Two-dimensional Plasma Crystals Research Articles

Amplitude modulation and surface wave generation in a complex plasma monolayer.

The response of a two-dimensional plasma crystal to an externally imposed initial perturbation has been explored using molecular dynamics (MD) simulations. A two-dimensional (2D) monolayer of micron-sized charged particles (dust) is formed in the plasma environment under certain conditions. The particles interacting via Yukawa pair potential are confined in the vertical (z[over ̂]) direction by an external parabolic confinement potential, which mimics the combined effect of gravity and the sheath electric field typically present in laboratory dusty plasma experiments. An external perturbation is introduced in the medium by displacing a small central region of particles in the vertical direction. The displaced particles start to oscillate in the vertical direction, and their dynamics get modulated through a parametric decay process generating beats. It has also been shown that the same motion is excited in the dynamics of unperturbed particles. A simple theoretical model is provided to understand the origin of the beat motions of particles. Additionally, in our simulations, concentric circular wavefronts propagating radially outward are observed on the surface of the monolayer. The physical mechanism and parametric dependence of the observed phenomena are discussed in detail. This research sheds light on the medium's ability to exhibit macroscopic softness, a pivotal characteristic of soft matter, while sustaining surface wave modes. Our findings are also relevant to other strongly coupled systems, such as colloids and classical one-component plasmas.

Stability of two-dimensional complex plasma monolayers in asymmetric capacitively coupled radio-frequency discharges.

In this article, the stability of a complex plasma monolayer levitating in the sheath of the powered electrode of an asymmetric capacitively coupled radio-frequency argon discharge is studied. Compared to earlier studies, a better integration of the experimental results and theory is achieved by operating with actual experimental control parameters such as the gas pressure and the discharge power. It is shown that for a given microparticle monolayer at a fixed discharge power there exist two threshold pressures: (i) above a specific pressure p_{cryst}, the monolayer always crystallizes; (ii) below a specific pressure p_{MCI}, the crystalline monolayer undergoes the mode-coupling instability and the two-dimensional complex plasma crystal melts. In between p_{MCI} and p_{cryst}, the microparticle monolayer can be either in the fluid phase or the crystal phase: when increasing the pressure from below p_{MCI}, the monolayer remains in the fluid phase until it reaches p_{cryst} at which it recrystallizes; when decreasing the pressure from above p_{cryst}, the monolayer remains in the crystalline phase until it reaches p_{MCI} at which the mode-coupling instability is triggered and the crystal melts. A simple self-consistent sheath model is used to calculate the rf sheath profile, the microparticle charges, and the microparticle resonance frequency as a function of power and background argon pressure. Combined with calculation of the lattice modes the main trends of p_{MCI} as a function of power and background argon pressure are recovered. The threshold of the mode-coupling instability in the crystalline phase is dominated by the crossing of the longitudinal in-plane lattice mode and the out-of plane lattice mode induced by the change of the sheath profile. Ion wakes are shown to have a significant effect too.

Buckling of two-dimensional plasma crystals with nonreciprocal interactions.

Laboratory realizations of two-dimensional (2D) plasma crystals typically involve monodisperse microparticles confined into horizontal monolayers in radio-frequency (rf) plasma sheaths. This gives rise to the so-called plasma wakes beneath the microparticles. The presence of wakes renders the interactions in such systems nonreciprocal, a fact that can lead to a quite different behavior from the one expected for their reciprocal counterparts. Here we examine the buckling of a hexagonal 2D plasma crystal, occurring as the confinement strength is decreased, taking explicitly into account the nonreciprocity of the system via a well-established point-wake model. We observe that for a finite wake charge, the monolayer hexagonal crystal undergoes a transition first to a bilayer hexagonal structure, unrealizable in harmonically confined reciprocal Yukawa systems, and subsequently to a bilayer square structure. Our theoretical results are confirmed by molecular dynamics simulations for experimentally relevant parameters, indicating the potential of their observation in state-of-the-art experiments with 2D complex plasmas.

