Effect of ion motion on parametric oscillations of a cold plasma in a magnetic field

Dispersion relations for first-order oscillations in an infinite homogeneous two- component plasma, in response to an externally applied constant magnetic field and a right-hand circularly polarized external electric field, and with propagation vector parallel to the magnetic field, has been obtained. The external electric field, assumed to be spatially homogeneous, is perpendicular to the applied magnetic field. It has been shown that the left-hand mode is excited and is unstable when its frequency ν-ω^ρ, where ν is the frequency of the external electric field and ω^ρ is the characteristic plasma frequency. When the applied magnetic field is large, both the left- and right-hand modes are excited and may be unstable when their frequencies Ω_ic - ω_ρ where Ω_ic represent the electron (i = 1) and the ion (i = 2) cyclotron frequencies. The principal criterion for the validity of these results is the condition of spatial homogeneity of the external electric field.