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.
Techniques have been developed to improve the unifoimity of the laser focal profile, to reduce the ablative Rayleigh-Taylor &stability, and to suppress the various laser-plasma instabilities. There are now three diiectdrive ignition target designs that utilize these techniques. Evaluation of these designs is still ongoing. Some of them may achieve the gains above 100 that are necessary for a fusion reactor. Two laser systems have been proposed that niay meet all of the requirements for a fusion reactor.
The linear stability analysis of accelerated ablation fronts is carried out self-consistently by retaining the effect of finite thermal conductivity. Its temperature dependence along with the density gradient scale length are adjusted to fit the density profiles obtained in the one-dimensional simulations. The effects of diffusive radiation transport are included through the nonlinear thermal conductivity (κ∼Tν). The growth rate is derived by using a boundary layer analysis for Fr≫1 (Fr is the Froude number) and a WKB approximation for Fr≪1. The self-consistent Atwood number depends on the mode wavelength and the power law index for thermal conduction. The analytic growth rate and cutoff wave number are in good agreement with the numerical solutions for arbitrary ν≳1.
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