Self-consistent stability analysis of ablation fronts with large Froude numbers

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.