Electrostatic instabilities driven by ion beams

Electrostatic instabilities in a plasma composed of an ion beam moving in a stationary background of electrons and ions are considered. Analytical expressions for the ion-acoustic and ion-ion acoustic instabilities are derived. These expressions consist of a system of two algebraic coupled equations, which do not shed much light on the nature of the unstable modes. However, when the system is complemented with the condition for marginal instability, they provide a simple graphic method to understand the nature of the instabilities. It is shown that kinetic Landau effects are responsible for the fact that the growth rate of the ion-ion acoustic instability can grow larger than the growth rate of the ion-acoustic mode. This result, which follows from the graphic method developed here, helps to resolve unambiguously an ongoing controversy concerning the nature of the ion-ion acoustic instability. (author)