Nonlinear Evolution of two Gravitational Instabilities and Thermal Conduction Loss at Fractal Interface

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1. We have developed a weakly nonlinear theory of ablative Rayleigh-Taylor (RT) instability with a finite bandwidth Included self-consistently. The theory includes up to third order nonlinearity that results in saturation of linear growth and determines weakly nonlinear growth. It is found that the ablation effects reduce both the saturation amplitude of the linear growth and the weakly nonlinear growth. They are evaluated for plastic and DT targets. The weakly nonlinear growth is shown given by the product pf the linear growth and the saturation amplitude.2. A third order nonlinear theory of Richtmyer-Meshkov (RM) instability has been developed by treating unstable interface as a vortex sheet with density jump. Nonlinear growth rates of spike and bubble are shown to agree well with hydrodynamic simulations. Circulation varies locally with time due to the density jump at the sheet and it introduces stretching and shrinking of the interface locally.3. We have developed a molecular dynamic simulation program to treat RM instability in a cylindrical geometry, that conventional hydrodynamic codes fails to simulate. With the use of the code, we have investigated the stability of converging shocks and the nonlinear growth of RM instability, We have shown the increase of the nonlinear growth due to multiple shocks rebounded at the center and its dependence on mode number.4. We have developed self-similar solutions of laser implosion in which thermal conduction plays an important rote by using Lie group theory. This model has been applied for hydrodynamically equivalent implosions in order to design future experimental facility for ignition and high gain in inertial fusion energy research.