Yukawa Balls Research Articles

Experimental determination of phase transitions by means of configurational entropies in finite Yukawa balls.

The phase transition of finite Yukawa balls (ordered systems of microspheres in a gaseous plasma environment) with less than 100 particles is studied experimentally by means of configurational entropies. We have developed cylindrical two- and three-particle-correlation functions to measure these entropies for multiple cluster sizes over a wide temperature range. The cluster temperature is finely tuned using a stochastic laser heating setup. It is shown that the correlation functions give a detailed insight into the structural properties of the cluster. The derived configurational entropies give a clear indication of the transition temperature from a solid-like to a fluid-like state. Comparing the transition temperatures of different sized clusters it is found that the transition temperature increases with cluster size in general agreement with theoretical predictions.

Plasma crystals: experiments and simulation

Dusty plasmas are a well accessible system to study crystallization of charged-particle systems at room temperature. The large mass compared to atomic particles dramatically slows down the particle velocities. The high transparency of the system allows to trace simultaneously the motion of all particles with quasi-atomic resolution. After a brief overview, the progress in this field is exemplified by studies of spherical three-dimensional plasma crystals, the so-called Yukawa balls. The static structure and eigenmodes are explained in simple terms. It is shown that shielding modifies the expansion of a Yukawa ball from a self-similar explosion to a continuous ablation process that starts at the surface. The experimental progress with three-dimensional diagnostics and laser heating and sophisticated methods for visualising the order inside the shell structure are described. Together with quantifying the diffusion coefficient these investigations reveal the details of the solid-liquid phase transition. Besides thermodynamic aspects, the liquid phase of dusty plasmas also gives access to hydrodynamic phenomena at the individual particle scale.

Collisional and collisionless expansion of Yukawa balls

The expansion of Yukawa balls is studied by means of molecular dynamics simulations of collisionless and collisional situations. High computation speed was achieved by using the parallel computing power of graphics processing units. When the radius of the Yukawa ball is large compared to the shielding length, the expansion process starts with the blow-off of the outermost layer. A rarefactive wave subsequently propagates radially inward at the speed of longitudinal phonons. This mechanism is fundamentally different from Coulomb explosions, which employ a self-similar expansion of the entire system. In the collisionless limit, the outer layers carry away most of the available energy. The simulations are compared with analytical estimates. In the collisional case, the expansion process can be described by a nonlinear diffusion equation that is a special case of the porous medium equation.

Crystal and fluid modes in three-dimensional finite dust clouds

The spectral properties of three-dimensional dust clusters confined in gaseous discharges are investigated using both a fluid mode description and the normal mode analysis (NMA). The modes are analysed for crystalline clusters as well as for laser-heated fluid-like clusters. It is shown that even for clusters with low particle numbers and under presence of damping fluid modes can be identified. Laser-heating leads to the excitation of several, mainly transverse, modes. The mode frequencies are found to be nearly independent of the coupling parameter and support the predictions of the underlying theory. The NMA and the fluid mode spectra demonstrate that the wakefield attraction is present for the experimentally observed Yukawa balls at low pressure. Both methods complement each other, since NMA is more suitable for crystalline clusters, whereas the fluid modes allow to explore even fluid-like dust clouds.

Ion-streaming induced order transition in three-dimensional dust clusters

Dust dynamics simulations utilizing a dynamical screening approach are performed to study the effect of ion-streaming on the self-organized structures in a three-dimensional spherically confined complex (dusty) plasma. Varying the Mach number M, the ratio of ion drift velocity to the sound velocity, the simulations reproduce the experimentally observed cluster configurations in the two limiting cases: at M = 0 strongly correlated crystalline structures consisting of nested spherical shells (Yukawa balls) and, for M ⩾ 1, flow-aligned dust chains, respectively. In addition, our simulations reveal a discontinuous transition between these two limits. It is found that already a moderate ion drift velocity (M ≈ 0.1 for the plasma conditions considered here) destabilizes the highly ordered Yukawa balls and initiates an abrupt melting transition. The critical value of M is found to be independent of the cluster size.

Melting scenarios for three-dimensional dusty plasma clusters

The melting transition of finite three-dimensional dust clouds (Yukawa balls) from a solid-like to a liquid-like state is systematically studied with high spatial and temporal resolution of the individual grains by means of stereoscopy. Two different melting scenarios are reported: Melting is induced first by an increase of plasma power, and second by laser-induced heating. The experiments confirm that melting starts with a loss of orientational correlation, followed by a loss of the radial order upon further heating. While the plasma-power melting is driven via the ion wakefield, laser heating provides a more equilibrium scenario. The internal loss of correlations is well captured by the triple correlation function (TCF) which is insensitive to particle exchanges and the rotation of the cluster as a whole. The critical Coulomb coupling parameter for N=35 is determined as Γ(crit)≈570. The experimental findings are in good agreement with thermodynamic Monte Carlo simulations.

On the influence of wakefields on three-dimensional particle arrangements

The role of wakefields on the three-dimensional (3D) particle arrangement in finite dust clouds at low neutral gas pressures is investigated experimentally. Using a novel stereoscopic digital in-line holography approach for the instantaneous measurement of the 3D particle positions, the structural properties of finite dust clouds are studied. The competition of a nested shell structure (known from Yukawa balls) and vertical particle chains (known for particle clouds confined in the plasma sheath) results in a markedly different particle arrangement. With experiments studying the dynamical response in a two-particle system for identical plasma and confinement conditions, we show that the presence of an ion focus in the wake of the particle is responsible for the observed structural differences.

