Spray amplification in inertial confinement fusion*

The mitigation of the nonlinear laser-plasma interactions and control of the energy deposition remains among the main challenges in inertial confinement fusion both in the direct and indirect drive approach. Hard to model in a self-consistent way on experimental scales, the mitigation of parametric instabilities based on spatial laser beam smoothing using random phase plates and temporal smoothing using spectral dispersion are largely empirical and not sufficiently supported by theory. The two leading theoretical models based on the random phase approximation and the hypothesis of independent speckles are incomplete, and their predictive capabilities are uncertain.

We propose a novel technique [1] for modeling parametric instabilities in a temporally and spatially smoothed laser beam using the statistical approach and applying it to the near-forward Brillouin scattering (FSBS). The wave mixing equations are treated with the statistical properties of the laser beam, thus accounting for the effect of the speckle correlations [2]. In agreement with three dimensional paraxial simulations, it is demonstrated that FSBS amplification of a smoothed laser beam scales as the square of the average gain coefficient if the beam power is large enough [3]. These results are in agreement with recent experimental results on laser beam spraying [4] and indicate that a significant growth is expected in hohlraums. This also opens the way for developing reduced modelling of beam spray amplification in radiation hydrodynamics codes.