Longitudinal and transverse waves in Yukawa crystals

Melting curve of two-dimensional Yukawa systems predicted by isomorph theory

The analytical expression for the conditions of the solid-fluid phase transition, i.e., the melting curve, for two-dimensional (2D) Yukawa systems is derived theoretically from the isomorph theory. To demonstrate that the isomorph theory is applicable to 2D Yukawa systems, molecular dynamical simulations are performed under various conditions. Based on the isomorph theory, the analytical isomorphic curves of 2D Yukawa systems are derived using the local effective power-law exponent of the Yukawa potential. From the obtained analytical isomorphic curves, the melting curve of 2D Yukawa systems is directly determined using only two known melting points. The determined melting curve of 2D Yukawa systems well agrees with the previous obtained melting results using completely different approaches.

Universal scaling of transverse sound speed and its isomorphic property in Yukawa fluids

Molecular dynamical simulations are performed to investigate the scaling of the transverse sound speed in two-dimensional (2D) and 3D Yukawa fluids. From the calculated diagnostics of the radial distribution function, the mean-squared displacement, and the Pearson correlation coefficient, the approximate isomorphic curves for 2D and 3D liquidlike Yukawa systems are obtained. It is found that the structure and dynamics of 2D and 3D liquidlike Yukawa systems exhibit the isomorphic property under the conditions of the same relative coupling parameter Γ/Γ_{m}=const. It is demonstrated that the reduced transverse sound speed, i.e., the ratio of the transverse sound speed to the thermal speed, is an isomorph invariant, which is a quasiuniversal function of Γ/Γ_{m}. The obtained isomorph invariant of the reduced transverse sound speed can be useful to estimate the transverse sound speed, or determine the coupling strength, with applications to dusty (complex) plasma or colloidal systems.

Observation of fast sound in two-dimensional dusty plasma liquids

Equilibrium molecular dynamics simulations are performed to study two-dimensional (2D) dusty plasma liquids. Based on the stochastic thermal motion of simulated particles, the longitudinal and transverse phonon spectra are calculated, and used to determine the corresponding dispersion relations. From there, the longitudinal and transverse sound speeds of 2D dusty plasma liquids are obtained. It is discovered that, for wavenumbers beyond the hydrodynamic regime, the longitudinal sound speed of a 2D dusty plasma liquid exceeds its adiabatic value, i.e., the so-called fast sound. This phenomenon appears at roughly the same length scale of the cutoff wavenumber for transverse waves, confirming its relation to the emergent solidity of liquids in the nonhydrodynamic regime. Using the thermodynamic and transport coefficients extracted from the previous studies, and relying on the Frenkel theory, the ratio of the longitudinal to the adiabatic sound speeds is derived analytically, providing the optimal conditions for fast sound, which are in quantitative agreement with the current simulation results.

Phonon spectra of a two-dimensional solid dusty plasma modified by two-dimensional periodic substrates

Phonon spectra of a two-dimensional (2D) solid dusty plasma modulated by 2D square and triangular periodic substrates are investigated using Langevin dynamical simulations. The commensurability ratio, i.e., the ratio of the number of particles to the number of potential well minima, is set to 1 or 2. The resulting phonon spectra show that propagation of waves is always suppressed due to the confinement of particles by the applied 2D periodic substrates. For a commensurability ratio of 1, the spectra indicate that all particles mainly oscillate at one specific frequency, corresponding to the harmonic oscillation frequency of one single particle inside one potential well. At a commensurability ratio of 2, the substrate allows two particles to sit inside the bottom of each potential well, and the resulting longitudinal and transverse spectra exhibit four branches in total. We find that the two moderate branches come from the harmonic oscillations of one single particle and two combined particles in the potential well. The other two branches correspond to the relative motion of the two-body structure in each potential well in the radial and azimuthal directions. The difference in the spectra between the square and triangular substrates is attributed to the anisotropy of the substrates and the resulting alignment directions of the two-body structure in each potential well.

Fluctuation theorem convergence in a viscoelastic medium demonstrated experimentally using a dusty plasma

The convergence of the steady-state fluctuation theorem (SSFT) is investigated in a shear-flow experiment performed in a dusty plasma. This medium has a viscoelastic property characterized by the Maxwell relaxation time τ_{M}. Using measurements of the time series of the entropy production rate, for subsystems of various sizes, it is discovered that the SSFT convergence time decreases with the increasing system size until it eventually reaches a minimum value of τ_{M}, no matter the size of the subsystem. This result indicates that the convergence of the SSFT is limited by the energy-storage property of the viscoelastic medium.

