Measurements of the weak warm beam instability

Experiments are described on the interaction of a weak warm beam with a broad spectrum of unstable waves on a traveling wave tube. The wave–particle interactions are similar to those in beam–plasma systems, and are traditionally described by quasilinear theory. The precise wave evolution is obtained by launching a specified waveform, allowing it to interact with the beam, and analyzing the received waveform. Significant mode coupling is observed, resulting in saturated waves correlated less than 0.5 with their launch values. Experimentally, each wave is separated into a component proportional to the launch amplitude and a component due solely to mode coupling. The measured properties of these separate components agree quantitatively with a four-wave coupling model. Strongest coupling is observed between waves whose wave numbers match within about an inverse turbulent trapping length. In the linear growth regime, the measured ensemble-averaged wave growth rates and beam velocity diffusion rates agree reasonably with quasilinear and resonance-broadening theory; in the nonlinear regime near saturation, the discrepancies become larger.