Thermal conductivity analysis of two-dimensional complex plasma liquids and crystals

A novel homogeneous perturbed non-equilibrium molecular dynamics (HPMD) scheme, proposed by Evan-Gillan, has been employed to calculate the thermal conductivity of two-dimensional (2D) complex plasma liquids and crystals (CPLCs). The thermal conductivity has been reported using an improved HPMD method under the influence of constant external perturbation with different system sizes (N) and combinations of plasma parameters (Γ, κ). The current HPMD scheme provides precise outcomes with fast convergence for small-to-large N effects over a complete range of (Γ, κ). Temperature scaling law is tested for 2D thermal conductivity with appropriate Einstein frequency and found excellent behaviors. New simulations show that the thermal conductivity of CPLCs depends on (Γ, κ) and N and a slightly decreasing behavior is noted for thermal conductivity with increasing Γ and N, but, overall, thermal conductivity becomes constant at intermediate-to-large Γ. The reported thermal conductivity obtained from present HPMD method, in the limit of low equilibrium perturbation, has established a reasonable agreement with that obtained from earlier known 2D numerical and experimental data. It is demonstrated that the present HPMD method is an alternative efficient tool to compute the thermal conductivity of 2D CPLCs and can be a suitable method for complete trends of complex plasmas.

Electric field in two-dimensional complex plasma crystal: Ideal lattices

Electric field in two-dimensional complex plasma crystal: Ideal lattices

Experimental studies of two-dimensional complex plasma crystals: waves and instabilities

A review of experimental studies on waves, phonon dispersion relations, and mode-coupling instability in two-dimensional complex plasma crystals is presented. An improved imaging method allowing simultaneous measurements of the three wave modes (compression in-plane, shear in-plane, and out-of-plane) is given. This method is used to evidence the formation of hybrid modes and the triggering of the mode-coupling instability due to wake-mediated interactions. The main stages of the mode-coupling instability are analyzed. In the early stages, synchronization of microparticle motion at the hybrid mode frequency is reported. The spatial orientation of the observed synchronization pattern correlates well with the directions of the maximal increment of the shear-free hybrid mode. When the instability is fully developed, a melting front is formed. The propagation of the melting front has similarities with flame propagation in ordinary reactive matter. Finally, it is experimentally demonstrated that an external mechanical excitation of a stable 2D complex plasma crystal can trigger the mode-coupling instability and lead to the full melting of a two-dimensional complex plasma crystal.

Experimental investigation of test particle induced micro-structural changes in a finite two-dimensional complex plasma crystal

The microstructural changes induced in a two dimensional complex plasma crystal by the movement of a single extra particle existing below it are investigated experimentally using a DC glow discharge device. The finite monolayer crystal consisting of monodispersive melamine formaldehyde particles is created in the background of an Argon plasma. The crystal formation is frequently found to be accompanied by the presence of one or more slightly heavier particles suspended a little below the monolayer. The interplay of one such test particle with the crystal is investigated for two distinct cases—(i) when the particle remains confined (trapped) in the space below the crystal and (ii) when it interacts for a short while with the crystal and then moves out of the vicinity. The trapped particle orbit induces permanent structural changes in the crystal in the form of microcracks, and these changes are identified using a variety of diagnostic analyses. The cracks can be enhanced by energizing the test particle with an incident laser. The passing particle, on the other hand, induces only transient changes in the crystal from which it is able to recover and return to its initial state in a clear demonstration of the viscoelastic property of a strongly coupled system.

Melting transition of two-dimensional complex plasma crystal in the DC glow discharge

The formation of self-consistent dust crystal and its melting is a well- known phenomenon in rf generated plasmas but remains challenging in DC glow discharge plasmas. Here, we report the melting of a two- dimensional dusty plasma crystal, suspended in the cathode sheath of a DC glow discharge plasma. The experiments are carried out in a Dusty Plasma Experimental (DPEx) device which consists of a circular powered electrode and an extended grounded cathode tray. A stationary crystal of melamine formaldehyde particles is formed in a background of Argon plasma between a pair of confining strips that are placed on the cathode. The stable structure breaks and transition to a fluid state when the neutral pressure is reduced. The neutral pressure range where this melting transition is observed is an order of magnitude less than what is typically reported in rf discharge plasma. The transition is confirmed by evaluating the variation in different characteristic parameters such as the pair correlation function, Voronoi diagram, local bond order parameter, defect fraction and dust kinetic temperature as a function of background neutral pressure. For instance, the average bond order parameter (Ψ6) reduces from 0.87 to 0.4 when the neutral pressure is reduced from 15 to 11 Pa. The asymmetry of the electrode is a special feature that is believed to enable the formation of the plasma crystal.

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.

