Richtmyer - Meshkov instability in a spherical target with density variation

TL;DR

This paper investigates the Richtmyer-Meshkov instability in a spherical target considering density variation, revealing how interface perturbations evolve during implosion in inertial confinement fusion and aligning well with experimental data.

Contribution

It extends the analysis of RM instability to spherical geometry with density variation, providing analytical insights into interface behavior during ICF implosion.

Findings

Interface perturbations decrease then increase over time.

Density peaks correspond to minimum interface radius.

Results agree qualitatively with experiments and simulations.

Abstract

The motion of unstable fluid interface due to Richtmyer - Meshkov (RM) instability incorporating with density variation has been studied in a spherical target using Lagrangian formulation. During the compression in Inertial Confinement Fusion (ICF)process, the density of deuterium - tritium (DT) fuel increases 1000 times greater than the density of gaseous DT fuel within the core of spherical target. We have extended the feature of density variation [PRA,84-Mikaelian & Lindl] in spherical geometry.Due to convergent shock impingement, the perturbed interface will be nonspherical which leads to the density variation in both radial as well as in polar angle. We have shown that the interface of perturbed surface decreases with time to reach a minimum and then kick back to gradual increase. As the perturbed radius decreases, the density increases and reaches a maxima corresponding to a minima of perturbed radius. This is the practical situation of density characteristics during implosion of ICF. The numerical results based on our analytical work show a good qualitative agreement with some experimental as well as simulation results.