Dust Coulomb balls: three-dimensional plasma crystals

Melting curve of two-dimensional Yukawa systems predicted by isomorph theory

The analytical expression for the conditions of the solid-fluid phase transition, i.e., the melting curve, for two-dimensional (2D) Yukawa systems is derived theoretically from the isomorph theory. To demonstrate that the isomorph theory is applicable to 2D Yukawa systems, molecular dynamical simulations are performed under various conditions. Based on the isomorph theory, the analytical isomorphic curves of 2D Yukawa systems are derived using the local effective power-law exponent of the Yukawa potential. From the obtained analytical isomorphic curves, the melting curve of 2D Yukawa systems is directly determined using only two known melting points. The determined melting curve of 2D Yukawa systems well agrees with the previous obtained melting results using completely different approaches.

Universal scaling of transverse sound speed and its isomorphic property in Yukawa fluids

Molecular dynamical simulations are performed to investigate the scaling of the transverse sound speed in two-dimensional (2D) and 3D Yukawa fluids. From the calculated diagnostics of the radial distribution function, the mean-squared displacement, and the Pearson correlation coefficient, the approximate isomorphic curves for 2D and 3D liquidlike Yukawa systems are obtained. It is found that the structure and dynamics of 2D and 3D liquidlike Yukawa systems exhibit the isomorphic property under the conditions of the same relative coupling parameter Γ/Γ_{m}=const. It is demonstrated that the reduced transverse sound speed, i.e., the ratio of the transverse sound speed to the thermal speed, is an isomorph invariant, which is a quasiuniversal function of Γ/Γ_{m}. The obtained isomorph invariant of the reduced transverse sound speed can be useful to estimate the transverse sound speed, or determine the coupling strength, with applications to dusty (complex) plasma or colloidal systems.

Structure of a two-dimensional superparamagnetic system in a quadratic trap

Ground-state structures of a two-dimensional (2D) system composed of superparamagnetic charged particles are investigated by means of molecular dynamics simulation. The charged particles trapped in a quadratic potential interact with each other via the repulsive, attractive, and magnetic dipole-dipole forces. Simulations are performed within two regimes: a one-component system and a two-component system where the charged particles have the identical charge-to-mass ratio. The effects of magnetic dipole-dipole interaction, mixing ratio of the two species and confinement frequency on the ground-state structures are discussed. It is found that as the strength of the magnetic dipole increases, the charged particles tend to self-organize into chainlike structures. The two species particles exhibit different structural features, depending on the competition of electrostatic repulsive interaction, magnetic dipole-dipole interaction and confinement force. The potential lanes are observed through analyzing the global potential of the magnetic particles, which guide the unmagnetic particles aligning themselves in the direction of the potential lanes.

Experimental determination of shock speed versus exciter speed in a two-dimensional dusty plasma

A shock that is continuously driven by a moving exciter will propagate at a speed that depends on the exciter speed. We obtained this dependence experimentally, in a strongly coupled dusty plasma that was prepared as a single two-dimensional layer of charged microparticles. Attaining this result required an experimental advance, developing a method of driving a shock continuously, which we did using an exciter moving at a constant supersonic speed, analogous to a piston in a cylinder. The resulting compressional pulse was a shock that propagated steadily without weakening, ahead of the moving exciter. We compare our experimental results to an empirical form M_{shock}=1+sM_{exciter}, and to the prediction of a recent simulation.

Distinguishing noisy crystalline structures using bond orientational order parameters

The bond orientational order parameters originally introduced by Steinhardt et al. (Phys. Rev. B 28, 784 (1983)) are a common tool for local structure characterization in soft matter studies. Recently, Mickel et al. (J. Chem. Phys. 138, 044501 (2013)) highlighted problems of the bond orientational order parameters due to the ambiguity of the underlying neighbourhood definition. Here we show the difficulties to distinguish common structures like FCC- and BCC-based structures with the suggested neighbourhood definitions when noise is introduced. We propose a simple improvement to the neighbourhood definition that results in robust and continuous bond orientational order parameters with which we can accurately distinguish crystal structures even when noise is present.

