Fokker-Planck multi-species equations in the adiabatic asymptotics

The main concern of the present paper is the study of the multi-scale dynamics of thermonuclear fusion plasmas via a multi-species Fokker-Planck kinetic model. One of the goals is the generalization of the standard Fokker-Planck collision operator to a multispecies one, conserving mass, total momentum and energy, as well as satisfying Boltzmann's H-theorem. Secondly, the paper investigates in more details the reduced model used for the electron description in present simulations, and which considers the electrons in a thermodynamic equilibrium (adiabatic regime), whereas the ions are kept kinetic. On the one hand, we perform some mathematical asymptotic limits to obtain in the electron/ion low mass ratio limit the above-mentioned electron adiabatic regime. On the other hand, we develop a numerical scheme , based on a Hermite spectral method, and perfom numerical simulations to illustrate and investigate in more details this asymptotics.