The self-consistent relaxation theory is employed to describe the collective ion dynamics in strongly coupled Yukawa classical one-component plasmas. The theory is applied to equilibrium states corresponding to intermediate screening regimes with appropriate values of the structure and coupling parameters. The information about the structure (the radial distribution function and the static structure factor) and the thermodynamics of the system is sufficient to describe collective dynamics over a wide range of spatial ranges, namely, from the extended hydrodynamic to the microscopic dynamics scale. The main experimentally measurable characteristics of the equilibrium collective dynamics of ions -- the spectrum of the dynamic structure factor, the dispersion parameters, the speed of sound and the sound attenuation -- are determined within the framework of the theory without using any adjustable parameters. The results demonstrate agreement with molecular dynamics simulations. Thus a direct realization is presented of the key idea of statistical mechanics: for the theoretical description of the collective particle dynamics of equilibrium fluids it is sufficient to know the interparticle interaction potential and the structural characteristics. Comparison with alternative or complementary theoretical approaches is provided.
In dusty (complex) plasmas, containing mesoscopic charged grains, the grain-grain interaction in many cases can be well described through a Yukawa potential. In this Review we summarize the basics of the computational and theoretical approaches capable of describing many-particle Yukawa systems in the liquid and solid phases and discuss the properties of the dynamical density and current correlation spectra of three- and two-dimensional strongly coupled Yukawa systems, generated by molecular dynamics simulations. We show details of the $ω(k)$ dispersion relations for the collective excitations…
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 \cite{henning.pre06}. While the MF results are more accurate for weak screening, LDA with correlations included yields the proper description for large screening. By comparison with first-principle simulations for three-dimensional spherical Yukawa crystals we demonstrate that both approximations complement each other. …
Small three-dimensional strongly coupled clusters of charged particles in a spherical confinement potential arrange themselves in nested concentric shells. If the particles are immersed into a background plasma the interaction is screened. The cluster shell configuration is known to be sensitive to the screening strength. With increased screening an increased population of the inner shell(s) is observed. Here, we present a detailed analysis of the ground state shell configurations and configuration changes in a wide range of screening parameters for clusters with particle numbers $N$ in the ra…
Sound velocities in classical single-component fluids with Yukawa (screened Coulomb) interactions are systematically evaluated and analyzed in one-, two-, and three spatial dimensions (${\mathcal D}=1,2,3$). In the strongly coupled regime the convenient sound velocity scale is given by $\sqrt{Q^2/Δm}$, where $Q$ is the particle charge, $m$ is the particle mass, $n$ is the particle density, and $Δ=n^{-1/{\mathcal D}}$ is the unified interparticle distance. The sound velocity can be expressed as a product of this scaling factor and a dimension-dependent function of the screening parameter, $κ=Δ/…
The results of a recent fluid theory for the multipole modes of a Yukawa plasma in a spherical confinement [H. Kählert and M. Bonitz, Phys. Rev. E \textbf{82}, 036407 (2010)] are compared with molecular dynamics simulations and 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. The relations between the br…
The evolution of isotropic, nondispersive, inertial wave, emerging from an unsteady initial coherent vortex is studied for strongly correlated Yukawa medium using 2D molecular dynamics simulation. In this study, the effect of azimuthal speed of vortex source, strong correlation, large screening and the compressibility of the medium over the propagation of generated inertial wave have been presented. It has been observed that these inertial waves only exist when the speed of the vortex source (U_0) is larger or equal to the longitudinal sound speed of the system. Estimated speed of the nonlinea…
We analyze via theoretical approaches and molecular dynamics simulations the collective mode structure of strongly coupled two-dimensional binary Yukawa systems, for selected density, mass and charge ratios, both in the liquid and crystalline solid phases. Theoretically, the liquid phase is described through the Quasi-Localized Charge Approximation (QLCA) approach, while in the crystalline phase we study the centered honeycomb and the staggered rectangular crystal structures through the standard harmonic phonon approximation. We identify "longitudinal" and "transverse" acoustic and optic modes…
We propose a simple two-step approximation for the radial distribution function of a one-component two-dimensional Yukawa fluid. This approximation is specified by the key parameters of the system: coupling parameter and screening parameter. On the basis of this approximation, analytical expressions are obtained for the same thermodynamic quantities as internal energy, internal pressure, excess entropy in the two-particle approximation, and also longitudinal sound velocity. The theoretical results show an agreement with the results obtained in the case of a true radial distribution function.
