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Slow dynamics in an amorphous quasi-two-dimensional complex plasma, comprised of microparticles of two different sizes, was studied experimentally. The motion of individual particles was observed using video microscopy, and the self-part of the intermediate scattering function as well as the mean-squared particle displacement was calculated. The long-time structural relaxation reveals the characteristic behavior near the glass transition. Our results suggest that binary complex plasmas can be an excellent model system to study slow dynamics in classical supercooled fluids.

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)], 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., Comment: 7 pages, 4 figures, PRL (https://journals.aps.org/prl/), updated version with correct author affiliations

Complex (dusty) plasmas are composed of a weakly ionized gas and charged microparticles and represent the plasma state of soft matter. Complex plasmas have several remarkable features: Dynamical time scales associated with microparticles are ``stretched'' to tens of milliseconds, yet the microparticles themselves can be easily visualized individually. Furthermore, since the background gas is dilute, the particle dynamics in strongly coupled complex plasmas is virtually undamped, which provides a direct analogy to regular liquids and solids in terms of the atomistic dynamics. Finally, complex plasmas can be easily manipulated in different ways---also at the level of individual particles. Altogether, this gives us a unique opportunity to go beyond the limits of continuous media and study---at the kinetic level---various generic processes occurring in liquids or solids, in regimes ranging from the onset of cooperative phenomena to large strongly coupled systems. In the first part of the review some of the basic and new physics are highlighted which complex plasmas enable us to study, and in the second (major) part strong coupling phenomena in an interdisciplinary context are examined. The connections with complex fluids are emphasized and a number of generic liquid and solid-state issues are addressed. In summary, application oriented research is discussed.

A theory of the mode-coupling instability (MCI) in a fluid two-dimensional complex plasma is developed. In analogy to the point-wake model of the wake-mediated interactions commonly used to describe MCI in two-dimensional crystals, the layer-wake model is employed for fluids. It is demonstrated that the wake-induced coupling of wave modes occurs in both crystalline and fluid complex plasmas, but the confinement-density threshold, which determines the MCI onset in crystals, virtually disappears in fluids. The theory shows excellent qualitative agreement with available experiments and provides certain predictions to be verified.

We study the onset and characteristics of vortices in complex (dusty) plasmas using two-dimensional simulations in a setup modeled after the PK-3 Plus laboratory. A small number of microparticles initially self-arranges in a monolayer around the void. As additional particles are introduced, an extended system of vortices develops due to a non-zero curl of the plasma forces. We demonstrate a shear-thinning effect in the vortices. Velocity structure functions and the energy and enstrophy spectra show that vortex flow turbulence is present that is in essence of the "classical" Kolmogorov type., 5 pages, 6 figures

Implications of the recently discovered effect of channeling of upstream extra particles for transport phenomena in a two-dimensional plasma crystal are discussed. Upstream particles levitated above the lattice layer and tended to move between the rows of lattice particles. An example of heat transport is considered, where upstream particles act as moving heat sources, which may lead to anomalous heat transport. The average channeling length observed was 15–20 interparticle distances. Other features of the channeling process are also reported.

We study 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 $45^\circ$. To demonstrate importance of the obtained results for experiments, we plot spectral densities of the longitudinal and transverse waves revealing 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)., Comment: 10 pages, 6 figures

Experiments under microgravity conditions were carried out to study 'condensed' (liquid and crystalline) states of a colloidal plasma (ions, electrons, and charged microspheres). Systems with approximately 10(exp 6) microspheres were produced. The observed systems represent new forms of matter--quasineutral, self-organized plasmas--the properties of which are largely unexplored. In contrast to laboratory measurements, the systems under microgravity are clearly three dimensional (as expected); they exhibit stable vortex flows, sometimes adjacent to crystalline regions, and a central 'void,' free of microspheres.

