Improved equation of state for the classical one-component plasma

Slattery, W. L.; Doolen, Gary D.; DeWitt, H. E.

doi:10.1103/physreva.21.2087

Cited by 580 publications

(238 citation statements)

References 8 publications

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“…., and γ is the Euler's constant. The analytical Abe expansion seems to be fairly accurate for Γ up to 0.1 [14]. The next few terms for the Γ → 0 expansion calculated in Ref.…”

Section: Introductionmentioning

confidence: 72%

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Accurate First‐Principle Equation of State for the One‐Component Plasma

Brilliantov

1998

Contrib. Plasma Phys.

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Accurate "first-principle" expressions for the excess free energy F ex and internal energy U ex of the classical one-component plasma (OCP) are obtained.We use the Hubbard-Schofield transformation that maps the OCP Hamiltonian onto the Ising-like Hamiltonian, with coefficients expressed in terms of equilibrium correlation functions of a reference system. We use the ideal gas as a reference system for which all the correlation functions are known. Explicit calculations are performed with the high-order terms in the Ising-like Hamiltonian omitted. For small values of the plasma parameter Γ the DebyeHuckel result for F ex and U ex is recovered. For Γ ≫ 1, these depend linearly on Γ in accordance with the Monte Carlo findings for the OCP. The MC data for the internal energy are reproduced fairly well by the obtained analytical expression.

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“…., and γ is the Euler's constant. The analytical Abe expansion seems to be fairly accurate for Γ up to 0.1 [14]. The next few terms for the Γ → 0 expansion calculated in Ref.…”

Section: Introductionmentioning

confidence: 72%

“…Extensive numerical studies have been performed by Monte Carlo (MC) [5,14,[18][19][20][21] and Molecular Dynamics [22] technique. To fit available "experimental" data for the excess thermodynamic functions simple analytical fits were proposed [23]:…”

Section: Introductionmentioning

confidence: 99%

Accurate First‐Principle Equation of State for the One‐Component Plasma

Brilliantov

1998

Contrib. Plasma Phys.

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“…Here we define D ≡ n −1/3 , where n is the particle density, consistent with recent studies [42]. However, other pioneering studies on OCP freezing [40,41] use a slightly different definition of the interparticle distance, D * ≡ (4πn/3) −1/3 ; this results in a small change to the coupling parameter definition: * ≡ Z 2 λ B /D * ≈ 1.61 . These studies show that a Coulomb lattice is the most favourable configuration when the coupling parameter exceeds a critical value, * 171 [41].…”

Section: Appendixmentioning

confidence: 84%

“…4. The OCP crystallizes if > 106 [40,41] (see Appendix), where the OCP coupling parameter is defined as ≡ Z 2 OCP λ B n 1/3 ; this threshold yields a simple new freezing criterion that takes the standard PB cell-model calculations as input. Therefore, to calculate the phase boundaries for comparison with the experimental data, we solve numerically for = 106 using ρ bg , as obtained from the numerical solution of Eq.…”