Structure and Phase Transitions of Yukawa Balls

AbstractIn this review, an overview of structural properties and phase transitions in finite spherical dusty (complex) plasma crystals – so‐called Yukawa balls – is given. These novel kinds of Wigner crystals can be directly analyzed experimentally with video cameras. The experiments clearly reveal a shell structure and allow to determine the shell populations, to observe metastable states and transitions between configurations as well as phase transitions. The experimental observations of the static properties are well explained by a rather simple theoretical model which treats the dust particles as being confined by a parabolic potential and interacting via an isotropic Yukawa pair potential. The excitation properties of the Yukawa balls such as normal modes and the dynamic behavior, including the time‐dependent formation of the crystal requires, in addition, to include the effect of friction between the dust particles and the neutral gas. Aside from first‐principle molecular dynamics and Monte Carlo simulations several analytical approaches are reviewed which include shell models and a continuum theory. A summary of recent results and theory‐experiment comparisons is given and questions for future research activities are outlined (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modes of three-dimensional dust crystals in dusty plasmas

Three-dimensional finite systems of charged dust particles confined to concentric spherical shells in a dusty plasma, so-called "Yukawa balls," have been studied experimentally with respect to their dynamic properties. For that purpose, the three-dimensional thermal Brownian motion of the dust particles around their equilibrium positions was reconstructed with high accuracy. From that the dynamic properties in the form of mode patterns and frequencies are obtained from singular value decomposition and normal mode analysis. The dynamics of the Yukawa balls was found to be dominated by large-scale low-frequency shearlike modes.

Plasma Crystals - Structure and Dynamics

This overview describes the confinement and structure of two-dimensional plasma crystals. Phonons and Mach cones in monolayer systems can be used for diagnostic purposes. Three-dimensional plasma crystals are found as multilayer systems or as Yukawa balls. The differences between Coulomb and Yukawa balls are described by means of a simple model. Optical diagnostic methods for studying dynamical phenomena in three-dimensional plasma crystals are discussed.

Simulation of dust voids in complex plasmas

In dusty radio-frequency (RF) discharges under micro-gravity conditions often a void is observed, a dust free region in the discharge center. This void is generated by the drag of the positive ions pulled out of the discharge by the electric field. We have developed a hydrodynamic model for dusty RF discharges in argon to study the behaviour of the void and the interaction between the dust and the plasma background. The model is based on a recently developed theory for the ion drag force and the charging of the dust.With this model, we studied the plasma inside the void and obtained an understanding of the way it is sustained by heat generated in the surrounding dust cloud. When this heating mechanism is suppressed by lowering the RF power, the plasma density inside the void decreases, even below the level where the void collapses, as was recently shown in experiments on board the International Space Station. In this paper we present results of simulations of this collapse.At reduced power levels the collapsed central cloud behaves as an electronegative plasma with corresponding low time-averaged electric fields. This enables the creation of relatively homogeneous Yukawa balls, containing more than 100 000 particles. On earth, thermophoresis can be used to balance gravity and obtain similar dust distributions.

Energy landscape in 3D finite dust clusters derived from shell transitions

Experiments on three-dimensional (3D) spherical arrangements of charged dust particles ina plasma confinement (Yukawa balls) are presented. The plasma trap provides a3D isotropic harmonic confinement in which a small number of dust particles,N<100, are trapped. The particle arrangement is recorded using stereoscopic imaging. Transitionsbetween different configurations of Yukawa balls are observed that allow us todetermine the energy landscape in such a finite cluster. The experiments have beencompared to molecular dynamics (MD) simulations with very good agreement.

Shell transitions between metastable states of Yukawa balls

Spherical dust clusters composed of several concentric shells are experimentally investigated with particular interest on transitions between different configurations and transitions of particles between different shells. Transitions between different ground and metastable configurations are frequently observed. The experimental analysis allows us to derive the energy differences of different configurations from particles traveling between shells. The observed transitions and transition probabilities are compared to molecular dynamics simulations.

Experiments on metastable states of three-dimensional trapped particle clusters

Small three-dimensional charged-dust clusters, so-called Yukawa balls, are analyzed with regard to their construction principle. For that purpose, in an experimental approach, different (metastable) configurations of clusters with fixed particle number (N&amp;lt;100) have been generated under identical plasma and trapping conditions. Metastable states are frequently observed. In combination with molecular dynamics simulations, it is shown that particle interaction with screening strongly affects the appearance probabilities of metastable configurations. Small clusters show different average density distributions with screened interaction compared to pure Coulomb, although having the same ground state configurations.

Structural and dynamical properties of Yukawa balls

To study the structural and dynamical properties of finite 3D dust clouds (Yukawa balls) new diagnostic tools have been developed. This contribution describes the progress towards 3D diagnostics for measuring the particle positions. It is shown that these diagnostics are capable of investigating the structural and dynamical properties of Yukawa balls and gaining insight into their basic construction principles.

Stereoscopy on Yukawa Balls in Dusty Plasmas

The static properties and the dynamics of spherically symmetric 3-D particle clusters (Yukawa balls) are determined experimentally. For that purpose, the stereoscopy with two standard video cameras as well as a three-camera high-speed system is used to simultaneously measure the positions of all particles in a Yukawa ball. The order phenomena, like shell configuration and occupation numbers, are found to be in agreement with the models and simulations. The normal modes' analysis for the Yukawa ball is presented

Three-dimensional stereoscopy of Yukawa (Coulomb) balls in dusty plasmas

A stereoscopic approach with standard video cameras for positioning and tracking of micrometer sized polymer particles in a radio-frequency gas discharge is presented. The stereoscopy is applied to simultaneously determine the positions of all particles in a three-dimensional strongly coupled spherical dusty plasma (Yukawa ball). The accuracy of the stereoscopic method is discussed. The shell structure and the occupation number of various Yukawa balls are determined and compared to recent simulations and models.