Absolute instability thresholds for parametric-decay interactions in plasmas

An analytical expression for the threshold of absolute growth for a parametric-decay instability is given for the simplest three-frequency interaction in a homogeneous plasma. The validity of this expression as compared to the results of a four-frequency interaction (including the upshifted frequency) at densities near critical is investigated using saddle-point mapping criteria. The investigation is carried out using pump intensities sufficiently large so that the effects of the oscillating-two-stream interaction should be manifest in the dispersion mapping for the parametric decay interaction. It is found that the absolute decay instability is preserved through a regime of parameters corresponding to intensities of ${10}^{14}$ ${\mathrm{W}/\mathrm{c}\mathrm{m}}^2$ and a critical parameter of $\frac{{\omega }_{\mathrm{pe}}}{{\omega }_0}=0.999\mathrm{}$. No parametric-decay instability is found for an overdense plasma. Finally, for a typical laser plasma, minimum threshold intensities are shown to exist for absolute instability of the parametric decay interaction at subcritical densities which are closer to the critical density than the previously known minimum thresholds for convective growth.