One-component Plasma Research Articles

Dynamic local field correction of the one-component plasma

The dynamic local field correction (LFC) of the classical one component plasma is studied with molecular dynamics simulations and analytical theory. Simulation results are obtained for a wide range of frequencies and wavenumbers in the strongly coupled regime. The dynamic LFC generally differs significantly from both the zero and high-frequency limits. The latter is attained at increasingly lower frequencies as the coupling grows. In the long wavelength limit, the frequency dependence of the LFC is studied in detail. Pronounced structure is observed in the vicinity of the plasma frequency and its first harmonic. The results provide access to the plasmon dispersion and are used to test the accuracy of various theoretical approaches. In the low-frequency limit, the simulation data are compared with the predictions of hydrodynamics, which connects the LFC with thermodynamic and transport coefficients. While a direct comparison is typically hindered by the finite size of the simulations, good agreement is found at strong coupling for a relation that connects the imaginary part of the LFC with the viscosity.

The high dust density regime of dusty plasma: Theory and simulations

It is shown that the dust density regimes in the dusty plasma are characterized by two complementary screening processes: (i) the low dust density regime where the Debye screening is the dominant process and (ii) the high dust density regime where the “Coulomb screening” is the dominant process. The Debye regime is characterized by a state where all dust particles carry an equal and constant charge. The high dust density regime or the “Coulomb plasma” regime is characterized by (a) “Coulomb screening” where the dust charge depends on the spatial location and is screened by other dust particles in the vicinity by charge reduction, (b) “asymptotic freedom” where dust particles, which on an average carry minimal electric charge, are asymptotically free in the high dust density limit, (c) uniform dust charge density and plasma potential, (d) dust charge neutralization by a uniform background of hot ions, and (e) dust is weakly coupled due to strong Coulomb screening. Thus, the dusty plasma is essentially a weakly coupled, one-component plasma with screening in the high dust density limit. Molecular dynamics (MD) simulations verify these properties. The MD simulations are performed, using a recently proposed Hamiltonian formalism to study the dynamics of Yukawa particles carrying variable electric charge. A hydrodynamic model for describing the collective properties of Coulomb plasma and its characteristic acoustic mode called the “Coulomb acoustic mode” arising due to imperfect Coulomb screening is given.

Bulk viscosity of the rigid rotor one-component plasma.

Bulk viscosity of a plasma consisting of strongly coupled diatomic ions is computed using molecular dynamics simulations. The simulations are based on the rigid rotor one-component plasma, which is introduced as a model system that adds two degrees of molecular rotation to the traditional one-component plasma. It is characterized by two parameters: the Coulomb coupling parameter, Γ, and the bond length parameter, Ω. Results show that the long-range nature of the Coulomb potential can lead to long rotational relaxation times, which in turn yield large values for bulk viscosity. The bulk-to-shear viscosity ratio is found to span from small to large values depending on the values of Γ and Ω. Although bulk viscosity is often neglected in plasma modeling, these results motivate that it can be large in molecular plasmas with rotational degrees of freedom.

Crossover in densities of confined particles with finite range of interaction

We study a one-dimensional classical system of N particles confined within a harmonic trap. Interactions among these particles are dictated by a pairwise potential V(x), where x is the separation between two particles. Each particle can interact with a maximum of d neighbouring particles on either side (left or right), if available. By adjusting the parameter d, the system can be made nearest neighbour (d=1) to all-to-all (d=N−1) interacting. As suggested by prior studies, the equilibrium density profile of these particles is expected to undergo shape variations as d is changed. In this paper, we investigate this crossover by tuning the parameter f(=d/N) from 1 to 0 in the large N limit for two distinct choices of interaction potentials, V(x)=−|x| and V(x)=−log⁡(|x|) which correspond to 1d one-component plasma and the log-gas model, respectively. For both models, the system size scaling of the density profile for fixed f turns out to be the same as in their respective all-to-all case. However, the scaling function exhibits diverse shapes as f varies. We explicitly compute the average density profile for any f∈(0,1] in the 1d plasma model, while for the log-gas model, we provide approximate calculations for large (close to 1) and small (close to 0) f. Additionally, we present simulation results to numerically demonstrate the crossover and compare these findings with our theoretical results.

