Adiabatic equation of state and ionization equilibrium of dense plasma

Beule, Dieter; Ébeling, W.; Förster, A.

doi:10.1016/s0378-4371(97)00168-4

Cited by 15 publications

(23 citation statements)

References 8 publications

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“…Then for any given temperature and density one has to minimize t h e free energy with respect to t h e abundancies of t h e various free and composite particles. We achieve this by a simulated annealing procedure t h a t finds t h e optimal numbers of free and composite particles within certain ensemble [61].…”

Section: Discussionmentioning

confidence: 99%

Quasiclassical Statistical Thermodynamics and New Padé Approximations for the Free Charges in Strongly‐Coupled Plasma

Ébeling

Stolzmann

Förster

et al. 1999

Contrib. Plasma Phys.

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HNC equations in combination with effective quasi-classical potentials are used to calculate correlation functions and the thermodynamic properties of the free charges in semi-classical non-degenerate quant.um plasmas. The interactions of the free particles are taken into account via effective potentials obtained from the Slater sum method. Analytical formulae reproducing the known limits and the HNC-results are constructed. Finally quantum effects are included as corrections by using known analytical results. This method is used to develope new Pad6 approximations for the subsystem of the free charges in mass-symmetrical as well as for' mass-unsymmetrical hydrogen-like plasmas. The most essential result of our investigations is, that in the classical limit the scaling properties correspond to the OCP, e.g. the thermodynamic functions follow for large coupling strength r a Berlin-MontrollRosenfeld asymptotics via a r + br" + c In I? + d. Including quantum effects, the coefficients depend on the temperature, e.g. the slope a(T) increases with decreasing T converging to the classical limit. The new formulae are compared with earlier variants.

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Section: Discussionmentioning

confidence: 99%

Quasiclassical Statistical Thermodynamics and New Padé Approximations for the Free Charges in Strongly‐Coupled Plasma

Ébeling

Stolzmann

Förster

et al. 1999

Contrib. Plasma Phys.

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“…A widespread form of this model is known as the lambda approximation. 8,15 In the lambda approximation, the same analytical formulation as the Debye-Hückel theory is used with the replacement of the classical parameter a by a temperature-dependent quantum length…”

Section: B Thermodynamic Functions and Nonideality Correctionsmentioning

confidence: 99%

“…If one takes the internal energy of an unionized ideal gas at T 0 Kelvin ͑usually chosen as 298. 15 K͒ as the reference level, then the specific internal energy per unit mass can be written as…”

Section: ͑16͒mentioning

confidence: 99%

A consistent model for the equilibrium thermodynamic functions of partially ionized flibe plasma with Coulomb corrections

Zaghloul

2003

Physics of Plasmas

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Flibe (2LiF–BeF2) is a molten salt that has been chosen as the coolant and breeding material in many design studies of the inertial confinement fusion (ICF) chamber. Flibe plasmas are to be generated in the ICF chamber in a wide range of temperatures and densities. These plasmas are more complex than the plasma of any single chemical species. Nevertheless, the composition and thermodynamic properties of the resulting flibe plasmas are needed for the gas dynamics calculations and the determination of other design parameters in the ICF chamber. In this paper, a simple consistent model for determining the detailed plasma composition and thermodynamic functions of high-temperature, fully dissociated and partially ionized flibe gas is presented and used to calculate different thermodynamic properties of interest to fusion applications. The computed properties include the average ionization state; kinetic pressure; internal energy; specific heats; adiabatic exponent, as well as the sound speed. The presented results are computed under the assumptions of local thermodynamic equilibrium (LTE) and electro-neutrality. A criterion for the validity of the LTE assumption is presented and applied to the computed results. Other attempts in the literature are assessed with their implied inaccuracies pointed out and discussed.

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“…Combining these two expressions we may get the usual EOS p = p(ρ, T ) as well as the isentropic (adiabatic) EOS p = p(s, T ), where ρ is the total mass density and s = S/N k B the specific entropy per proton (N = N p is the total number of protons in the plasma including the protons bound in H and in H 2 ). In earlier work we calculated the isentropic EOS based on the chemical picture [34,43]. We leave a detailed discussion of the isentropic EOS to future work.…”

Section: Discussion Of the Thermodynamics Functions And Phase Transitmentioning

confidence: 99%

“…In earlier work we calculated the isentropic EOS based on the chemical picture [34,43]. We leave a detailed discussion of the isentropic EOS to future work.…”

Section: The Ionization Equilibriummentioning

confidence: 99%

Thermodynamics and Phase Transitions in Dense Hydrogen – the Role of Bound State Energy Shifts

Ébeling¹,

Redmer

Reinholz

et al. 2008

Contrib. Plasma Phys.

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In recent papers we have investigated the effects of Pauli blocking on the energy shifts in dense hydrogen. As Pauli blocking we denote effects on the shifts which result from the antisymmetry of the electronic wave functions. Here we study of the thermodynamic properties of dense hydrogen including the influence of energy shifts. Of special interest is the region where a transition from insulating behavior to metal-like conductivity has been shown experimentally. In this region, Pauli blocking effects have a deciding influence on this transition. Assuming that the system is a gas-like mixture of chemical species, the ionization equilibrium is treated by an advanced chemical approach. We calculate the Pauli and Fock shifts by perturbation theory and variational methods and construct useful interpolation formulae. Results for the ionization equilibrium are presented for temperatures between 4 000 K < T < 20 000 K and densities in the range n = (2 − 6) × 10 23 cm −3 where the transition from a neutral hydrogen gas to a highly ionized plasma occurs. The results for the equation of state and the relative pressure indicate that the transition to a highly conducting state is softer than derived in earlier work.

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Adiabatic equation of state and ionization equilibrium of dense plasma

Cited by 15 publications

References 8 publications

Quasiclassical Statistical Thermodynamics and New Padé Approximations for the Free Charges in Strongly‐Coupled Plasma

Quasiclassical Statistical Thermodynamics and New Padé Approximations for the Free Charges in Strongly‐Coupled Plasma

A consistent model for the equilibrium thermodynamic functions of partially ionized flibe plasma with Coulomb corrections

Thermodynamics and Phase Transitions in Dense Hydrogen – the Role of Bound State Energy Shifts

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