The second-order theory of electromagnetic hot ion beam instabilities

The present investigation is concerned with the application of a second-order theory for electromagnetic instabilities in a collisionless plasma to two modes which resonate with hot ion beams. The application of the theory is strictly limited to the linear growth phase. However, the application of the theory may be extended to obtain a description of the beam at postsaturation if the wave-beam resonance is sufficiently broad in velocity space. Under the considered limitations, it is shown that, as in the cold beam case, the fluctuating fields do not gain appreciable momentum and that the primary exchange of momentum is between the beam and main component.