Forward scattering and filamentation of a spatially smoothed laser pulse in the hydrodynamic and kinetic frameworks

We address the scattering of a high energy laser pulse on a large wavelength acoustic turbulence of relevance for Laser M'egajoule or National Ignition Facility-class experiments. Both kinetic and hydrodynamic frameworks are adopted and combined with a linearized description of the laser propagation. The resulting dispersion relations display important kinetic contributions to the growth of the forward Brillouin instability. Moreover, proof is made that the spatial incoherence often used in high energy laser facilities is, for cold enough plasmas or in the multi-ion species case, not enough to reach full control of the laser filamentation. Comparisons with experimental results and dedicated hydrodynamic simulations confirm our results. The derived dispersion relations present new tools for assessing the propagation quality and energy deposition region of high energy laser pulses. They also underline the importance of accounting for kinetic effects, even in the millimeter and nanosecond scale of many inertial confinement fusion or high-energy-density experiments.