Bispectral analysis of nonlinear compressional waves in a two-dimensional dusty plasma crystal

Bispectral analysis was used to study the nonlinear interaction of compressional waves in a two-dimensional strongly coupled dusty plasma. A monolayer of highly charged polymer microspheres was suspended in a plasma sheath. The microspheres interacted with a Yukawa potential and formed a triangular lattice. Two sinusoidal pump waves with different frequencies were excited in the lattice by pushing the particles with modulated Ar+ laser beams. Coherent nonlinear interaction of the pump waves was shown to be the mechanism of generating waves at the sum, difference, and other combination frequencies. However, coherent nonlinear interaction was ruled out for certain combination frequencies, in particular, for the difference frequency below an excitation-power threshold, as predicted by theory.

Shear viscosity of two-dimensional Yukawa systems in the liquid state

The shear viscosity of a two-dimensional (2D) liquid was calculated using molecular dynamics simulations with a Yukawa potential. The viscosity has a minimum at a Coulomb coupling parameter Gamma of about 17, arising from the temperature dependence of the kinetic and potential contributions. Previous calculations of 2D viscosity were less extensive as well as for a different potential. The stress autocorrelation function was found to decay rapidly, contrary to earlier work. These results are useful for 2D condensed matter systems and are compared to a dusty plasma experiment.

Phonons in a one-dimensional Yukawa chain: dusty plasma experiment and model

Phonons in a one-dimensional chain of charged microspheres suspended in a plasma were studied in an experiment. The phonons correspond to random particle motion in the chain; no external manipulation was applied to excite the phonons. Two modes were observed, longitudinal and transverse. The velocity fluctuations in the experiment are analyzed using current autocorrelation functions and a phonon spectrum. The phonon energy was found to be unequally partitioned among phonon modes in the dusty plasma experiment. The experimental phonon spectrum was characterized by a dispersion relation that was found to differ from the dispersion relation for externally excited phonons. This difference is attributed to the presence of frictional damping due to gas, which affects the propagation of externally excited phonons differently from phonons that correspond to random particle motion. A model is developed and fit to the experiment to explain the features of the autocorrelation function, phonon spectrum, and the dispersion relation.

Shear flows and shear viscosity in a two-dimensional Yukawa system (dusty plasma)

The shear viscosity of a two-dimensional liquid-state dusty plasma was measured experimentally. A monolayer of highly charged polymer microspheres, with a Yukawa interaction, was suspended in a plasma sheath. Two counterpropagating Ar+ laser beams pushed the particles, causing shear-induced melting of the monolayer and a shear flow in a planar Couette configuration. By fitting the particle velocity profiles in the shear flow to a Navier-Stokes model, the kinematic viscosity was calculated; it was of order 1 mm(2) s(-1), depending on the monolayer's parameters and shear stress applied.

Characterizing potentials using the structure of a one-dimensional chain demonstrated using a dusty plasma crystal

A procedure was developed to characterize the interparticle potential in a lattice that is confined by an external potential. The first of the two steps is to characterize the confining potential, which can be done using various schemes involving observations of particle motion. The second step is to characterize the interparticle potential using measurements of the equilibrium particle positions. This can be done with either of two methods developed here, a force-balance method or a simpler equation-of-state method. To demonstrate and test these methods, an experiment and a molecular dynamics simulation were performed with a one-dimensional Coulomb chain of particles confined in a parabolic potential. The experiment used a dusty plasma consisting of charged microspheres levitated in the plasma sheath above a narrow groove in a lower electrode.

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.

Transverse optical mode in a one-dimensional Yukawa chain

A transverse optical mode was observed in a one-dimensional Yukawa chain. Charged particles, suspended in a strongly coupled dusty plasma, were arranged in a 1D periodic structure. Particle displacement in the direction perpendicular to the chain was restored by the confining potential. The dispersion relation of phonons was measured, verifying that the optical mode has negative dispersion, with phase and group velocities that are oppositely directed. A theoretical dispersion relation is presented and compared to the experiment and a molecular dynamics simulation.

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.

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.

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.

