Thermodynamics of dense high-temperature plasmas: Semiclassical approach

The electric microfield distributions at the location of an ion have been calculated using a coupling parameter integration technique for Li + plasma proposed by Ortner et al. [4] and Molecular Dynamics simulations. Electric microfield distributions are studied in a frame of the Hellmann-Gurskii-Krasko pseudopotential model, taking into account the quantum-mechanical effects and the ion shell structure [34]. The screened Hellmann-GurskiiKrasko pseudopotential taking into account not only the quantum-mecanical effects, the ion shell structure but screening field effects has been derived by means of Bogoljubow method [40] and [42]. The screened pseudopotential is represented by a Fourier transform. For the Hellmann-Gurskii-Krasko pseudopotential model the results obtained for the microfield in the framework of the Ortner model are found in a good agreement with the Molecular Dynamics simulations.

Section: Screening Of the Hellmann-gurskii-krasko Potentialmentioning

confidence: 99%

Section: Screening Of the Hellmann-gurskii-krasko Potentialmentioning

confidence: 99%

Section: Screening Of the Hellmann-gurskii-krasko Potentialmentioning

confidence: 99%

“…We derive the screened Hellmann-Gurskii-Krasko potential by using Bogoljubow's method as described e.g. in [39], [40], [41] and [42].…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Electric Microfield Distributions in Li + Plasma With Account of the Ion Structure

Sadykova¹,

Ébeling

Valuev

et al. 2009

Pseudopotential theory of a partially ionized hydrogen plasma

Arkhipov

Baimbetov

Davletov

2003

Key words Neutrals in plasma, partially ionized plasma, pseudopotential model PACS 52.25.YaIn the framework of the BBGKY hierarchy the main features of interparticle interactions in a partially ionized hydrogen plasma are extensively studied. The theory developed is quite analogous to the Debye-Hückel approximation of a fully ionized plasma.Of interest in the theory of modern plasma physics is the study of thermodynamic properties of partially ionized plasmas. It is evident that the ionization degree is determined by the direct competition of the thermal ionization process and the opposite process of recombimation. In the thermodynamic equilibrium, though, the ionization degree does not depend on details of those processes and can principally be calculated from the pure thermodynamic point of view. The basic procedure here is to assume the free energy and, then, minimize it [1,2].We propose by this a somewhat different approach to the problem that is aimed at studying correlation phenomena in a partially ionized hydrogen plasma consisting of neutrals (atoms), protons and electrons that are referred to in the following by the subscripts n, p and e, respectively. We describe the system of interest by the Wigner-Seitz radiusand, then, introduce the number density parameterHere n = n n + n p is the total amount of protons in the system, a B =h 2 /m e e 2 signifies the first Bohr radius,h is the Planck constant, m e and −e refer to the electron mass and charge, respectively.To characterize the importance of interparticle interactions the coupling parameter is introduced aswhere T is the plasma temperature and k B designates the Boltzmann constant. Fixing two parameters r s and Γ does not determine completely the composition of the plasma medium and, thus, the following Saha equation is added n e n p n n = 2πm e k B T h 2 3/2with the ionization energy I = m e e 4 /2h 2 of the ground state of the hydrogen atom.

Self‐Consistent Chemical Model of Partially Ionized Hydrogen Plasmas: Electrical Conductivity

Arkhipov

Baimbetov

Davletov

2007

Self Cite

The Bogolyubov hierarchy for equilibrium distribution functions is employed to define a chemical model for partially ionized hydrogen plasmas. The Helmholtz free energy is found in a self-consistent manner beyond the linear mixing rule allowing one to determine not only the ionization equilibrium but the correlation functions as well. Particle interactions are effectively treated such that the charged and neutral components of the plasma are closely interrelated which results in short-range order formation in the system of interest. The method proposed is an analog of the Debye-Hückel theory of fully ionized gases and allows one to study both thermodynamics and transport phenomena in a partially ionized hydrogen. Plasma parametersThis paper deals with a partially ionized hydrogen plasma consisting of electrons with the number density n e , protons with the number density n p and atoms with the number density n n . The system of interest is thus treated in the framework of the so-called chemical picture initially proposed in [1] (see also [2] for an overview).To characterize the state of the plasma we define the Wigner-Seitz radius as a = (3/4πn) 1/3 and introduce the density parameter r s = (3/4πn) 1/3 m e e 2 / 2 = a/a B , where n = n p + n n is the total number density of protons in the system, a B = 2 /m e e 2 designates the Bohr radius, signifies the Planck constant, m e and −e stand for the electron mass and electric charge, respectively. Note that knowledge of the density parameter is sufficient to determine the total number of protons and atoms but not their exact proportion. To describe the strength of interparticle interactions the Coulomb coupling parameter is defined as Γ = e 2 /(ak B T ), where T is the plasma temperature and k B denotes the Boltzmann constant. Helmholtz free energy and ionization equilibriumThe basic equation to be used is a consequence of the Bogolyubov hierarchy in the pair correlation approximation and reads [3,4]:where a r i is the i'th particle coordinate of sort a, i refers to the Laplace operator. Here ϕ ab (r) corresponds to the micropotential and Φ ab (r) represents the macropotential taking into account the collective events in the medium.