Simple dispersion relations for Coulomb and Yukawa fluids

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.Comment: To be published in a special issue of IEEE Trans. Plasma Sci. devoted to ICPDP 2017 in Pragu

Note: Melting criterion for soft particle systems in two dimensions

A simple criterion for melting of two-dimensional crystals with soft long-ranged interactions is proposed. It states that the ratio of the transverse sound velocity of an ideal crystalline lattice to the thermal velocity is a quasi-universal number close to $4.3$ at melting. This criterion is arrived by reference to the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young theory of two-dimensional melting, combined with the observation that the ratio of transverse-to-longitudinal sound velocities is small in the soft interaction limit. Application of this criteria allows estimating melting lines in a simple yet relatively accurate manner. Two-dimensional weakly screened Yukawa systems represent one relevant example considered.Comment: 2 pages note in JC

Accurate transport cross sections for the Lennard-Jones potential

Physically motivated expressions for the transport cross sections describing classical scattering in the Lennard-Jones potential are proposed. These expressions, which agree with the numerical results better than to within $\pm 1$, can be easy implemented in practical situations. Some relevant examples are provided.Comment: 6 page

Classical scattering in strongly attractive potentials

Scattering in central attractive potentials is investigated systematically, in the limit of strong interaction, when large-angles scattering dominates. In particular, three important model interactions (Lennard-Jones, Yukawa, and exponential), which are qualitatively different from each other, are studied in detail. It is shown that for each of these interactions the dependence of the scattering angle on the properly normalized impact parameter exhibits a quasi-universal behavior. This implies simple scaling of the transport cross sections with energy in the considered limit. Accurate fits for the momentum transfer cross section are suggested. Applications of the obtained results are discussed.Comment: Phys. Rev. E (in press

Gr\"uneisen parameter for strongly coupled Yukawa systems

The Gr\"uneisen parameter is evaluated for three-dimensional Yukawa systems in the strongly coupled regime. Simple analytical expression is derived from the thermodynamic consideration and its structure is analysed in detail. Possible applications are briefly discussed

Electron and ion thermal forces in complex (dusty) plasmas

Expressions for the ion and electron thermal forces acting on a charged grain, suspended in a weakly ionized plasma subject to temperature gradients, are derived. The main emphasize is on the conditions pertinent to the investigations of complex (dusty) plasmas in gas discharges. Estimates show that for the electron temperature gradients $\sim {\mathcal O}$(eV/cm) typically encountered in laboratory gas discharges, the electron thermal force can become an important player among other forces acting on micron-size grains.Comment: 6 pages, 1 figur

Effective Coulomb Logarithm for One Component Plasma

An expression for the effective Coulomb logarithm in one-component-plasma is proposed, which allows to extend the applicability of the classical formula for the self-diffusion coefficient to the strongly coupled regime. The proposed analytical approximation demonstrates reasonable agreement with previous numerical simulation results. Relevance to weakly screened Yukawa systems (and, in particular, complex plasmas) is discussed.Comment: 4 pages, 3 figure

Dispersion relations of Yukawa fluids at weak and moderate coupling

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.Comment: 9 pages, 7 figure

Practical expressions for the internal energy and pressure of Yukawa fluids

Simple practical expressions are put forward, which allow to estimate thermodynamic properties of Yukawa fluids in a wide range of coupling, up to the fluid-solid phase transition. These expressions demonstrate excellent agreement with the available results from numerical simulations. The approach provides simple and accurate tool to estimate thermodynamic properties of Yukawa fluids and related systems in a broad range of parameters.Comment: To be published in Phys. Rev.

Fluid approach to evaluate sound velocity in Yukawa systems (complex plasmas)

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 coupled dusty (complex) plasmas. It is shown that, within the present approach, the sound velocity is completely determined by particle-particle correlations and the neutralizing medium (plasma), apart from providing screening of the Coulomb interaction, has no other effect on the sound propagation. The ratio of the actual sound velocity to its "ideal gas" (weak coupling) scale only weakly depends on the coupling strength in the fluid regime, but exhibits a pronounced decrease with the increase of the screening strength. The limitations of the present approach in applications to real complex plasmas are briefly discussed.Comment: Physical Review E (in press