Analysis of Rayleigh-Taylor instability by nonlinear statistics methods for the tasks of laser thermonuclear fusion

Abstract

A consideration of turbulent mixing is especially important in the laser fusion problems where the intensities of shock waves and acceleration fields achieve great values and the arising instabilities lead to a considerable reduction of thermonuclear yield. A standard set of thermodynamic values is insufficient to describe a process of turbulent mixing because a classical set averaging takes no account of the coherent structures, which are essential for the process. However, there is supposed to be a certain "reasonable" number of parameters characterizing a further development of turbulent process, as evidenced by numerical calculations and experimental data. An attempt has been made to determine numerically the turbulent mixing steady-state formation at an example of two-dimensional Rayleigh-Taylor problems. In order to define such hidden characteristics one applied a mathematical apparatus of artificial intellect used effectively in fuzzy logic problems. The process states were coded by wavelet transform allowing one to consider spatially localized structures. The processes under study were determined by numerical calculations. As a result one obtained a steady-state representation of an RT-mixing process. The stable parameters are expressed through linear combinations of wavelet coefficients and Fourier transforms of the physical fields.