Principles of the radiative ablation modeling

Abstract

Indirectly driven inertial confinement fusion (ICF) rests on the setting up of a radiation temperature within a laser cavity and on the optimization of the capsule implosion ablated by this radiation. In both circumstances, the ablation of an optically thick medium is at work. The nonlinear radiation conduction equations that describe this phenomenon admit different kinds of solutions called generically Marshak waves. In this paper, a completely analytic model is proposed to describe the ablation in the subsonic regime relevant to ICF experiments. This model approximates the flow by a deflagrationlike structure where Hugoniot relations are used in the stationary part from the ablation front up to the isothermal sonic Chapman–Jouguet point and where the unstationary expansion from the sonic point up to the external boundary is assumed quasi-isothermal. It uses power law matter properties. It can also accommodate arbitrary boundary conditions provided the ablation wave stays very subsonic and the surface temperature does not vary too quickly. These requirements are often met in realistic situations. Interestingly, the ablated mass rate, the ablation pressure, and the absorbed radiative energy depend on the time history of the surface temperature, not only on the instantaneous temperature values. The results compare very well with self-similar solutions and with numerical simulations obtained by hydrodynamic code. This analytic model gives insight into the physical processes involved in the ablation and is helpful for optimization and sensitivity studies in many situations of interest: radiation temperature within a laser cavity, acceleration of finite size medium, and ICF capsule implosion, for instance.