Minimizing perturbation growth along interfaces accelerated by large pressure waves

Large pressure waves passing through an interface separating a heavy and light fluid can cause hydrodynamically unstable perturbations to grow. Minimizing this growth is crucial for achieving the high-pressure regimes required for a sustained nuclear reaction in inertial confinement fusion (ICF). In ICF, the laser-driven pressure waves typically consist of a shock front followed by a decompression wave caused by the termination of the laser pulse, causing the interface to evolve under the influence of a complex combination of Richtmyer-Meshkov and Rayleigh-Taylor instability growth. Our objective is to find initial pressure profiles that minimize perturbation growth for a given interface. As a model pressure wave, we consider a shock front being overtaken by a rarefaction wave. Our analysis indicates that perturbation growth can be minimized if the shock-induced phase inversion, which initially causes the perturbations to decrease in amplitude, is counteracted by the rarefaction-induced growth. We further identify the relationship between the shock strength, rarefaction strength, and rarefaction length that minimizes growth. Our analysis, which is grounded in analytical techniques from gas dynamics, is verified by comparison to high-order-accurate numerical simulations.