A simple analytical model is presented to study hydrodynamic perturbation growths driven by nonuniform laser ablation in the start-up phase in laser fusion. Propagation of a rippled shock and deformation of an ablation surface are studied for cases of initial target roughness and nonuniform laser irradiation. The study of the perturbation growth in the start-up phase is very important because it seeds the Rayleigh-Taylor instability in the subsequent acceleration and stagnation phases. Analytical solutions are obtained for temporal evolutions of the shock front ripple and the ablation surface deformation. As a result, it is seen that the shock front ripples oscillate and decay in both cases. On the other hand, there is an asymptotic amplitude of the ablation surface deformation in the case of uniform laser irradiation on a target with a rippled surface, and an asymptotic growth rate of the ablation surface ripple in the case of nonuniform laser irradiation on a smooth target. In both cases, it can be shown that a high intensity of laser irradiation causes the ablation surface to distort, and a shore wavelength laser inhibits its deformation. Approximate formulas expressing the temporal behaviors of the shock front and the ablation surface are obtained in the weak shack limit. Those formulas are also applicable to a relatively strong shock. Analytical results agree quite well with recent experimental data for the shock front ripple and the areal mass density perturbation in the initial target roughness case. The behaviors of the shock front ripple and the ablation surface deformation are also investigated in the case where the nonuniformity of the laser irradiation oscillates with time. It can be seen that the deformation of the ablation surface is inhibited for a high oscillation frequency of the laser nonuniformity. [References: 27]
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