Non-modal linear stability analysis of ablation flows relative to inertial confinement fusion

International audienceThe hydrodynamic stability of ablation flows is a key issue in laser-driven inertial confinementfusion (ICF) where a sufficiently symmetric implosion of a spherical pellet is expected to achievethermonuclear burn. Such flows which originate from exposing the pellet outer shell to a growingincident heat flux, present the radial structure of an inward-propagating deflagration, or ‘ablation’,wave where a shock wave precedes a subsonic heat front that coindices with the leading edge ofthe heated material expansion wave. Inherently unsteady, these flows are compressible, stronglyaccelerated and highly nonuniform with a steep heat front, owing to the strong nonlinearity of theheat transport and the intense incident heating. These features, in addition to non-trivial boundaryconditions at the shell external surface and shock front, are sources of non-modal thermo-acousticseffects [1, 2]. However non-modal instability growth in ablation flows relevant to ICF has neverbeen studied so far. The development of instabilities leading to non-linear phenomena in ablationflows could result into the loss of symmetry of the implosion and could finally inhibit ignition.Transition mechanisms in ablation flows are therefore of primary importance to ICF ignition.Here we investigate non-modal effects in planar radiative ablation waves by using self-similarablation solutions to the Euler equations with nonlinear heat conduction without further approxi-mation as model base flows representative of the early stage of an ICF pellet implosion [3]. Pseudo-spectra of the local approximation of the perturbation evolution operator reveal a potential forstrong transient growth. Because of the base flow unsteadiness, our non-modal linear stabilityanalysis relies on a direct-adjoint method. The flow boundary deformations, at the material ex-ternal surface and shock front, as well as their adjoint variable counterparts enter this methodformulation. Both optimal initial conditions and receptivity to perturbations of the incident heatflux and external surface pressure are considered. Different definitions of objective functionalsare investigated, some in relation with experimentally measurable quantities. Optimal responsecomputations are carried out for terminal times and perturbation transverse wavelengths whichare determined on the basis of pellet implosion features. Computed optimal responses are physi-cally analysed in terms of diffusion and propagation, with the help of a decomposition into linearhyperbolic waves — corresponding to acoustic, entropy, vorticity and radiation-conductivity waves[3] — for a nonuniform heat-conducting flow.References[1] K. Wieczorek, C. Sensiau, W. Polifke, F. Nicoud, Phys. Fluids. 23, (2011)[2] F. Nicoud, L. Benoit, C. Sensiau, T. Poinsot, AIAA J. 45, (2007)[3] J. M. Clarisse, J. L. Pfister, S. Gauthier, C. Boudesocque-Dubois, J. Fluid Mech. 848, (2018