Reduction of increment of Rayleigh-Taylor instability in specially designed multilayer inertial-confinement-fusion targets

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The problem of hydrodynamic stability and mixing is very important for inertial-confinement-fusion (ICF) systems based upon high compression of fuel before ignition. The ablative drive of foils and compression of shells are unstable. The fundamental isobaric ${f}^{\ensuremath{-}}$ mode is the most destructive one. It conserves pressures in the Lagrangian particles. A way to remove this dangerous mode is presented, based on special distributions of mass among subshells in the multishell target. The obtained solution follows from a consideration of new, inverse-density polytropes that have negative values of the polytropic index $N$, $\ensuremath{\rho}(r)\ensuremath{\propto}(r\ensuremath{-}{r}_{V}{)}^{N}$, where ${r}_{V}$ is the radius of an inner, low-pressure cavity filled with a fuel. Polytropes describe inhomogeneous incompressible and compressible cases. Density of material $\ensuremath{\rho}$ does not vanish in these distributions, as in the case of usual polytropes with $N>0$ considered previously in geophysics and astrophysics. Conversely $\ensuremath{\rho}$ rises when we approach the boundary with vacuum. This property allows us to simulate multilayer distributions of $\ensuremath{\rho}$ that are typical for ICF targets. In these targets the high-density subshells surround the low pressure or vacuum cavity, while the outer subshells are made from low-density materials such as plastics, foams, and/or from composite materials. The proposed distributions are self-similar. Therefore their linear dynamics is scale invariant. New acoustic fundamental modes ${f}_{P}^{\ifmmode\pm\else\textpm\fi{}}$ are found and an interesting correspondence between acoustic and gravity modes is presented. (The ${f}^{\ifmmode\pm\else\textpm\fi{}}$ or ${f}_{G}^{\ifmmode\pm\else\textpm\fi{}}$ fundamental modes are the well-known gravity modes.)