Vertical wave packets observed in a crystallized hexagonal monolayer complex plasma

Amplitude modulation and surface wave generation in a complex plasma monolayer

The response of a two-dimensional plasma crystal to an externally imposed initial perturbation has been explored using molecular dynamics (MD) simulations. A two-dimensional (2D) monolayer of micron-sized charged particles (dust) is formed in the plasma environment under certain conditions. The particles interacting via Yukawa pair potential are confined in the vertical (z[over ̂]) direction by an external parabolic confinement potential, which mimics the combined effect of gravity and the sheath electric field typically present in laboratory dusty plasma experiments. An external perturbation is introduced in the medium by displacing a small central region of particles in the vertical direction. The displaced particles start to oscillate in the vertical direction, and their dynamics get modulated through a parametric decay process generating beats. It has also been shown that the same motion is excited in the dynamics of unperturbed particles. A simple theoretical model is provided to understand the origin of the beat motions of particles. Additionally, in our simulations, concentric circular wavefronts propagating radially outward are observed on the surface of the monolayer. The physical mechanism and parametric dependence of the observed phenomena are discussed in detail. This research sheds light on the medium's ability to exhibit macroscopic softness, a pivotal characteristic of soft matter, while sustaining surface wave modes. Our findings are also relevant to other strongly coupled systems, such as colloids and classical one-component plasmas.

Stability of two-dimensional complex plasma monolayers in asymmetric capacitively coupled radio-frequency discharges

In this article, the stability of a complex plasma monolayer levitating in the sheath of the powered electrode of an asymmetric capacitively coupled radio-frequency argon discharge is studied. Compared to earlier studies, a better integration of the experimental results and theory is achieved by operating with actual experimental control parameters such as the gas pressure and the discharge power. It is shown that for a given microparticle monolayer at a fixed discharge power there exist two threshold pressures: (i) above a specific pressure p_{cryst}, the monolayer always crystallizes; (ii) below a specific pressure p_{MCI}, the crystalline monolayer undergoes the mode-coupling instability and the two-dimensional complex plasma crystal melts. In between p_{MCI} and p_{cryst}, the microparticle monolayer can be either in the fluid phase or the crystal phase: when increasing the pressure from below p_{MCI}, the monolayer remains in the fluid phase until it reaches p_{cryst} at which it recrystallizes; when decreasing the pressure from above p_{cryst}, the monolayer remains in the crystalline phase until it reaches p_{MCI} at which the mode-coupling instability is triggered and the crystal melts. A simple self-consistent sheath model is used to calculate the rf sheath profile, the microparticle charges, and the microparticle resonance frequency as a function of power and background argon pressure. Combined with calculation of the lattice modes the main trends of p_{MCI} as a function of power and background argon pressure are recovered. The threshold of the mode-coupling instability in the crystalline phase is dominated by the crossing of the longitudinal in-plane lattice mode and the out-of plane lattice mode induced by the change of the sheath profile. Ion wakes are shown to have a significant effect too.

Tracking and Linking of Microparticle Trajectories During Mode-Coupling Induced Melting in a Two-Dimensional Complex Plasma Crystal

In this article, a strategy to track microparticles and link their trajectories adapted to the study of the melting of a quasi two-dimensional complex plasma crystal induced by the mode-coupling instability is presented. Because of the three-dimensional nature of the microparticle motions and the inhomogeneities of the illuminating laser light sheet, the scattered light intensity can change significantly between two frames, making the detection of the microparticles and the linking of their trajectories quite challenging. Thanks to a two-pass noise removal process based on Gaussian blurring of the original frames using two different kernel widths, the signal-to-noise ratio was increased to a level that allowed a better intensity thresholding of different regions of the images and, therefore, the tracking of the poorly illuminated microparticles. Then, by predicting the positions of the microparticles based on their previous positions, long particle trajectories could be reconstructed, allowing accurate measurement of the evolution of the microparticle energies and the evolution of the monolayer properties.

