Instabilities in Parametric Oscillations of a Plasma in a Magnetic Field

A dispersion relation for transverse waves with a propagation vector along the direction of a constant magnetic field pervading a plasma medium in response to an externally applied circularly polarized or hybrid electric field with the electric vector perpendicular to the magnetic field has been obtained. The zero‐order state of the plasma is defined by these external fields with a zero‐order plasma current and a zero‐order external current, both of which have oscillatory parts with frequencies $\nu$ (frequency of the applied field) and Ω (the electron cyclotron frequency). It has been shown that in all cases the left‐hand mode is excited with frequency ${\mathrm{\simeq \hspace{0.17em}\Omega \hspace{0.17em}-\hspace{0.17em}\omega }}_0$ , where ${\omega }_0$ is the electron plasma frequency, and instabilities may occur provided Ω is large. Excitation and instabilities are also possible with frequency ${\mathrm{\simeq \hspace{0.17em}\nu \hspace{0.17em}-\hspace{0.17em}\omega }}_0$ in both modes under certain restrictions. The principal criterion for these restrictions is the validity of the assumption of spatial homogeneity of the imposed electric field.