The linear Darrieus-Landau and Rayleigh-Taylor instabilities in inertial confinement fusion revisited

Within the framework of the quasi-isobaric approximation (low Mach number), a self-consistent stability analysis of ablation fronts in inertial confinement fusion is performed for all the modes with a wavelength larger than the conduction length in the cold material. The validity domain is ranging from short to long wavelength modes, shorter and larger than the total thickness of the thermal wave, respectively. The analysis leads to a single analytical expression for the dispersion relation valid in the whole range of modes, including the transition regime (wavelength of the same order of magnitude as the total thickness). The hydrodynamic instabilities of ablation fronts are thus described by a unified theory in a large domain of conditions, ranging from weak acceleration in the early stage of irradiation to strong acceleration during the main implosion phase. In the weak acceleration regime, the transition between Darrieus-Landau unstable modes and damped oscillatory modes is described. Comparison with numerical results shows a good agreement. Comparison with the previous analyses sheds new light on the stabilization mechanism. The result of the sharp boundary model is recovered in the limit of large power index for thermal conduction.