Oscillating two-stream and parametric decay instabilities in a weakly magnetized plasma

The effects of a weak ambient magnetic field on the oscillating two-stream and parametric decay instabilities, with particular emphasis on the dependence of the angular variation of the instability thresholds and growth rates on the magnetic field, are considered. A dispersion relation is derived in the limit in which ωe≳≳Ωe (where ωe and Ωe are the electron plasma and cyclotron frequencies, respectively), and is solved for dipole and monochromatic pump spectra. The analysis shows that the presence of a magnetic field can substantially enhance thresholds and reduce growth rates for waves propagating at an oblique angle with respect to the ambient magnetic field and k2λ2e∼Ω2e/ω2e (where k is the wave vector of the perturbation and λe is the Debye length). Thus, the magnetic field has a stabilizing influence on the off-parallel propagating modes.