High-Order Wave Mixing in Beam-Plasma Instabilities

Abstract

When two waves, ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{1}+\ensuremath{\Delta}\ensuremath{\omega}$, are externally driven in an unstable beam-plasma system, they are found to couple in the nonlinear regime to produce up to ten waves, with frequencies given by ${\ensuremath{\omega}}_{1}\ifmmode\pm\else\textpm\fi{}n\ensuremath{\Delta}\ensuremath{\omega}$ and amplitudes comparable to the driver amplitudes. This situation is described in terms of third- and higher-order wave-interaction processes. It is suggested that this phenomenon is responsible for nonlinear broadening of the amplified noise spectrum.