Absolute and convective nature of Raman instability in relativistic hot plasmas

The modulational and Raman instabilities are investigated in the relativistic regime, for a large amplitude electromagnetic wave propagating in a hot plasma of arbitrary density. Temporal growth rates and the number of unstable branches are determined when the plasma temperature, density, and the amplitude of the wave vary. The convective or absolute nature of the Raman instabilities is then determined. The present paper extends previous results by Guérin et al. [Phys. Plasmas 2, 2807 (1995)] and Couairon and Mora [Phys. Plasmas 8, 3434 (2001)]. It is shown that for any temperature, the Raman instability is convectively unstable at low density and low intensity, and absolutely unstable when the intensity or the density exceeds a threshold that we determine as a function of the temperature. In contrast with the cold plasma case, the threshold for absolute instability does not coincide with the merging of branches found by a classical temporal stability analysis.