Complex structures generated by competing interactions in harmonically confined colloidal suspensions

We investigate the structural properties of colloidal particle systems interacting via an isotropic pair potential and confined by a three-dimensional harmonic potential. The interaction potential has a repulsive-attractive-repulsive profile that varies with the interparticle distance (also known as a 'mermaid' potential). We performed Langevin dynamics simulations to find the equilibrium configurations of the system. We show that particles can self-assemble in complex structural patterns, such as compact disks, fringed disks, rods, spherical clusters with superficial entrances among others. Also, for particular values of the parameters of the interaction potential, we could identify that some configurations were formed by quasi two-dimensional (2D) structures which are stable for 2D systems.

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.

Brownian motion of a circle swimmer in a harmonic trap

We study the dynamics of a Brownian circle swimmer with a time-dependent self-propulsion velocity in an external temporally varying harmonic potential. For several situations, the noise-free swimming paths, the noise-averaged mean trajectories, and the mean-square displacements are calculated analytically or by computer simulation. Based on our results, we discuss optimal swimming strategies in order to explore a maximum spatial range around the trap center. In particular, we find a resonance situation for the maximum escape distance as a function of the various frequencies in the system. Moreover, the influence of the Brownian noise is analyzed by comparing noise-free trajectories at zero temperature with the corresponding noise-averaged trajectories at finite temperature. The latter reveal various complex self-similar spiral or rosette-like patterns. Our predictions can be tested in experiments on artificial and biological microswimmers under dynamical external confinement.

Finite-temperature quantum effects on confined charges

A quantum system of N Coulomb charges confined within a harmonic trap is considered over a wide range of densities and temperatures. A recently described construction of an equivalent classical system is applied in order to exploit the rather complete classical description of harmonic confinement via liquid-state theory. Here, the effects of quantum mechanics on that representation are described with attention focused on the origin and nature of shell structure. The analysis extends from the classical strong Coulomb coupling conditions of dusty plasmas to the opposite limit of low temperatures and large densities characteristic of "warm, dense matter."

Shell formation in short like-charged polyelectrolytes in a harmonic trap

Inspired by recent experiments and simulations on pattern formation in biomolecules by optical tweezers, a theoretical description based on the reference interaction site model (RISM) is developed to calculate the equilibrium density profiles of small polyelectrolytes in an external potential. The formalism is applied to the specific case of a finite number of Gaussian and rodlike polyelectrolytes trapped in a harmonic potential. The density profiles of the polyelectrolytes are studied over a range of lengths and numbers of polyelectrolytes in the trap, and the strength of the trap potential. For smaller polymers we recover the results for point charges. In the mean field limit the longer polymers, unlike point charges, form a shell at the boundary layer. When the interpolymer correlations are included, the density profiles of the polymers show sharp shells even at weaker trap strengths. The implications of these results are discussed.

Electron energy distribution in a dusty plasma: analytical approach

Analytical expressions describing the electron energy distribution function (EEDF) in a dusty plasma are obtained from the homogeneous Boltzmann equation for electrons. The expressions are derived neglecting electron-electron collisions, as well as transformation of high-energy electrons into low-energy electrons at inelastic electron-atom collisions. At large electron energies, the quasiclassical approach for calculation of the EEDF is applied. For the moderate energies, we account for inelastic electron-atom collisions in the dust-free case and both inelastic electron-atom and electron-dust collisions in the dusty plasma case. Using these analytical expressions and the balance equation for dust charging, the electron energy distribution function, the effective electron temperature, the dust charge, and the dust surface potential are obtained for different dust radii and densities, as well as for different electron densities and radio-frequency (rf) field amplitudes and frequencies. The dusty plasma parameters are compared with those calculated numerically by a finite-difference method taking into account electron-electron collisions and the transformation of high-energy electrons at inelastic electron-neutral collisions. It is shown that the analytical expressions can be used for calculation of the EEDF and dusty plasma parameters at typical experimental conditions, in particular, in the positive column of a direct-current glow discharge and in the case of an rf plasma maintained by an electric field with frequency f=13.56MHz.

