This book covers a variety of topics related to kinetic theory in neutral gases and magnetized plasmas, with extensions to other systems such as quantum plasmas and granular flows. A comprehensive presentation is given for the Boltzmann equations and other kinetic equations for a neutral gas, together with the derivations of compressible and incompressible fluid dynamical systems, and their rigorous justification. Several contributions are devoted to collisionless magnetized plasmas. Rigorous results concerning the well-posedness of the Vlasov-Maxwell system are presented. Special interest is devoted to asymptotic regimes where the scales of variation of the electromagnetic field are clearly separated from those associated with the gyromotion of the particles. This volume collects lectures given at the Short Course and Workshop on Kinetic Theory organized at the Fields Institute of Mathematical Sciences in Toronto during the Spring of 2004.
Hydrodynamic limits of kinetic models by F. Golse and C. D. Levermore Collisionless plasmas and the Vlasov Maxwell system by R. T. Glassey Irreversible behaviours in Vlasov equation and many-body Hamiltonian dynamics: Landau damping, chaos and granularity by Y. Elskens Introduction to the guiding center theory by P. L. Sulem Variational formulations of exact and reduced Vlasov-Maxwell equations by A. J. Brizard A short introduction to general gyrokinetic theory by H. Qin Introduction to gyrokinetic theory with applications in magnetic confinement research in plasma physics by W. M. Tang From kinetic to fluid descriptions of plasmas by T. Passot Nonlocal closures in long mean free path regimes by A. I. Smolyakov, M. Yagi, and J. D. Callen How to model quantum plasmas by G. Manfredi Inelastic kinetic theory: The granular gas by I. Goldhirsch.