High order resolution of the Maxwell–Fokker–Planck–Landau model intended for ICF applications

A high order, deterministic direct numerical method is proposed for the non-relativistic 2 D x × 3 D v Vlasov–Maxwell system, coupled with Fokker–Planck–Landau collision operators. The magnetic field is perpendicular to the 2 D x plane surface of computation, whereas the electric fields occur in this plane. Such a system is devoted to modelling of electron transport and energy deposition in the general frame of Inertial Confinement Fusion applications. It is able to describe the kinetics of the plasma electrons in the nonlocal equilibrium regime, and permits to consider a large anisotropy degree of the distribution function. We develop specific methods and approaches for validation, that might be used in other fields where couplings between equations, multiscale physics, and high dimensionality are involved. Fast algorithms are employed, which makes this direct approach computationally affordable for simulations of hundreds of collisional times.