Angular melting scenarios in binary dusty-plasma Coulomb balls: magic versus normal clusters

Molecular-dynamic simulations were performed in order to investigate the melting processes of isotropically confined binary systems. We considered two species of particles, which differ by their amount of electric charge. A Lindemann type of criterion was used to determine the angular melting temperature. We demonstrate that the magic-to-normal cluster transition can evolve in two distinct ways, that is, through a structural phase transition of the first order or via a smooth transition where an increase of the shells' width leads to a continuous decreasing mechanical stability of the system. Moreover, for large systems, we demonstrate that the internal cluster exerts a minor effect on the mechanical stability of the external shell. Furthermore, we show that highly symmetric configurations, such as those found for multiple ring structures, have large mechanical stability, i.e., high angular melting temperature.

Computer tomography of large dust clouds in complex plasmas

The dust density is a central parameter of a dusty plasma. Here, a tomography setup for the determination of the three-dimensionally resolved density distribution of spatially extended dust clouds is presented. The dust clouds consist of micron-sized particles confined in a radio frequency argon plasma, where they fill almost the entire discharge volume. First, a line-of-sight integrated dust density is obtained from extinction measurements, where the incident light from an LED panel is scattered and absorbed by the dust. Performing these extinction measurements from many different angles allows the reconstruction of the 3D dust density distribution, analogous to a computer tomography in medical applications.

Structural properties of anisotropically confined binary Coulomb balls

We investigate the structural properties of a small binary system of dusty plasma subjected to an anisotropic external confinement. We have found that the ground state can form various symmetrical configurations, which generally correspond to variations of a multiple-ring structure. The presence of such structures is given through a detailed phase diagram constructed for the systems with N=18 and 24 particles. Furthermore, we show that the configurations of multiple rings can present a persistent behavior for the case in which the number of less-charged particles is equal to a multiple of the number of particles per ring. Finally, we discuss the main characteristics of the transitions of first and second orders since these are related to the main configurational changes of the ground states.

Symbolic transfer entropy analysis of the dust interaction in the presence of wakefields in dusty plasmas

The method of symbolic transfer entropy has been applied to analyze the behavior of charged-particle systems under the influence of an ion focus (wakefield) in a dusty plasma. Using long-run experiments under various plasma and trapping conditions, it is revealed from the transfer entropy that information is transported from the upper particle in an ion flow to the lower. The information transfer increases with smaller interparticle distance and with reduced height in the sheath. This can be consistently explained by the formation of the ion focus by an ion flow in the sheath. From the analysis of two-particle and many-particle systems, the symbolic entropy transfer can be judged as a reliable measure for information asymmetry, and hence interaction asymmetry, in dusty plasma systems.

Network analysis of three-dimensional complex plasma clusters in a rotating electric field

Network analysis was used to study the structure and time evolution of driven three-dimensional complex plasma clusters. The clusters were created by suspending micron-size particles in a glass box placed on top of the rf electrode in a capacitively coupled discharge. The particles were highly charged and manipulated by an external electric field that had a constant magnitude and uniformly rotated in the horizontal plane. Depending on the frequency of the applied electric field, the clusters rotated in the direction of the electric field or remained stationary. The positions of all particles were measured using stereoscopic digital in-line holography. The network analysis revealed the interplay between two competing symmetries in the cluster. The rotating cluster was shown to be more cylindrical than the nonrotating cluster. The emergence of vertical strings of particles was also confirmed.

