Response to “Comment on ‘On the ionization equilibrium of hot hydrogen plasma and thermodynamic consistency of formulating finite partition functions’ ” [Phys. Plasmas 17, 124705 (2010)]

Zaghloul, Mofreh R.

doi:10.1063/1.3531707

Cited by 6 publications

(4 citation statements)

References 6 publications

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“…The evaluation of the internal partition function for the composite structured particles has been thoroughly discussed and investigated in Refs [17,[29][30][31][32]]. An essential concern in modeling thermodynamic equilibrium at high density is associated with the need to consistently and smoothly truncate the internal partition functions of the ensemble of bound states.…”

Section: Free Energy Componentsmentioning

confidence: 99%

Equation-of-state, critical constants, and thermodynamic properties of lithium at high energy density

Zaghloul

Hassanein

2019

Physics of Plasmas

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High-density lithium plasmas are expected to be generated in the Inertial Confinement Fusion (ICF) reactor chamber due to energy deposition of the prompt X-rays and ion debris in the first wall. These dense plasmas are encountered in many other applications as well.The design and optimization of such lithium-based applications requires information about the thermodynamic properties of Li fluid over a wide range of parameters including the high-energy-density regime.A model that takes into account all essential features of strongly-coupled plasmas of metal vapors is developed and used to predict the equation-of-state (EOS), critical constants, thermodynamic functions, and principal shock Hugoniot of hot dense lithium fluid.Predictions and computational results from the present model are analyzed and presented and are available in electronic form suitable for use to interested researchers and scientists.

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Section: Free Energy Componentsmentioning

confidence: 99%

Equation-of-state, critical constants, and thermodynamic properties of lithium at high energy density

Zaghloul

Hassanein

2019

Physics of Plasmas

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“…In these applications the numbers N n of atoms in the electronically excited state E n are retained as independent thermodynamic variables. Some criticisms are presently raised concerning the consistency of some expressions of the free energy used by the occupation probability methods [24]- [26]. These criticisms do not apply to the present derivation since our thermodynamic model is limited to diluted conditions and, above all, has a single variable N H to describe the total number of all neutral atoms, irrespective of their state of electronic excitation.…”

Section: 10)mentioning

confidence: 94%

A simple thermodynamic model of diluted hydrogen gas/plasma for CFD applications

Quartapelle

Muzzio²

2015

Eur. Phys. J. D

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This work describes a simple thermodynamic model of the hydrogen gas at low densities and for temperatures going from those involving quantum rotations of ortho-and para-hydrogen up to the fully ionized state. The closed-form energy levels of Morse rotating oscillator given in Harris and Bertolucci [14] (but not those in Morse's original paper) are shown to provide an internal partition function of H2 that is a sufficiently accurate representation of that exploiting the state-of-the-art spectrum of roto-vibrational levels calculated by Pachucki and Komasa [13]. A system of two coupled quadratic equations for molecular dissociation and atomic ionization at thermodynamical and chemical equilibrium is derived according to the statistical mechanics by assuming that the system is an ideal mixture containing molecules, neutral atoms and noninteracting protons and electrons. The system of two equations reduces to a single quartic equation for the ionization unknown, with the coefficients dependent on the temperature and the specific volume. Explicit relations for specific energy and entropy of the hydrogen ideal gas/plasma model are derived. These fully compatible equations of state provide a complete thermodynamic description of the system, uniformly valid from low temperatures up to a fully ionized state, with electrons and ions relaxed to one and the same temperature. The comparison with results of other models developed in the framework of the physical and chemical pictures shows that the proposed elementary model is adequate for computational fluid dynamics purposes, in applications with the hydrogen gas under diluted conditions and when the dissociation and ionization can be assumed at thermodynamical and chemical equilibrium.

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“…Dissociation and ionization equilibria are considered with a special interest devoted to the pressure dissociation and pressure ionization phenomena. The model implements our newly proposed formulation for the establishment of statistical-thermodynamically consistent finite bound-state partition functions, [37][38][39] where an occupational probability is prescribed in advance to assure a smooth truncation of the electronic partition function and manifestation of the phenomenon of pressure ionization. An analogous occupational probability is proposed herein for a smooth truncation of the vibrational-rotational molecular partition function of deuterium molecules.…”

Section: Introductionmentioning

confidence: 99%

Dissociation and ionization equilibria of deuterium fluid over a wide range of temperatures and densities

Zaghloul

2015

Physics of Plasmas

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We investigate the dissociation and ionization equilibria of deuterium fluid over a wide range of temperatures and densities. The partition functions for molecular and atomic species are evaluated, in a statistical-mechanically consistent way, implementing recent developments in the literature and taking high-density effects into account. A new chemical model (free energy function) is introduced in which the fluid is considered as a mixture of diatomic molecules, atoms, ions and free electrons. Intensive short range hard core repulsion is taken into account together with partial degeneracy of free electrons and Coulomb interactions among charged particles. Samples of computational results are presented as a set of isotherms for the degree of ionization, dissociated fraction of molecules, pressure, and specific internal energy for a wide range of densities and temperatures. Predictions from the present model calculations show an improved and sensible physical behavior compared to other results in the literature. I -INTRODUCTIONThe equation-of-state of deuterium, over a wide range of densities and temperatures, is of central importance to many fundamental and applied topics and has been under intensive investigation over the past four decades . Accurate prediction of the equation-of-state and thermodynamic properties of deuterium at ultrahigh pressures and a wide range of temperatures is of great interest to ICF research and astrophysical applications. Since the compressibility of a material is determined by its equation-of-state, the accurate estimation of the EOS of the deuterium or deuterium-tritium fusion fuel is critical for designing ICF ignition targets and for predicting the performance of the target during ICF implosions. Besides, both of the planets Jupiter and Saturn contain large amount of very dense hydrogen and information about deuterium EOS is, therefore, essential in the study of these planets.

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Response to “Comment on ‘On the ionization equilibrium of hot hydrogen plasma and thermodynamic consistency of formulating finite partition functions’ ” [Phys. Plasmas 17, 124705 (2010)]

Abstract: Dissociation and ionization equilibria of deuterium fluid over a wide range of temperatures and densities

Cited by 6 publications

References 6 publications

Equation-of-state, critical constants, and thermodynamic properties of lithium at high energy density

Equation-of-state, critical constants, and thermodynamic properties of lithium at high energy density

A simple thermodynamic model of diluted hydrogen gas/plasma for CFD applications

Dissociation and ionization equilibria of deuterium fluid over a wide range of temperatures and densities

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