Abstract

The focus of this lecture lays in the interplay  of  nonlinear analysis  and numerical approximations to mean field models in particle physics where kinetic transport flows in momentum are strongly nonlinearly  modified by macroscopic quantities in classical or spectral density spaces. We will present several examples in weakly and highly plasmas where, just a scaling parameter choses widely different asymptotic regimes. One is the classical Landau fluid flow models, another is and entropy diminishing computational schemes for Boltzmann Poisson systems subject to periodic boundary conditions. The last one, is the Quasi-Linear diffusion model for magnetized fast electrons in momentum space in a toroidal domain results from stimulated emission and absorption of waves packets via wave-particle resonances. Such model consists in solving the dynamics of a coupled system of classical kinetic diffusion processes described by the balance equations for electron probability density functions (electron pdf) coupled to the time dynamics on spectral energy waves  (quasi-particles) in a quantum process of their resonant interaction. Such description results in a ‘mean field’ model where diffusion coefficients are determined by the local spectral energy density of excited waves whose perturbations depend on flux averages of the electron pdf.  Analytical calculations and some Numerical  simulations show a strong hot tail anisotropy  formation and stabilization for the iteration in a three dimensional cylindrical model. The semi-discrete scheme preserves the total system mass, momentum and energy.  Work in collaboration with Clark Pennie,  Jose Morales Escalante,  Kun Huang, Michael Abdelmalik.