Decharging of complex plasmas: first kinetic observations

The first experiment on the decharging of a complex plasma in microgravity conditions was conducted. After switching off the rf power, in the afterglow plasma, ions and electrons rapidly recombine and leave a cloud of charged microparticles. Because of microgravity, the particles remain suspended in the experimental chamber for a sufficiently long time, allowing precise measurements of the rest particle charge. A simple theoretical model for the decharging is proposed which agrees quite well with the experiment results and predicts the rest charge at lower gas pressures.

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.

Particle interaction measurements in a Coulomb crystal using caged-particle motion

A technique for characterizing the particle interaction potential of a Coulomb crystal is developed. The mean-square displacement (MSD) is measured, showing both caged- and superdiffusive-particle motions. By subtracting the center of mass of neighboring particles in computing MSD, only short-wavelength particle motions are retained. This yields the lattice Einstein frequency, which contains information about the interparticle forces and potentials. Video measurements of particle motions in a complex (dusty) plasma are used to demonstrate the technique.

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.

Experimental test of two-dimensional melting through disclination unbinding

A two-dimensional (2D) melting transition has been studied in a nonequilibrium experimental model system. The system used was a complex or dusty plasma consisting of microspheres suspended in a glow-discharge plasma, where we have mapped the topological defects during the transition. The role of the defects in the melting transition is evaluated and the arrangement of the defects in the lattice is quantified in a new way. It is found that defect density increases dramatically during the melting; at all stages the defects tend to be clustered together rather than widely dispersed; the clustering tends to take the form of chain or string-like structures. We compare these results for the defect structure with the assumptions of the popular 2D melting theory of Halperin and Nelson, rather than the predictions, as is more common.

Theory of collision-dominated dust voids in plasmas

A dust void, i.e., the dust-free region in a dusty plasma, results from the balance of the electrostatic and plasma (such as the ion drag) forces acting on a dust particle. The properties of dust voids depend on the ratio of the void size to the mean free path of plasma ions colliding with neutral species of a weakly ionized plasma. For many plasma-processing and plasma-crystal experiments, the size of the void is much larger than the ion-neutral mean free path. The theory and numerical results are presented for such a collisional case including the situations in which the plasma is quasineutral in the void region or the plasma quasineutrality is violated, as well as the case in which the ion ram pressure is insignificant.

Long-range attractive and repulsive forces in a two-dimensional complex (dusty) plasma

An interaction of a negatively biased wire with a monolayer lattice of negatively charged particles has been studied experimentally. The particles levitated at the height of the wire in a sheath of an rf discharge. It was found that the particles close to the wire were repelled from it electrostatically, while the far particles were attracted due to the drag of the ion flow deflected toward the wire. The ion drag force prevails far from the wire, whereas the electrostatic force is stronger close to the wire. The range of the forces is one to two orders of magnitude greater than the screening length.

Three-dimensional strongly coupled plasma crystal under gravity conditions

Experiments were carried out to investigate a three-dimensional (3D) plasma crystal. A method of determining the positions of each individual microparticle has been developed. A crystal volume of about 2x10(4) particles in 19 horizontal planes was analyzed. Direct imaging and the 3D pair correlation function show that "domains" of fcc and hcp lattices coexist in the crystal. Other structures, in particular, the theoretically predicted bcc lattice, were not observed.

Laser-excited mach cones in a dusty plasma crystal

Experimental studies of the formation and structure of Mach cones in a plasma crystal are presented. Plasma crystals are ordered structures of charged microspheres trapped in the sheath of an rf discharge plasma. Using a monolayer crystal with a hexagonal lattice, Mach cones were excited by the radiation pressure of a focused laser beam. The beam was swept at a supersonic speed through the crystal, in a controlled and repeatable manner. A multiple Mach cone structure was observed, with at least three distinct Mach cones. The Mach angle relation was verified over a wide range of Mach numbers, for both the first and second cones. The sound speed, measured from the first Mach angle, was found to increase with the particle number density. Two methods of determining the particle charge and screening distance are developed, making use of the sound speed and an assumption of a Yukawa interparticle potential. Molecular-dynamics simulations of the experiment were carried out, using a monolayer of particles interacting through a Yukawa potential, and these show close agreement with the experiment.

