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.

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.

Instabilities in bilayer complex plasmas: Wake-induced mode coupling.

Stability principles for bilayer complex plasmas are studied. To mimic bilayer crystals and identify the main melting mechanism of such structures, a simple binary-chain model is employed. This approach provides adequate representation of the collective effects and accurate description of the interaction nonreciprocity, associated with the wake-mediated interparticle forces. It is shown that the wake-induced coupling of the wave modes sustained in different crystalline layers can trigger the dynamical instability. Furthermore, the mode coupling is demonstrated to be a universal instability mechanism, operating also in bilayer fluids. General stability criteria for the crystalline and fluid bilayers are derived.

Flame propagation in two-dimensional solids: Particle-resolved studies with complex plasmas.

Using two-dimensional (2D) complex plasmas as an experimental model system, particle-resolved studies of flame propagation in classical 2D solids are carried out. Combining experiments, theory, and molecular dynamics simulations, we demonstrate that the mode-coupling instability operating in 2D complex plasmas reveals all essential features of combustion, such as an activated heat release, two-zone structure of the self-similar temperature profile ("flame front"), as well as thermal expansion of the medium and temperature saturation behind the front. The presented results are of relevance for various fields ranging from combustion and thermochemistry, to chemical physics and synthesis of materials.

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.

Simple estimation of thermodynamic properties of Yukawa systems.

A simple analytical approach to estimate thermodynamic properties of model Yukawa systems is presented. The approach extends the traditional Debye-Hückel theory into the regime of moderate coupling and is able to qualitatively reproduce thermodynamics of Yukawa systems up to the fluid-solid phase transition. The simplistic equation of state (pressure equation) is derived and applied to the hydrodynamic description of the longitudinal waves in Yukawa fluids. The relevance of this study to the topic of complex (dusty) plasmas is discussed.

Mode-coupling instability in a fluid two-dimensional complex plasma.

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.

Synchronization of particle motion induced by mode coupling in a two-dimensional plasma crystal.

The kinematics of dust particles during the early stage of mode-coupling induced melting of a two-dimensional plasma crystal is explored. It is found that the formation of the hybrid mode causes the particle vibrations to partially synchronize at the hybrid frequency. Phase- and frequency-locked hybrid particle motion in both vertical and horizontal directions (hybrid mode) is observed. The system self-organizes in a rhythmic pattern of alternating in-phase and antiphase oscillating chains of particles. The spatial orientation of the synchronization pattern correlates well with the directions of the maximal increment of the shear-free hybrid mode.

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

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

High-voltage nanosecond pulses in a low-pressure radio-frequency discharge.

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 µs (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.

Onset of cavity deformation upon subsonic motion of a projectile in a fluid complex plasma.

We study the deformation of a cavity around a large projectile moving with subsonic velocity in the cloud of small dust particles. To solve this problem, we employ the Navier-Stokes equation for a compressible fluid with due regard for friction between dust particles and atoms of neutral gas. The solution shows that due to friction, the pressure of a dust cloud at the surface of a cavity around the projectile can become negative, which entails the emergence of a considerable asymmetry of the cavity, i.e., the cavity deformation. Corresponding threshold velocity is calculated, which is found to decrease with increasing cavity size. Measurement of such velocity makes it possible to estimate the static pressure inside the dust cloud.

Anisotropic shear melting and recrystallization of a two-dimensional complex plasma.

A two-dimensional plasma crystal was melted by suddenly applying localized shear stress. A stripe of particles in the crystal was pushed by the radiation pressure force of a laser beam. We found that the response of the plasma crystal to stress and the eventual shear melting depended strongly on the crystal's angular orientation relative to the laser beam. Shear stress and strain rate were measured, from which the spatially resolved shear viscosity was calculated. The latter was shown to have minima in the regions with highest strain rate, thus demonstrating shear thinning. Shear-induced reordering was observed in the steady-state flow, where particles formed strings aligned in the flow direction.

Coulomb expansion: analytical solutions.

Exact and approximate analytical solutions are presented, describing expansion of a cloud of charged particles in one, two, and three dimensions (assuming the planar, axial, and spherical symmetries, respectively). The expansion occurs in a gas or dilute plasma, where the screening is unimportant, so that particles interact with each other via Coulomb repulsive forces. It is shown that, irrespective of dimensionality, the density distribution remains homogeneous across the cloud and the velocity increases linearly towards the cloud boundary. The density evolution obeys a universal dependence, asymptotically decreasing with time as t(-1). It is also shown that in the presence of an inhomogeneous external field the interparticle repulsion becomes negligible at an early stage of expansion and then the density decreases with time exponentially.

Kinetics of the melting front in two-dimensional plasma crystals: Complementary analysis with the particle image and particle tracking velocimetries.

Melting of a two-dimensional plasma crystal occurring due to a mode-coupling instability is studied using particle tracking and particle image velocimetry techniques. By combining these techniques, it is possible to identify the location of a propagating melting front and find a characteristic scale length for the temperature gradient across the front. It is found that the measurements of heat transport are consistent with a simple two-dimensional model allowing us to estimate the thermal diffusivity. The measured values for the thermal diffusivity are consistent with previously measured values.

Fluid-solid phase transitions in three-dimensional complex plasmas under microgravity conditions.

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.

Nonviscous motion of a slow particle in a dust crystal under microgravity conditions.

Subsonic motion of a large particle moving through the bulk of a dust crystal formed by negatively charged small particles is investigated using the PK-3 Plus laboratory onboard the International Space Station. Tracing the particle trajectories shows that the large particle moves almost freely through the bulk of the plasma crystal, while dust particles move along characteristic α-shaped pathways near the large particle. In the hydrodynamic approximation, we develop a theory of nonviscous dust particle motion about a large particle and calculate particle trajectories. Good agreement with experiment validates our approach.

Microstructure of a liquid two-dimensional dusty plasma under shear.

The microstructure of a strongly coupled liquid undergoing a shear flow was studied experimentally. The liquid was a shear melted two-dimensional plasma crystal, i.e., a single-layer suspension of micrometer-size particles in a rf discharge plasma. Trajectories of particles were measured using video microscopy. The resulting microstructure was anisotropic, with compressional and extensional axes at around ±45° to the flow direction. Corresponding ellipticity of the pair correlation function g(r) or static structure factor S(k) gives the (normalized) shear rate of the flow.

Freezing and melting of 3D complex plasma structures under microgravity conditions driven by neutral gas pressure manipulation.

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. The evolution of complex plasma structural properties upon pressure variation is studied. Theoretical estimates allow us to identify the main factors responsible for the observed behavior.

Complex plasmas in external fields: the role of non-hamiltonian interactions.

Dedicated experiments with strongly coupled complex plasmas in external electric fields were carried out under microgravity conditions using the PK-4 dc discharge setup. The focus was put on the comparative analysis of the formation of stringlike anisotropic structures due to reciprocal (hamiltonian) and nonreciprocal (non-hamiltonian) interactions between microparticles (induced by ac and dc fields, respectively). The experiments complemented by numerical simulations demonstrate that the responses of complex plasmas in these two regimes are drastically different. It is suggested that the observed difference is a manifestation of intrinsic thermodynamic openness of driven strongly coupled systems.

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

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