Numerical simulations of the ablative Rayleigh-Taylor instability in planar inertial-confinement-fusion targets using the FastRad3D code

Abstract

The ablative Rayleigh-Taylor (RT) instability is a central issue in the performance of laser-accelerated inertial-confinement-fusion targets. Historically, the accurate numerical simulation of this instability has been a challenging task for many radiation hydrodynamics codes, particularly when it comes to capturing the ablatively stabilized region of the linear dispersion spectrum and modeling ab initio perturbations. Here, we present recent results from two-dimensional numerical simulations of the ablative RT instability in planar laser-ablated foils that were performed using the Eulerian code FastRad3D. Our study considers polystyrene, (cryogenic) deuterium-tritium, and beryllium target materials, quarter- and third-micron laser light, and low and high laser intensities. An initial single-mode surface perturbation is modeled in our simulations as a small modulation to the target mass density and the ablative RT growth-rate is calculated from the time history of areal-mass variations once the target reaches a steady-state acceleration. By performing a sequence of such simulations with different perturbation wavelengths, we generate a discrete dispersion spectrum for each of our examples and find that in all cases the linear RT growth-rate γ is well described by an expression of the form γ=α [kg/(1+ϵ kLm)]1/2−βkVa, where k is the perturbation wavenumber, g is the acceleration of the target, Lm is the minimum density scale-length, Va is the ablation velocity, and ϵ is either one or zero. The dimensionless coefficients α and β in the above formula depend on the particular target and laser parameters and are determined from two-dimensional simulation results through the use of a nonlinear curve-fitting procedure. While our findings are generally consistent with those of Betti et al. (Phys. Plasmas 5, 1446 (1998)), the ablative RT growth-rates predicted in this investigation are somewhat smaller than the values previously reported for the same target and laser parameters. It is speculated that differences in the equation-of-state and opacity models are largely responsible for the discrepancy. Resolution of this issue awaits the development of better experimental diagnostics capable of measuring small-wavelength (5–20 μm) perturbation growth due to the ablative RT instability in the linear regime.