First direct measurement of optical phonons in 2D plasma crystals

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.

Dissipative solitary waves in a two-dimensional complex plasma: Amorphous versus crystalline

The propagation of a dissipative soliton was experimentally studied in a two-dimensional binary complex plasma. The crystallization was suppressed in the center of the particle suspension where two types of particles were mixed. The motions of individual particles were recorded using video microscopy, and the macroscopic properties of the solitons were measured in the amorphous binary mixture in the center and in the plasma crystal in the periphery. Although the overall shape and parameters of solitons propagating in amorphous and crystalline regions were quite similar, their velocity structures at small scales as well as the velocity distributions were profoundly distinct. Moreover, the local structure rearranged drastically in and behind the soliton, which was not observed in the plasma crystal. Langevin dynamics simulations were performed, and the results agreed with the experimental observations.

Auto-correlations of microscopic density fluctuations for Yukawa fluids in the generalized hydrodynamics framework with viscoelastic effects

The present work develops a theoretical procedure for obtaining transport coefficients of Yukawa systems from density fluctuations. The dynamics of Yukawa systems are described in the framework of the generalized hydrodynamic (GH) model that incorporates strong coupling and visco-elastic memory effects by using an exponentially decaying memory function in time. A hydrodynamic matrix for such a system is exactly derived and then used to obtain an analytic expression for the density autocorrelation function (DAF)-a marker of the time dynamics of density fluctuations. The present approach is validated against a DAF obtained from numerical data of Molecular Dynamics (MD) simulations of a dusty plasma system that is a practical example of a Yukawa system. The MD results and analytic expressions derived from the model equations are then used to obtain various transport coefficients and the latter are compared with values available in the literature from other models. The influence of strong coupling and visco-elastic effects on the transport parameters are discussed. Finally, the utility of our calculations for obtaining reliable estimates of transport coefficients from experimentally determined DAF is pointed out.

Self-sustained non-equilibrium co-existence of fluid and solid states in a strongly coupled complex plasma system

A complex (dusty) plasma system is well known as a paradigmatic model for studying the kinetics of solid-liquid phase transitions in inactive condensed matter. At the same time, under certain conditions a complex plasma system can also display characteristics of an active medium with the micron-sized particles converting energy of the ambient environment into motility and thereby becoming active. We present a detailed analysis of the experimental complex plasmas system that shows evidence of a non-equilibrium stationary coexistence between a cold crystalline and a hot fluid state in the structure due to the conversion of plasma energy into the motion energy of microparticles in the central region of the system. The plasma mediated non-reciprocal interaction between the dust particles is the underlying mechanism for the enormous heating of the central subsystem, and it acts as a micro-scale energy source that keeps the central subsystem in the molten state. Accurate multiscale simulations of the system based on combined molecular dynamics and particle-in-cell approaches show that strong structural nonuniformity of the system under the action of electostatic trap makes development of instabilities a local process. We present both experimental tests conducted with a complex plasmas system in a DC glow discharge plasma and a detailed theoretical analysis.

Wave spectroscopy in a driven granular material

Driven granular media constitute model systems in out-of-equilibrium statistical physics. By assimilating the motions of granular particles to those of atoms, by analogy, one can obtain macroscopic equivalent of phase transitions. Here, we study fluid-like and crystal-like two-dimensional states in a driven granular material. In our experimental device, a tunable magnetic field induces and controls remote interactions between the granular particles. We use high-speed video recordings to analyse the velocity fluctuations of individual particles in stationary regime. Using statistical averaging, we find that the particles self-organize into collective excitations characterized by dispersion relations in the frequency-wavenumber space. These findings thus reveal that mechanical waves analogous to condensed matter phonons propagate in driven granular media. When the magnetic coupling is weak, the waves are longitudinal, as expected for a fluid-like phase. When the coupling is stronger, both longitudinal and transverse waves propagate, which is typically seen in solid-like phases. We model the dispersion relations using the spatial distribution of particles and their interaction potential. Finally, we infer the elastic parameters of the granular assembly from equivalent sound velocities, thus realizing the spectroscopy of a granular material.

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.

Frequency-dependent complex viscosity obtained for a liquid two-dimensional dusty plasma experiment

Strongly coupled plasmas in a liquid phase can be characterized by a complex viscosity η(ω), which is a function of frequency. Data from a single experiment with dusty plasma were analyzed to compare η(ω) obtained by two fundamentally distinct methods. In a nonequilibrium method, a pair of counterpropagating laser beams, separated by a gap, applied a sinusoidal shear to a two-dimensional liquid, and η(ω) was determined using the constitutive relation. In an equilibrium method, there was no externally applied shear, so η(ω) could be calculated with a generalized Green-Kubo relation. The results for these two methods are compared for the real and imaginary parts of η(ω). For both parts, it is confirmed that the two methods yield results that agree qualitatively in their trends with frequency, with the real part diminishing with ω and the imaginary part increasing with ω, as expected for viscoelastic liquids. Quantitatively, the values of η(ω) obtained by the two methods differ slightly. For the experiment that we analyze, values for the real and imaginary parts of η(ω) are substantially greater than those reported in an earlier experiment, which we attribute to shear thinning effects in the earlier experiment. The experiment we analyze was designed to minimize shear thinning, unlike the earlier experiment.