Taking into account the statistical charge fluctuations on microspheres embedded in a low-pressure gas discharge, a stochastic differential equation for the one-dimensional dust lattice wave is derived. Using this equation, the nonstochastic differential equations for the mean particle displacement and for the second moments of the displacement and velocity are obtained. The analysis of the equation for the second moments shows that for sufficiently small gas pressure the charge fluctuations can result in exponential growth of the average energy of lattice oscillations.

Using the standard reductive perturbation technique, a nonlinear Schr\"odinger equation is derived to study the modulational instability of finite amplitude dust-acoustic (DA) and dust-ion-acoustic (DIA) waves against oblique perturbations (with respect to the propagation direction of the carrier waves) in an unmagnetized dusty plasma. It is shown that both the DA and DIA waves are modulationally unstable. Possible stationary states of the wave packets can appear as envelope solitons.

The internal structures of most periodic crystalline solids contain defects. This affects various important mechanical and thermal properties of crystals. Since it is very difficult and expensive to track the motion of individual atoms in real solids, macroscopic model systems, such as complex plasmas, are often used. Complex plasmas consist of micrometer-sized grains immersed into an ion-electron plasma. They exist in solidlike, liquidlike, and gaseouslike states and exhibit a range of nonlinear and dynamic effects, most of which have direct analogies in solids and liquids. Slabs of a monolayer hexagonal complex plasma were subjected to a cycle of uniaxial compression and decompression of large amplitudes to achieve plastic deformations, both in experiments and simulations. During the cycle, the internal structure of the lattice exhibited significant rearrangements. Dislocations (point defects) were generated and displaced in the stressed lattice. They tended to glide parallel to their Burgers vectors under load. It was found that the deformation cycle was macroscopically reversible but irreversible at the particle scale.

We describe a series of experiments on dust particles flows in a positive column of a horizontal dc discharge operating in laboratory and microgravity conditions. The main observation is that the particle flow velocities in laboratory experiments are systematically higher than in microgravity experiments, for otherwise identical discharge conditions. The paper provides an explanation for this interesting and unexpected observation. The explanation is based on a physical model, which properly takes into account main plasma-particle interaction mechanisms relevant to the described experimental study. Comparison of experimentally measured particle velocities and those calculated using the proposed model demonstrates reasonable agreement, both in laboratory and microgravity conditions, in the entire range of discharge parameters investigated., Comment: 9 pages, 7 figures

An influence of a high-voltage (3-17 kV) 20 ns pulse on a weakly-ionized low-pressure (0.1-10 Pa) capacitively-coupled radiofrequency (RF) argon plasma is studied experimentally. The plasma evolution after pulse exhibits two characteristic regimes: a bright flash, occurring within 100 ns after the pulse (when the discharge emission increases by 2-3 orders of magnitude over the steady-state level), and a dark phase, lasting a few hundreds \mu s (when the intensity of the discharge emission drops significantly below the steady-state level). The electron density increases during the flash and remains very large at the dark phase. 1D3V particle-in-cell simulations qualitatively reproduce both regimes and allow for detailed analysis of the underlying mechanisms. It is found that the high-voltage nanosecond pulse is capable of removing a significant fraction of plasma electrons out of the discharge gap, and that the flash is the result of the excitation of gas atoms, triggered by residual electrons accelerated in the electric field of immobile bulk ions. The secondary emission from the electrodes due to vacuum UV radiation plays an important role at this stage. High-density plasma generated during the flash provides efficient screening of the RF field (which sustains the steady-state plasma). This leads to the electron cooling and, hence, onset of the dark phase.

Experimental evidence is presented for a scale-free transition from an unordered to an ordered state in a 2D complex plasma that differs from the KTHNY theory of phase transitions in 2D systems. The transition is characterized by the formation and growth of ordered domains. A fractal relationship is found between the domain areas and domain boundary lengths, which can be explained by a recent theoretical model. The experimental findings are supported by a molecular dynamics simulation of a 2D particle system.

