On the spectrum of longitudinal plasma oscillations

Abstract

Longitudinal plasma oscillations are investigated in the presence of a beam of electrons possessing a large velocity component V⊥0 perpendicular to the external magnetic field B0. The angle between the wave vector k and the external magnetic field is taken equal to π/2. If the wave frequency ω is large compared with the gyration frequency of the beam electrons and the wavelength is small compared with their gyration radius, the instability appears under the resonance condition ω = kv⊥0. With ω kv⊥0 in a rather dense plasma, the Langmuir frequency Ωp exceeds considerably the gyration frequency ωc, and the oscillations are excited with frequencies close to the half-integral harmonics of the gyration frequency. In the case when the wavelength is of the order of the beam electron gyration radius, it is oscillations with frequencies near the hybrid one, √(Ωp2 + ωc2) that appear unstable (herein, √(Ωp2 + ωc2) = Lωc, L = 2, 3,...).