We exhibit and detail the properties of self-similar solutions for inviscid compressible ablative flows in slab symmetry with nonlinear heat conduction which are relevant to inertial confinement fusion (ICF). These solutions have been found after several contributions over the last four decades. We first derive the set of ODEs – a nonlinear eigenvalue problem – which governs the self-similar solutions by using the invariance of the Euler equations with nonlinear heat conduction under the two-parameter Lie group symmetry. A sub-family which leaves the density invariant is detailed since these solutions may be used to model the ‘early-time’ period of an ICF implosion where a shock wave travels from the front to the rear surface of a target. A chart allowing us to determine the starting point of a numerical solution, knowing the physical boundary conditions, has been built. A physical analysis of these unsteady ablation flows is then provided, the associated dimensionless numbers (Mach, Froude and Péclet numbers) being calculated. Finally, we show that self-similar ablation fronts generated within the framework of the above hypotheses (electron heat conduction, growing heat flux at the boundary, etc.) and for large heat fluxes and not too large pressures at the boundary do not satisfy the low-Mach-number criteria. Indeed both the compressibility and the stratification of the hot-flow region are too large. This is, in particular, the case for self-similar solutions obtained for energies in the range of the future Laser MegaJoule laser facility. Two particular solutions of this latter sub-family have been recently used for studying stability properties of ablation fronts.

Exact similarity solutions for inviscid compressible ablative flows in slab symmetry with nonlinear heat conduction are proposed for studying unsteadiness and compressibility effects on the hydrodynamic stability of ablation fronts relevant to inertial confinement fusion. Both the similarity solutions and their linear perturbations are numerically computed with a dynamical multidomain Chebyshev pseudospectral method. Herewith the first analysis of laser-imprinting based on a dynamic solution is presented, showing that maximum perturbation amplification occurs for a laser-intensity modulation of zero transverse wave number, with growth dominated by the mean flow stretching.

Self-similar solutions to the compressible Euler equations with nonlinear conduction are considered as particular instances of unsteady radiative deflagration – or ‘ablation’ – waves with the goal of characterizing the actual hydrodynamic properties that such flows may present. The chosen family of solutions, corresponding to the ablation of an initially quiescent perfectly cold and homogeneous semi-infinite slab of inviscid compressible gas under the action of increasing external pressures and radiation fluxes, is well suited to the description of the early ablation of a target by gas-filled cavity X-rays in experiments of high energy density physics. These solutions are presently computed by means of a highly accurate numerical method for the radiative conduction model of a fully ionized plasma under the approximation of a non-isothermal leading shock wave. The resulting set of solutions is unique for its high fidelity description of the flows down to their finest scales and its extensive exploration of external pressure and radiative flux ranges. Two different dimensionless formulations of the equations of motion are put forth, yielding two classifications of these solutions which are used for carrying out a quantitative hydrodynamic analysis of the corresponding flows. Based on the main flow characteristic lengths and on standard characteristic numbers (Mach, Péclet, stratification and Froude numbers), this analysis points out the compressibility and inhomogeneity of the present ablative waves. This compressibility is further analysed to be too high, whether in terms of flow speed or stratification, for the low Mach number approximation, often used in hydrodynamic stability analyses of ablation fronts in inertial confinement fusion (ICF), to be relevant for describing these waves, and more specifically those with fast expansions which are of interest in ICF. Temperature stratification is also shown to induce, through the nonlinear conductivity, supersonic upstream propagation of heat-flux waves, besides a modified propagation of quasi-isothermal acoustic waves, in the flow conduction regions. This description significantly departs from the commonly admitted depiction of a quasi-isothermal conduction region where wave propagation is exclusively ascribed to isothermal acoustics and temperature fluctuations are only diffused.

A family of exact similarity solutions for inviscid compressible ablative flows in slab symmetry with nonlinear heat conduction is proposed for studying unsteadiness and compressibility effects on the hydrodynamic stability of ablation fronts relevant to inertial confinement fusion. Dynamical multi-domain Chebyshev spectral methods are employed for computing both the similarity solution and its time-dependent linear perturbations. This approach has been exploited to analyse the linear stability properties of two self-similar ablative configurations subjected to direct laser illumination asymmetries. Linear perturbation temporal and reduced responses are analysed, evidencing a maximum instability for illumination asymmetries of zero transverse wavenumber as well as three distinct regimes of ablation-front distortion evolution, and emphasizing the importance of the mean flow unsteadiness, compressibility and stratification.