Pair and bond-orientational correlation functions and structure factors, as used in colloidal science, are applied as quantitative indicators of the phase of the newly discovered "plasma crystals." These Coulomblattice structures are formed by charged microspheres levitated in glow discharge plasmas and are imaged photographically. Static structural analysis is demonstrated on the experimental data of Thomas et al. [Phys. Rev. Lett. 73, 652, (1994)] and interpreted in the context of a two-dimensional (2D) dislocation-unbinding melting theory and a 2D density-wave melting theory.

The observation of a well-developed treelike string structure supported by a gas flow in a three-dimensional dc complex plasma is presented. The dynamically stable strings, comprising 10-20 particles, were up to 5 mm long. The experiments were performed using neon gas at a pressure of 100 Pa and melamine-formaldehyde particles with a diameter of 3.43 μm. Inside the discharge glass tube a nozzle had been built in to supply the controllable gas (plasma) flux intensity distribution along the tube. The walls of the nozzle were transparent for the laser light illuminating the particles. That gave the opportunity to closely study the particle dynamics deep inside the nozzle.

Phase behavior of large three-dimensional (3D) complex plasma systems under microgravity conditions onboard the International Space Station is investigated. The neutral gas pressure is used as a control parameter to trigger phase changes. Detailed analysis of structural properties and evaluation of three different melting-freezing indicators reveal that complex plasmas can exhibit melting by increasing the gas pressure. Theoretical estimates of complex plasma parameters allow us to identify main factors responsible for the observed behavior. The location of phase states of the investigated systems on a relevant equilibrium phase diagram is estimated. Important differences between the melting process of 3D complex plasmas under microgravity conditions and that of flat 2D complex plasma crystals in ground based experiments are discussed.

A macroscopic Coulomb crystal of solid particles in a plasma has been observed. Images of a cloud of $7\ensuremath{-}\ensuremath{\mu}m$ "dust" particles, which are charged and levitated in a weakly ionized argon plasma, reveal a hexagonal crystal structure. The crystal is visible to the unaided eye. The particles are cooled by neutral gas to 310 K, and their charge is $g9800e$, corresponding to a Coulomb coupling parameter $\ensuremath{\Gamma}g20 700$. For such a large $\ensuremath{\Gamma}$ value, strongly coupled plasma theory predicts that the particles should organize in a Coulomb solid, in agreement with our observations.

Freezing and melting of large three-dimensional complex plasmas under microgravity conditions is investigated. The neutral gas pressure is used as a control parameter to trigger the phase changes: Complex plasma freezes (melts) by decreasing (increasing) the pressure. Evolution of complex plasma structural properties upon pressure variation is studied. Theoretical estimates allow us to identify main factors responsible for the observed behavior., Phys. Rev. Lett. (in press); 4 pages, 4 figures

The liquid-solid phase transition of the Lennard-Jones (LJ) system is investigated. It is found that the properly normalized second derivative of the interaction potential is practically constant at freezing. Using this relation a simple equation for the freezing curve is derived. The obtained equation is used to estimate the triple-point parameters of the LJ system. Results are compared with available numerical simulation studies.

Using experiments and combining theory and computer simulations, we show that binary complex plasmas are particularly good model systems to study the kinetics of fluid-fluid demixing at the "atomistic" (individual particle) level. The essential parameters of interparticle interactions in complex plasmas, such as the interaction range(s) and degree of nonadditivity, can be varied significantly, which allows systematic investigations of different demixing regimes. The critical role of competition between long-range and short-range interactions at the initial stage of the spinodal decomposition is discussed.

We propose a simple method to approximately predict the freezing (fluid-solid) phase transition in systems of particles interacting via purely repulsive potentials. The method is based on the striking universality of the freezing curve for the model Yukawa and inverse-power-law interactions. This method is applied to draw an exemplary phase diagram of complex plasmas. We suggest that it can also be used to locate freezing transition in other substances with similar properties of interaction.

