Self-consistent chemical model of partially ionized plasmas

Nonideal effect of free electrons on ionization equilibrium and radiative property in dense plasmas

The thermodynamic as well as optical properties of strongly coupled plasmas depend crucially on the average degree of ionization and the ionic state composition, which, however, cannot be determined by using the normal Saha equation usually used for the ideal plasmas. Hence, an adequate treatment of the ionization balance and the charge state distribution of strongly coupled plasmas is still a challenge for theory due to the interactions between the electrons and ions and among the electrons themselves. Based on a local density temperature-dependent ion-sphere model, the Saha equation approach is extended to the regime of strongly coupled plasmas by taking into account the free-electron-ion interaction, the free-free-electron interaction, the nonuniform free-electron space distribution, and the free-electron quantum partial degeneracy. All the quantities, including the bound orbitals with ionization potential depression, free-electron distribution, and bound and free-electron partition function contributions, are calculated self-consistently in the theoretical formalism. This study shows that the ionization equilibrium is evidently modified by considering the above nonideal characteristics of the free electrons. Our theoretical formalism is validated by the explanation of a recent experimental measurement of the opacity of dense hydrocarbon.

Influence of dust particles on ionization equilibrium in partially ionized plasmas

A chemical model is proposed for a dusty plasma consisting of electrons, ions, neutrals, and positively charged dust particles all being at thermodynamic equilibrium. An expression is derived for the Helmholtz free energy, which comprises the ideal part, taking into account the charge of dust particles, and the excess part, evaluated in the framework of the self-consistent chemical model [Phys. Rev. E 83, 016405 (2011)PLEEE81539-375510.1103/PhysRevE.83.016405]. The ionization potential depression for a dust-free partially ionized hydrogen is analytically evaluated for weakly and strongly ionized states to consistently account for the presence of charged and neutral components. An ad hoc interpolation of the ionization potential depression, valid across the whole ionization region, is put forward and subsequent solution of the generalized Saha equation is found to be in a perfect agreement with exact calculations. Minimization of the Helmholtz free energy of dusty plasmas provides the number densities of free electrons, free ions, neutrals, and the dust electric charge as well. Based on consideration of weakly and strongly ionized states, a straightforward comparison is made of the ionization equilibrium in a partially ionized plasma with and without dust particles to demonstrate that at thermal equilibrium positively charged dusts are responsible for an increase in the number density of free electrons and a decrease in the number density of free ions. It is analytically proved that nonideality effects result in a growth of the number densities of free electrons and ions by obtaining the so-called electron and proton ionization potential depressions. Electric charge of dust particles is systematically studied as a full plasma component rather than considering a detailed balance of the electron and ion fluxes on the surface of a solitary dust grain.

Multipole expansion in plasmas: Effective interaction potentials between compound particles

In this paper, the multipole expansion method is used to determine effective interaction potentials between particles in both classical dusty plasma and dense quantum plasma. In particular, formulas for interactions of dipole-dipole and charge-dipole pairs in a classical nondegenerate plasma as well as in degenerate quantum and semiclassical plasmas were derived. The potentials describe interactions between atoms, atoms and charged particles, dust particles in the complex plasma, atoms and electrons in the degenerate plasma, and metals. Correctness of the results obtained from the multipole expansion is confirmed by their agreement with the results based on other methods of statistical physics and dielectric response function. It is shown that the method of multipole expansion can be used to derive effective interaction potentials of compound particles, if the effect of the medium on the potential of individual particles comprising compound particles is known.

Effective potentials of interactions and thermodynamic properties of a nonideal two-temperature dense plasma

In this article a dense nonideal, nonisothermal plasma is considered. New effective screened interaction potentials taking into account quantum-mechanical diffraction and symmetry effects have been obtained. The effective potential of the ion-ion interaction in plasmas with a strongly coupled ion subsystem and semiclassical electron subsystem is presented. Based on the obtained effective potentials the analytical expressions for internal energy and the pressure of the considered plasma were obtained.

Thermodynamics of atomic and ionized hydrogen: analytical results versus equation-of-state tables and Monte Carlo data

We compute thermodynamical properties of a low-density hydrogen gas within the physical picture, in which the system is described as a quantum electron-proton plasma interacting via the Coulomb potential. Our calculations are done using the exact scaled low-temperature (SLT) expansion, which provides a rigorous extension of the well-known virial expansion-valid in the fully ionized phase-into the Saha regime where the system is partially or fully recombined into hydrogen atoms. After recalling the SLT expansion of the pressure [A. Alastuey et al., J. Stat. Phys. 130, 1119 (2008)], we obtain the SLT expansions of the chemical potential and of the internal energy, up to order exp(-|E_{H}|/kT) included (E_{H}≃-13.6 eV). Those truncated expansions describe the first five nonideal corrections to the ideal Saha law. They account exactly, up to the considered order, for all effects of interactions and thermal excitations, including the formation of bound states (atom H, ions H^{-} and H_{2}^{+}, molecule H_{2},⋯) and atom-charge and atom-atom interactions. Among the five leading corrections, three are easy to evaluate, while the remaining ones involve well-defined internal partition functions for the molecule H_{2} and ions H^{-} and H_{2}^{+}, for which no closed-form analytical formula exist currently. We provide accurate low-temperature approximations for those partition functions by using known values of rotational and vibrational energies. We compare then the predictions of the SLT expansion, for the pressure and the internal energy, with, on the one hand, the equation-of-state tables obtained within the opacity program at Livermore (OPAL) and, on the other hand, data of path integral quantum Monte Carlo (PIMC) simulations. In general, a good agreement is found. At low densities, the simple analytical SLT formulas reproduce the values of the OPAL tables up to the last digit in a large range of temperatures, while at higher densities (ρ∼10^{-2} g/cm^{3}), some discrepancies among the SLT, OPAL, and PIMC results are observed.