Density Gradient Effect on the Non-Linear Spectrum of the Rayleigh–Taylor Instability

Nonlinear spectrum of the deceleration phase Rayleigh–Taylor instability (RTI) has been investigated in the inertial confinement fusion. Growth rate of the deceleration phase RTI has been expressed well in the form of γk=α2kg1+kLm-β2kua,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \upgamma_{\text{k}} =\upalpha_{2} \sqrt {\frac{\text{kg}}{{1 + {\text{kL}}_{\text{m}} }}} -\upbeta_{2} {\text{ku}}_{\text{a}} , $$\end{document} where α and β are constants. g, k, Lm and ua are the target acceleration, the wave number, the finite density gradient scale length and the ablation velocity, respectively (Betti et al. in Phys Plasmas 5:1446, 1998). Analytically obtained results indicate that the mass power spectrum can be described as an inverse power law with an approximate spectral index of 2.3 in the limit of kL0≪1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\text{kL}}_{0} \ll 1 $$\end{document}, where k is the wave number and L0 is the ablation front thickness and we have shown that power-law slope for kLm ≫ 1 is the most that it is changing with k−4. Furthermore, it has been found that nonlinear power spectrum decreases slowly by increasing of the hot spot radius. Our obtained value is in agreement with theoretical findings (Keskinen et al. in Phys. Plasmas 14:012705, 2007).