Hierarchy of beam plasma instabilities up to high beam densities for fast ignition scenario

The hierarchy of electromagnetic instabilities suffered by a relativistic electron beam passing through a plasma is investigated. The fluid approximation is used and beam densities up to the plasma one are considered. The hierarchy between instabilities is established in terms of two parameters only: the beam relativistic factor and the ratio nb∕np of the beam density to the plasma one. It is found that for nb∕np≲0.53, the most unstable modes are a mix between filamentation and two-stream instabilities. Beyond this limit, filamentation instability may dominate, depending on the beam relativistic factor. The largest growth rates are found for a beam density slightly smaller than the plasma one.