Experiment and model for a Stokes layer in a strongly coupled dusty plasma

A Stokes layer, which is a flow pattern that arises in a viscous fluid adjacent to an oscillatory boundary, was observed in an experiment using a two-dimensional strongly coupled dusty plasma. Liquid conditions were maintained using laser heating, while a separate laser manipulation applied an oscillatory shear that was localized and sinusoidal. The evolution of the resulting flow was analyzed using space-time diagrams. These figures provide an intuitive visualization of a Stokes layer, including features such as the depth of penetration and wavelength. Another feature, the characteristic speed for the penetration of the oscillatory flow, also appears prominently in space-time diagrams. To model the experiment, the Maxwell-fluid model of a Stokes layer was generalized to describe a two-phase liquid. In our experiment, the phases were gas and dust, where the dust cloud was viscoelastic due to strong Coulomb coupling. The model is found to agree with the experiment, in the appearance of the space-time diagrams, and in the values of the characteristic speed, depth of penetration, and wavelength.

Reflection and transmission of an incident solitary wave at an interface of a binary complex plasma in a microgravity condition

Theoretical results are given in the present paper, which can well explain the experimental observations performed under microgravity conditions in the PK-3 Plus Laboratory on board the International Space Station about the propagation of a solitary wave across an interface in a binary complex plasma. By using the traditional reductive perturbation method and the continuity conditions of both the electric potential and the momentum at the interface, we obtain the equivalent "initial conditions" for both the transmitted wave and the reflected waves from the incident wave. Then we obtain the numbers of the reflected and the transmitted solitary waves as well as all the wave amplitudes by using the inverse scattering method. The ripples of both reflection and transmission have also been given by using the Fourier series. The number of the reflected and the transmitted solitary waves produced by interface, as well as all the solitary wave amplitudes, depend on the system parameters such as the number density, electric charge, mass of the dust particles, and the effective temperature in both regions. The analytical results agree with observations in the experiments.

Rotating vortices in two-dimensional inhomogeneous strongly coupled dusty plasmas: Shear and spiral density waves

Dusty plasma experiments can be performed quite easily in a strong coupling regime. In our previous work [V. S. Dharodi, S. K. Tiwari, and A. Das, Physics of Plasmas 21, 073705 (2014)]PHPAEN1070-664X10.1063/1.4888882, we numerically explored such plasmas with constant density and observed the transverse shear (TS) waves from the rotating vortex. Laboratory dusty plasmas are good examples of homogeneous plasmas; however, heterogeneity (e.g., density, temperature, and charge) may be due to the existence of voids, different domains with different orientations, presence of external forces like magnetic and/or electric, size or charge imbalance, etc. Here, we examine how the density heterogeneity in dusty plasmas responds to the circularly rotating vortex monopoles, specifically, smooth and sharp cutoff. For this purpose, we have carried out a series of two-dimensional fluid simulations in the framework of the incompressible generalized hydrodynamics fluid model. The rotating vortices are placed at the interface of two incompressible fluids with different densities. The smooth rotating vortex causes two effects: First, the regions are stretched to form the spiral density waves; second, there is a shear in flows which consequently induces the TS waves. The TS waves move slower in the denser side than in the lighter side. The difference in speeds of the waves induces the net flow of the medium towards the lower density side. We notice that the spiral density arms are distinguishable in the early time while later they get smeared out. In sharp flows, the interplay between the TS waves and the vortices of Kelvin-Helmholtz instability distorts the formation of the regular spiral density arms around the rotor.

Configurational temperature in dusty plasmas

The temperature of a dust ensemble in a dusty plasma is one of its most fundamental properties. Here, we present experiments using the configurational temperature as a for the temperature analysis in dusty plasmas. Using a model of the particle interactions, the configurational temperature allows us to determine the temperature of the dust ensemble from measurements of the particle positions, rather than particle velocities. The basic concept will be presented and the technique is applied to two-dimensional finite clusters as well as three-dimensional data from an extended dust cloud. Additionally, the configurational temperature can be used to derive the particle charge and the screening length from a comparison with the standard kinetic temperature.

