Instabilities in Parametric Oscillations of a Plasma

Dispersion relations for longitudinal and transverse waves propagated perpendicularly to an externally applied high‐frequency electric field in a fully ionized plasma has been obtained. It has been shown that in addition to ${\mathrm{\omega \; \sim \; \omega }}_0$ (${\omega }_0$ is the characteristic electron frequency), the longitudinal mode may be excited with frequencies ${\mathrm{\omega \; \simeq \; \Omega }}_k\mathrm{\pm \; \nu }$ (${\Omega }_k^2{\mathrm{\hspace{0.17em}=\hspace{0.17em}c}}^2{k}^2{\mathrm{\hspace{0.17em}+\hspace{0.17em}\omega }}_0^2$ , ν is the external field frequency); and under certain conditions the excitation near ${\omega }_0$ may be unstable. For the transverse mode instabilities may occur owing to resonance between a backward and a forward moving wave of the same frequency and vice versa. Apparently these are owing to the periodic nature of the dispersion relations found and to the mode‐mode coupling present.