Nonlinear Mode Competition in Beam-Plasma Instability

Abstract

In a cold beam-plasma system unstable for $f>{f}_{\mathrm{ce}}$, two waves are launched, one at ${f}_{0}$, with large growth rate, and a small test wave at ${f}_{T}$, with small growth rate. The wave at ${f}_{0}$ saturates because of beam trapping, independent of the test-wave amplitude. After the beam is trapped, the test wave ceases growing and exhibits amplitude oscillations in phase with large wave. This is consistent with a linear interaction of the test wave with the modified electron beam.