An analytical model that shows the conditions for the existence of the Landau-Darrieus instability of an ablation front is presented. The model seems to agree with recently claimed simulation results ͓L. Masse et al., Proceedings of the 1st International Conference on Inertial Fusion Sciences and Applications ͑Elsevier, Paris, 2000͒, p. 220͔. The model shows that the ablation front can be unstable in absence of gravity when the thermal flux is inhibited within the supercritical region of the corona.

An analytical model for the implosion of a multilayered cylindrical target driven by an intense heavy ion beam has been developed. The target is composed of a cylinder of frozen hydrogen or deuterium, which is enclosed in a thick shell of solid lead. This target has been designed for future high-energy-density matter experiments to be carried out at the Gesellschaft für Schwerionenforschung, Darmstadt. The model describes the implosion dynamics including the motion of the incident shock and the first reflected shock and allows for calculation of the physical conditions of the hydrogen at stagnation. The model predicts that the conditions of the compressed hydrogen are not sensitive to significant variations in target and beam parameters. These predictions are confirmed by one-dimensional numerical simulations and thus allow for a robust target design.

We have developed an analytical model for the implosion of a heavy ion beam driven multilayered cylindrical target. The target consists of a thick metallic shell, typically made of lead which is filled with a low density material, for example frozen hydrogen, and it is axially irradiated with a heavy ion beam with an annular focal spot. The model describes the expansion of the absorption region, the implosion of the pusher, the trajectories of the incident and reflected shocks and the final quasi-isentropic compression. The model is expected to be very helpful to optimize detailed simulations of such problems which are of close relevance to the GSI plasma physics experimental program, planned for the future upgraded accelerator facilities.

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