Quantum-Mechanical Plasma Transport Theory

Abstract

The quantum-mechanical convergent kinetic equation of Gould and DeWitt is used for the calculation of static transport coefficients through first order in the plasma parameter for a fully ionized, nondengenerate, two-component plasma near thermal equilibrium. The equation is solved with the standard Chapman-Enskog procedure using a three-term Sonine polynomial expansion. Since close collisions and dynamic screening effects are treated correctly, the results contain both logarithmic (dominant) and nonlogarithmic (subdominant) terms evaluated exactly to first order in the plasma parameter. Since close collisions are treated quantum mechanically the transport coefficients obtained are valid for a wide range of temperatures. For the case where only one Sonine polynomial is used in the evaluation of the electrical conductivity, the result obtained here reduces to that of Kivelson and DuBois in the high-temperature limit (kT ≫ Ry) and to that of Gould and DeWitt in the low-temperature, classical limit (kT ≪ Ry). Using more than one Sonine polynomial in the expansion of the distribution function, we obtain for the electrical conductivity σ(χ) = c(χ)σ(1), where χ is the number of terms in the Sonine expansion and σ(1) is the result for one term. In the limit where the Coulomb logarithm is large, c(3) = 1.95 and c(∞) = 1.973, so that our results are accurate to 1 or 2% for a wide range of temperatures (including kT ∼ Ry).