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.

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.

Wake-Mediated Propulsion of an Upstream Particle in Two-Dimensional Plasma Crystals

The wake-mediated propulsion of an "extra" particle in a channel of two neighboring rows of a two-dimensional plasma crystal, observed experimentally by Du et al. [Phys. Rev. E 89, 021101(R) (2014)PRESCM1539-375510.1103/PhysRevE.89.021101], is explained in simulations and theory. We use the simple model of a pointlike ion wake charge to reproduce this intriguing effect in simulations, allowing for a detailed investigation and a deeper understanding of the underlying dynamics. We show that the nonreciprocity of the particle interaction, owing to the wake charges, is responsible for a broken symmetry of the channel that enables a persistent self-propelled motion of the extra particle. We find good agreement of the terminal extra-particle velocity with our theoretical considerations and with experiments.

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.

Connecting the wakefield instabilities in dusty plasmas

The wakefield, or ion focus, formed by ions streaming past dust particles trapped in the plasma sheath leads to two types of instabilities: the Schweigert instability in multilayer systems and the mode-coupling instability that already appears in single-layer dust systems. Here, a model is presented that treats both types of instability in a common description. The parameter space for the onset of the instabilities is determined. A new variant of the mode-coupling instability is found to arise from the interaction among the layers. For weak confinement, all instabilities continuously merge into each other. For stronger confinement of the dust mainly the Schweigert type of instability is observed.

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.

Wakes in inhomogeneous plasmas

The Debye shielding of a charge immersed in a flowing plasma is an old classic problem. It has been given renewed attention in the last two decades in view of experiments with complex plasmas, where charged dust particles are often levitated in a region with strong ion flow. Efforts to describe the shielding of the dust particles in such conditions have been focused on the homogeneous plasma approximation, which ignores the substantial inhomogeneity of the levitation region. We address the role of the plasma inhomogeneity by rigorously calculating the point charge potential in the collisionless Bohm sheath. We demonstrate that the inhomogeneity can dramatically modify the wake, making it nonoscillatory and weaker.

Effect of strong wakes on waves in two-dimensional plasma crystals

We study the effects of the particle-wake interactions on the dispersion and polarization of dust lattice wave modes in two-dimensional plasma crystals. Most notably, the wake-induced coupling between the modes causes the branches to "attract" each other, and their polarizations become elliptical. Upon the mode hybridization the major axes of the ellipses (remaining mutually orthogonal) rotate by 45°. To demonstrate the importance of the obtained results for experiments, we plot representative particle trajectories and spectral densities of the longitudinal and transverse waves. These characteristics reveal distinct fingerprints of the mixed polarization. Furthermore, we show that at strong coupling the hybrid mode is significantly shifted towards smaller wave numbers, away from the border of the first Brillouin zone (where the hybrid mode is localized for a weak coupling).

Nonequilibrium finite dust clusters: connecting normal modes and wakefields

The dynamic properties of finite three-dimensional dust clusters in a dusty plasma under the influence of an ion focus are studied by normal modes. The mode analysis has been extended to account for the ion focus using the point-charge model for the horizontal interaction of the dust particles. From that, an analytical model for a few-particle system is derived accounting for three distinct dynamical regimes at different focus strengths, namely, absolutely unstable and fully stable configurations as well as an unstable oscillatory regime. The techniques of normal mode analysis (NMA) and instantaneous normal modes (INM) extended by the ion focus have been applied to dust systems in the experiment and compared to the model. From this, the ion focus strength has been derived. The specific sensitivity of NMA and INM allows one to identify equilibrium configurations in this nonequilibrium environment for these finite clusters.

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.

Instability of ion kinetic waves in a weakly ionized plasma

The fundamental higher-order Landau plasma modes are known to be generally heavily damped. We show that these modes for the ion component in a weakly ionized plasma can be substantially modified by ion-neutral collisions and a dc electric field driving ion flow so that some of them can become unstable. This instability is expected to naturally occur in presheaths of gas discharges at sufficiently small pressures and thus affect sheaths and discharge structures.

Direct observation of mode-coupling instability in two-dimensional plasma crystals

Dedicated experiments on melting of two-dimensional plasma crystals were carried out. The melting was always accompanied by spontaneous growth of the particle kinetic energy, suggesting a universal plasma-driven mechanism underlying the process. By measuring three principal dust-lattice wave modes simultaneously, it is unambiguously demonstrated that the melting occurs due to the resonance coupling between two of the dust-lattice modes. The variation of the wave modes with the experimental conditions, including the emergence of the resonant (hybrid) branch, reveals exceptionally good agreement with the theory of mode-coupling instability.