Motivated by the shock ignition approach to improving the performance of inertial fusion targets, we make a series of studies of the stability of hydrodynamic shock waves.
We first examine the behaviour of shocks moving through perturbations in background fluid in planar and 2D converging geometries, representing the ‘ignition’ shock moving through strongly perturbed material. To do this we follow the behaviour of finite amplitude perturbations on a 2D spherically converging shock wave, through convergence, reflection at its minimum radius and then into the expansion phase. We then extend this to pressure perturbations for converging shocks, representing asymmetries in the drive profile.
These are then extended to 3D where we examine a uniquely 3D asymmetry, collapse and reflection of perturbed shock fronts without axial symmetry.
We find that finite amplitude perturbations are transferred with little change through convergence into expansion, recovering their approximate ingoing form and find that shock fronts are robust against a range of asymmetries, specifically that the shock front is broadly stable against moderate perturbation, with only minor deviations from the symmetric behaviour.
Even under fairly extreme, 3D perturbations in multiple parameters in convergent geometry the shock front remains robust and transfers with little change through convergence into expansion and recovers its approximate ingoing form.
This stability of shock waves is at the root of the robustness of shock ignition and suggests this robustness is fully 3D.