Rippled shock propagation and hydrodynamic perturbation growth in laser implosion

Abstract

Abstract A simple analytical model is presented to study hydrodynamic perturbation growth in the start-up phase in laser fusion, namely propagation of a rippled shock driven by nonuniform laser ablation induced by initial target roughness or nonuniform laser irradiation. These perturbation growths are very important, because they seed the Rayleigh–Taylor instability in the subsequent acceleration and stagnation phases. We investigate temporal evolutions of the shock front and the ablation surface. As a result, we have found that the shock front ripples oscillate and decay in both the case of uniform laser irradiation on a target with a rippled surface and that of nonuniform laser irradiation on a smooth target. It was also found that there is an asymptotic value of the ablation surface deformation in the former case and an asymptotic growth rate of the ablation surface ripple in the latter case. Approximate formulae expressing both temporal evolutions of the shock front and the ablation surface are obtained in the weak shock limit. These formulae are also applicable in a relatively strong shock. We also investigate the case of oscillating nonuniform laser irradiation with time. The oscillation frequency dependences of the shock front ripple and the growth rate of the ablation surface ripple are discussed.