Partial suppression of hydrodynamic mixing in profiled shells

Abstract

The problems of stability and mixing are important in the physics of high-energy densities. Ablation-induced acceleration of foils and compression of liners entail loss of symmetry and the development of instability. The most destructive instability is the fundamental f ⁻ mode, which conserves the pressure in Lagrangian particles. A means has been proposed to eliminate this dangerous mode, based on special profiling of the mass distribution among the subshells. The presence of this mode has led to novel proposals for limiting the degree of instability and optimization of the shells by profiling in the important case of very large density ratios at the ablation front. The solution is based on a class of new polytropes with an inverted density profile and a negative polytrope index N. In this class the density ρ of the material does not decrease towards the boundary with the vacuum, as for ordinary polytropes with N>0, but rather increases. This permits modeling multilayer distributions of ρ typical of inertial confinement fusion systems in which the high-density subshells form an inner core surrounding a low-pressure cavity, and the outer layers are made from low-density materials (plastic, foam type materials, composites). It is emphasized that the distributions are self-similar, and hence both the linear and the turbulent dynamics are scale-invariant. The spectral problem of perturbations in an incompressible fluid has a hidden symmetry. Isospectral deformations of the density profile I{ρ ₀(_y)} are known that leave the spectrum unchanged. It is of interest to apply the transformation I to the invariant f ^± modes, since they are not tied to any specific profile of ρ ₀(y). This paper analyzes a new type of invariant mode obtained in this way.