Micro, kinetic and fluid descriptions—Hierarchy of plasma descriptions

Abstract This chapter describes the hierarchical development of classical plasma dynamic model equations. In any macroscopic physical system containing many individual particles, there are basically three levels of classical dynamics descriptions: the exact microscopic description, the kinetic theory description, and the macroscopic or fluid description. The chapter's analysis of classical plasma dynamic model equations spans from the microscopic Liouville–Klimontovich equations, and its Bogoliubov, Born, Green, Kirkwood, Yvon (BBGKY) hierarchy of coupled statistical correlations, to their reduction to the fluid kinetic equations (Boltzmann and Vlasov–Fokker–Planck), to the hydrodynamic moment equations and the various reduced hydrodynamic equations used in preceding chapters. In particular, the chapter also puts in perspective the collisionless kinetic Vlasov equation and Vlasov–Fokker–Planck, Boltzmann equations, which are used to study the dynamics of plasma.