Nonlinear Mode Competition in Beam-Plasma Instability

In a cold beam-plasma system unstable for $f>\mathrm{}{f}_{\mathrm{ce}}$, 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.