Nonlinear heat conductivity in plasmas

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Abstract
It is shown that the modified moment method applied to the Vlasov–Landau equation is adequate for accounting for the heat flux inhibition in laser-driven plasmas, if the temperature profile is properly taken into account in calculating the heat flux. The temperature profiles are obtained by solving the steady-state mass, momentum, and energy balance equations in which the heat flux is a nonlinear function of the temperature gradient derived from the kinetic equation by means of the modified moment method. There can be two different temperature profiles, depending on the Mach number of the fluid speed. When the temperature profiles thus calculated are self-consistently used in the heat flux formula, the heat flux limit factors are derived. The factors are of the same order of magnitude as the experimentally inferred value of 0.03. For example, in the case of the hydrogen plasma the factor is less than 0.05 for the supersonic branch.