Hierarchy of beam plasma instabilities up to high beam densities for Fast Ignition Scenarii

We investigate the hierarchy of electromagnetic instabilities suffered by a relativistic electron beam(REB) passing through a plasma. We work in a fluid approximation and consider beam densities up to plasma ones. The hierarchy between instabilities is established in terms of only two parameters: beam relativistic Gamma factor and ratio Nb/Np of beam to plasma densities. For Nb/Np $<$ 0.53, most unstable modes are a mix of Filamentation and 2-Stream instabilities. Beyond that limit, Filamentation may be dominating, depending on beam Gamma factor. Growth rates behavior for Nb/Np $\sim $ 1 leads to conclude that a Fast Ignition Scenario REB could experience a very high instability level at earliest stages of its journey through supercompressed DT core.