Nonequilibrium finite dust clusters: connecting normal modes and wakefields

The dynamic properties of finite three-dimensional dust clusters in a dusty plasma under the influence of an ion focus are studied by normal modes. The mode analysis has been extended to account for the ion focus using the point-charge model for the horizontal interaction of the dust particles. From that, an analytical model for a few-particle system is derived accounting for three distinct dynamical regimes at different focus strengths, namely, absolutely unstable and fully stable configurations as well as an unstable oscillatory regime. The techniques of normal mode analysis (NMA) and instantaneous normal modes (INM) extended by the ion focus have been applied to dust systems in the experiment and compared to the model. From this, the ion focus strength has been derived. The specific sensitivity of NMA and INM allows one to identify equilibrium configurations in this nonequilibrium environment for these finite clusters.

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.

Structural ordering of trapped colloids with competing interactions

The structure of colloids with competing interactions which are confined in a harmonic external trap potential is analyzed numerically by energy minimization in two spatial dimensions. A wealth of different cluster structures is found to be stable including clusters with a fringed outer rim (reminiscent to an ornamental border), clusters perforated with voids, as well as clusters with a crystalline core and a disordered rim. All cluster structures occur in a two-dimensional parameter space. The structural ordering can therefore be efficiently tuned by changing few parameters only providing access to a controlled fabrication of colloidal clusters.

Thermal energy density of dust in dusty plasmas: experiment and theory

A surprising observation in dusty plasma experiments is that the dust thermal energy density, P_{d}∝n_{d}T_{d}, is typically much greater than n_{d}T_{n} (where n_{d} and T_{d} are the dust density and temperature, and T_{n} is the neutral temperature), even though the dust particles would be expected to be in thermal equilibrium with the neutrals. We show here, theoretically and experimentally, that the anomalously high dust thermal energy density can be accounted for if electrostatic interactions between the dust particles and the background plasma are taken into account. Thus, the dust pressure in dusty plasma is mostly of electrostatic origin.

Single string based global optimizer for geometry optimization in strongly coupled finite clusters: An adaptive mutation-driven strategy

We propose and implement a simple adaptive heuristic to optimize the geometries of clusters of point charges or ions with the ability to find the global minimum energy configurations. The approach uses random mutations of a single string encoding the geometry and accepts moves that decrease the energy. Mutation probability and mutation intensity are allowed to evolve adaptively on the basis of continuous evaluation of past explorations. The resulting algorithm has been called Completely Adaptive Random Mutation Hill Climbing method. We have implemented this method to search through the complex potential energy landscapes of parabolically confined 3D classical Coulomb clusters of hundreds or thousands of charges--usually found in high frequency discharge plasmas. The energy per particle (EN∕N) and its first and second differences, structural features, distribution of the oscillation frequencies of normal modes, etc., are analyzed as functions of confinement strength and the number of charges in the system. Certain magic numbers are identified. In order to test the feasibility of the algorithm in cluster geometry optimization on more complex energy landscapes, we have applied the algorithm for optimizing the geometries of MgO clusters, described by Coulomb-Born-Mayer potential and finding global minimum of some Lennard-Jones clusters. The convergence behavior of the algorithm compares favorably with those of other existing global optimizers.

From transport to disorder: thermodynamic properties of finite dust clouds

The quantities entropy and diffusion are measured for two- and three-dimensional (3D) dust clusters in the fluid state. Entropy and diffusion are predicted to be closely linked via unstable modes. The method of instantaneous normal modes is applied for various laser-heated clusters to determine these unstable modes and the corresponding diffusive properties. The configurational entropy is measured for 2D and 3D clusters from structural rearrangements. The entropy shows a threshold behavior at a critical temperature for the 2D clusters, allowing us to estimate a configurational melting temperature. Further, the entropic disorder increases for larger clusters. Finally, the predicted relation between entropy and unstable modes has been confirmed from our experiments for 2D systems, whereas 3D systems do not show such a clear correlation.

