Instabilities in Parametric Oscillations of a Plasma in a Magnetic Field

Abstract

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 ν (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 ≃ Ω − ω0, where ω0 is the electron plasma frequency, and instabilities may occur provided Ω is large. Excitation and instabilities are also possible with frequency ≃ ν − ω0 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.