Modeling hydrodynamic instabilities in inertial confinement fusion targets

Abstract

In inertial confinement fusion experiments, a cold target material is accelerated by a hot, low-density plasma. The interface between the heavy and light materials is Rayleigh–Taylor (RT) unstable. To estimate the perturbation growth in accelerated targets, a postprocessor to the results of one-dimensional codes is developed. The postprocessor is based on the sharp-boundary model that takes into account time variation in the unperturbed state, mode interaction of neighboring interfaces in the target, effects of spherical convergence, and the mass ablation. The model reveals a new stabilizing effect of ablation for modes with wavelengths longer than the shell thickness. For such modes with γcl>Va/d, the perturbation growth is reduced to η∼m(t)/m(0)e∫dt′γcl2−kVblVa/(2d), where γcl=kg is the classical RT growth rate of interface perturbations in the semi-infinite slab subject to gravitational field g, k is the wave number, d and m(t) are the slab thickness and mass, and Va and Vbl are the ablation and blowoff velocities, respectively. The perturbation evolution calculated by using the developed postprocessor is shown to be in good agreement with the results of two-dimensional hydrodynamic simulations.

Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified cylindrical shells

“…The results differed by less than 5%, probably because the density of 100-fold compressed air, 0.12 g /cm 3 , is still much less than the density of the gelatin ring at 1g /cm 3 . At higher compressions one must modify the perturbation equations as has been done in spherical geometry 40 .…”

Linear and nonlinear Rayleigh-Taylor growth at strongly convergent spherical interfaces

“…In the context of ICF research, models of the type inspired by Haan have proven highly useful in the design of implosion targets, e.g., Ref. [30][31][32][33][34]. Despite the considerable advances in computing power and in numerical techniques, the direct numerical simulation of multimode nonlinear RT growth on an imploding capsule remains a tedious endeavor, and one fraught with uncertainty.…”

Harmonic growth of spherical Rayleigh-Taylor instability in weakly nonlinear regime

“…42,43 Both the RTI and the BP effects are important to the outcome of implosion experiments in the ICF. 44, 45 Epstein 46 discussed that the BP effects based on a simple model are formulated in terms of the mass amplitude of interface perturbations, and work by Mikaelian 47 gives the differential equations in cylindrical and spherical coordinates for the stability of the cylindrical and spherical shells, presents a linearized analysis for different geometries, and the case of concentric shells of fluid undergoing implosion or explosion is considered. This linearized analysis is extended to the case of compressible fluids by Yu and Livescu.…”