Scale-free crystallization of two-dimensional complex plasmas: Domain analysis using Minkowski tensors

Experiments of the recrystallization processes in two-dimensional complex plasmas are analyzed to rigorously test a recently developed scale-free phase transition theory. The "fractal-domain-structure" (FDS) theory is based on the kinetic theory of Frenkel. It assumes the formation of homogeneous domains, separated by defect lines, during crystallization and a fractal relationship between domain area and boundary length. For the defect number fraction and system energy a scale-free power-law relation is predicted. The long-range scaling behavior of the bond-order correlation function shows clearly that the complex plasma phase transitions are not of the Kosterlitz, Thouless, Halperin, Nelson, and Young type. Previous preliminary results obtained by counting the number of dislocations and applying a bond-order metric for structural analysis are reproduced. These findings are supplemented by extending the use of the bond-order metric to measure the defect number fraction and furthermore applying state-of-the-art analysis methods, allowing a systematic testing of the FDS theory with unprecedented scrutiny: A morphological analysis of lattice structure is performed via Minkowski tensor methods. Minkowski tensors form a complete family of additive, motion covariant and continuous morphological measures that are sensitive to nonlinear properties. The FDS theory is rigorously confirmed and predictions of the theory are reproduced extremely well. The predicted scale-free power-law relation between defect fraction number and system energy is verified for one more order of magnitude at high energies compared to the inherently discontinuous bond-order metric. It is found that the fractal relation between crystalline domain area and circumference is independent of the experiment, the particular Minkowski tensor method, and the particular choice of parameters. Thus, the fractal relationship seems to be inherent to two-dimensional phase transitions in complex plasmas. Minkowski tensor analysis turns out to be a powerful tool for investigations of crystallization processes. It is capable of revealing nonlinear local topological properties, however, still provides easily interpretable results founded on a solid mathematical framework.

Full melting of a two-dimensional complex plasma crystal triggered by localized pulsed laser heating

The full melting of a two-dimensional plasma crystal was induced in a principally stable monolayer by localized laser stimulation. Two distinct behaviors of the crystal after laser stimulation were observed depending on the amount of injected energy: (i) below a well-defined threshold, the laser melted area recrystallized; (ii) above the threshold, it expanded outwards in a similar fashion to mode-coupling instability-induced melting, rapidly destroying the crystalline order of the whole complex plasma monolayer. The reported experimental observations are due to the fluid mode-coupling instability, which can pump energy into the particle monolayer at a rate surpassing the heat transport and damping rates in the energetic localized melted spot, resulting in its further growth. This behavior exhibits remarkable similarities with impulsive spot heating in ordinary reactive matter.

Coupling of Noncrossing Wave Modes in a Two-Dimensional Plasma Crystal

We report an experimental observation of the coupling of the transverse vertical and longitudinal in-plane dust-lattice wave modes in a two-dimensional complex plasma crystal in the absence of mode crossing. A new large-diameter rf plasma chamber was used to suspend the plasma crystal. The observations are confirmed with molecular dynamics simulations. The coupling manifests itself in traces of the transverse vertical mode appearing in the measured longitudinal spectra and vice versa. We calculate the expected ratio of the trace to the principal mode with a theoretical analysis of the modes in a crystal with finite temperature and find good agreement with the experiment and simulations.

Plasma crystal dynamics measured with a three-dimensional plenoptic camera

Three-dimensional (3D) imaging of a single-layer plasma crystal was performed using a commercial plenoptic camera. To enhance the out-of-plane oscillations of particles in the crystal, the mode-coupling instability (MCI) was triggered in it by lowering the discharge power below a threshold. 3D coordinates of all particles in the crystal were extracted from the recorded videos. All three fundamental wave modes of the plasma crystal were calculated from these data. In the out-of-plane spectrum, only the MCI-induced hot spots (corresponding to the unstable hybrid mode) were resolved. The results are in agreement with theory and show that plenoptic cameras can be used to measure the 3D dynamics of plasma crystals.

