The stability of a uniform relativistic beam of particles injected into a plasma is studied using the previously developed linear transport theory. Velocity distribution in the beam and electron-ion collisions in the plasma are considered. For wave propagation in the beam direction, an exact treatment is given, while for oblique angles between plasma waves and the beam two kinds of perturbation theory are developed. We find that the two electromagnetic modes of beam-plasma oscillation are always stable, but that growing electrostatic oscillations are possible for long enough wavelengths. For short wavelengths or high temperatures this mode is also stable. Boundary effects and the effects of static fields are not considered.
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Bludman et al. (1960) studied this question.
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