An Extension of Spitzer-Härm Theory on Thermal Transport to Steep Temperature Gradient Case. II. Integral Representation

The electron distribution function in a plasma with the steep temperature gradient is obtained from the Fokker-Planck equation by the Green's function method, extending the previous differential formula [J. Phys. Soc. Jpn. 52 (1983) 3389]. The formula describes the nonlocal effects on the thermal transport over the range of \(λₑ/L{}0.1 (λₑ\): electron mean free path, L : temperature scale length). The formula includes the self-consistent electrostatic potential and exactly recovers the Spitzer-Härm thermal conductivity in the long scale length limit, λ e / L →0. As an example, the heat wave propagation is numerically analyzed by employing the integral formula and the nonlocal properties of the heat flux, which is obtained in the Fokker-Planck simulation, are well reproduced.