Экспериментальные исследования двумерных комплексных плазменных кристаллов: волны и неустойчивости

Экспериментальные исследования двумерных комплексных плазменных кристаллов: волны и неустойчивости

New radio-frequency setup for studying large 2D complex plasma crystals

Complex plasma crystals are popular model systems where various plasma-specific or generic phenomena can be studied at the level of individual particles. Addressing the growing need for larger two-dimensional (2D) plasma crystals, a new plasma setup was built at the DLR Institute of Materials Physics in Space. The setup allows obtaining larger than before, highly ordered 2D plasma crystals and exploring new parameter ranges. It is based on a relatively large (90 cm in diameter) vacuum chamber where a capacitively coupled radio-frequency discharge is used to levitate polymer microparticles. The discharge is created between the lower rf electrode and the grounded chamber walls, the particles levitate in the plasma (pre)sheath above the electrode and are observed by video microscopy through the large top glass window and through the side windows. The first observations of plasma crystals in the new setup are reported.

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.

Electric field in two-dimensional complex plasma crystal: Simulated lattices

We focus on molecular dynamics simulated two-dimensional complex plasma crystals. We use rigid walls as a confinement force and produce square and rectangular crystals. We report various types of two-row crystals. The narrow and long crystals are likely to be used as wigglers; therefore, we simulate such crystals. Also, we analyze the electric fields of simulated crystals. A bit change in lattice parameters can change the internal structures of crystals and their electric fields notably. These parameters are the number of grains, grains charge, length, and width of the crystal. With the help of electric fields, we show the details of crystal structures.

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.

Narrowband attenuation at 157 GHz by a plasma photonic crystal

A plasma photonic crystal operating as a notch filter at 157 GHz () has been demonstrated. Comprising a 5 × 10 array of microplasma jets, having a pitch and jet diameter of 1 mm and 400 µm, respectively, this two-dimensional plasma crystal exhibits an unexpectedly narrow stopband (Δ = 1.0 GHz (FWHM) = 0.6% ) and a maximum, time-averaged attenuation of 5% at 157.0 GHz. Simulations accurately predict the position of line center, and the assumption of a time-averaged electron density of 3 × 1013 cm−3 is necessary for the predicted magnitude of peak attenuation (at 157 GHz) to be in agreement with experiment. Reconfigurable plasma photonic crystals, synthesized from microcavity plasmas and providing electromagnetic functionality in the 100 GHz–1 THz spectral region (300 µm ⩽ λ ⩽ 3 mm), are now feasible.

Determination of yield stress of 2D (Yukawa) dusty plasma

Elastic and plastic deformations of a two-dimensional (2D) dusty plasma crystal under shear stresses are investigated using a numerical simulation. Our simulation mimics experiments that start with a crystal that is then manipulated by a pair of laser beams separated by a gap. In a pair of rectangular regions, we apply two equal but oppositely directed forces, to induce a shear deformation in the gap between. These external forces are increased incrementally to examine the elastic behavior, plasticity, and liquid flows. In the low-force elastic limit, a measurement of the shear modulus is obtained, which agrees with a theoretical value based on a sound speed. For larger forces resulting in plastic deformation, we determine the yield stress, which is found to agree with a common theoretical model for the critical yield stress, after accounting for the dimensionality for 2D.

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 etal. [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.

Forced mode coupling in 2D complex plasmas

It is demonstrated experimentally that the plasma-wake–mediated resonant coupling of the longitudinal in-plane and out-of-plane collective motion in two-dimensional plasma crystals can be induced by applying an external forcing. The experimental observations are supported by numerical analysis of the forced collective dynamics of particles with the wake-mediated interactions.

Anisotropic confinement effects in a two-dimensional plasma crystal.

The spectral asymmetry of the wave-energy distribution of dust particles during mode-coupling-induced melting, observed for the first time in plasma crystals by Couëdel etal. [Phys. Rev. E 89, 053108 (2014)PLEEE81539-375510.1103/PhysRevE.89.053108], is studied theoretically and by molecular-dynamics simulations. It is shown that an anisotropy of the well confining the microparticles selects the directions of preferred particle motion. The observed differences in intensity of waves of opposed directions are explained by a nonvanishing phonon flux. Anisotropic phonon scattering by defects and Umklapp scattering are proposed as possible reasons for the mean phonon flux.

Wave modes in shear-deformed two-dimensional plasma crystals.

A theory of wave modes in shear-deformed two-dimensional plasma crystals is presented. Modification of the dispersion relations upon the pure and simple shear, and the resulting effect on the onset of the mode-coupling instability, are studied. In particular, it is explained why the velocity fluctuation spectra measured in experiments with sheared crystals exhibit asymmetric "hot spots": It is shown that the coupling of the in-plane compressional and the out-of-plane modes, leading to the formation of an unstable hybrid mode and generation of the hot spots, is enhanced in a certain direction determined by deformation.