An entropic approach to magnetized nonlocal transport and other kinetic phenomena in high-energy-density plasmas

Hydrodynamic simulations in high-energy-density physics and inertial confinement fusion require a detailed description of energy fluxes. The leading mechanism is the electron transport, which can be a nonlocal phenomenon that needs to be described with quasistationary and simplified Fokker-Planck models in large scale hydrodynamic codes. My thesis is dedicated to the development of a new nonlocal transport model based on a fast-moving-particles collision operator and on a first moment Fokker-Planck equation, simplified with an entropic closure relation. Such a closure enables a better description of the electron distribution function in the limit of high anisotropies, where small scale electrostatic instabilities could be excited. This new model, so called M1, is successfully compared with the well known nonlocal electron transport model proposed by Schurtz, Nicolai and Busquet, using different collision operators, and with the reduced Fokker-Planck model, based on a small-anisotropies polynomial closure relation (P1). Several typical configurations of heat transport are considered. We show that the M1 entropic model may operate in two and three dimensions and is able to account for electron transport modifications in external magnetic fields. Moreover, our model enables to compute realistic electron distribution functions, which can be used for kinetic studies, as for the plasma stability in the transport zone. It is demonstrated that the electron energy transport may strongly modify damping of Langmuir and ion acoustic waves, while the simplified nonlocal transport models are not able to describe accurately the modifications of the distribution function and plasma wave damping. The structure of the M1 model allows to naturally take into account self-generated magnetic fields, which play a crucial role in multidimensional simulations. Moreover, magnetic fields could also be used for the focusing of energetic particles in alternative ignition schemes. The M1 model reproduces the results of the local transport theory in plasma, developed by Braginskii, in a broad range of degrees of magnetization and predicts new results in the nonlocal regime. This work constitutes a first validation of the entropic closure assumption in the weakly-anisotropic regime. It can be added to the existing tests, in the strongly-anisotropic regimes. (author)