Relaxation of collisionless plasmas

Abstract

We present a new theory for the relaxation of two-dimensional collisionless quasi-neutral plasmas by mixing in phase space. In general, mixing in phase space does not lead to equilibrium states in the framework of exact, collisionless theory. However, filamentation on smaller and smaller scales can result in stationary states from a macroscopic (coarse-grained) point of view. In a first step we discuss a general technique to calculate suitably stable equilibria of collisionless plasmas. In a second step we develop a model relaxation that yields a simple transition to a description on macroscopic scales without following the details of the complicated mixing dynamics. Combination of both results allows calculation of final states of collisionless relaxation. We illustrate our approach with the help of a one-dimensional sheet configuration as a simple example.