The Yukawa one-component plasma (OCP) is a paradigm model for describing plasmas that contain one component of interest and one or more other components that can be treated as a neutralizing, screening background. In appropriately scaled units, interactions are characterized entirely by a screening parameter, $κ$. As a result, systems of similar $κ$ show the same dynamics, regardless of the underlying parameters (e.g., density and temperature). We demonstrate this behavior using ultracold neutral plasmas (UNP) created by photoionizing a cold ($T\le10$ mK) gas. The ions in UNP systems are well …
The conventional fluid description of multi-component plasma, supplemented by an appropriate equation of state for the macroparticle component, is used to evaluate the longitudinal sound velocity of Yukawa fluids. The obtained results are in very good agreement with those obtained earlier employing the quasi-localized charge approximation and molecular dynamics simulations in a rather broad parameter regime. Thus, a simple yet accurate tool to estimate the sound velocity across coupling regimes is proposed, which can be particularly helpful in estimating the dust-acoustic velocity in strongly …
Spiral wave formations are ubiquitous in nature. In the present paper, the excitation of spiral waves in the context of driven two-dimensional dusty plasma (Yukawa system) has been demonstrated at particle level using molecular dynamics simulations. The interaction amidst dust particles is modeled by Yukawa potential to take account of the shielding of dust charges by the lighter electron and ions species. Spatiotemporal evolution of these spiral waves has been characterized as a function of frequency and amplitude of the driving force, dust neutral collisions etc. The effect of strong couplin…
In this work, we present a phenomenological study of the complete analytical solution to the bound eigenstates and eigenvalues of the Yukawa potential obtained previously using the hidden supersymmetry of the system and a systematic expansion of the Yukawa potential in terms of $δ=a_{0}/D$, where $a_{0}$ is the Bohr radius and $D$ is the screening length. The eigenvalues, $ε_{nl}(δ)$, are given in the form of Taylor series in $δ$ which can be systematically calculated to the desired order $δ^{k}$. Coulomb $l$-degeneracy is broken by the screening effects and, for a given $n$, $ε_{nl}(δ)$ is la…
Application of the ion sphere model (ISM), well known in the context of the one-component-plasma, to estimate thermodynamic properties of model Yukawa systems is discussed. It is shown that the ISM approximation provides fairly good estimate of the internal energy of the strongly coupled Yukawa systems, in both fluid and solid phases. Simple expressions for the excess pressure and isothermal compressibility are derived, which can be particularly useful in connection to wave phenomena in strongly coupled dusty plasmas. It is also shown that in the regime of strong screening a simple considerati…
Strongly coupled systems occupying the transitional range between the Wigner crystal and fluid phases are most dynamic constituents of the nature. Highly localized but strongly interacting elements in this phase posses enough thermal energy to trigger the transition between a variety of short to long range order phases. Nonlinear excitations are often the carriers of proliferating structural modifications in the strongly coupled Yukawa systems. Well represented by a laboratory dusty plasma, these systems show explicit propagation of nonlinear shocks and solitary structures both in experiments …
Thermally excited phonon spectra of 2D Yukawa solids and liquids in the presence of an external magnetic field are studied using computer simulations. Special attention is paid to the variation of wave spectra in terms of several key parameters, such as the strength of coupling, the screening parameter, and the intensity of the magnetic field. In addition, comparisons are made with several analytical theories, including random-phase approximation, quasi-localized charge approximation, and harmonic approximation, and the validity of those theories is discussed in the present context.
The equilibrium structure and the dispersion relations of collective excitations in trilayer Yukawa systems in the strongly coupled liquid regime are examined. The equilibrium correlations reveal a variety of structures in the liquid phase, reminiscent of the corresponding structures in the solid phase. At small layer separation substitutional disorder becomes the governing feature. Theoretical dispersion relations are obtained by applying the Quasi-Localised Charge Approximation (QLCA) formalism, while numerical data are generated by micro-canonical molecular dynamics (MD) simulations. The di…
Very simple explicit analytical expressions, which are able to describe the dispersion relations of collective modes in strongly coupled plasma fluids, are summarized. The accuracy of these expressions is demonstrated using the comparison with available results from benchmark numerical simulations.
