Scaling laws of the Rayleigh-Taylor ablation front mixing zone evolution in inertial confinement fusion

A theoretical model for the ablatively driven Rayleigh-Taylor (RT) instability single-mode and multimode mixing fronts is presented. The effect of ablation is approximately included in a Layzer-type potential flow model, yielding the description of both the single-mode evolution and the two-bubble nonlinear competition. The reduction factor of the linear growth rate due to ablative stabilization obtained by the model is similar to the Takabe formula. The single-bubble terminal velocity is found to be similarly reduced by ablation, in good agreement with numerical simulations. Two-bubble competition is calculated, and a statistical mechanics model for multimode fronts is presented. The asymptotic ablation correction to the classical RT αgt² mixing zone growth law is derived. The effect of ablative stabilization on the allowed in-flight aspect ratio of inertial confinement fusion pellets is estimated using the results of the statistical mechanics model.