We examine the properties of perturbed spherically imploding shock waves in an ideal fluid through the collapse, bounce, and development into an outgoing shock wave. We find broad conservation of the size and shape of ingoing and outgoing perturbations when viewed at the same radius. The outgoing shock recovers the velocity of the unperturbed shock outside the strongly distorted core. The results are presented in the context of the robustness of the shock ignition approach to inertial fusion energy. DOI: 10.1103/PhysRevLett.110.185002 PACS numbers: 52.57.Kk, 47.20.Ma, 47.40.Nm, 52.57.Fg Shock ignition [1] is a variant on fast ignition [2] of inertial fusion targets which improves target performance by burning the deuterium-tritium fuel on a lower adiabat (and therefore with less input energy) than is possible using central ignition [1]. Shock ignition occurs as the result of the temperature increase at the surface of collision of two shock waves. The ingoing ''ignition'' shock is the result of a rapid late time increase in driver power and the outgoing shock is the earlier ''compression'' shock. This compression shock converges, reflects at its minimum radius, and then expands before colliding with the ignition shock. Full radiation hydrodynamics calculations [3] show that shock ignition is reasonably tolerant of departures from spherical symmetry. This is perhaps surprising since it is known [4,5] that spherically converging shock waves are unstable to perturbations of their surface.The purpose of this Letter is to study an idealized problem relating to the compression shock, namely, the behavior of finite amplitude perturbations on a converging shock wave, to follow this shock through convergence, reflection at its minimum radius, and then into the expansion phase. We examine the underlying hydrodynamics with a uniform ideal gas, in the absence of heat conduction and other sources and sinks of energy. The relevance to shock ignition is that this approximates the behavior of the compression shock. Pure hydrodynamics is something of a worst case for these perturbed shocks-much of the additional physics will be dissipative and favor greater stability against perturbation growth. The results may also be of interest in the study of the symmetry of supernovae explosions with the proviso that the present work has no input of thermonuclear energy.Previous work has established that during convergence the shock is unstable to perturbations on its surface [4,5], and that during the subsequent blast wave the perturbations are likely to decay [6]. We show that the perturbations are transferred with little change through convergence into expansion, recovering their approximate ingoing form. This ability of the spherical shock waves to recover their ingoing form is at the root of the robustness of shock ignition.Analytic solutions for spherically symmetric converging shocks are used to validate the computer models for these shocks in 1D spherical and 2D axial symmetry. The 2D models then have small perturbations applied ...

Motivated by the shock ignition approach to improve the performance of inertial fusion targets, we make a series of studies of the stability of shock waves in planar and converging geometries. We examine stability of shocks moving through distorted material and driving shocks with nonuniform pressure profiles. We then apply a fully 3D perturbation, following this spherically converging shock through collapse to a distorted plane, bounce and reflection into an outgoing perturbed, broadly spherical shock wave. We find broad shock stability even under quite extreme perturbation. V C 2014 AIP Publishing LLC. [http://dx

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