Influence of random phase plates temporal smoothing on the growth of the Backward stimulated Brillouin scatter

Based on a previous work [1], we derive analytical dispersion relations of the backward stimulated Brillouin scattering (BSBS) that accounts for spatial temporal beam smoothing and the phase plate randomness [2]. Quantifying the instability variability that results from the phase plates is shown to be crucial for understanding quantitatively the backscattering temporal and spatial growth as well as the asymptotic reflectivity. A simple analytical correction to the plane wave spatial gain is extracted from our theory for a simple and effective reflectivity prediction that includes the impact of smoothing techniques. Validated by a large number of three dimensional hydrodynamic paraxial (Hera) simulations [3] and experimental data [4], our model shades a new light on the long-time studied BSBS deleterious to many high energy experimental studies related to the physics of inertial confinement fusion [5].

[1] C. Ruyer, A. Debayle et. al., Phys. Plasmas 28, 052701 (2021)

[2] H. A. Rose and D. F. DuBois, Phys. Fluids B 5, 590 (1993)

[3] P. Loiseau, O. Morice, et. al., Phys. Rev. Lett. 97, 205001 (2006)

[4] L. Divol, R. L. Berger et. al., Phys. Plasmas 15, 056313 (2008)

[5] C. Ruyer, R. Capdessus et. al., submitted to PRX