Pearl-necklace-like structures of microparticle strings observed in a dc complex plasma

The observation of a well-developed treelike string structure supported by a gas flow in a three-dimensional dc complex plasma is presented. The dynamically stable strings, comprising 10-20 particles, were up to 5 mm long. The experiments were performed using neon gas at a pressure of 100 Pa and melamine-formaldehyde particles with a diameter of 3.43 μm. Inside the discharge glass tube a nozzle had been built in to supply the controllable gas (plasma) flux intensity distribution along the tube. The walls of the nozzle were transparent for the laser light illuminating the particles. That gave the opportunity to closely study the particle dynamics deep inside the nozzle.

Madelung energy of Yukawa lattices

We propose a method to obtain an approximate closed form expression for the Madelung energy (ME) of Yukawa lattices. Such a method is applied for lattices of different topologies and dimensions. The obtained Madelung energies have a satisfactory accuracy for all ranges of the screening parameter κ of the Yukawa potential, and it becomes exact in the asymptotic limits κ→0 and κ→+∞. For instance, for the triangular lattice, the maximum relative error of the ME given by the method is about 0.0047. Also, satisfactory results are obtained for the one-component plasma limit. The Madelung constants of the two-dimensional hexagonal BN and square NaCl and the three-dimensional cubic NaCl crystals are estimated with a relative error of 0.004, 0.006, and 0.03, respectively. Finally, different ways to improve the method are presented and discussed.

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.

Resonant behavior of trapped Brownian particles in an oscillatory shear flow

The response of harmonically trapped Brownian particles to an externally imposed oscillatory shear flow is explored by theory and computer simulation. The special case of a single trapped particle is solved analytically. We present explicit results for the time-dependent density and the velocity distribution. The response of the many-body problem is studied by computer simulations. In particular, we investigate the influence of oscillatory shear flow on the internal modes of the cluster. As a function of the shear oscillation frequency, we find resonant behavior for certain (antisymmetric) normal modes, implying that they can be efficiently excited by oscillatory shear. Our results are verifiable in experiments on dusty plasmas and trapped colloidal dispersions.

Density functional theory for the ground state of spherically confined dusty plasma

The spatial structure of dusty plasma confined in a spherical microcavity has been investigated by use of the density functional theory for classical fluids, in which all particles undergo an isotropic harmonic potential and the interparticle interaction is described by the hard-core Yukawa potential. The fundamental measure theory of Rosenfeld and its modified versions have been used in the energy functional to incorporate hard-core interactions between particles. Based on the variational principle, the equilibrium density profile can be obtained by use of an iteration calculation with the average density of particles as an input. In terms of density profiles presented under various conditions, the roles of the trapped parameter, coupling parameter, screening parameter, and the average number density of particles are discussed, and significant influences of these factors on the structure of confined dusty plasma are found.

Synchronization mechanism and Arnold tongues for dust density waves

The nonlinear phenomenon of synchronization is characterized experimentally for dust density waves, i.e., dust acoustic waves, which are self-excited due to an ion streaming instability. The waves propagate in a dust cloud with a natural frequency of 22 Hz. We synchronize these waves to a different frequency using a driving electrode that sinusoidally modulates the ion density. We study four synchronized states, with frequencies that are multiples of 1, 2, 3, and 1/2 of the driving frequency. Comparing to phenomena that are typical of the van der Pol paradigm, we find that synchronization of our waves exhibit the signature of the suppression mechanism but not that of the phaselocking mechanism. Additionally, synchronization of our waves exhibits three characteristics that differ from the van der Pol paradigm: a threshold amplitude that can be seen in the Arnold tongue diagram, a branching of the 1:1 harmonic tongue at its lower extremity, and a nonharmonic state. The latter state appears to be a nonlinear oscillation; it is neither at the natural frequency nor a synchronized state.

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.

