Ground state of a confined Yukawa plasma

Isotropic and Anisotropic Monolayer Structures in RF Discharge Plasma

We present the results of an experimental and analytical study of the structural and dynamic properties of a monolayer consisting of dust grains in an electrostatic trap in an RF discharge plasma. The possibility of forming a monolayer with an isotropic distribution for interparticle distance and kinetic energy of particles in the structure has been experimentally shown. Isotropy has crucial importance for the study of various processes in such systems, including the kinetics of phase transitions, the formation of directed flows, wave propagation, and others.

Schrödinger-Poisson systems under gradient fields

A singularity-free generalisation of Newtonian gravity can be constructed (Lazar in Phys Rev D 102:096002, 2020) within the framework of gradient field theory. This procedure offers a straightforward regularisation of Newtonian gravity and remains equally well applicable to other fields, such as electromagnetic fields. Here, with the aim of finding potentially measurable effects of gradient fields on the dispersion properties of various media, we present a quantum kinetic treatment of matter under gradient fields. The method is based on the application of the Wigner–Moyal procedure to the modified Schrödinger–Poisson equation emerging in the framework of gradient field theory. This allows us to treat, on equal footing, three different scenarios, namely self-gravitating systems, plasmas, and cold atoms in magneto-optical traps. We address the signature of gradient fields in the elementary excitations of these media. In particular, we estimate this effect to be accessible in state-of-the-art plasma-based experiments. We discuss in detail the classical kinetic and hydrodynamic limits of our approach and obtain a class of generalised Lane–Emden equations, in the context of gradient field theory, which remain valid in the three scenarios discussed here.

Self-sustained non-equilibrium co-existence of fluid and solid states in a strongly coupled complex plasma system

A complex (dusty) plasma system is well known as a paradigmatic model for studying the kinetics of solid-liquid phase transitions in inactive condensed matter. At the same time, under certain conditions a complex plasma system can also display characteristics of an active medium with the micron-sized particles converting energy of the ambient environment into motility and thereby becoming active. We present a detailed analysis of the experimental complex plasmas system that shows evidence of a non-equilibrium stationary coexistence between a cold crystalline and a hot fluid state in the structure due to the conversion of plasma energy into the motion energy of microparticles in the central region of the system. The plasma mediated non-reciprocal interaction between the dust particles is the underlying mechanism for the enormous heating of the central subsystem, and it acts as a micro-scale energy source that keeps the central subsystem in the molten state. Accurate multiscale simulations of the system based on combined molecular dynamics and particle-in-cell approaches show that strong structural nonuniformity of the system under the action of electostatic trap makes development of instabilities a local process. We present both experimental tests conducted with a complex plasmas system in a DC glow discharge plasma and a detailed theoretical analysis.

Plasma anisotropy around a dust particle placed in an external electric field

A self-consistent model of plasma polarization around an isolated micron-sized dust particle under the action of an external electric field is presented. It is shown that the quasineutral condition is fulfilled and the formed volume charge totally screens the dust particle. The ion focusing and wake formation behind the dust particle are demonstrated for different ion mean free paths and the external electric fields. It is obtained that at low values of the external electric field the trapped ions play the main role in the screening of the dust particle charge. For high external electric fields, the density of trapped ions decreases and the dust particle is screened mainly by the free ions.

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.

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.

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.

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.

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.

Higher harmonics of the magnetoplasmon in strongly coupled Coulomb and Yukawa systems

The generation of higher harmonics of the magnetoplasmon frequency which has recently been reported in strongly coupled two-dimensional Yukawa systems is investigated in detail and, in addition, extended to two-dimensional Coulomb systems. We observe higher harmonics over a much larger frequency range than before and compare the theoretical prediction with the simulations. The influence of the coupling, structure, and thermal energy on the excitation of these modes is examined in detail. We also report on the effect of friction on the mode spectra to make predictions about the experimental observability of this new effect.

Shell model of assemblies of equicharged particles subject to radial confining potentials

A shell model of an assembly of N equicharged particles subject to an arbitrary radial confining potential N W(r), where W(r) is parameterized in terms of an auxiliary function Λ(t), is presented. The validity of the model requires that Λ(t) is strictly increasing and concave for any t ∈ (0, 1), Λ'(0) is infinite, and Λ(t) = -t(-1) Λ'(t)/Λ''(t) is finite at t = 0. At the bulk limit of N → ∞, the model is found to correctly reproduce the energy per particle pair and the mean crystal radius R(N), which are given by simple functionals of Λ(t) and Λ'(t), respectively. Explicit expressions for an upper bound to the cohesive energy and the large-N asymptotics of R(N) are obtained for the first time. In addition, variational formulation of the cohesive energy functional leads to a closed-form asymptotic expression for the shell occupancies. All these formulae involve the constant ξ that enters the expression -(ξ/2) n(3/2) for the leading angular-correlation correction to the minimum energy of n electrons on the surface of a sphere with a unit radius (the solution of the Thomson problem). The approximate energies, which constitute rigorous upper bounds to their exact counterparts for any value of N, include the cohesive term that is not accounted for by the mean-field (fluidlike) theory and its simple extensions but completely neglect the surface-energy correction proportional to N.

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.

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.

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.

Ground state of a confined Yukawa plasma including correlation effects

The ground state of an externally confined one-component Yukawa plasma is derived analytically using the local density approximation (LDA). In particular, the radial density profile is computed. The results are compared with the recently obtained mean-field (MF) density profile [Henning et al., Phys. Rev. E 74, 056403 (2006)]. While the MF results are more accurate for weak screening, the LDA with correlations included yields the proper description for large screening. By comparison with first-principles simulations for three-dimensional spherical Yukawa crystals, we demonstrate that the two approximations complement each other. Together they accurately describe the density profile in the full range of screening parameters.