Dusty plasma experiment to confirm an expression for the decay of autocorrelation functions

Statistical physicists recently proposed an expression for an autocorrelation function (ACF) [Belousov and Cohen, Phys. Rev. E 94, 062124 (2016)2470-004510.1103/PhysRevE.94.062124] that has, until now, not been tested experimentally. The expression captures the early behavior of the ACF decay, when the ACF is flattened. Using experimental data from a nonequilibrium steady-state dusty plasma, we confirm that the expression's use extends to liquidlike strongly coupled plasmas. A transition in the shape of the ACF is identified, and we suggest that it corresponds to the onset of collisional scattering.

Overestimation of Viscosity by the Green-Kubo Method in a Dusty Plasma Experiment

The Green-Kubo (GK) method is widely used in simulations of strongly coupled plasmas to obtain the viscosity coefficient. However, the method's applicability, which is often taken for granted, has not been tested experimentally. We report an experimental test using a two-dimensional strongly coupled dusty plasma. We find that the GK viscosity is ≈60% larger than the result of a benchmark hydrodynamic method, obtained in the same experiment with the same conditions except for the presence of shear.

Ion-wake-induced anomaly of dust lattice mode in the presence of an external magnetic field

We report a theoretical investigation of the dust lattice (DL) mode in two-dimensional Yukawa crystals in the presence of asymmetric ion flow and an external magnetic field perpendicular to the crystal plane. Two mutually perpendicular modes are found to be coupled due to Lorentz force. Interaction among the dust grains along the vertical direction of ion flow is strongly affected due to the formation of an ion wake. This causes anisotropy in interaction strength along two mutually perpendicular directions. Both hybrid modes are studied as characteristics of different ion flow speeds and magnetic field strengths. The study shows a fluctuation in DL mode frequency driven by the strength of the particle-wake interaction. The effect of ion flow on polarization of the hybrid wave amplitudes is discussed in detail. Results show a possible mechanism of anomalous phase transition in dusty plasma.

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.

Coulomb double helical structure

Structures of Coulomb clusters formed by dust particles in a plasma are studied by numerical simulation. Our study reveals the presence of various types of self-organized structures of a cluster confined in a prolate spheroidal electrostatic potential. The stable configurations depend on a prolateness parameter for the confining potential as well as on the number of dust particles in a cluster. One-dimensional string, two-dimensional zigzag structure and three-dimensional double helical structure are found as a result of the transition controlled by the prolateness parameter. The formation of stable double helical structures resulted from the transition associated with the instability of angular perturbations on double strings. Analytical perturbation study supports the findings of numerical simulations.

Green-Kubo relation for viscosity tested using experimental data for a two-dimensional dusty plasma

The theoretical Green-Kubo relation for viscosity is tested using experimentally obtained data. In a dusty plasma experiment, micron-sized dust particles are introduced into a partially ionized argon plasma, where they become negatively charged. They are electrically levitated to form a single-layer Wigner crystal, which is subsequently melted using laser heating. In the liquid phase, these dust particles experience interparticle electric repulsion, laser heating, and friction from the ambient neutral argon gas, and they can be considered to be in a nonequilibrium steady state. Direct measurements of the positions and velocities of individual dust particles are then used to obtain a time series for an off-diagonal element of the stress tensor and its time autocorrelation function. This calculation also requires the interparticle potential, which was not measured experimentally but was obtained using a Debye-Hückel-type model with experimentally determined parameters. Integrating the autocorrelation function over time yields the viscosity for shearing motion among dust particles. The viscosity so obtained is found to agree with results from a previous experiment using a hydrodynamical Navier-Stokes equation. This comparison serves as a test of the Green-Kubo relation for viscosity. Our result is also compared to the predictions of several simulations.

Effects of polarization force and effective dust temperature on dust-acoustic solitary and shock waves in a strongly coupled dusty plasma

A strongly coupled dusty plasma containing strongly correlated negatively charged dust grains and weakly correlated (Maxwellian) electrons and ions has been considered. The effects of polarization force (which arises due to the interaction between thermal ions and highly negatively charged dust grains) and effective dust temperature (which arises from the electrostatic interactions among highly negatively charged dust and from the dust thermal pressure) on the dust-acoustic (DA) solitary and shock waves propagating in such a strongly coupled dusty plasma are taken into account. The DA solitary and shock waves are found to exist with negative potential only. It has been shown that the strong correlation among the charged dust grains is a source of dissipation and is responsible for the formation of the DA shock waves. It has also been shown that the effects of polarization force and effective dust-temperature significantly modify the basic features (e.g., amplitude, width, and speed) of the DA solitary and shock waves. It has been suggested that a laboratory experiment be performed to test the theory presented in this work.

