Propagation of a rippled shock wave driven by nonuniform laser ablation

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. Analytical results agree quite well with experimental data for the rippled shock propagation in the case of uniform irradiation on a rough surface. Approximate formulas expressing both the time evolution of the shock front and the asymptotic behavior of the ablation front are obtained in the weak shock limit.