Theoretical description of spherically confined, strongly correlated Yukawa plasmas

A theoretical description of the radial density profile for charged particles with Yukawa interaction in a harmonic trap is described. At strong Coulomb coupling shell structure is observed in both computer simulations and experiments. Correlations responsible for such shell structure are described here using a recently developed model based in density functional theory. A wide range of particle number, Coulomb coupling, and screening lengths is considered within the fluid phase. A hypernetted chain approximation shows the formation of shell structure, but fails to give quantitative agreement with Monte Carlo simulation results at strong coupling. Significantly better agreement is obtained within the hypernetted chain structure using a renormalized coupling constant, representing bridge function corrections.

Cavity dynamics and particle alignment in the wake of a supersonic projectile penetrating a dusty plasma

The penetration of a projectile into a strongly coupled dusty plasma was studied in a radio-frequency discharge under microgravity conditions. A supersonic projectile produces an elongated dust-free cavity in its wake. The dynamics of the cavity is analyzed and compared with Langevin dynamics simulations. Besides a three-dimensional Mach cone structure, the simulation shows that the cavity dynamics can be subdivided into three phases: An opening phase with fixed time scale, a closing phase, whose duration is affected by the projectile speed and, finally, a phase of particle realignment in the target cloud, which persists for a long time after the closure of the cavity.

Polygon construction to investigate melting in two-dimensional strongly coupled dusty plasma

The polygon construction method of Glaser and Clark is used to characterize melting and crystallization in a two-dimensional (2D) strongly coupled dusty plasma. Using particle positions measured by video microscopy, bonds are identified by triangulation, and unusually long bonds are deleted. The resulting polygons have three or more sides. Geometrical defects, which are polygons with more than three sides, are found to proliferate during melting. Pentagons are found in liquids, where they tend to cluster with other pentagons. Quadrilaterals are a less severe defect, so that disorder can be characterized by the ratio of quadrilaterals to pentagons. This ratio is found to be less in a liquid than in a solid or a superheated solid. Another measure of disorder is the abundance of different kinds of vertices, according to the type of polygons that adjoin there. Unexpectedly, spikes are observed in the abundance of certain vertex types during rapid temperature changes. Hysteresis, revealed by a plot of a disorder parameter vs temperature, is examined to study sudden heating. The hysteresis diagram also reveals features suggesting a possibility of latent heat in the melting and rapid cooling processes.

Binary dusty plasma Coulomb balls

We investigated the mixing and segregation of a system consisting of two different species of particles, having different charges, interacting through a pure Coulomb potential, and confined in a three-dimensional parabolic trap. The structure of the cluster and its normal mode spectrum are analyzed as a function of the relative charge and the relative number of different types of particles. We found that (a) the system can be in a mixed or segregated state depending on the relative charge ratio parameter and (b) the segregation process is mediated by a first or second order structural phase transition which strongly influences the magic cluster properties of the system.

Collective excitations of a spherically confined Yukawa plasma

The complete spectrum of eigenmodes of a spherically confined Yukawa plasma is presented, based on first-principle molecular dynamics simulations. These results are compared with a recent fluid theory for the multipole modes of this system [H. Kählert and M. Bonitz, Phys. Rev. E 82, 036407 (2010)] and with the exact N-particle eigenmodes in the crystalline phase. Simulations confirm the existence of high-order modes found in cold fluid theory. We investigate the influence of screening, coupling, and friction on the mode spectra in detail. Good agreement between theory and simulation is found for weak to moderate screening and low-order modes. In addition, a number of new modes are observed which are missing in the fluid theory. The relations between the breathing mode in the fluid theory, simulation, and the crystal eigenmode are investigated in further detail.

Structural transitions in laterally compressed two-dimensional Coulomb clusters

We model structural transitions of small-size Wigner crystals in laterally compressed two-dimensional traps. Ground and metastable configurations are calculated and their transformations are linked to conspicuous changes in the heat capacity of the system. We show that various types of structural transitions are reflected by characteristic features in the behavior of the heat capacity. For deeper understanding, results produced by the Monte Carlo numerical calculations are compared to predictions of simple one-dimensional models.