In numerous realizations of complex plasmas, dust-dust interactions are characterized by two screening lengths and are thus better described by a combination of Yukawa potentials. The present work investigates the static correlations and the thermodynamics of repulsive dense bi-Yukawa fluids based on the fact that such strongly coupled systems exhibit isomorph invariance. The strong virial-potential energy correlations are demonstrated with the aid of molecular dynamics simulations, an accurate analytical expression for the isomorph family of curves is obtained and an empirical expression for …
In this paper we compare different theoretical approaches to describe the dispersion of collective modes in Yukawa fluids when the inter-particle coupling is relatively weak, so that kinetic and potential contributions to the dispersion relation compete. Thorough comparison with the results from molecular dymamics simulation allows us to conclude that in the regime investigated the best description is provided by the sum of the generalized excess bulk modulus and the Bohm-Gross kinetic term.
We analyze the acoustic collective excitations in two- and three-dimensional binary Yukawa systems, consisting of two components with different masses. Theoretical analysis reveals a profound difference between the weakly and strongly correlated limits: at weak coupling the two components interact via the mean field only and the oscillation frequency is governed by the light component. In the strongly correlated limit the mode frequency is governed by the combined mass, where the heavy component dominates. Computer simulations in the full coupling range extend and confirm the theoretical resul…
We have analyzed the Vlasov dispersion relation for Yukawa plasmas in three and two dimensions primarily for the purpose of identifying coupling parameter domains where the existence of well-developed collective excitations is forbidden or allowed. First, we have established a rigorous lower bound for the coupling parameter, below which there can be no real solution to the dispersion relation. In the coupling domain where weakly damped solutions do exist, we have focused on the long-wavelength acoustic regime where we have established more restrictive lower-bound estimates of the coupling para…
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 [Block et al., Physics of 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 p…
We report accurate molecular dynamics calculations of the shear stress relaxation in a two-dimensional strongly coupled Yukawa liquid over a wide range of the Coulomb coupling strength $Γ$ and the Debye screening parameter $κ$. Our data on the relaxation times of the ideal- , excess- and total shear stress auto-correlation ($τ^{id}_M, τ^{ex}_M, τ_M$ respectively) along with the lifetime of local atomic connectivity $τ_{LC}$ leads us to the following important observation. Below a certain crossover $Γ_c(κ)$, $τ_{LC} \rightarrow τ^{ex}_M$, directly implying that here $τ_{LC}$ is the microscopic …
The layered crystal formation in dusty plasma medium depicted by the Yukawa interaction amidst dust has been investigated using Molecular Dynamics simulations. The multilayer structures are shown to form in the presence of a combined gravitational and external electric field force (representing the sheath field in experiments) along the ^ z direction. A detailed study of the dependence of the number of crystal layer formation, their width etc., on various system parameters (viz., the external field profile and the screening length of Yukawa interaction) have been analyzed. The structural prope…
We analyze the Vlasov dispersion relation for Yukawa plasmas in three dimensions for the purpose of identifying coupling parameter domains where the Vlasov approach is justified and the existence of a well-developed RPA type collective excitation is allowed. We establish a rigorous lower bound for the coupling parameter, below which there can be no real solution to the Vlasov dispersion relation. In the coupling domain, where weakly damped solutions do exist, we have focused on the long-wavelength acoustic regime where we establish more restrictive estimates for the lower bound of the coupling…
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 $κ$ the inverse screening length. The eigenfrequencies increase monotonically with $ξ$ and saturate in the limit $ξ\to\infty$. Compared with the results in the Coulomb limit~[D. H. E. Dubin, Phys. Rev. Lett. \textbf{66},…
We derive an effective coupling parameter for two-dimensional Yukawa systems based on the height of the first maximum of the pair distribution function. Two variants -- one valid in the high-coupling range, the other for arbitrary couplings of the liquid -- are derived. Comparison to previous approaches to Yukawa coupling parameters shows that the present concept is more general and more accurate. Using, in addition, dynamical information contained in the velocity autocorrelation function, we outline a reference data method that can be employed as a non-invasive measurement scheme of the plasm…
We study the impact of plasma correlation effects on nonresonant thermonuclear reactions for various stellar objects, namely in the liquid envelopes of neutron stars, and the interiors of white dwarfs, low-mass stars, and substellar objects. We examine in particular the effect of electron screening on the enhancement of thermonuclear reactions in dense plasmas within and beyond the linear mixing rule approximation as well as the corrections due to quantum effects at high density. In addition, we examine some recent unconventional (Yukawa-potential and "quantum-tail") theoretical results on ste…
The effect of plasma screening on the electronic and vibrational properties of the H2+ molecular ion was analyzed within the Born-Oppenheimer approximation. When a molecule is embedded in a plasma, the plasma screens the electrostatic interactions. This screening is accounted for in the Schrödinger equation by replacing the Coulomb potentials with Yukawa potentials that incorporate the Debye length as a screening parameter. Variational expansions in confocal elliptical coordinates were used to calculate energies of the 1ssg and the 2psu states over a range of Debye lengths and bond distances. …
An analysis of superdiffusion in two-dimensional strongly correlated Yukawa liquids is presented. In particular, we report a regular, montonic behavior of the diffusion exponent on the screening parameter.