Simulation of a Langevin-dynamics model demonstrates emergence of critical fluctuations and anomalous grain transport which have been observed in experiments on "soft" quasi-two-dimensional dusty plasma clusters. It has been suggested that these anomalies derive from particular non-equilibrium physics, but our model does not contain such physics: the grains are confined by an external potential, interact via static Yukawa forces, and are subject to stochastic heating and dissipation from neutrals. One remarkable feature is emergence of leptokurtic probability distributions of grain displacements $\xi(\tau)$ on time-scales $\tau^{1/2}$ approaches the mean inter-grain distance $\Delta$. Others are development of humps in the distributions on multiples of $\Delta$, anomalous Hurst exponents, and transitions from leptokurtic towards Gaussian displacement distributions on time scales $\tau>\tau_{\Delta}$. The latter is a signature of intermittency, here interpreted as a transition from bursty transport associated with hopping on intermediate time scales to vortical flows on longer time scales., Comment: 12 pages, 9 figures

We present a model-independent method to test for scale-dependent non-Gaussianities in combination with scaling indices as test statistics. Therefore, surrogate data sets are generated, in which the power spectrum of the original data is preserved, while the higher order correlations are partly randomized by applying a scale-dependent shuffling procedure to the Fourier phases. We apply this method to the Wilkinson Microwave Anisotropy Probe data of the cosmic microwave background and find signatures for non-Gaussianities on large scales. Further tests are required to elucidate the origin of the detected anomalies.

The dispersion relation and damping of an electrostatic dust-lower-hybrid mode has been derived using both the fluid and kinetic models of plasmas in magnetized dusty plasmas with a background of neutral atoms and streaming electrons and ions. This mode can be excited in a laboratory experiment when the streaming velocity of electrons and ions in the direction of the magnetic field exceeds the parallel phase velocity.

We report on the first three-dimensional (3D) complex plasma structure analysis for an experiment that was performed in an elongated discharge tube in the absence of striations. The low frequency discharge was established with 1 kHz alternating dc current through a cylindrical glass tube filled with neon at 30 Pa. The injected particle cloud consisted of monodisperse microparticles. A scanning laser sheet and a camera were used to determine the particle position in 3D. The observed cylindrical-shaped particle cloud showed an ordered structure with a distinct outer particle shell. The observations are in agreement with performed molecular dynamics simulations.

We present a shear instability, which can be triggered in compressible fluids with density-dependent viscosity at shear rates above critical. The instability mechanism is generic: It is based on density-dependent viscosity, compressibility, as well as flow two-(three-)dimensionality that provides coupling between streamwise and transversal velocity components and density variations. The only factor stabilizing the instability is fluid elasticity. The corresponding eigenvalue problem for a plane Couette flow is solved analytically in the limiting cases of large and small wave numbers.

The heat transport in a two-dimensional complex (dusty) plasma undergoing a phase transition was studied experimentally. A single layer of highly charged polymer microspheres was suspended in a plasma sheath. A part of this lattice was heated by two counterpropagating focused laser beams that moved rapidly around in the lattice and provided short intense random kicks to the particles. Above a threshold, the lattice locally melted. The spatial profiles of the particle kinetic temperature were analyzed to find a thermal conductivity, which did not depend on temperature.

The onset of free thermal convection in complex fluids with background friction is theoretically investigated. It is shown that in the limit when friction prevails--opposite to the classic Rayleigh-Bénard case--the onset is determined by a renormalized Rayleigh number and also depends on the Prandtl number. Such convection should be observable in experiments with complex plasmas.

Experimental results on self-excited density waves in a complex plasma are presented. An argon plasma is produced in a capacitively coupled rf discharge at a low power and gas pressure. A cloud of microparticles is subjected to effective gravity in the range of 1-4 g by thermophoresis. The cloud is stretched horizontally (width/height approximately 45 mm/8 mm). The critical pressure for the onset of the waves increases with the temperature gradient. The waves are propagating in the direction of the ion drift. The wave frequency, phase velocity, and wavelength are measured, and particle migrations affected by the waves are analyzed at a time scale of 1 ms/frame and a subpixel space resolution.

