Coupling of non-crossing wave modes in a two-dimensional plasma crystal

We report an experimental observation of 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.Comment: 4 figures, 5 pages, accepted for publication in PRL Nov 201

Observation of particle pairing in a two-dimensional plasma crystal

The observation is presented of naturally occurring pairing of particles and their cooperative drift in a two-dimensional plasma crystal. A single layer of plastic microspheres was suspended in the plasma sheath of a capacitively coupled rf discharge in argon at a low pressure of 1 Pa. The particle dynamics were studied by combining the top-view and side-view imaging of the suspension. Cross analysis of the particle trajectories allowed us to identify naturally occurring metastable pairs of particles. The lifetime of pairs was long enough for their reliable identification.Comment: 5 pages, 4 figure

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 et al. [Phys. Rev. E 89, 021101(R) (2014)], is explained in simulations and theory. We use the simple model of a pointlike ion wake charge to reproduce this intriguing effect in simulations, allowing for a detailed investigation and a deeper understanding of the underlying dynamics. We show that the nonreciprocity of the particle interaction, owing to the wake charges, is responsible for a broken symmetry of the channel that enables a persistent self-propelled motion of the extra particle. We find good agreement of the terminal extra-particle velocity with our theoretical considerations and with experiments.Comment: 7 pages, 4 figures, PRL (https://journals.aps.org/prl/), updated version with correct author affiliation

Autowaves in a dc complex plasma confined behind a de Laval nozzle

Experiments to explore stability conditions and topology of a dense microparticle cloud supported against gravity by a gas flow were carried out. By using a nozzle shaped glass insert within the glass tube of a dc discharge plasma chamber a weakly ionized gas flow through a de Laval nozzle was produced. The experiments were performed using neon gas at a pressure of 100 Pa and melamine-formaldehyde particles with a diameter of 3.43 {\mu}m. The capturing and stable global confining of the particles behind the nozzle in the plasma were demonstrated. The particles inside the cloud behaved as a single convection cell inhomogeneously structured along the nozzle axis in a tube-like manner. The pulsed acceleration localized in the very head of the cloud mediated by collective plasma-particle interactions and the resulting wave pattern were studied in detail.Comment: 6 pages, 4 figure

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, comparison with theory showed good agreement. The effect of the plasma wakes on the dispersion relation is briefly discussed.Comment: submitted to Physical Review Letter

Wave mode coupling due to plasma wakes in two-dimensional plasma crystals: In-depth view

Experiments with two-dimensional (2D) plasma crystals are usually carried out in rf plasma sheaths, where the interparticle interactions are modified due to the presence of plasma wakes. The wake-mediated interactions result in the coupling between wave modes in 2D crystals, which can trigger the mode-coupling instability and cause melting. The theory predicts a number of distinct fingerprints to be observed upon the instability onset, such as the emergence of a new hybrid mode, a critical angular dependence, a mixed polarization, and distinct thresholds. In this paper we summarize these key features and provide their detailed discussion, analyze the critical dependence on experimental parameters, and highlight the outstanding issues

Formation of singularities on the surface of a liquid metal in a strong electric field

The nonlinear dynamics of the free surface of an ideal conducting liquid in a strong external electric field is studied. It is establish that the equations of motion for such a liquid can be solved in the approximation in which the surface deviates from a plane by small angles. This makes it possible to show that on an initially smooth surface for almost any initial conditions points with an infinite curvature corresponding to branch points of the root type can form in a finite time.Comment: 14 page

On separable Fokker-Planck equations with a constant diagonal diffusion matrix

We classify (1+3)-dimensional Fokker-Planck equations with a constant diagonal diffusion matrix that are solvable by the method of separation of variables. As a result, we get possible forms of the drift coefficients $B_1(\vec x),B_2(\vec x),B_3(\vec x)$ providing separability of the corresponding Fokker-Planck equations and carry out variable separation in the latter. It is established, in particular, that the necessary condition for the Fokker-Planck equation to be separable is that the drift coefficients $\vec B(\vec x)$ must be linear. We also find the necessary condition for R-separability of the Fokker-Planck equation. Furthermore, exact solutions of the Fokker-Planck equation with separated variables are constructedComment: 20 pages, LaTe

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

Dedicated experiments on melting of 2D 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 (DL) wave modes simultaneously, it is unambiguously demonstrated that the melting occurs due to the resonance coupling between two of the DL 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.Comment: 4 pages, submitted to Physical Review Letter