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A high order, deterministic direct numerical method is proposed for thenonrelativistic $2D_{\bf x} \times 3D_{\bf v}$ Vlasov-Maxwell system, coupledwith Fokker-Planck-Landau type operators. Such a system is devoted to themodelling of electronic transport and energy deposition in the general frame ofInertial Confinement Fusion applications. It describes the kinetics of plasmaphysics in the nonlocal thermodynamic equilibrium regime. Strong numericalconstraints lead us to 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. Parallelisation (MPIcommunication standard) and fast algorithms such as the multigrid method areemployed, that make this direct approach be computationally affordable forsimulations of hundreds of picoseconds, when dealing with configurations thatpresent five dimensions in phase space.

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