chapter  2
17 Pages

Kinetic Equations

ByS. Ichimaru

Plasma physics involves a rich class of phenomena related to the dynamical processes in statistical mechanics. This chapter begins with a discussion of the Vlasov equation: It will be derived from the Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy; in the process, its validities and limitations will also be studied. This is particularly important in view of the fact that the Vlasov equation is used most frequently in the theoretical investigation of the plasma phenomena. The chapter presents consideration of the collision term in the kinetic equation; this involves a study of the particle correlations, which are not included in a treatment based on the Vlasov equation. It is worth noticing that the Balescu–Lenard collision term conserves the mean kinetic energy only and does not concern itself with the interaction energy. This stems from the fact that the theory has taken account of only the first-order effects in the plasma parameter.