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.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

Graduate students interested in physics and applied mathematics and research mathematicians interested in kinetic theory of dilute gases and magnetized plasmas.

Table of Contents

• F. Golse and C. D. Levermore -- Hydrodynamic limits of kinetic models
• R. T. Glassey -- Collisionless plasmas and the Vlasov Maxwell system
• Y. Elskens -- Irreversible behaviours in Vlasov equation and many-body Hamiltonian dynamics: Landau damping, chaos and granularity
• P. L. Sulem -- Introduction to the guiding center theory
• A. J. Brizard -- Variational formulations of exact and reduced Vlasov-Maxwell equations
• H. Qin -- A short introduction to general gyrokinetic theory
• W. M. Tang -- Introduction to gyrokinetic theory with applications in magnetic confinement research in plasma physics
• T. Passot -- From kinetic to fluid descriptions of plasmas
• A. I. Smolyakov, M. Yagi, and J. D. Callen -- Nonlocal closures in long mean free path regimes
• G. Manfredi -- How to model quantum plasmas
• I. Goldhirsch -- Inelastic kinetic theory: The granular gas