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confidence: 99%

Crystallization and reentrant melting of charged colloids in nonpolar solvents

Kanai

Boon

et al. 2015

Phys. Rev. E

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We explore the crystallization of charged colloidal particles in a nonpolar solvent mixture. We simultaneously charge the particles and add counterions to the solution with aerosol-OT (AOT) reverse micelles. At low AOT concentrations, the charged particles crystallize into body-centered-cubic (bcc) or face-centered-cubic (fcc) Wigner crystals; at high AOT concentrations, the increased screening drives a thus far unobserved reentrant melting transition. We observe an unexpected scaling of the data with particle size, and account for all behavior with a model that quantitatively predicts both the reentrant melting and the data collapse. Colloidal particles can spontaneously form structures that exhibit long-range ordered states, making them a fascinating system for fundamental studies of crystal phase behavior [1][2][3][4]. The majority of studies focus on colloids which model the hard-sphere interaction, a strong repulsion that prevents particles from overlapping, whose range is restricted to contact [5]. Hard-sphere crystallization is driven through purely entropic effects, and the phase behavior is well studied [5][6][7][8][9]. Typically, the colloids used for these studies are stericallystabilized polymeric particles in nonaqueous solvents, which can match both the density ρ and refractive index n of the particles, enabling confocal microscopy to be used for these investigations. Even earlier studies focused on charged particles, where crystallization is driven by strong long-range repulsive interactions arising from Coulombic charges on the particles [1,[10][11][12][13][14][15][16][17][18][19][20][21][22]. These studies were performed on particles in aqueous solvents, which makes charge effects much easier to induce, but precludes index matching, limiting the use of optical techniques except at very low densities. Instead, x-ray scattering studies [23] showed a fascinating phase behavior of Wigner crystals, including a body-centered-cubic (bcc) phase at low concentration, and a solid-solid transition to a face-centered-cubic (fcc) phase at higher densities [15][16][17][18]24,25]. It is also possible to induce charge on particles in nonaqueous solvents through the addition of charge control agents [21,[26][27][28]. However, in this case, there is strong coupling between the charge on the particle surface and the ions in solution. Charge-induced crystallization should still be expected, although new behavior may also occur as a consequence of this coupling. Nevertheless, these systems have never been investigated experimentally, and the range of potential behavior has not yet been explored.In this Rapid Communication, we investigate the crystallization behavior of colloidal particles in nonpolar solvents. By adding aerosol-OT (AOT) reverse micelles, we both charge the particles and add ions to the solution. As AOT concentration increases from zero, the system undergoes a first transition from fluid to a charge-stabilized bcc Wigner crystal, and * Corresponding author: plu@fas.harvard.edu then a second solid-sol...

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“…For values of Γ i of the order of 1 or larger, correlation effects become important and the plasma is then called strongly coupled. The expression for u(Γ i ) can be given for κ → 0 (where κ, to be explained later, is the ratio of the interparticle distance to the ion Debye length) as [15,16] …”

Section: Analysis a Basic Equationsmentioning

confidence: 99%

Stability and evolution of wave packets in strongly coupled degenerate plasmas

Misra

Shukła

2012

Phys. Rev. E

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We study the nonlinear propagation of electrostatic wave packets in a collisional plasma composed of strongly coupled ions and relativistically degenerate electrons. The equilibrium of ions is maintained by an effective temperature associated with their strong coupling, whereas that of electrons is provided by the relativistic degeneracy pressure. Using a multiple scale technique, a (3+1)-dimensional coupled set of nonlinear Schrödinger-like equations with nonlocal nonlinearity is derived from a generalized viscoelastic hydrodynamic model. These coupled equations, which govern the dynamics of wave packets, are used to study the oblique modulational instability of a Stoke's wave train to a small plane wave perturbation. We show that the wave packets, though stable to the parallel modulation, becomes unstable against oblique modulations. In contrast to the long-wavelength carrier modes, the wave packets with short-wavelengths are shown to be stable in the weakly relativistic case, whereas they can be stable or unstable in the ultra-relativistic limit. Numerical simulation of the coupled equations reveals that a steady state solution of the wave amplitude exists together with the formation of a localized structure in (2+1) dimensions. However, in the (3+1)-dimensional evolution, a Gaussian wave beam self-focuses after interaction and blows up in a finite time. The latter is, however, arrested when the dispersion predominates over the nonlinearities. This occurs when the Coulomb coupling strength is higher or a choice of obliqueness of modulation, or a wavelength of excitation is different. Possible application of our results to the interior as well as in an outer mantle of white dwarfs are discussed.

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Improved equation of state for the classical one-component plasma

Cited by 580 publications

References 8 publications

Accurate First‐Principle Equation of State for the One‐Component Plasma

Accurate First‐Principle Equation of State for the One‐Component Plasma

Crystallization and reentrant melting of charged colloids in nonpolar solvents

Stability and evolution of wave packets in strongly coupled degenerate plasmas

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