Nonlinear Resonance Phenomena of Electron Plasma Oscillations by Beam Modulation

A longitudinal electron plasma oscillation having a narrow spectral width was spontaneously excited in a beam plasma system. As the frequency of the beam modulation approaches that of the spontaneous electron plasma oscillation, we observed that the electron plasma oscillation suffered catastropic suppression, while the oscillation with the same frequency as the modulation one was enhanced suddenly. Asymmetry and hysteresis of oscillation amplitude were observed. These nonlinear phenomena are well explained by an equation of the van der Pol type including a driving term and a cubic nonlinear term. The magnitude of the nonlinear term was estimated.