Self-consistent Analytical Model of the Rayleigh-Taylor Instability in Inertial Confinement Fusion

The model presented overcomes past inconsistencies by applying asymptotic techniques. The obtained growth rate, $\ensuremath{\gamma}\ensuremath{\approx}\ensuremath{\alpha}(k)\sqrt{\mathrm{kg}}\ensuremath{-}2k{\ensuremath{\nu}}_{a}$ (where ${\ensuremath{\nu}}_{a}=\mathrm{ablation}$ velocity, $\ensuremath{\alpha}(k)\ensuremath{\equiv}\sqrt{1\ensuremath{-}{(\frac{k}{{k}_{c}})}^{r}}$ represents the stabilization heat conduction effect, and the cutoff wave number ${k}_{c}$ is much smaller than the inverse of the density scale length at the ablation front), reproduces numerical simulations and experiments in a more complete way than the so-called Takabe formula, $\ensuremath{\gamma}=0.9\sqrt{\mathrm{kg}}\ensuremath{-}3k{\ensuremath{\nu}}_{a}$.