Theory of double resonance parametric excitation in plasmas. Part 2

Using a simpler formalism than in the original paper on this subject, we verify the earlier result 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 t being Δ2Ω –Γ for equal pump amplitudes, where Γ is the ion-acoustic wave damping rate and Γ « Ω. The analysis presented in a recent paper 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 (T_e/T_i » 1).