Test Wave Coexisting with a Large-Amplitude Electron Plasma Wave

The behavior of a small test wave launched simultaneously with a large-amplitude electron plasma wave is calculated by treating the test wave as a slow modulation of the larger wave's amplitude and phase. Test-wave experiments show agreement with the calculation when the test-wave frequency is between the large wave's frequency (${\omega }_0$) and ${\omega }_0-\frac{4\pi }{T}$, where $T$ is the main wave's transit time through the experiment. When the spontaneously unstable lower sideband frequency is within this range, the sideband's slow amplitude oscillations agree with the calculation.