Some Investigations of Nonlinear Behavior in One-Dimensional Plasmas

Abstract

Numerical experiments on a one-dimensional electron plasma were used to obtain an insight into nonlinear plasma phenomena. Three experiments were carried out. The first dealt with the damping of a large-amplitude wave which is found to be much stronger than that predicted by linear theory. A rough theory for the damping is presented. The second experiment examined mode-mode coupling. Quantitative agreement was found with theory after precautions were taken to avoid other effects, in particular, “trapped” particles. A rough theory for “trapping” is given. The third experiment examined the weak turbulence produced by a small bump in the tail of the distribution function, and present theory appears inadequate to describe this behavior. After initial growth, the unstable modes fluctuate on a time scale of 10ωp−1. The bump in the tail of the velocity distribution flattens out in a short time (20ωp−1), and then evolves into a hot Gaussian tail which coexists with the main plasma for a long time (≳ 1000 ωp−1). Particles in the tail have been observed with four times the initial average energy of the beam electron. A discussion of the physical effects which appear to be involved in this experiment is given, and estimates of their importance for three-dimensional plasmas are presented.