Some Investigations of Nonlinear Behavior in One-Dimensional Plasmas

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 ${\text{10ω}}_p^{\text{−1}}$ . The bump in the tail of the velocity distribution flattens out in a short time ${\text{(20ω}}_p^{\text{−1}})$ , and then evolves into a hot Gaussian tail which coexists with the main plasma for a long time ${\text{(≳ 1000 ω}}_p^{\text{−1}})$ . 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.