No abstract

A simple procedure is developed to determine the Froude number Fr, the effective power index for thermal conduction , the ablation-front thickness L 0 , the ablation velocity V a , and the acceleration g of laser-accelerated ablation fronts. These parameters are determined by fitting the density and pressure profiles obtained from one-dimensional numerical simulations with the analytic isobaric profiles of Kull and Anisimov ͓Phys. Fluids 29, 2067 ͑1986͔͒. These quantities are then used to calculate the growth rate of the ablative Rayleigh-Taylor instability using the theory developed by Goncharov et al. ͓Phys. Plasmas 3, 4665 ͑1996͔͒. The complicated expression of the growth rate ͑valid for arbitrary Froude numbers͒ derived by Goncharov et al. is simplified by using reasonably accurate fitting formulas.

The linear stability analysis of accelerated ablation fronts is carried out self-consistently by retaining the effect of finite thermal conductivity. Its temperature dependence is included through a power law (κ∼Tν) with a power index ν≳1. The growth rate is derived for Fr≫1 (Fr is the Froude number) by using a boundary layer analysis. The self-consistent Atwood number and the ablative stabilization term depend on the mode wavelength, the density gradient scale length, and the power index ν. The analytic formula for the growth rate is shown to be in excellent agreement with the numerical fit of Takabe, Mima, Montierth, and Morse [Phys. Fluids 28, 3676 (1985)] for ν=2.5 and the numerical results of Kull [Phys. Fluids B 1, 170 (1989)] over a large range of ν’s.