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, $\gamma \approx \alpha \mathrm{}\left(k\right)\mathrm{}\sqrt{\mathrm{kg}}-2k{\nu }_a$ (where ${\nu }_a=\mathrm{ablation}$ velocity, $\alpha \mathrm{}\left(k\right)\mathrm{}\equiv \sqrt{1-{\left(\frac{k}{k_c}\right)}^r}$ 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, $\gamma =0.9\mathrm{}\sqrt{\mathrm{kg}}-3k{\nu }_a$.