Theoretical investigation of collective motion in some liquid metals using pseudopotential approach

The collective motions are studied using a recently created pseudopotential and some elastic constants. This paper involves the calculations of the collective motions like phonon dispersion curves (PDCs) for longitudinal and transverse frequencies ([Formula: see text] and [Formula: see text]), longitudinal sound velocity ([Formula: see text]), transverse sound velocity ([Formula: see text]), isothermal bulk modulus (B), modulus of rigidity (G), Young’s modulus (Y), Poisson’s ratio [Formula: see text], Debye temperature ([Formula: see text]) of some monovalent (Na), divalent (Mg) and polyvalent liquid metals (Al, Pb, Bi). This investigation is based upon the theory of pseudopotential of second-order approach via the equations of Hubbard and Beeby (HB). [Formula: see text] The pair correlation function is calculated from the different mean spherical approximation (MSA), one-component plasma (OCP) and optimized random phase approximation (ORPA) structure factors employed in this work. Three different types of local field correction (screening) functions proposed by Hartree (H), Taylor (T) and Nagy (N) are utilized in this paper. The current findings are found to be in qualitative accord with experimental and theoretical data.

Comparative studies of role of different structure factors in various physical properties of some simple liquid metals

In the current work, the comparison of the structure factors and pair correlation functions produced by using eight different theoretical models based on the Perckus-Yevick Hard Sphere (PYHS), Hard Sphere Yukawa (HSY), Mean Spherical Approximation (MSA), Generalized Mean Spherical Approximation (GMSA), Soft Sphere (SS), One-Component Plasma (OCP), Optimized Random Phase Approximation (ORPA) and Charged Hard Sphere (CHS) models for liquid metals viz. Li, Na, K, Rb, Cs, Mg, Zn, Ca, Al, Ga, In, Pb, Sn, Bi and Sb are carried out. Our own model potential is used with the Taylor (TY) screening function in the present computation. With this, certain physical properties such as electrical transport (electrical resistivity), vibrational property (phonon dispersion), dynamical property (velocity autocorrelation function (VACF)) and static (long wavelength of structure factor) properties has also been calculated. When the several theoretical models of the structure factors of the researched simple liquid metals are compared, it is discovered that the experimental data is consistent and in good agreement with the theoretical models.

Shoving model and the glass transition in one-component plasma.

A modified shoving model is applied to estimate the location of the glass transition in a one-component plasma. The estimated value of the coupling parameter Γ ≃ 570 at the glass transition is compared with other predictions available in the literature.

Variational principles for the hydrodynamics of the classical one-component plasma

Hydrodynamic equations for a one-component plasma are derived as a unification of the Euler equations with long-range Coulomb interaction. By using a variational principle, these equations self-consistently unify thermodynamics, dispersion laws, nonlinear motion, and conservation laws. In the moderate and strong coupling limits, it is argued that these equations work down to the length scale of the interparticle spacing. The use of a variational principle also ensures that closure is achieved self-consistently. Hydrodynamic equations are evaluated in both the Eulerian frame, where the fluid variables depend on the position in the laboratory, and the Lagrangian frame, where they depend on the position in some reference state, such as the initial position. Each frame has its advantages and our final theory combines elements of both. The properties of longitudinal and transverse dispersion laws are calculated for the hydrodynamic equations. A simple step function approximation for the pair distribution function enables simple calculations that reveal the structure of the equations of motion. The obtained dispersion laws are compared to molecular dynamics simulations and the theory of quasilocalized charge approximation. The action, which gives excellent agreement for both longitudinal and transverse dispersion laws for a wide range of coupling strengths, is elucidated. Agreement with numerical experiments shows that such a hydrodynamic approach can be used to accurately describe a one-component plasma at very small length scales comparable to the average interparticle spacing. The validity of this approach suggests considering nonlinear flows and other systems with long-range interactions in the future.

On the study of electrical transport properties of some liquid metals by pseudopotential method

ABSTRACT Our recently evolved pseudopotential is used to study the electrical transport properties such as electrical resistivity ( ρ ), thermal conductivity ( σ ) and thermoelectric power ( TEP ) of some monovalent (Li, Na, K, Rb, Cs), divalent (Mg, Zn, Ca) and polyvalent (Al, Ga, In, Pb, Sn, Bi, Sb) liquid metals. The model potential theory in conjunction with Ziman, mean free path, t-matrix, and Kubo models are implemented in the above-mentioned work for the first time. The Taylor’s local field correction function (T) is taken for observing the exchange and correlation effect with one component plasma (OCP) structure factor method of liquid metals with Hartree dielectric function (H). The presently computed findings are extremely comparable with available data, either theoretical or experimental results that exist in the literature.

