Rippled shock propagation and hydrodynamic perturbation growth in laser implosion

A simple analytical model is presented to study hydrodynamic perturbation g rowth in the start-up phase in laser fusion, namely propagation of a ripple d shock driven by nonuniform laser ablation induced by initial target rough ness or nonuniform laser irradiation. These perturbation growths are very i mportant, because they seed the Rayleigh-Taylor instability in the subseque nt acceleration and stagnation phases. We investigate temporal evolutions o f 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 la ser irradiation on a target with a rippled surface and that of nonuniform l aser irradiation on a smooth target. It was also found that there is an asy mptotic 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 formu lae are also applicable in a relatively strong shock. We also investigate t he case of oscillating nonuniform laser irradiation with time. The oscillat ion frequency dependences of the shock front ripple and the growth rate of the ablation surface ripple are discussed. (C) 1999 Elsevier Science S.A. A ll rights reserved.