Plasma transport coefficients in a magnetic field by direct numerical solution of the Fokker–Planck equation

Abstract

Significant departures from standard transport coefficients [e.g., Sov. Phys. JETP 6, 338 (1958)] have been found for the electron current and heat flux in a fully ionized plasma. These have been discovered by carrying out a direct and accurate numerical solution of the linearized Fokker–Planck equation using a Cartesian tensor expansion of the distribution function. The results, which were carried out for plasmas of various atomic numbers, show the presence of major inaccuracies (errors of up to 65%) in Braginskii coefficients β_■, κ_⊥, and κ_■ (as conventionally defined) for Hall parameters ωτ in the range 0.3≲ωτ≲30. Surprisingly, α_■ and β_⊥ are found to depend on τ/(ωτ)^2/3 and 1/(ωτ)^5/3, and not on τ/(ωτ) and 1/(ωτ)², respectively, as ωτ→∞. An analytic expansion for large ωτ verifies this result, showing that the relatively cold unmagnetized electrons in the distribution function play a dominant role in the cross‐field transport. The numerical results are fitted to within 15% to a polynomial in ωτ for various values of Z.