The Study Of Laser Ablative Rayleigh-Taylor Instability

In this paper, hydrodynamic linear stability theory and weakly nonlinear theory are adopted to study the Rayleigh-Taylor instability at the laser ablation front in the preheat case. In the stability analysis, the numerically solved steady state flow field is used as the basic flow, and the ablation front is treated as a continuous flow field so as to take into account the broaden thickness of the ablation front. In this paper, amplitude distribution and amplitude evolvement of the laser ablative Rayleigh-Taylor instability is the main focus.First, the behavior of the laser-driven CH ablation target is analyzed using a direct numerical simulation which is second order in space. The thickness of the CH target is 200μm, the laser intensity linearly grows 4 ns to it maximum of 1014 W/cm2, and then keeps on. The constantly accelerating equilibrium of the ablation CH target is obtained. Based on the ablation parameters, the steady state flow field at the reference frame of the constantly accelerating ablation front is given and compared with the result of direct numerical simulation. The hydrodynamic linear stability theory and weakly nonlinear theory are used to study the ablative Rayleigh-Taylor instability based on the steady state flow field, and the results are tested through comparison with a direct numerical simulation which is fourth order accurate in space. And the following conclusions can be drawn:1. The constantly accelerating equilibrium of the laser ablation front can be represented by the corresponding steady state flow field at the reference frame of the constantly accelerating ablation front which is obtained using the same ablation parameters.2. The linear growth of the ablative Rayleigh-Taylor instability is studied using the linear stability theory. The Eigen-Functions of the instable perturbations are presented, and the characteristics of the Eigen-Functions are analyzed. The growth rate of the linear stability theory is in agreement with the modified Lindl formula, and is almost identical to that of direct numerical simulation.3. In the weakly nonlinear theory, a new method is proposed to determine the Landau constant for the perturbations with relatively larger growth rates. The method is that the shape function of the regenerated fundamental mode is bi-orthogonal to the Eigen-function of the ad-joint linear stability problem. This method can be easily applied for higher order expansion (in the weakly nonlinear theory).4. The weakly nonlinear growth of ablative Rayleigh-Taylor instability is studied using the weakly nonlinear theory by Stuart. Shape functions of each harmonic are presented and their characteristics are analyzed. The Landau constant curve is given by the weakly nonlinear theory. It is negative when the wave number is small and positive when the wave number is large. The weakly nonlinear theory shows that the Landau constant has relatively smaller correction to the first harmonic, whereas the regenerated fundamental mode plays the dominant role.5. In the weakly nonlinear theory, a new expansion method with respect to the linear amplitude of the fundamental mode is proposed. Compared with the expansion method by Stuart, the new method has the following advantages: the amplitude equations no longer contains the Landau constant, no extra condition is needed to determine the Landau constant, and the equations can be solved directly. The expansion method is simpler, and is convenient for higher order expansion. The compassion with direct numerical simulation shows that: when the nonlinear effect is relatively stronger, the new method can describe the ablative Rayleigh-Taylor instability more accurately in a certain sense.