Simple model for ablative stabilization

We present a simple analytic model for ablative stablization of the Rayleigh-Taylor instability. In this model the effect of ablation is to move the peak of the perturbations to the location of peak pressure. This mechanism enhances the density-gradient stabilization, which is effective at short wavelengths, and it also enhances the stabilization of long-wavelength perturbations due to finite shell thickness. We consider the following density profile: exponential blowoff plasma with a density gradient β, followed by a constant-density shell of thickness δt. For perturbations of arbitrary wave number k, we present an explicit expression for the growth rate γ as a function of k, β, and δt. We find that ‘‘thick’’ shells defined by β δt≥1 have ${\gamma }^2$≥0 for any k, while ‘‘thin’’ shells defined by β δt${\gamma }^2$small k, reflecting stability by proximity to the back side of the shell. We also present lasnex simulations that are in good agreement with our analytic formulas.