Vlasov Description of a Plasma
The formal identity between Vlasov's and Liouville's equations makes it frequently useful to refer to properties of single-particle motion to gain insight into the behavior of the solutions of the Vlasov equation. One should bear in mind, when doing so, that particle discreteness has been erased by the neglect of correlations. When the phase velocity of a wave is comparable to the plasma thermal velocity, however, the response of particles moving at different velocities is highly nonuniform: the particle response becomes local in velocity space as well as coordinate space. An important nonlinear phenomenom is the trapping of particles by a finite-amplitude electrostatic potential. The shuffling property has important consequences for the stability of Vlasov plasmas. The background distribution may be separated into a part that is constant on surfaces of constant energy, and a small, spatially oscillating part that results from the difference between surfaces of constant energy and velocity.