Self-consistent analytical model of the Rayleigh-Taylor instability in inertial confinement fusion

Abstract

The model presented overcomes past inconsistencies by applying matching asymptotic techniques. The obtained growth rate, $\ensuremath{\gamma}\ensuremath{\approx}\ensuremath{\alpha}(k)\sqrt{\mathrm{kg}}\ensuremath{-}2k{\ensuremath{\nu}}_{a}$ (where ${\ensuremath{\nu}}_{a}$ is the ablation velocity), could reproduce numerical simulations and experiments in a more complete way than the Takabe formula [Phys. Fluids 28, 3676 (1985)] $\ensuremath{\gamma}=0.9\sqrt{\mathrm{kg}}\ensuremath{-}3k{\ensuremath{\nu}}_{a}$. Here $\ensuremath{\alpha}(k)\ensuremath{\equiv}{[1\ensuremath{-}{(\frac{k}{{k}_{c}})}^{r}]}^{\frac{1}{2}}$, 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. Such a rigorously derived stabilization mechanism clarifies many of the numerical, analytical, and simulation results found in the literature.