Amplitude modulation and surface wave generation in a complex plasma monolayer.

The response of a two-dimensional plasma crystal to an externally imposed initial perturbation has been explored using molecular dynamics (MD) simulations. A two-dimensional (2D) monolayer of micron-sized charged particles (dust) is formed in the plasma environment under certain conditions. The particles interacting via Yukawa pair potential are confined in the vertical (z[over ̂]) direction by an external parabolic confinement potential, which mimics the combined effect of gravity and the sheath electric field typically present in laboratory dusty plasma experiments. An external perturbation is introduced in the medium by displacing a small central region of particles in the vertical direction. The displaced particles start to oscillate in the vertical direction, and their dynamics get modulated through a parametric decay process generating beats. It has also been shown that the same motion is excited in the dynamics of unperturbed particles. A simple theoretical model is provided to understand the origin of the beat motions of particles. Additionally, in our simulations, concentric circular wavefronts propagating radially outward are observed on the surface of the monolayer. The physical mechanism and parametric dependence of the observed phenomena are discussed in detail. This research sheds light on the medium's ability to exhibit macroscopic softness, a pivotal characteristic of soft matter, while sustaining surface wave modes. Our findings are also relevant to other strongly coupled systems, such as colloids and classical one-component plasmas.

Hyperuniformity of the two-dimensional one-component plasma

Hyperuniformity of the two-dimensional one-component plasma

The use of one-component plasma in the icp-rie etching process of periodic structures for applications in photodetector arrays

The paper presents the effect of ICP-RIE etching time using one-component plasma on various parameters of an InAs/GaSb type II superlattice matrix. In the studies, two samples used at different BCl3 gas flow rates were compared and it was found that using a lower flow rate of 7 sccm results in obtaining a smoother sidewall morphology. Next, five periodic mesa-shaped structures were etched under identical conditions, but using a different time. The results indicated that the ICP-RIE method using a BCl3 flow rate of 7 sccm, ICP:RIE power ratio of 300W:270W allowed the ICP:RIE formation of a periodic mesa-shaped structure with smooth and perpendicular sidewalls.

Expanding the Fourier Transform of the Scaled Circular Jacobi beta Ensemble Density

The family of circular Jacobi beta ensembles has a singularity of a type associated with Fisher and Hartwig in the theory of Toeplitz determinants. Our interest is in the Fourier transform of the corresponding N rightarrow infty bulk scaled spectral density about this singularity, expanded as a series in the Fourier variable. Various integrability aspects of the circular Jacobibeta ensemble are used for this purpose. These include linear differential equations satisfied by the scaled spectral density for beta = 2 and beta = 4, and the loop equation hierarchy. The polynomials in the variable u=2/beta which occur in the expansion coefficents are found to have special properties analogous to those known for the structure function of the circular beta ensemble, specifically in relation to the zeros lying on the unit circle |u|=1 and interlacing. Comparison is also made with known results for the expanded Fourier transform of the density about a guest charge in the two-dimensional one-component plasma.

Connection between Polytropic Index and Heating

The paper derives the one-to-one connecting relationships between plasma heating and its polytropic index, and addresses the consequences through the transport equation of temperature. Thermodynamic polytropic processes are classified in accordance to their polytropic index, the exponent of the power-law relationship of thermal pressure expressed with respect to density. These processes generalize the adiabatic one, where no heating is exchanged between the system and its environment. We show that, in addition to heating terms, the transport equation of temperature depends on the adiabatic index, instead of a general, nonadiabatic polytropic index, even when the plasma follows nonadiabatic processes. This is because all the information regarding the system's polytropic index is contained in the heating term, even for a nonconstant polytropic index. Moreover, the paper (i) defines the role of the polytropic index in the context of heating; (ii) clarifies the role of the nonadiabatic polytropic index in the transport equation of temperature; (iii) provides an alternative method for deriving the turbulent heating through the comparably simpler polytropic index path; and, finally, (iv) shows a one-component plasma proof-of-concept of this method and discusses the implications of such derived connecting relationships in the solar wind plasma in the heliosphere.

