scattering. Due to the low charge-to-mass ratio of the dust particles, the wave frequency is typically only a few tens of hertz. The wave is self-excited by an ion-streaming instability [1].We performed an experiment to observe nonlinear phenomena, which occur because the wave grows to a large amplitude. We observed wave synchronization where the wave's frequency changes in response to an external modulation of the plasma conditions [2]- [4]. We study the same synchronization phenomenon as in [4], but here we rely on space-time diagrams, prepared as in [5], as our analysis method.An argon glow discharge plasma was ignited by applying a 13.56-MHz radio frequency voltage with 57 V peak-to-peak amplitude to a horizontal lower electrode [ Fig. 1(a)]. Dust particles, which were 4.8-µm melamine formaldehyde spheres, were dropped into the plasma using a dispenser with a single hole. The dust particles were negatively charged by collecting more electrons than ions, and they levitated under the action of naturally occurring electric fields. To vertically elongate the dust cloud, we used a glass box that enhanced the horizontal component of the electric field. The vertical component of this electric field drove a downward ion flow, which was the energy source for exciting the DAW. The 120-mTorr gas pressure was low enough that gas damping did not prevent the DAW from growing to large amplitudes with significant nonlinearities. The natural frequency of the wave, meaning its frequency without any modulation present, was 20.5 Hz. Our primary diagnostic was planar laser-light scattering for imaging the dust cloud [6]. The intensity of the scattered light was proportional to the dust number density n d , because the dust cloud was optically thin. A vertical cross section of the cloud was illuminated with a sheet of 532-nm laser light. A movie was recorded at 256 frames/s using a Phantom v5.2 camera. A still image is shown in Fig. 1(b). We analyzed the intensity within a region of interest (ROI) [ Fig. 1(b)]. The wavefronts were planar in the ROI, so that we can average the int...