Self-consistent stability analysis of ablation fronts in inertial confinement fusion

Abstract

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.