When an oscillating electric field is applied along a plasma density gradient, an enhanced field is resonantly excited where the electron plasma frequency approximately equals the frequency of the applied field. The measured, time-averaged distribution function of the electrons accelerated by the enhanced field in a plasma-filled capacitor includes a high-energy component that agrees with calculations.

When a fast electron beam transits a high frequency, localized electric field in a plasma, the beam is dispersed in energy, and no net energy is transferred between the beam and the field. The time-averaged distribution function of the beam is a source of information about the localized field strength and width.

The nonlinear behavior of two unstable waves that grow simultaneously at closely spaced frequencies on a low density, initially monoenergetic beam-plasma system is calculated. The exponential spatial growth of both waves stops in the region where the beam is trapped by the waves. When the initial amplitude ratio ‖ε‖ (⩽1) of the two waves exceeds 0.4, both waves play a significant role in the trapping, so the larger wave saturates at a lower potential than when launched alone. The behavior of an intermodulation product is calculated as a contribution to the spectral broadening, and the total energy in this wave plus the two launched waves is shown to evolve spatially in approximately the same way as the energy of a single frequency wave that is launched alone.

When a small test wave is launched near the frequency of a large amplitude electron plasma wave, the behavior of the test wave is determined by the nonlinear dynamics of the electrons that are trapped by the large amplitude wave. Consequently, the amplitude of the test wave oscillates coherently with the trapping oscillations in the amplitude of the main wave. The behavior of a small, launched, test wave at frequency ω is observed as a function of its frequency separation from a large amplitude electron plasma wave at frequency ω0. The initial damping and subsequent amplitude oscillations of the test wave are compared with a calculation in which the test wave is treated as a slow modulation of the amplitude and phase of the main wave. Test wave experiments agree with the calculation when ω0 − 4π/T < ω < ω0 + π/T, where T is the transit time of the main wave through the experiment. When the spontaneously unstable frequency of the lower sideband is within this range, the slow amplitude oscillations of the sideband agree with the calculation. When the frequency of the test wave is sufficiently far below ω0 − 4π/T, the test wave damps according to linear theory. The phase velocity at which the test wave behaves essentially linearly determines the velocity of the fastest electrons that interact strongly with the wave.

The unstable modes on a low-density, cold-electron-beam-plasma system are treated as an ensemble of Van der Pol oscillators. This model predicts the observed amplitude limiting of unstable waves at the neighboring frequencies of a launched wave that traps the beam electrons.