Parametric Effects of Radiation on a Plasma

The parametric excitation of the modes of an infinite plasma by intense incident radiation is studied on the basis of the Vlasov equation. It is found that the modes can be driven into unstable oscillations for incident frequencies in the three regions ${\omega }_0\simeq {\omega }_{\mathrm{pe}}$, ${\omega }_{\mathrm{pe}}+{\omega }_i$, and $2{\omega }_{\mathrm{pe}}$, where ${\omega }_{\mathrm{pe}}$ is the electron plasma frequency, and ${\omega }_i$ is the ion acoustic frequency. In the limit of weak intensities, the features of the two resonances ${\omega }_0\simeq {\omega }_{\mathrm{pe}}+{\omega }_i$ and $2{\omega }_{\mathrm{pe}}$ are found to be in substantial agreement with the results of DuBois and Goldman. For larger intensities it is found that the resonance ${\omega }_0\simeq {\omega }_{\mathrm{pe}}+{\omega }_i$ is restricted to frequencies ${\omega }_0$ which are not more than $4{\omega }_{\mathrm{pi}}$ above or ${\omega }_i$ below this value, and has a maximum growth rate of $0.05{\omega }_{\mathrm{pe}}$. The resonance near ${\omega }_0\simeq {\omega }_{\mathrm{pe}}$ is found to be dominated by collisional damping if $\frac{\gamma }{{\omega }_{\mathrm{pe}}}>{10}^{-4\mathrm{}}$, and limited to a range of frequencies ${\omega }_0$ of only $\frac{{\omega }_{\mathrm{pi}}}{100}$. The present results do not generally agree with the results obtained by Silin. These results indicate that the usual harmonic approximation for the plasma is justified except in the above-mentioned frequency regions.