Self-consistent cutoff wave number of the ablative Rayleigh–Taylor instability

The cutoff wave number of the ablative Rayleigh–Taylor instability is calculated self-consistently by including the effects of finite thermal conduction. The derived cutoff wave number is quite different from the one obtained with the incompressible fluid (∇⋅ṽ=0) or sharp boundary models, and it is strongly dependent on thermal conductivity (K∼Tν) and the Froude number (Fr). The derivation is carried out for values of ν≳1, Fr≳1, and it is valid for some regimes of interest to direct and indirect-drive inertial confinement fusion (ICF). The analytic formula for the cutoff wave number is in excellent agreement with the numerical results of Kull [Phys. Fluids B 1, 170 (1989)].