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∼T ν) 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)].