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 {δ}t. For perturbations of arbitrary wave number k, we present an explicit expression for the growth rate {γ} as a function of k, {β}, and {δ}t. We find that ``thick'' shells defined by {β} {δ}t{≥}1 have γ²{≥}0 for any k, while ``thin'' shells defined by {β} {δ}t1 can have γ²0 for 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.