Transverse waves in a two-dimensional screened-coulomb crystal (Dusty plasma)

Transverse shear waves were observed experimentally in a two-dimensional screened Coulomb crystal. They were excited by applying a chopped laser beam to a 2D dusty plasma, i.e., a monolayer of charged microspheres levitated in a plasma. Measurements of the dispersion relation reveal an acoustic, i.e., nondispersive, character over the entire range of wave numbers measured, 0.2<k(r)a/pi<0.7, where a is the interparticle spacing. Comparison to theory provides a measurement of the particles' charge.

Mach cone shocks in a two-dimensional Yukawa solid using a complex plasma

Mach cones were studied experimentally in a two-dimensional Yukawa solid consisting of charged micrometer particles suspended as a layer in a plasma. These cones were V-shaped shocks produced spontaneously by a supersonic particle moving below the main two-dimensional particle layer. The cones had a double structure. The first cone was compressional and particles moved forward, and it was followed by a second cone, which was rarefactional, where particles moved backward. Over the limited range of speed V attained by the supersonic particles in this experiment, the angle mu of the cone was found to obey the Mach cone rule sin mu = c/V, where c is the medium's sound speed. The cones caused only elastic deformations in the crystal lattice, except in a narrow track behind the cone's vertex. The wings of the cones can be analyzed as linear shocks in two dimensions. Using spatially resolved measurements of the particle number density and velocity and applying the Hugoniot relations for shocks in two dimensions, we found that the pressure inside the first Mach cone was greater than in the undisturbed medium by a factor of 1.3-1.6. The cone angle was also used to measure the charge in this experiment.

Rigid and differential plasma crystal rotation induced by magnetic fields

Observations show that plasma crystals, suspended in the sheath of a radio-frequency discharge, rotate under the influence of a vertical magnetic field. Depending on the discharge conditions, two different cases are observed: a rigid-body rotation (all the particles move with a constant angular velocity) and sheared rotation (the angular velocity of particles has a radial distribution). When the discharge voltage is increased sufficiently, the particles may even reverse their direction of motion. A simple analytical model is used to explain qualitatively the mechanism of the observed particle motion and its dependence on the confining potential and discharge conditions. The model takes into account electrostatic, ion drag, neutral drag, and effective interparticle interaction forces. For the special case of rigid-body rotation, the confining potential is reconstructed. Using data for the radial dependence of particle rotation velocity, the shear stresses are estimated. The critical shear stress at which shear-induced melting occurs is used to roughly estimate the shear elastic modulus of the plasma crystal. The latter is also used to estimate the viscosity contribution due to elasticity in the plasma liquid. Further development is suggested in order to quantitatively implement these ideas.

Theory of dust voids in plasmas

Dusty plasmas in a gas discharge often feature a stable void, i.e., a dust-free region inside the dust cloud. This occurs under conditions relevant to both plasma processing discharges and plasma crystal experiments. The void results from a balance of the electrostatic and ion drag forces on a dust particle. The ion drag force is driven by a flow of ions outward from an ionization source and toward the surrounding dust cloud, which has a negative space charge. In equilibrium the force balance for dust particles requires that the boundary with the dust cloud be sharp, provided that the particles are cold and monodispersive. Numerical solutions of the one-dimensional nonlinear fluid equations are carried out including dust charging and dust-neutral collisions, but not ion-neutral collisions. The regions of parameter space that allow stable void equilibria are identified. There is a minimum ionization rate that can sustain a void. Spatial profiles of plasma parameters in the void are reported. In the absence of ion-neutral collisions, the ion flow enters the dust cloud's edge at Mach number M=1. Phase diagrams for expanding or contracting voids reveal a stationary point corresponding to a single stable equilibrium void size, provided the ionization rate is constant. Large voids contract and small voids expand until they attain this stationary void size. On the other hand, if the ionization rate is not constant, the void size can oscillate. Results are compared to recent laboratory and microgravity experiments.