  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.