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.

Wave spectra of two-dimensional dusty plasma solids and liquids

Brownian dynamics simulations were carried out to study wave spectra of two-dimensional dusty plasma liquids and solids for a wide range of wavelengths. The existence of a longitudinal dust-thermal mode was confirmed in simulations, and a cutoff wave number in the transverse mode was measured. Dispersion relations, resulting from simulations, were compared with those from analytical theories, such as the random-phase approximation (RPA), the quasilocalized charged approximation (QLCA), and the harmonic approximation (HA). An overall good agreement between the QLCA and simulations was found for wide ranges of states and wavelengths after taking into account the direct thermal effect in the QLCA, while for the RPA and HA, good agreement with simulations was found in the high and low-temperature limits, respectively.

Heat transport in a two-dimensional complex (dusty) plasma at melting conditions

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.

Supersonic dislocations observed in a plasma crystal

Experimental results on the dislocation dynamics in a two-dimensional plasma crystal are presented. Edge dislocations were created in pairs in lattice locations where the internal shear stress exceeded a threshold and then moved apart in the glide plane at a speed higher than the sound speed of shear waves, C(T). The experimental system, a plasma crystal, allowed observation of this process at an atomistic (kinetic) level. The early stage of this process is identified as a stacking fault. At a later stage, supersonically moving dislocations generated shear-wave Mach cones.

Cutoff wave number for shear waves in a two-dimensional Yukawa system (dusty plasma)

The cutoff wave number for shear waves in a liquid-state strongly coupled plasma was measured experimentally. The phonon spectra of random particle motion were measured at various temperatures in a monolayer dusty plasma, where microspheres interact with a Yukawa potential. In the liquid state of this particle suspension, shear waves were detected only for wavelengths smaller than 20 to 40 Wigner-Seitz radii, depending on the Coulomb coupling parameter. The temperature of the suspension was controlled using a laser-heating method.

Excitation of Mach cones and energy dissipation by charged particles moving over two-dimensional strongly coupled dusty plasmas

We present a theoretical model for studying the interactions of charged particles with two-dimensional strongly coupled dusty plasmas, based on the quasilocalized charge approximation in which the static pair distribution function of a dust layer is determined from a molecular dynamics simulation. General expressions are derived for the perturbed dust-layer density, the induced potential in plasma, and the energy loss of a charged particle moving parallel to the dust layer. Numerical results show that the structure of Mach cones, excited in the dust layer by the charged particle, strongly depends on the plasma parameters such as the coupling parameter, the screening parameter, and the discharge pressure, as well as on the particle speed. In addition, it is found that the energy dissipation suffered by slow charged particles can be significantly enhanced in strongly coupled dusty plasmas when compared to the dissipation in weakly coupled plasmas.

Wave dispersion relation of two-dimensional plasma crystals in a magnetic field

The wave dispersion relation in a two-dimensional strongly coupled plasma crystal is studied by theoretical analysis and molecular dynamics simulation taking into account a constant magnetic field parallel to the crystal normal. The expression for the wave dispersion relation clearly shows that high-frequency and low-frequency branches exist as a result of the coupling of longitudinal and transverse modes due to the Lorenz force acting on the dust particles. The high-frequency and the low-frequency branches are found to belong to right-hand and left-hand polarized waves, respectively.

Normal modes of a quasi-one-dimensional multichain complex plasma

We studied equally charged particles, suspended in a complex plasma, which move in a plane and interact with a screened Coulomb potential (Yukawa type) and with an additional external confining parabolic potential in one direction, which makes the system quasi-one-dimensional (Q1D). The normal modes of the system are studied in the presence of dissipation. We also investigated how a perpendicular magnetic field couples the phonon modes with each other. Two different ways of exciting the normal modes are discussed: (1) a uniform excitation of the Q1D lattice, and (2) a local forced excitation of the system in which one particle is driven by, e.g., a laser. Our results are in very good agreement with recent experimental findings on a finite single chain system [Phys. Rev. Lett. 91, 255003 (2003)]]. Predictions are made for the normal modes of multichain structures in the presence of damping.

