Around the electronic M1 model

Sébastien Guisset

Angular moments closures are widely used in numerical solutions of kinetic equations. The first part of this presentation is devoted to introduce the validity domain of the M1 model and its extensions, the two populations M1 and the M2 angular moments models for the collisionless kinetic physics applications. Three typical kinetic plasmas effects are considered, which are the charged particle beams interaction, the Landau damping and the electromagnetic wave absorption in an overdense semi-infinite plasma. For each case, a perturbative analysis is performed and the dispersion relation is established using the moments models.

For collisional regimes applications, one must propose collisional operators for the electronic M1 model. However, the moment extraction of the electron-electron collision operator from the kinetic collision operator is challenging and some approximations are required. In the second part of the presentation, characterisations of the electron-electron and electron-ion collision operators proposed for the electronic M1 model are given and the electron plasma transport coefficients derivation is detailed. It is shown that in the high Z limit the electronic M1 model and the Fokker-Planck-Landau equation coincide in the case of near equilibrium. Also, in general, the electron-electron collision operator proposed for the electronic M1 model recovers accurate electron transport plasma coefficients.

A multi-dimensional finite volume Lagrangian scheme

Gabriel Georges

Solving the gas dynamics equations under the Lagrangian formalism enables to model complex flows with strong shock waves. This formulation is well suited to the simulation of multi-material compressible fluid flows such as those encountered in the domain of High Energy Density Physics (HEDP) and Inertial Confinement Fusion (ICF). These flows can present complex geometries and 3D aspects such as hydrodynamical perturbations which require 3D simulations. In this presentation, we will focus on the 3D extension of such a Lagrangian scheme. In particular, the definition of the cells geometry and the limitation of a reconstructed field in the case of a second-order extension appear to be challenging. Solutions will be proposed and tested on several academic test cases. Finally, we will see the application of this new scheme on the study of Rayleigh-Taylor instabilites in a supernova remnants in 3D.