How correct is the EOS of weakly nonideal hydrogen plasmas?

Abstract

Helioseismology opens new possibility to check EOS of weakly nonideal hydrogen plasmas with high precision, using reconstructed local sound velocities within 10 −4 accuracy. A comparison of different theoretical models with experiment permits to verify the existing methods of calculation bound states and continuum contribution to the second virial coefficient within the framework of physical nature.The regular way of the deduction expression for EOS is presented and generalization of the EOS for broad atomic states and two temperature non-equilibrium case is proposed. cannot be considered as a convincing proof -each step contains infinities for the pure Coulomb case.To calculate thermodynamic functions of weakly nonideal hydrogen plasmas it is convenient to use KadanoffBaym-Keldysh technique [8,9]. From [8] it is possible to obtain correction δp to the ideal gas pressure p 0 :where S a -spin value of the particle a, integration over λ parameter corresponds to integration over charge e 2 → e 2 λ, Σ > a -mass operator (Σ +− in Keldysh notations) represents decay rate of excited a-particle state with momentum p and frequency ω; G < a -kinetics Green's function (G −+ in Keldysh notations); β = T −1 , T -temperature in energy units.From (1) we obtain contribution from e − i system to thermodynamical potential in grand canonical ensembleHere µ a -chemical potential of a particle of a-kind,λ a -thermal de-Broigle wavelength,λ a =

Pair fluctuations in nonideal plasma and their restriction at the ionization threshold

“…Then the lifetime of pairs in equilibrium plasma is (30) where averaging 〈…〉 is performed over the Maxwellian distribution. If the lifetime is expressed in periods of plasma oscillation τ e , then (31) where f(ε) is the density of distribution of pair fluctuations with respect to bond energies (19), normalized to unity. We assume the temperature dependence of the factor ln(kT/|ε|) to be weak and select f(ε) for ideal plasma f(ε) = g(ε)exp(-ε/kT), where the function g(ε) similar to "spread-out" statistical weight depends on ε, to derive from Eq.…”

“…The history of the problem goes back to Planck [15], Fermi [16], and Brillouin [17]. The simultaneous consideration of free and pair "bound states" (atoms) turned out to be possible owing to the application of quantum statistical physics [2,3,[18][19][20] (however, only in the ideal plasma limit) and produced a convergent expression for Z [1][2][3]. The assumption of interaction between continuous spectrum of collective excitations of free electrons and discrete spectrum of excited atoms is discussed in [ In the present paper, an attempt is made at simultaneous consideration of free and pair "bound states" (highly excited atoms) in nonideal plasma.…”

Max Planck and Albrecht Unsöld on plasma partition functions and lowering of ionization energy

“…Note here that there are also other approaches to this problem: for example, Khomkin and Shumikhin suggested choosing the weight factor based on a nearest neighbour approximation . In a different approach to the problem, as put forward by Starostin and Roerich, the authors arrived even at the conclusion that the PBL partition function is wrong. Following Onsager, we would prefer to apply the terms correct or wrong not to the bound state partition function but only to expressions for complete thermodynamic functions containing a sum of bound‐state and free‐state contributions.…”

Account of Atomic and Molecular Contributions in the Equation of‐State for a Weakly Non‐Ideal Hydrogen Plasmas

“…1 the temperature dependences of heat capacity c V along the lines of constant density are shown for the model EOS with (solid lines) and without (dots) last term in the molecular PF (8). As can be seen, the influence is more pronounced at higher values of density ρ > 10 −2 g·cm −3 .…”