Hydrodynamic instabilities of laser indirect-drive inertial-confinement-fusion implosion

Abstract

Hydrodynamic instabilities (HI) occurring at interfaces of a capsule in the process of laser indirect-drive inertial-confinement-fusion (ICF) implosion, plays an essential role in the success of the fusion ignition. In order to deeply understand the generation and growth of the HI and their influence on the fusion ignition, we have successfully developed the LARED-S code which is a high-order twodimensional (local three-dimensional) radiation hydrodynamic code. The LARED-S code has been improved in our research of the HI in the past decades. It is shown that the results of LARED-S code agree well with the results of the linear and weakly nonlinear theories and the nonlinear shock tube experiments. Using the LARED-S code, we carry out a lot of numerical simulation research, obtaining a large amount of important result and physical understanding of the growth and evolution of the HI. The analytic expressions of the linear growth rate of Rayleigh-Taylor (RT) and Kelvin-Helmholtz (KH) instabilities considering the profiles of density, velocity, and magnetic field, and the their weakly nonlinear solutions in the limit of incompressible fluids, are derived. The relation of the RT instability (RTI) competing against the KH instability (KHI) is clearly shown, at different Froude numbers and widths of the density transition layer and the velocity shear layer. It is found that the jet-like spike in the ablative RTI (ARTI) in the presence of weak preheating can be ruptured by the nonlinear growth of the second harmonic. Moreover, jet-like spike pattern can be formed in the ARTI with strong preheating where a bubble acceleration process can be observed. The growth of high harmonics initiated by single-mode perturbation of the ablative KHI (AKHI) is effectively mitigated and the flow is stabilized in comparison with its classical counterpart. However, with a two-mode perturbation, the vortex pairing of the AKHI is reinforced, which would strength the mixing of materials. A serial of ARTI experiments have been performed in the Shenguang Ⅱ laser facility of China. The simulation results from the LARED-S code for the planar foil trajectory experiment indicates that the energy flux at the hohlraum wall is obviously less than that at the laser entrance hole (LEH). Furthermore, the non-Planckian spectra of X-ray source can affect the dynamics of the foil flight and the perturbation growth. The image of evident growth of the ARTI initiated by a small-amplitude perturbation and the spike-bubble pattern initiated by large-amplitude perturbation are observed. The data of the growth of the second and the third harmonics is also obtained by increasing the spatial resolution in the experiments. The simulation results are in general consistent with the experimental results. The reliability of the LARRED-S code has been tested and validated through the comparison with experiment results. Based on the physical understanding mentioned above, we have achieved the physical research of ICF fusion ignition target, including the effects of the perturbation seeded on the outer and inner surfaces of the shell, of the radiation asymmetry, of the hot-spot boundary instability, of the M-band from the hohlraum radiation, and of the low-mode areal density inhomogeneity, on the ICF implosion. Regarding the perturbation seeded on the ablator outer surface and on the deuterium-tritium (DT) ice inner surface and the radiation asymmetry, we have obtained the growth rule of the instabilities and improved the full understandings of the influence of the hot-spot interfacial growth on the fusion ignition and of the effect of the M-band of the X-ray spectra on the implosion stability. The simulation results show that the areal density inhomogeneity of the DT fuel severely affects the efficiency of the conversion of the implosion kinetic energy into the fuel internal energy and the implosion inertial confinement time. Our studies will play an important role not only in the research of ICF implosion ignition, but also in fundamental understanding of the HI which occur at the nature phenomena and the celestial bodies.