The dynamical structure factor (DSF) of strongly coupled ions in dense plasmas with partially and strongly degenerate electrons is investigated. The main focus is on the impact of electronic correlations (non-ideality) on the ionic DSF. The latter is computed by carrying out molecular dynamics (MD) simulations with a screened ion-ion interaction potential. The electronic screening is taken into account by invoking the Singwi-Tosi-Land-Sjölander approximation, and compared to the MD simulation data obtained considering the electronic screening in the random phase approximation and using the Yuk…
The dynamic Friedel sum rule (FSR) is derived within the second-order Born (B2) approximation for an ion that moves in a fully degenerate electron gas and for an arbitrary spherically-symmetric electron-ion interaction potential. This results in an implicit equation for the dynamic B2 screening parameter which depends on the ion atomic number $Z_{1}$ unlike the first-order Born (B1) dynamic screening parameter reported earlier by some authors. Furthermore, for typical metallic densities our analytical results for the Yukawa and hydrogenic potentials are compared, for both positive and negative…
A many-body system of charged particles interacting via a pairwise Yukawa potential, the so-called Yukawa One Component Plasma (YOCP) is a good approximation for a variety of physical systems. Such systems are completely characterized by two parameters; the screening parameter, $κ$, and the nominal coupling strength, $Γ$. It is well known that the collective spectrum of the YOCP is governed by a longitudinal acoustic mode, both in the weakly and strongly coupled regimes. In the long-wavelength limit the linear term in the dispersion (\textit{i.e.} $ω= s k$) defines the sound speed $s$. We stud…
In a non-ideal classical Coulomb one-component plasma (OCP) all thermodynamic properties are known to depend only on a single parameter -- the coupling parameter $Γ$. In contrast, if the pair interaction is screened by background charges (Yukawa OCP) the thermodynamic state depends, in addition, on the range of the interaction via the screening parameter $κ$. How to determine in this case an effective coupling parameter has been a matter of intensive debate. Here we propose a consistent approach for defining and measuring the coupling strength in Coulomb and Yukawa OCPs based on a fundamental …
A classical dusty plasma experiment was performed using two different dust grain sizes to form a strongly coupled asymmetric bilayer (two closely spaced interacting monolayers) of two species of charged dust particles. The observation and analysis of the thermally excited particle oscillations revealed the collective mode structure and wave dispersion in this system; in particular the existence of the theoretically predicted $k=0$ energy (frequency) gap was verified. Equilibrium molecular dynamics simulations were performed to emulate the experiment, assuming Yukawa type inter-particle interac…
We show that strong coupling between ions in an ultracold neutral plasma is limited by electron screening. While electron screening reduces the quasi-equilibrium ion temperature, it also reduces the ion-ion electrical potential energy. The net result is that the ratio of nearest-neighbor potential energy to kinetic energy in quasi-equilibrium is constant and limited to approximately 2 unless the electrons are heated by some external source. We support these conclusions by reporting new measurements of the ion velocity distribution in an ultracold neutral calcium plasma. These results match pre…
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\geq1, flow-aligned dust chains, respectively. In addition, our simulations revea…
The effect of Coulomb interaction screening on non-relativistic free-free absorption is investigated by integrating the numerical continuum wave functions. The screened potential is taken to be in Debye-Hűckel (Yukawa) form with a screening length D. It is found that the values of the free-free Gaunt factors for different Debye screening lengths D for a given initial electron energy \eps_i and absorbing photon energy ω, generally lie between those of the pure Coulomb field and field-free case. However, for initial electron energies below 0.1 Ry and fixed photon energy, the Gaunt factors show d…
