Evolution of the rippled inner-interface-initiated ablative Rayleigh-Taylor instability in laser-ablating high-Z doped targets

Rippled interface between the ablator and DT ice can feedout and form the perturbation seeds for the ablative Rayleigh-Taylor (ART) instability, which negatively affects direct-drive inertial confinement fusion (ICF). However, the evolution of instability remains insufficiently studied, and the effect of high-Z dopant on it remains unclear. In this paper, we develop a theoretical model to calculate the feedout seeds and describe this instability. Our theory suggests that the feedout seeds are determined by the ablation pressure and the adiabatic index, while the subsequent growth mainly depends on the ablation velocity. Two-dimensional radiation hydrodynamic simulations confirm our theory. It is shown that high-Z doped targets exhibit more severe feedout seeds, because of their higher ionization compared to undoped targets. However, the X-ray pre-ablation in high-Z doped targets significantly suppresses the subsequent growth, leading to the suppression of short-wavelength perturbations. But for long-wavelength perturbations, this suppression weakens, resulting in an increased instability in the high-Z doped targets. The results are helpful for understanding the inner-interface-initiated instability and the influence of high-Z dopant on it, providing valuable insights for target design and instability control in ICF.