Absolute and convective nature of the modulational and Raman instabilities in the relativistic regime

The nature (convective or absolute) of the modulational and Raman instabilities is investigated in the relativistic regime, for a large amplitude electromagnetic wave propagating in a plasma of arbitrary density. The present paper extends previous results by Guérin et al. [Phys. Plasmas 2, 2807 (1995)]. Stability diagrams are obtained and compared to the stability properties found by a classical temporal stability analysis. It is shown that the modulational and the (forward and backward) Raman instabilities are individually convective. However, the Raman instability is absolute for large density and high intensity when the forward and backward Raman branches have merged into a hybrid Raman branch. Near quarter critical density, this hybrid branch is destabilized and is absolute from the threshold. The plasma equilibrium is convectively unstable between quarter critical and critical density at low intensity.