Corrections to the Electrical Conductivity of the Fully Ionized Plasma at Moderate Values of the Degeneracy Parameter

Abstract

The influence of the electronic degeneration on the electrical conductivity of the fully ionized low-density hightemperature plasma is investigated. The consideration basis is the following: the linear response theory in the formulation of Zubarev, Lenard-Balescu-type collision integrals with dynamical screening of the Coulomb interaction, the first Born approximation in the thermodynamic Green's functions technique. Asymptotic expansions for correlation functions for electron-ion and electron-electron scattering as functions of the degeneracy parameter Θ = kBT /EF in the range from Θ 1 to Θ → 1 are obtained. The results presented are improved approximation formulas for the correlation functions and the electrical conductivity. The Spitzer factors for the electrical conductivity are slightly corrected.

Contribution of electron-atom collisions to the plasma conductivity of noble gases

“…Within the LinearResponse-Theory (LRT) the treatment and inclusion of different collision mechanisms is vivid. In recent years, the influence of electron-electron (e-e) collisions at arbitrary degeneracy was discussed in Born approximation for a fully ionized plasma (FIP) by Reinholz et al [4] and Karakhtanov [5], leading to a systematic interpolation between the Spitzer and the Ziman limit, see also Esser et al [6]. A correction factor is obtained which depends in contrast to the Spitzer value on density and temperature.…”

Virial Expansion of the Electrical Conductivity of Hydrogen Plasmas

“…1, see also [39]. The line including e − e collisions obeys the same asymptote (x → 0) as that of Karakhtanov [28]. With increasing x = 1/ ln(Θ/Γ), small deviations from the linear behavior are seen.…”

“…Inspecting Fig. 2, values for 10 g/cm 3 (17) for hydrogen plasma as a function of x = 1/ ln(Θ/Γ): QMD simulations of Lambert et al [38] (the orange line points to the value for n = 80 g/cm 3 , kBT = 300 eV), DFT-MD simulations of Desjarlais et al [27] and of this work, experimental values of Günther and Radtke [44], and Lenard-Balescu results of Karakhtanov [28]. ρ Spitzer 1 = 0.846 and ρ Lorentz 1 = 0.492 are defined in the text.…”

“…Considering screening in the random-phase approximation leads to the quantum Lenard-Balescu (QLB) expression. Thus, at very high temperatures where the dynamically screened Born approximation becomes valid, we obtain the QLB result, see [27][28][29],…”

“…To extract the first and second virial coefficient from calculated or measured dc conductivities, we plot the ex- Lenard-Balescu results of Karakhtanov [28] as well as QLB results [27] including the e − e interaction (dashed) and without (only e − i: dot-dashed) are also shown. The values ρ Spitzer 1 , ρ Lorentz 1 , and ρ Ziman 1 are defined in the text.…”