It is shown that the electrostatic interaction potential between a pair of positively charged particles embedded in a highly collisional plasma has a long-range attractive asymptote. The effect is due to continuous plasma absorption on the particles. The relevance of this result to experimental investigations of complex (dusty) plasmas is discussed.

The interaction forces between particles have been studied in a 3D plasma cluster under weak external confinement. A suitable combination of dc and rf applied to a small electrode provided gravity compensation, uniform over dimensions much larger than the cluster itself. The forces acting on the particles could be reconstructed due to unique three-dimensional diagnostics, which allow us to obtain coordinates and velocities of all the particles simultaneously. The measurements yield a maximum (external) confinement force of 1.4 x 10(-15)N and interparticle force that is repulsive at short distances and attractive at larger distances, with a maximum attractive force of 2.4 X 10(-14)N at particle separation 195 microm.

The occurrence of liquid-vapor phase transition and the possible existence of a critical point in complex plasmas--systems that consist of charged micrograins in a neutralizing plasma background--is investigated theoretically. An analysis based on the consideration of the intergrain interaction potential suggests that under certain conditions systems near and at the critical point should be observable. Measurements under microgravity conditions would appear to be required. The analysis aims at determining the plasma parameter regime most suitable for planned experimental investigations.

An experimental determination of particle charge in a bulk dc discharge plasma covering a wide range of neutral gas pressures, was recently reported [S. Ratynskaia et al., Phys. Rev. Lett. 93, 085001 (2004)]. The charges obtained were several times smaller than the predictions of collisionless orbital motion limited theory. This discrepancy was attributed to the effect of ion-neutral collisions. In the present paper a more detailed description of this experiment is provided and additional experimental results obtained with particles of different sizes are reported. The measurements are compared with molecular dynamics simulations of particle charging for conditions similar to those of the experiment, with other available experimental data on particle charge in the bulk of gas discharges, and with a simple analytical model accounting for ion-neutral collisions. All the considered evidence indicates that ion-neutral collisions represent a very important factor, which significantly affects (reduces) the particle charge under typical discharge conditions.

Heating and heat transfer were studied in a two-dimensional crystalline complex plasma at the kinetic level. The lattice was formed of microspheres levitated in a plasma sheath. One half of the crystal was heated anisotropically to obtain higher kinetic temperatures in one direction and heat conduction was observed in real time. It was found that the longitudinal phonons conduct heat better than the transverse. The thermometric conductivity coefficient was measured to be $53\text{ }\text{ }{\mathrm{mm}}^{2}/\mathrm{s}$ for longitudinal heating and $30\text{ }\text{ }{\mathrm{mm}}^{2}/\mathrm{s}$ for transverse heating. Heat decay lengths and energy exchange times between the temperature components were determined.

Observations of complex plasmas under microgravity conditions onboard the International Space Station performed with the Plasma-Kristall experiment-Nefedov facility are reported. A weak instability of the boundary between the central void (region free of microparticles) and the microparticle cloud is observed at low gas pressures. The instability leads to periodic injections of a relatively small number of particles into the void region (by analogy this effect is called the "trampoline effect"). The trajectories of injected particles are analyzed providing information on the force field inside the void. The experimental results are compared with theory which assumes that the most important forces inside the void are the electric and the ion drag forces. Good agreement is found clearly indicating that under conditions investigated the void formation is caused by the ion drag force.

The coupling between transverse and longitudinal dust-lattice modes due to the particle-wake interactions and vertical dust charge gradient is considered. It is shown that the dust-lattice waves can be subjected to a specific instability, the criterion for which has been derived. This instability can explain experimentally observed spontaneous excitation of vibrational modes in a plasma crystal when the pressure is decreased below a critical value.

The linear kinetic approach to calculate the ion drag force in a collisional plasma is generalized. The model collision integral (for ion-neutral collisions) is discussed and employed to calculate the plasma response for arbitrary velocity of the plasma flow and arbitrary frequency of the collisions. The derived plasma response is used to calculate the self-consistent force on the test charged particle. The obtained results are compared to those of the traditional pair collision approach, and the importance of the self-consistent kinetic consideration is highlighted. In conclusion, the applicability of the proposed approach is discussed.