Nonlinear interaction of compressional waves in a 2D dusty plasma crystal

Nonlinear mixing and harmonic generation of compressional waves were studied in a 2D Yukawa (screened Coulomb) triangular lattice. The lattice was a monolayer of highly charged polymer microspheres levitated in a plasma sheath. Two sinusoidal waves with different frequencies were excited in the lattice by pushing the particles with modulated Ar+ laser beams. Waves at the sum and difference frequencies and harmonics were observed propagating in the lattice. Phonons interacted nonlinearly only above an excitation-power threshold due to frictional damping, as predicted by theory.

Two-dimensional Yukawa liquids: correlation and dynamics

A combined theoretical and molecular dynamics (MD) simulation study of the collective modes and their dispersion in a two-dimensional Yukawa system in the strongly coupled liquid state is presented. The theoretical analysis relies upon the quasilocalized charge approximation; the MD simulation generates static pair correlation functions and dynamical current-current correlation spectra.

Compressional and shear wakes in a two-dimensional dusty plasma crystal

Wakes composed of compressional and shear waves were studied experimentally in a two-dimensional screened-Coulomb crystal. Highly charged microspheres suspended in a plasma settled in a horizontal monolayer and arranged in a triangular lattice with a repulsive interparticle potential. Wakes were excited by a moving spot of Ar+ laser light. Depending on the laser spot speed, compressional waves formed a Mach cone and multiple lateral or transverse wakes, similar to ship wakes on the water surface, due to a combination of acoustic and dispersive properties. Shear waves, however, formed only a Mach cone, due to their nearly acoustic, i.e., dispersionless character. The experimental results show agreement with a recently developed theory and with molecular dynamics simulations, which assume a binary Yukawa interparticle potential. A generally useful method is presented for calculating the real part of the dispersion relation of the compressional waves based on the analysis of the spatial structure of a phonon wake. Fitting the resulting dispersion relation provides an independent measure of the interparticle potential, parametrized by the screening parameter kappa and particle charge Q.

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

The formation of a two-dimensional (2D) Coulomb crystal in a typical experimental environment was simulated with a computer code called BOX_TREE. The dispersion properties of a novel dust lattice wave (DLW) mode, the out-of-plane transverse wave, were obtained. The dispersion relation was determined to be an opticlike inverse dispersion when wave number k is lower than a critical value k(critical), and a positive dispersion when k>k(critical). The negative group velocity of the wave for k<k(critical) depends on the kappa value (with kappa=a/lambda(D), where a is the interparticle spacing and lambda(D) is the Debye length) and the positive group velocity for k>k(critical) depends on the propagation direction. The value of k(critical) depends on both kappa and propagation direction, but changes very little for all propagation directions and the range of kappa investigated. An analytical method has also been used to derive the dispersion relations assuming a hexagonal 2D lattice and Yukawa interparticle potential. These dispersion relations compare favorably with the simulation results. The dispersion relation for a 1D string was also obtained via BOX_TREE simulation and shown to agree with the analytical result given by Vladimirov [Physica A 315, 222 (2002)]. Comparison shows that the out-of-plane transverse DLW in a 2D lattice when k<k(critical) has a negative group velocity much larger than that of the 1D string, given the same particle parameters and operating environment. Again k(critical) for 1D string and 2D lattice are in the same range.

Nonlinear compressional waves in a two-dimensional Yukawa lattice

A modified Korteweg-de Vries (KdV) equation is obtained for studying the propagation of nonlinear compressional waves and pulses in a chain of particles including the effect of damping. Suitably altering the linear phase velocity makes this equation useful also for the problem of phonon propagation in a two-dimensional (2D) lattice. Assuming a Yukawa potential, we use this method to model compressional wave propagation in a 2D plasma crystal, as in a recent experiment. By integrating the modified KdV equation the pulse is allowed to evolve, and good agreement with the experiment is found. It is shown that the speed of a compressional pulse increases with its amplitude, while the speed of a rarefactive pulse decreases. It is further discussed how the drag due to the background gas has a crucial role in weakening nonlinear effects and preventing the emergence of a soliton.

Polarization of wave modes in a two-dimensional hexagonal lattice using a complex (dusty) plasma

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 longitudinal waves in a two-dimensional screened Coulomb crystal

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 omega-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.

