Large energetic laser facilities provide an amazing tool for bringing matter into high energy density states but achieving a good energy conversion requires to optically smooth the high-power laser beams. Optical smoothing reduces the laser spatial and temporal coherences, allowing to mitigate the development of unwanted laser–plasma instabilities (LPI). Two schemes have been mainly developed: polarization smoothing and smoothing by spectral dispersion. Here, we focus on the latter. Smoothing by spectral dispersion consists in broadening the spectrum usually through a sinusoidal phase modulation and dispersing it with an optical grating. It is usually considered that the modulation frequency should be equal to the inverse of the time delay of the grating, because it maximizes the number of uncorrelated speckles patterns at a given bandwidth. However, current optical smoothing designs are still not sufficient for mitigating LPI. Because the optical smoothing system possesses degrees of freedom, we propose to improve the optical smoothing efficiency by a better tuning of those parameters. Considering the Laser Mégajoule optical system framework, we show that an increase in the modulation frequency allows a better efficiency of the smoothing while keeping the same bandwidth. We assess the efficiency by looking at a better mitigation of the stimulated Brillouin scattering that, due to its dangerousness in hohlraums developed for inertial confinement fusion applications in the indirect drive scheme, serves as a witness instability.
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