In plasma physics domain, the electron transport is described with the Fokker-Planck-Landau equation. The direct numerical solution of the kinetic equation is usually intractable due to the large number of independent variables. That is why we propose in this paper a new model whose derivation is based on an angular closure in the phase space and retains only the energy of particles as kinetic dimension. To find a solution compatible with physics conditions, the closure of the moment system is obtained under a minimum entropy principle. This model is proved to satisfy the fundamental properties like a H theorem. Moreover an entropic discretization in the velocity variable is proposed on the semi-discrete model. Finally, we validate on numerical test cases the fundamental properties of the full discrete model.

We show that it is possible to construct a class of entropicschemes for the multicomponent Euler system describing a gas or fluidhomogeneous mixture at thermodynamic equilibrium by applying a relaxation technique. Afirst order Chapman–Enskog expansion shows that the relaxed systemformally converges when the relaxation frequencies go to the infinitytoward a multicomponent Navier–Stokes system with the classical Fick andNewton laws, with a thermal diffusion which can be assimilated to a Soret effect in the case of a fluid mixture,and with also a pressure diffusion or a density diffusion respectively for a gas or fluid mixture. We also discuss on the link between the convexity of the entropies of each species and the existence of the Chapman–Enskog expansion.