Symmetry of Spherically Converging Shock Waves through Reflection, Relating to the Shock Ignition Fusion Energy Scheme

Abstract

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 ...

Stability of shocks relating to the shock ignition inertial fusion energy scheme

“…II B. We extend our earlier "piston" verification 4 for convergent shocks to fully 3D geometries, additionally including 1D spherical and 2D axial geometries, in Sec. V A.…”

“…We construct an appropriate piston to drive the shock, closely recreating the Guderley solution and then perturb this piston and examine the evolving behaviour. 4 We provide an outline here of the construction of the symmetric piston, a more complete explanation can be found in Davie and Evans. 4 We first make use of a result by Ribeyre et al 13 who give an approximation to the velocity of a Lagrangian fluid element following the passage of a strong, spherically converging shock wave.…”

“…4 We provide an outline here of the construction of the symmetric piston, a more complete explanation can be found in Davie and Evans. 4 We first make use of a result by Ribeyre et al 13 who give an approximation to the velocity of a Lagrangian fluid element following the passage of a strong, spherically converging shock wave. This is used as a boundary condition in a 1D spherical fluid model, 14 set to follow an ideal fluid with no dissipation apart from the shock itself.…”

“…IV B, representing asymmetries in the drive profile. The basic stability against 2D perturbation of shock shape found by Davie and Evans, 4 broad conservation of size and shape of perturbation on a converging shock through collapse, bounce, and development into an outgoing shock wave is extended to 3D in Sec. V B.…”

“…This stability of SI has been shown to be present in the underlying hydrodynamics, within the limits of 2D hydrodynamics simulation. 4 In addition to the symmetry issues present in conventional Inertial Fusion Energy (IFE), the late-time ignition shock also influences stability. The reflected "compression" shock front is subject to shock front perturbation growth through reflection, including the potential collapse of the shock front away from the centre of convergence.…”