Anisotropic confinement effects in a two-dimensional plasma crystal

The spectral asymmetry of the wave-energy distribution of dust particles during mode-coupling-induced melting, observed for the first time in plasma crystals by Couëdel et al. [Phys. Rev. E 89, 053108 (2014)PLEEE81539-375510.1103/PhysRevE.89.053108], is studied theoretically and by molecular-dynamics simulations. It is shown that an anisotropy of the well confining the microparticles selects the directions of preferred particle motion. The observed differences in intensity of waves of opposed directions are explained by a nonvanishing phonon flux. Anisotropic phonon scattering by defects and Umklapp scattering are proposed as possible reasons for the mean phonon flux.

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.

Synchronization of particle motion induced by mode coupling in a two-dimensional plasma crystal

The kinematics of dust particles during the early stage of mode-coupling induced melting of a two-dimensional plasma crystal is explored. It is found that the formation of the hybrid mode causes the particle vibrations to partially synchronize at the hybrid frequency. Phase- and frequency-locked hybrid particle motion in both vertical and horizontal directions (hybrid mode) is observed. The system self-organizes in a rhythmic pattern of alternating in-phase and antiphase oscillating chains of particles. The spatial orientation of the synchronization pattern correlates well with the directions of the maximal increment of the shear-free hybrid mode.

Ideal gas behavior of a strongly coupled complex (dusty) plasma

In a laboratory, a two-dimensional complex (dusty) plasma consists of a low-density ionized gas containing a confined suspension of Yukawa-coupled plastic microspheres. For an initial crystal-like form, we report ideal gas behavior in this strongly coupled system during shock-wave experiments. This evidence supports the use of the ideal gas law as the equation of state for soft crystals such as those formed by dusty plasmas.

Three-dimensional structure of Mach cones in monolayer complex plasma crystals

The structure of Mach cones in a crystalline complex plasma has been studied experimentally using an intensity sensitive imaging, which resolved particle motion in three dimensions. This revealed a previously unknown out-of-plane cone structure, which appeared due to excitation of the vertical wave mode. The complex plasma consisted of micron sized particles forming a monolayer in a plasma sheath of a gas discharge. Fast particles, spontaneously moving under the monolayer, created Mach cones with multiple structures. The in-plane cone structure was due to compressional and shear lattice waves.

First direct measurement of optical phonons in 2D plasma crystals

Spectra of phonons with out-of-plane polarization were studied experimentally in a 2D plasma crystal. The dispersion relation was directly measured for the first time using a novel method of particle imaging. The out-of-plane mode was proven to have negative optical dispersion at small wave numbers, comparison with theory showed good agreement. The effect of the plasma wakes on the dispersion relation is briefly discussed.

Discrete breathers in hexagonal dusty plasma lattices

The occurrence of single-site or multisite localized vibrational modes, also called discrete breathers, in two-dimensional hexagonal dusty plasma lattices is investigated. The system is described by a Klein-Gordon hexagonal lattice characterized by a negative coupling parameter epsilon in account of its inverse dispersive behavior. A theoretical analysis is performed in order to establish the possibility of existence of single as well as three-site discrete breathers in such systems. The study is complemented by a numerical investigation based on experimentally provided potential forms. This investigation shows that a dusty plasma lattice can support single-site discrete breathers, while three-site in phase breathers could exist if specific conditions, about the intergrain interaction strength, would hold. On the other hand, out of phase and vortex three-site breathers cannot be supported since they are highly unstable.

High speed laser tomography system

A high speed laser tomography system was developed capable of acquiring three-dimensional (3D) images of optically thin clouds of moving micron-sized particles. It operates by parallel-shifting an illuminating laser sheet with a pair of galvanometer-driven mirrors and synchronously recording two-dimensional (2D) images of thin slices of the imaged volume. The maximum scanning speed achieved was 120,000 slices/s, sequences of 24 volume scans (up to 256 slices each) have been obtained. The 2D slices were stacked to form 3D images of the volume, then the positions of the particles were identified and followed in the consecutive scans. The system was used to image a complex plasma with particles moving at speeds up to cm/s.