Instabilities of ablation fronts in inertial confinement fusion : a comparison with flames

A comparison with flames sheds new light on the dynamics of ablation fronts in inertial confinement fusion (ICF). The mathematical formulation of the problem in ICF is the same as for flames propagating upwards. The difference concerns the Froude number Fr, yielding a different order of magnitude for the nondimensional wave number of the marginally stable disturbances. When the thermal conductivity varies strongly, as is the case in ICF, a wide range of characteristic (diffusive) lengths is involved across the wave structure. For disturbances with intermediate wavelengths, a "universal" diffusive relaxation rate of thermal waves is exhibited with no dependence on the heat conductivity. This is a key point for describing the dynamics of strongly accelerated ablation fronts whose marginally stable wavelength is much shorter than the total wave thickness. The coupling of hydrodynamics and heat conduction is analyzed in a way similar to flame theory, through the derivation of a kinematic relation for the ablation front including its thermal relaxation. A transition between the regimes of flames and ablation fronts in ICF is exhibited with decreasing Fr. For a moderate acceleration, Fr>>1, the result for flames is recovered. For a large acceleration, Fr of order unity, the thermal relaxation, when coupled with hydrodynamics, is shown to damp out the Darrieus–Landau instability, yielding the known result in ICF for strongly accelerated ablation fronts. For a wide class of models, including the simple two-length-scale model, the description is shown to be independent of the model. A weakly nonlinear analysis, valid irrespective of the number of unstable modes, is carried out for describing the early development of nonlinear structures of the ablation front in ICF. The role of the Darrieus–Landau instability at the early stage of irradiation is pointed ou