Fluid modes of a spherically confined Yukawa plasma

The normal modes of a three-dimensional Yukawa plasma in an isotropic harmonic confinement are investigated by solving the linearized cold fluid equations. The eigenmodes are found analytically and expressed in terms of hypergeometric functions. It is found that the mode frequencies solely depend on the dimensionless plasma parameter ξ=κR , where R is the plasma radius and κ is the inverse screening length. The eigenfrequencies increase monotonically with ξ and saturate in the limit ξ→∞ . Compared with the results in the Coulomb limit [D. H. E. Dubin, Phys. Rev. Lett. 66, 2076 (1991)10.1103/PhysRevLett.66.2076], we find an additional class of modes characterized by the number n which determines the number of radial nodes in the perturbed potential. These modes originate from the degenerate bulk modes of the Coulomb system. Analytical formulas for the eigenfrequencies are derived for limiting cases.

A two-component mixture of charged particles confined in a channel: melting

The melting of a binary system of charged particles confined in a quasi-one-dimensional parabolic channel is studied through Monte Carlo simulations. At zero temperature the particles are ordered in parallel chains. The melting is anisotropic and different melting temperatures are obtained according to the spatial direction, and the different kinds of particles present in the system. Melting is very different for the single-, two- and four-chain configurations. A temperature induced structural phase transition is found between two different four-chain ordered states which is absent in the mono-disperse system. In the mixed regime, where the two kinds of particles are only slightly different, melting is almost isotropic and a thermally induced homogeneous distribution of the distinct kinds of charges is observed.

How spherical plasma crystals form

The correlation buildup and the formation dynamics of the shell structure in a spherically confined one-component plasma are studied. Using Langevin dynamics simulations the relaxation processes and characteristic time scales and their dependence on the pair interaction and dissipation in the plasma are investigated. While in systems with Coulomb interaction (e.g., trapped ions) in a harmonic confinement shell formation starts at the plasma edge and proceeds inward, this trend is significantly weakened for dusty plasmas with Yukawa interaction. With a suitable change of the confinement conditions the crystallization scenario can be externally controlled.

Theoretical description of Coulomb balls: fluid phase

A theoretical description for the radial density profile of a finite number of identical charged particles confined in a harmonic trap is developed for application over a wide range of Coulomb coupling (or, equivalently, temperatures) and particle numbers. A simple mean-field approximation neglecting correlations yields a density profile which is monotonically decreasing with radius for all temperatures, in contrast to molecular dynamics simulations and experiments showing shell structure at lower temperatures. A more complete theoretical description including charge correlations is developed here by an extension of the hypernetted chain approximation, developed for bulk fluids, to the confined charges. The results reproduce all of the qualitative features observed in molecular dynamics simulations and experiments. These predictions are then tested quantitatively by comparison with benchmark Monte Carlo simulations. Quantitative accuracy of the theory is obtained by correcting the hypernetted chain approximation with a representation for the associated bridge functions.

Brownian dynamic of laser cooling and crystallization of electron-ion plasma

Laser cooling and crystallization of electron-ion plasma is studied using the Brownian dynamics simulation technique and taking into consideration the interaction of ions with the electron subsystem. It has been shown that the nonlinear dependence of laser friction force on the velocity of ions has to be taken into account in order to simulate in an adequate manner the cooling dynamics and obtain a correct estimate for minimum temperatures. It has been found that times required for formation of an ordered ionic structure can be much longer than the typical plasma cooling time.

Gas flow driven by thermal creep in dusty plasma

Thermal creep flow (TCF) is a flow of gas driven by a temperature gradient along a solid boundary. Here, TCF is demonstrated experimentally in a dusty plasma. Stripes on a glass box are heated by laser beam absorption, leading to both TCF and a thermophoretic force. The design of the experiment allows isolating the effect of TCF. A stirring motion of the dust particle suspension is observed. By eliminating all other explanations for this motion, we conclude that TCF at the boundary couples by drag to the bulk gas, causing the bulk gas to flow, thereby stirring the suspension of dust particles. This result provides an experimental verification, for the field of fluid mechanics, that TCF in the slip-flow regime causes steady-state gas flow in a confined volume.

