Nonlinear excitation of the ablative Rayleigh-Taylor instability for all wave numbers

Small-scale perturbations in the ablative Rayleigh-Taylor instability (ARTI) are often neglected because they are linearly stable when their wavelength is shorter than a linear cutoff. Using two-dimensional (2D) and three-dimensional (3D) numerical simulations, it is shown that linearly stable modes of any wavelength can be destabilized. This instability regime requires finite amplitude initial perturbations and linearly stable ARTI modes to be more easily destabilized in 3D than in 2D. It is shown that for conditions found in laser fusion targets, short wavelength ARTI modes are more efficient at driving mixing of ablated material throughout the target since the nonlinear bubble density increases with the wave number and small-scale bubbles carry a larger mass flux of mixed material.

Figure 1

(a) Initial equilibrium density profile in the $Z$ direction. (b) The time evolution of a linearly stable ARTI mode under different perturbation amplitudes, showing that it becomes unstable if the amplitude exceeds a critical value.

Figure 2

(a) Critical velocity perturbation amplitude versus wave number in 2D and 3D ARTI. The linear dispersion relation (red line) is indicated by the solid red line and $Y$ axis on the right. Linear wave number cutoff is $k_c^l=1$, while the nonlinear cutoff wave number is $k_c^{nl2\mathrm{D}}=2.1$ in 2D and $k_c^{nl3\mathrm{D}}=5.3$ in 3D. (b) Vorticity at the bubble vertex for different ARTI modes.

Figure 3

Comparison of the 2D vortex structures between ARTI modes (a) $\lambda =4\mu \mathrm{m}$ ($k=1.57$) and (b) $\lambda =2.5\mu \mathrm{m}$ ($k=2.5$) at different times. Initial perturbation amplitude is $V_p=3.6V_a$ for $\lambda =4\mu \mathrm{m}$, and $V_p=9.9V_a$ for $\lambda =2.5\mu \mathrm{m}$. The black line shows the ablation front interface. Panel (c) is the 3D isosurface of the density for $\lambda =4\mu \mathrm{m}$.

Figure 4

The bubble density profile for 2D and 3D ARTI modes along $Z$ in the deeply nonlinear stage.

Figure 5

(a) Time evolution of the bubble velocity normalized to the classical value. (b) Bubble mass flux for different wave numbers.