Theory of double resonance parametric excitation in plasmas

It is shown that for a pump frequency separation Δ approximately equal to twice the ion acoustic frequency Ω, the use of two long-wavelength pumps can reduce the threshold for parametric excitation of ion-acoustic waves when, and only when, the Langmuir wave damping rate γ is much larger than Ω. The threshold is then reduced by a factor of order Ω/ω, the optimum value of Δ being 2Ω-GAMMA for equal pump amplitudes, where GAMMA is the ion-acoustic wave damping rate and GAMMA << Ω. A recent analysis is shown to be valid only for γ << Ω, where the threshold reduction is quite small, vanishing in the limit of weak ion-acoustic wave damping (Tsub(e)/Tsub(i) >> 1). (author)