Dispersion properties of the out-of-plane transverse wave in a two-dimensional Coulomb crystal

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.

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.

Viscosity of two-dimensional strongly coupled dusty plasma modified by a perpendicular magnetic field

Transport properties of two-dimensional (2D) strongly coupled dusty plasmas have been investigated in detail, but never for viscosity with a strong perpendicular magnetic field; here, we examine this scenario using Langevin dynamics simulations of 2D liquids with a binary Yukawa interparticle interaction. The shear viscosity η of 2D liquid dusty plasma is estimated from the simulation data using the Green-Kubo relation, which is the integration of the shear stress autocorrelation function. It is found that, when a perpendicular magnetic field is applied, the shear viscosity of 2D liquid dusty plasma is modified substantially. When the magnetic field is increased, its viscosity increases at low temperatures, while at high temperatures its viscosity diminishes. It is determined that these different variational trends of η arise from the different behaviors of the kinetic and potential parts of the shear stress under external magnetic fields.

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.

Mode couplings and resonance instabilities in finite dust chains

Employing a numerical simulation, the normal modes are investigated for finite, one-dimensional horizontal dust chains in complex plasma. Mode couplings induced by the ion flow within the sheath are identified in the mode spectra and the coupling rules are determined. Two types of resonance-induced instabilities are observed, one bidirectional and one unidirectional. Bidirectional instability is found to cause melting of the chain with the melting proceeding via a two-step process which obeys the Lindemann criterion. The relationship between the normal mode spectra observed in finite systems and the wave dispersion relations seen in larger systems was also examined using a dust chain model. For this case, the dispersion relation was obtained through multiplication of the mode spectra matrix by a transition matrix. The resulting dispersion relations exhibit both the general features observed in larger crystals as well as several characteristics unique to finite systems, such as discontinuities and strong energy-density fluctuations.

Mode coupling and resonance instabilities in quasi-two-dimensional dust clusters in complex plasmas

Small quasi-two-dimensional dust clusters consisting of three to eleven particles are formed in an argon plasma under varying rf power. Their normal modes are investigated through their mode spectra obtained from tracking the particles' thermal motion. Detailed coupling patterns between their horizontal and vertical modes are detected for particle numbers up to 7 and discrete instabilities are found for dust clusters with particle number ⩾9, as predicted in previous theory on ion-flow induced mode coupling in small clusters. The instabilities are proven to be induced by resonance between coupled horizontal and vertical normal modes.

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.

Mode couplings and resonance instabilities in dust clusters

The normal modes for three to seven particle two-dimensional (2D) dust clusters in a complex plasma are investigated using an N-body simulation. The ion wakefield downstream of each particle is shown to induce coupling between horizontal and vertical modes. The rules of mode coupling are investigated by classifying the mode eigenvectors employing the Bessel and trigonometric functions indexed by order integers (m, n). It is shown that coupling only occurs between two modes with the same m and that horizontal modes having a higher shear contribution exhibit weaker coupling. Three types of resonances are shown to occur when two coupled modes have the same frequency. Discrete instabilities caused by both the first and third type of resonances are verified and instabilities caused by the third type of resonance are found to induce melting. The melting procedure is observed to go through a two-step process with the solid-liquid transition closely obeying the Lindemann criterion.

Collective modes in two-dimensional binary Yukawa systems

We analyze via theoretical approaches and molecular dynamics simulations the collective mode structure of strongly coupled two-dimensional binary Yukawa systems, for selected density, mass, and charge ratios, both in the liquid and crystalline solid phases. Theoretically, the liquid phase is described through the quasilocalized charge approximation (QLCA) approach, while in the crystalline phase we study the centered honeycomb and the staggered rectangular crystal structures through the standard harmonic phonon approximation. We identify "longitudinal" and "transverse" acoustic and optic modes and find that the longitudinal acoustic mode evolves from its weakly coupled counterpart in a discontinuous nonperturbative fashion. The low-frequency acoustic excitations are governed by the oscillation frequency of the average atom, while the high-frequency optic excitation frequencies are related to the Einstein frequencies of the systems.

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.

Mode coupling for phonons in a single-layer dusty plasma crystal

New modes in a dusty plasma result from coupling of differently polarized phonons. A single horizontal layer of charged microparticles, confined so that vertical as well as horizontal motions are possible, usually exhibits three modes. An experiment shows that mode coupling leads to a new hybrid mode and another new mode. Coupling also leads to a recently reported hybrid mode and nondispersive mode, shown here to occur in an unmelted lattice. A linear theory based on ion wakes is able to predict some, but not all, of these modes. Other multiphase systems could exhibit similar mode coupling.

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.

Vertical wave packets observed in a crystallized hexagonal monolayer complex plasma

Propagation of vertical wave packets was observed experimentally in a crystallized hexagonal monolayer complex plasma. It was found that the phase velocity exceeded the group velocity by a factor 65 and was directed into the opposite direction as expected for an inverse optical-like dispersion relation. The wave packets propagated keeping their width constant. The explanation of this behavior is based on three-dimensional equations of motion and uses a long-wavelength weak dispersion weak inhomogeneity approximation. While the wave dispersion causes the wave packet to spread, lattice inhomogeneity and neutral gas drag counteract spreading. A plasma diagnostic method was developed that is based on the ratio between vertical and dust-lattice wave speeds. This ratio is very sensitive to the lattice parameter kappa (ratio of the particle separation to the screening length) in a very useful range of kappa < or = 2 . It was found that only a two-dimensional lattice model can provide a quantitative description of the vertical waves, while a linear chain model gives only a qualitative agreement.

Structural phase transitions and out-of-plane dust lattice instabilities in vertically confined plasma crystals

The formation of plasma crystals confined in an external one-dimensional parabolic potential well is simulated for a normal experimental environment employing a computer code called BOX_TREE. Under appropriate conditions, crystals were found to form layered systems. The system's structural phase transitions, including transitions between crystals with differing numbers of layers and the same number of layers but different intralayer structures, were investigated and found to agree with previous theoretical and experimental research results. One- to two-layer transitions were examined in detail and shown to start at the point where the out-of-plane lattice instability appears. The resulting three layer system caused by this instability was observed at the center of the system. Finally, growth rates for this out-of-plane lattice instability were obtained using the BOX_TREE simulation with these results shown to agree with those obtained from analytical theory.

Collective modes of quasi-two-dimensional Yukawa liquids

Particles in dusty plasmas are often confined to a quasi-two-dimensional arrangement. In such layers--besides the formation of compressional and (in-plane) shear waves--an additional collective excitation may also show up, as small-amplitude oscillations of the particles perpendicular to the plane are also possible. We explore through molecular dynamics simulations the properties (fluctuation spectra, dispersion relation, Einstein frequency) of this out-of-plane transverse mode in the strongly coupled liquid phase of Yukawa systems.