Combined activity‐virial expansions

Rogers, F. J.; DeWitt, H. E.

doi:10.1002/ctpp.200310045

Cited by 5 publications

(5 citation statements)

References 7 publications

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“…Such data pushed the limits of the activity expansion method, and Forrest was characteristically excited by the data [58][59][60][61]. He revisited long-standing issues in pressure ionization and the molecular contribution to the EOS [62], as well as numerical improvements [63], reporting good agreement up to Γ ≈ 9. This is a formidable achievement for a perturbation expansion away from the ideal gas.…”

Section: Experimental Tests Of Theoretical Equation Of Statementioning

confidence: 93%

A tribute to pioneers of strongly coupled plasmas: Hugh E. DeWitt, Bernard Jancovici, and Forrest J. Rogers

Whitley

Alastuey

Gaffney

et al. 2014

Contrib. Plasma Phys.

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The field of strongly coupled Coulomb systems that stretches from dense plasma, to astrophysics, condensed matter and high energy physics has seen a dramatic development over the last four decades. At the beginning of this process were a few physicists whose work has had a high impact on many exciting developments of the recent years. Among them are Hugh E. DeWitt, Bernard Jancovici and Forrest J. Rogers who passed away in 2013–2014. Their important contributions to the field of strongly coupled Coulomb systems are summarized in this article. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Section: Experimental Tests Of Theoretical Equation Of Statementioning

confidence: 93%

A tribute to pioneers of strongly coupled plasmas: Hugh E. DeWitt, Bernard Jancovici, and Forrest J. Rogers

Whitley

Alastuey

Gaffney

et al. 2014

Contrib. Plasma Phys.

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“…From the partition function, we obtain the grand canonical thermodynamic potential J = −pV , which defines the pressure p = p(T, z i , z e ) in the fugacity representation. Thus, the pressure in the grand canonical ensemble serves as basic quantity for the description of the thermodynamics of plasmas [16,19,24,[28][29][30]. From this follows the expression for the densities…”

Section: The Methods Of Fugacity Inversion and Fermi-dirac Lawsmentioning

confidence: 99%

Hydrogen, helium and lithium plasmas at high pressures

Ébeling

Reinholz

Röpke

2020

Eur. Phys. J. Spec. Top.

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The equations of state (EoS) and other thermodynamic properties of plasmas of the light elements H, He, and Li, are calculated using inverted fugacity expansions. Fugacity expansions are known as an alternative to density expansions but show often an inferior convergence. If, however, the inversion can be solved, the fugacity representations may be very efficient. In particular, the contributions of deeply bound states are included in the fugacity expansion in a very effective way. The mathematical problems on nonlinearity connected with the inversion of fugacities to densities are reduced to solvable algebraic problems. The inversion of fugacities to densities is solved separately for two density regions: (i) In the low density, non-degenerate region we consider ring contributions describing screening effects and ladder contributions describing bound state formation. (ii) In the high density, degenerate region the electrons are described by the Fermi–Dirac distribution. Hartree–Fock contributions and Pauli blocking have to be taken into account. The ions are considered as classical, strongly correlated subsystem eventually forming a Wigner lattice. We solve the inversion problem for each of the regions. Near the crossing point, the separate solutions are connected to each other, either by smooth concatenation at the crossing point or by Padé approximations.

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“…Thus, the pressure in the grand canonical ensemble serves as basic quantity for the description of the thermodynamics of plasmas. [ 19,23,25,28,41–44 ] From this follows, the expression for the densities (

d \neq c

) is given as

n_{c} false(T, z_{i}, z_{e} false) = z_{c} {((), \frac{\partial p}{\partial z_{c}})}_{T, z_{d}} .

Within a quantum statistical approach using the method of Green's functions, typical approximations of the pressure of plasmas consist of three main contributions stemming diagrammatically in the lowest approximation from the free diagrams, the ring diagrams, and the ladder diagrams, [ 9 ] which represent the contributions of free states, modified by screening, and by the contribution of bound states, respectively,

p = p_{normalid} + p_{ring} + p_{bound} .

At higher temperatures, we may neglect the contributions of bound states completely and approximate the pressure by

p^{'} = p_{normalid} + p_{ring}

we are denoting this as a Debye‐like approach. In the grand canonical ensemble, we find the pressure contributions stemming from free and ring diagrams [ 9,25,28 ] :

β p^{'} = z_{e} + z_{i} - \frac{κ_{g}^{3}}{12 π} (1 - \frac{3 \sqrt{π}}{8} κ_{g} λ + \dots) .

The main nonideality term comes from ring diagrams depending on the fugacities instead of densities and correspondingly

κ_{g}

is the grand canonical Debye screening parameter.…”

Section: Representation In Grand Canonical Ensemblementioning

confidence: 99%

Equation of state of hydrogen, helium, and solar plasmas

Ébeling

Reinholz

Röpke

2021

Contributions to Plasma Physics

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The equation of state (EOS) for plasmas of the two lightest elements H and He, and mixtures as typical for the plasmas in the sun are calculated. The contributions of deep bound states are included by using inverted fugacity expansions. The inversion of fugacities to densities is reduced to solvable algebraic problems and expressed by rational polynomials. The calculation of relative pressures is carried out separately for low and high densities. Near the crossing point, in between, the separate solutions are connected to each other by smooth concatenation. Applications to hydrogen–helium plasmas in the sun including estimates for the isentropic EOS are discussed.

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Combined activity‐virial expansions

Abstract: We describe a mixed expansion method that combines the best features of the virial and activity expansions. The mixed expansion has the important feature that it can be applied to mixtures of plasma and neutrals that involve both attractive and repulsive interactions.

Cited by 5 publications

References 7 publications

A tribute to pioneers of strongly coupled plasmas: Hugh E. DeWitt, Bernard Jancovici, and Forrest J. Rogers

A tribute to pioneers of strongly coupled plasmas: Hugh E. DeWitt, Bernard Jancovici, and Forrest J. Rogers

Hydrogen, helium and lithium plasmas at high pressures

Equation of state of hydrogen, helium, and solar plasmas

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