Non-modal linear stability analysis of ablation flows relative to inertial confinement fusion
Résumé
The hydrodynamic stability of ablation flows is a key issue in laser-driven inertial confinement
fusion (ICF) where a sufficiently symmetric implosion of a spherical pellet is expected to achieve
thermonuclear burn. Such flows which originate from exposing the pellet outer shell to a growing
incident 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 of
the heated material expansion wave. Inherently unsteady, these flows are compressible, strongly
accelerated and highly nonuniform with a steep heat front, owing to the strong nonlinearity of the
heat transport and the intense incident heating. These features, in addition to non-trivial boundary
conditions at the shell external surface and shock front, are sources of non-modal thermo-acoustics
effects [1, 2]. However non-modal instability growth in ablation flows relevant to ICF has never
been studied so far. The development of instabilities leading to non-linear phenomena in ablation
flows 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-similar
ablation 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 for
strong transient growth. Because of the base flow unsteadiness, our non-modal linear stability
analysis 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 method
formulation. Both optimal initial conditions and receptivity to perturbations of the incident heat
flux and external surface pressure are considered. Different definitions of objective functionals
are investigated, some in relation with experimentally measurable quantities. Optimal response
computations are carried out for terminal times and perturbation transverse wavelengths which
are 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 linear
hyperbolic 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)
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