Dust-free regions around a Langmuir probe are studied in a complex plasma under microgravity. The dust particles settle in the presheath of the probe, where an equilibrium of the electric field force and the ion-drag force is established. The size and shape of the dust cloud are discussed with simple models. A more sophisticated presheath model is solved numerically to analyze the acting forces and the equilibrium position of the dust. The formation of distinct particle layers in the dust shell can be explained by the force gradients of the effective potential well.

Levitated particles are a new powerful diagnostic of the midplasma sheath region. They can reveal features undetectable either to plasma or to surface measurements. The equilibrium position of microparticles suspended in an oxygen plasma sheath, together with a model of the levitation force and Langmuir probe measurements, gives evidence of secondary electropositive plasmas in the already established plasma sheath, in the range of parameters where the modified Bohm criterion breaks down into multiple solutions.

Shock waves with a linear front were experimentally studied in a monolayer hexagonal Yukawa lattice which was formed from charged monodisperse plastic microspheres and levitated in the sheath of a radio-frequency discharge. It was found that the shock can cause phase transitions from a crystalline to gaslike and liquidlike states. Melting occurred in two stages. First, the lattice was compressed in the direction of shock propagation and second, the particle velocities were randomized a few lattice lines downstream. The Mach number of the shock reached 2.7.

We investigate the forces experienced by a microparticle immersed in a weakly ionized plasma with constant electric field. These are electric force and the forces associated with the momentum transfer from electrons and ions drifting in the field (electron and ion drag forces). It is shown that the effect of the electron drag, which is often neglected, can be substantial in a certain parameter range. Numerical calculation of the forces for a reasonable set of plasma parameters is performed to illustrate the importance of this effect.

The force on a charged test particle embedded in a flowing (electron-ion) plasma is calculated using the linear dielectric response formalism. This approach allows us to take into account ion-neutral collisions self-consistently. The effect of collisions on the ion drag force is analyzed. It is shown that collisions can play a major role and can enhance the force substantially.

Fluid flow around an obstacle was observed at the kinetic (individual particle) level using ``complex (dusty) plasmas'' in their liquid state. These ``liquid plasmas'' have bulk properties similar to water (e.g., viscosity), and a comparison in terms of similarity parameters suggests that they can provide a unique tool to model classical fluids. This allows us to study ``nanofluidics'' at the most elementary---the particle---level, including the transition from fluid behavior to purely kinetic transport. In this (first) experimental investigation we describe the kinetic flow topology, discuss our observations in terms of fluid theories, and follow this up with numerical simulations.

Wave spectra corresponding to the random particle motion in a monolayer Yukawa crystal were studied for various directions of propagation. It was found that there are two wave modes with a polarization alternating between the longitudinal and transverse. In the long-wavelength regime, the modes became purely longitudinal and transverse as was known before. In the short-wavelength regime the spectra strongly depended on the wavelength and the direction of propagation. The results obtained from the experiment, theory, and simulation agreed well with each other.

Nonlinear interactions of longitudinal waves were observed in a two-dimensional plasma crystal, i.e., a lattice composed of highly charged microspheres immersed in a plasma. The waves were launched by radiation pressure of a laser, and wave spectra in $\ensuremath{\omega}\ensuremath{-}\mathbf{k}$ space were analyzed at various amplitudes of waves. At a sufficiently large amplitude of wave, the second and third wave harmonics satisfying a dispersion relation were observed. As the second harmonic propagates from the excitation region, it was amplified for a small distance, and then damped. The experimental results were compared to a nonlinear wave theory and to a molecular dynamic simulation.

Melting of a monolayer plasma crystal in a radio-frequency discharge with no particles suspended above or below is studied. The experimental data are compared with results of molecular dynamics simulations and theory. It is shown that the melting is caused by the resonance coupling between the longitudinal and the transverse dust-lattice wave modes, due to the interaction of particles with the plasma wakes.