One-component fermion plasma on a sphere at finite temperature: the anisotropy of the path conformations

In our previous work (Fantoni 2018 Int. J. Mod. Phys. C 29 1850064) we studied, through a computer experiment, a one-component fermion plasma on a sphere at finite, non-zero temperature. We extracted thermodynamic properties, such as the kinetic and internal energy per particle, and structural properties, such as the radial distribution function, and produced some snapshots of the paths to study their shapes. Here, we revisit this study, giving more theoretical details explaining the path shape anisotropic conformation due to the inhomogeneity in the polar angle of the variance of the random walk diffusion from the kinetic action.

Electromagnetism of one-component plasmas of massless fermions

We present a theoretical study of two- and three-dimensional massless Dirac one-component plasmas embedded in a constant uniform magnetic field. We determine the wavefunctions and Landau energy levels of a massless Dirac fermion in a constant magnetic field. On this basis we consider magnetism of Fermi fluids of massless charged particles. We show that such a three-dimensional Dirac plasma consisting of fermions with the same helicity has its own magnetic moment. We also consider the limit of strong magnetic fields and investigate the De Haas–van Alphen effect. We derive the Kubo formula for the electrical conductivity tensor of massless Dirac plasmas and consider the Shubnikov–de Haas effect. In addition, we propose a model of the static conductivity tensor and employ the matrix version of the classical method of moments to derive a Drude-like formula for the dynamic conductivity tensor for massless Dirac plasmas. We find that the electrical conductivity tensor for Dirac fermions with the right helicity is not isotropic in the plane perpendicular to the magnetic field.

Collective ion dynamics in Coulomb one-component plasmas within the self-consistent relaxation theory.

In this paper, we present the theoretical formalism describing the collective ion dynamics of the nonideal Coulomb classical one-component plasmas on the basis of the self-consistent relaxation theory. The theory is adapted to account for correlations between the frequency relaxation parameters that characterize the three- and four-particle dynamics and the parameters associated with the two-particle dynamics. The dynamic structure factor spectra and dispersion characteristics calculated for a wide range of wave numbers are in agreement with the molecular dynamics simulation data and the results obtained with the theory of the frequency moments. The proposed formalism reproduces all the features inherent to the Coulomb one-component plasmas and requires only knowledge of the coupling parameter and the information about the structure.

Theoretical investigation on the structural and vibrational properties of some alkali liquid metals: A pseudopotential approach

Along with a few elastic constants, a recently created pseudopotential is employed to examine the vibrational properties of some simple alkali metals, i.e. Li, Na, K, Rb and Cs. The phonon dispersion curves (PDC) are computed in the text. (ωL and ωT), longitudinal sound velocity (vl), transverse sound velocity (vt), isothermal bulk modulus (B), modulus of rigidity (G), Young’s modulus (Y ), Debye temperature (θD) of some liquid alkali metals. The second order technique used in the current work, using Hubbard and Beeby (HB) equations, is based on pseudopotential theory. The various Percus-Yevick hard sphere (PYHS) and one-component plasma (OCP) structure factors used in the current investigation are used to construct the pair correlation function g(r). The current paper makes use of three distinct forms of local field correction functions developed by Hartree (H), Taylor (T), and Nagy (N). The current findings are found to qualitatively agree with the experimental and theoretical data that is currently available.

Superconducting Transition Temperature of the Bose One-Component Plasma.

We present results of numerically exact simulations of the Bose one-component plasma, i.e., a Bose gas with pairwise Coulomb interactions among particles and a uniform neutralizing background. We compute the superconducting transition temperature for a wide range of densities, in two and three dimensions, for both continuous and lattice versions of the model. The Coulomb potential causes the weakly interacting limit to be approached at high density, but gives rise to no qualitatively different behavior, vis-à-vis the superfluid transition, with respect to short-ranged interactions. Our results are of direct relevance to quantitative studies of bipolaron mechanisms of (high-temperature) superconductivity.

Theory of energy loss of charged projectiles in magnetized one-component plasmas

Theory of energy loss of charged projectiles in magnetized one-component plasmas