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

1.建立了有限带宽自洽烧蚀Rayleigh-Taylor(RT)不稳定性的弱非线性理论。该理论包括高达三阶非线性，它导致线性增长饱和，并决定弱非线性增长。结果表明，烧蚀效应降低了线性增长的饱和幅度和弱非线性增长的饱和幅度。它们被评估为塑料和DT目标。弱非线性增长由线性增长和饱和幅度的乘积给出。将不稳定界面视为具有密度跳跃的涡旋片，发展了Richtmyer-Meshkov(RM)不稳定性的三阶非线性理论。尖峰和气泡的非线性增长率与流体动力学模拟结果吻合较好。由于薄层密度的跳跃，局部环流随时间变化，并在局部引入界面的拉伸和收缩。我们已经开发了一个分子动力学模拟程序来处理圆柱几何中的RM不稳定性，这是传统的流体动力学程序无法模拟的。利用该程序研究了收敛激波的稳定性和RM不稳定性的非线性增长，得到了中心多次激波反弹引起的非线性增长及其对模数的依赖关系。利用李群理论，我们得到了激光内爆的自相似解，其中热传导起着重要作用。该模型已应用于流体力学等效内爆实验，为今后惯性聚变能量研究中点火和高增益实验装置的设计奠定了基础。

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.