Wave dispersion relations in two-dimensional Yukawa systems

Collective modes in a two-dimensional Yukawa system are investigated by molecular dynamics simulation in a wide range of coupling parameter Gamma and screening strength kappa. The dispersion relations and sound speeds of the transverse and longitudinal waves obtained for hexagonal lattice are in agreement with the theoretical results. The negative dispersion of the longitudinal wave is demonstrated. Frequency gaps are found on the dispersion curves of the transverse wave due to scattering of the waves on lattice defects for proper values of Gamma. The common frequency of transverse and longitudinal waves drops dramatically with the increasing screening strength kappa.

Self-consistent nonlinear resonance and hysteresis of a charged microparticle in a RF sheath

A self-consistent model is proposed to study nonlinear phenomena, such as secondary resonance and hysteresis in the vertical oscillations of a charged microparticle in a radio-frequency sheath. The motion of a single microparticle in the sheath is simulated by solving Newton's equation in which various forces acting on the particle are taken into account. The particle charging and the sheath electric field are described by a self-consistent model of the collisional radio-frequency sheath dynamics. It is found that the nonlinearity is related to the particle's charge, the sheath electric field, and the external excitation force, as well as the ion drag force and neutral-gas friction on the particle.

Experiments and molecular-dynamics simulation of elastic waves in a plasma crystal radiated from a small dipole source

The radiation of elastic waves from a localized source is observed experimentally in a two-dimensional plasma crystal. An initial shear stress applied by a laser forms a small dipole source. The emerging complex wave pattern is shown to consist of outgoing compressional and shear wave pulses. Subsequent structures are identified as inward-going waves due to the finite size of the source region, which reappear on the opposite side. The compressional wave forms a trailing wave train due to strong dispersion, while the nondispersive shear wave evolves into a vortex-antivortex pair on either side. The experiments are compared with a molecular-dynamics simulation.

Phonon spectrum in a plasma crystal

The Fourier spectra of longitudinal and transverse waves corresponding to random particle motion were measured in a two-dimensional plasma crystal. The crystal was composed of negatively charged microspheres immersed in a plasma at a low gas pressure. The phonons were found to obey a dispersion relation that assumes a Yukawa interparticle potential. The crystal was in a nonthermal equilibrium, nevertheless phonon energies were almost equally distributed with respect to wave number over the entire first Brillouin zone.

Dispersion relations of longitudinal and transverse waves in two-dimensional screened Coulomb crystals

Dispersion relations of longitudinal and transverse waves in two-dimensional (2D) screened-Coulomb crystals were investigated. The waves were excited in 2D crystals made from complex plasmas, i.e., dusty plasmas, by applying radiation pressure of laser light. The dependencies of the dispersion relation on the shielding parameter, the damping rate, and the wave propagation direction were experimentally measured. The measured dispersion relations agree reasonably with a recently developed theory, and the comparison yields the shielding parameter and the charge on particles.

Nonlinear compressional pulses in a 2D crystallized dusty plasma

Compressional pulses were launched in a two-dimensional Yukawa lattice, a hexagonal monolayer of polymer microspheres suspended in a plasma. The pulsed wave was excited by a laser beam, and nonlinear effects were observed for Mach numbers M>0.07 and for variation of particle number density delta(n)/n>0.1, but no steepening of the pulse was detected. The pulse propagation speed was found to be comparable to the sound speed of compressional waves launched with sinusoidal excitation.

Observation of shear-wave Mach cones in a 2D dusty-plasma crystal

Mach cones composed of shear waves were observed experimentally in a two-dimensional screened-Coulomb crystal. Highly charged microspheres suspended in a plasma and interacting with a repulsive Yukawa potential arranged themselves in a triangular lattice with hexagonal symmetry. Mach cones were excited by applying a force from the radiation pressure of a moving laser beam. They had a single-cone structure, which is explained by the almost dispersionless character of shear waves. The cone's opening angle obeyed the Mach-cone-angle relation. Results are compared to a molecular-dynamics simulation.

Laser-generated waves and wakes in rotating ion crystals

Locally excited plasma waves are generated in a Coulomb crystal by "pushing" with radiation pressure on a rotating cloud of laser-cooled 9Be+ ions. The waves form a stationary wake that is directly imaged through the dependence of the ion fluorescence on Doppler shifts, and theoretical calculations in a slab geometry are shown to accurately reproduce these images. The technique demonstrates a new method of exciting and studying waves in cold ion clouds.