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 non-uniform laser ablation induced by initial target roug
hness or non-uniform laser irradiation. These perturbation growths are very
important because they seed the Rayleigh-Taylor (RF) instability in the su
bsequent acceleration and stagnation phases. We investigate temporal evolut
ions of the shock front and the ablation surface. In the result, we have fo
und that the shock front ripples oscillate and decay in both cases of unifo
rm laser irradiation on a target with a rippled surface and non-uniform las
er irradiation on a smooth target surface. On the other hand, we obtain tha
t there is the asymptotic value of the ablation surface deformation in the
former case and the asymptotic growth rate of the ablation surface ripple i
n the latter case. Approximate formulas expressing both temporal evolutions
of the shock front and the ablation surface are obtained in the weak shock
limit. These formulas are also applicable in a relatively strong shock. We
also investigate the case of oscillating non-uniform laser irradiation wit
h time. The oscillation frequency dependences of the shock front ripple and
the growth rate of the ablation surface ripple are discussed. (C) 1999 Els
evier Science S.A. All rights reserved.