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Developments around a Maxwell Fokker-Planck kinetic model dedicated to the ICF physics

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Fully determinist approximations of kinetic models are of special interest for the Inertial Confinement Fusion, where an accurate description of microscopic scales is required. Two examples of such kinetic processes are the non-local hot electron transport at the target compression stage and the fast core heating by high current relativistic electron beams at the ignition stage. One difficulty is that strong electric and magnetic fields are generated and a detailed kinetic description is of crucial importance (Collective mecanisms, spontaneously induced by charge separation ; magnetic focusing of the beam ; electric deceleration of the beam ; resistive heating). Another difficulty lies in handling electron propagation both in collisional and non collisional regimes. The basic physical process includes both electron-electron and electron-ion collisions in the 3D velocity space, but also at least 2D physical space self-consistent magnetic and electric fields. Moreover, fast electrons require a relativistic treatment. Development of such a code is a serious challenge in Applied Mathematics. Here, we present a Vlasov-Maxwell kinetic model coupled with a Landau-Fokker-Planck collision operator, which is supposed to address the above mentioned physical effects in typical volumes of tens of micrometers and in the time scale of tens of picoseconds. Description of the numerical methods is performed. In particular focus is put on conservative and entropy decaying properties that are required by such physics. A validation strategy has been set up, where simple physical examples are discussed as numerical challenges. The Landau damping, the two-stream instability, and the electron energy transport (with and without magnetic fields) are treated. Both qualitative and quantitative results show good performance of the code by now.

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