Growth rates of parametric instabilities driven by two pump waves

The authors have calculated the parametric instability growth rates and the frequency spectrum for ion acoustic waves driven by two long wavelength pump fields with frequencies w1 and w2 = w1 - Δ near the Bohm Gross frequency w/sub k/, where Δ is of order of the ion acoustic frequency Ω. It has been shown previously that the stability threshold is lower, with two pumps rather than one, only when the Langmuir wave damping rate exceeds Ω. Here they explore the dependance of the growth rate on w1 and w2 and find that there are nulls when w1 and w2 are symmetrically located above and below w/sub k/ and also when Δ = 2Ω. Under some conditions, the nulls extend over a finite region (of w1, for fixed w2, or vice versa) giving a structure similar to that associated with the Mathieu equation. They also find that the peaks in the electron density spectrum resulting from a single pump show a characteristic splitting when the second pump is added