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.

Normal modes of a small bilayer system of binary classical charged particles trapped in a parabolic confinement potential

The normal modes and the melting character of a bilayer system consisting of binary charged particles with different charge and/or different mass, interacting through a Coulomb potential and confined in a parabolic trap are investigated. The normal mode spectrum is discussed as a function of the charge ratio (CR) and mass ratio (MR) of the two kinds of charged particles as well as the interlayer separation. We show that the dependence of the normal modes on the excited states can be tuned by varying the CR, the MR, and the interlayer distance. Once the interlayer distance is larger than a critical value, the first excited state corresponds only to the intershell rotation mode. In addition, the intershell rotation melting temperature is discussed as a function of the CR and MR as well as the interlayer separation.

Structural properties of complex plasmas in a homogeneous dc discharge

We report on the first three-dimensional (3D) complex plasma structure analysis for an experiment that was performed in an elongated discharge tube in the absence of striations. The low frequency discharge was established with 1 kHz alternating dc current through a cylindrical glass tube filled with neon at 30 Pa. The injected particle cloud consisted of monodisperse microparticles. A scanning laser sheet and a camera were used to determine the particle position in 3D. The observed cylindrical-shaped particle cloud showed an ordered structure with a distinct outer particle shell. The observations are in agreement with performed molecular dynamics simulations.

Probability of metastable configurations in spherical three-dimensional Yukawa crystals

Recently the occurrence probabilities of ground and metastable states of three-dimensional Yukawa clusters with 27 and 31 particles have been analyzed in dusty plasma experiments [D. Block, Phys. Plasmas 15, 040701 (2008)]. There it was found that, in many cases, the ground state appeared substantially less frequently than excited states. Here we analyze this question theoretically by means of molecular dynamics (MD) and Monte Carlo simulations and an analytical method based on the canonical partition function. We confirm that metastable states can occur with a significantly higher probability than the ground state. The results strongly depend on the screening parameter of the Yukawa interaction and the damping coefficient used in the MD simulations. The analytical method allows one to gain insight into the mechanisms being responsible for the occurrence probabilities of metastable states in strongly correlated finite systems.

Existence and vanishing of the breathing mode in strongly correlated finite systems

One of the fundamental eigenmodes of finite interacting systems is the mode of uniform radial expansion and contraction-the breathing mode (BM). Here we show in a general way that this mode exists only under special conditions: (i) for harmonically trapped systems with interaction potentials of the form 1/rgamma (gamma in R not equal 0) or log(r), or (ii) for some systems with special symmetry such as single-shell systems forming platonic bodies. Deviations from the BM are demonstrated for two examples: clusters interacting with a Lennard-Jones potential and parabolically trapped systems with Yukawa repulsion. We also show that vanishing of the BM leads to the occurrence of multiple monopole oscillations which is of importance for experiments.

Melting transitions in isotropically confined three-dimensional small Coulomb clusters

Molecular dynamic simulations are performed to investigate the melting process of small three-dimensional clusters (i.e., systems with one and two shells) of classical charged particles trapped in an isotropic parabolic potential. The confined particles interact through a repulsive potential. We find that the ground-state configurations for systems with N=6 , 12, 13, and 38 particles interacting through a Coulomb potential are magic clusters. Such magic clusters have an octahedral or icosahedral symmetry and are found to have a large stability against intrashell diffusion leading to an intershell melting transition prior to the intrashell and radial melting process. For systems with two shells a local radial melting of subshells is found at low temperatures resulting in a structural transition leading to an increased symmetry of the ordered system. Using Lindemann's criterion the different melting temperatures are determined and the influence of the screening of the interparticle interaction was investigated. A normal mode analysis is performed and some of the normal modes are found to be determinantal for the melting process.