Nonlinear Development of the Two-Stream Instability

The nonlinear development of the two-stream instability is investigated analytically and numerically using as a model two cold interpenetrating electron and ion streams. When periodic boundary conditions are chosen so that only one linearly unstable wave is excited, it is found that whether or not the instability levels off nonlinearly before overtaking is directly dependent upon the choice of the spatially averaged electric field E0. Simple choices of E0 are given for stabilization and no stabilization. Also, even though there is strong nonlinear coupling, there is no continuous flow of energy into higher harmonics, for those waves which stabilize.