Principles of the radiative ablation modeling

Abstract

Indirectly driven inertial confinement fusion ͑ICF͒ 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.

Full self-similar solutions of the subsonic radiative heat equations

“…Hammer and Rosen [12,13] proposed new solutions in this region, based on a perturbation theory. Self-similar solutions of the ablative subsonic regime in specific cases were obtained in many other works [14][15][16][17][18][19]. In particular, Garnier et.…”

“…Only naive approximations, considering a constant ablation pressure were used to describe the shock region [19,[22][23][24][25]. These approximations are inaccurate in many cases, where the ablation pressure varies significantly over time.…”

Investigation of supersonic heat-conductivity hyperbolic waves in radiative ablation flows

“…The present analysis of linear perturbation propagation in an ablation wave has confirmed the existence of heat-conductivity linear waves in the flow conduction region. This existence is the direct consequence of temperature and density stratification in the conduction region and therefore cannot be obtained from the standard modeling of radiation-driven ablation flows which assumes an isothermal expansion region (e.g [1,18]). Such waves correspond to the propagation of fluctuations of heat-flux perturbations [25]( § 4.2).…”

“…In order to investigate the deflagration structure of a non-uniform and unsteady ablation flow, we will consider the evolution of three dimensional linear perturbations of a self-similar ablation flow which exhibits a fast expansion of its conduction region, a situation typical of the shock transit phase of an ICF pellet implosion [18,23].…”

“…Due to the multiplicity of phenomena at stake in ablation waves, the standard modeling of radiation-driven ablation in ICF has relied on simplifying assumptions: i.e. an isothermal expansion, a stationary ablation region, and in certain cases an isobaric approximation for this region [1,18]. Nowadays, ICF ablation flows are routinely studied by means of multiple-physics simulations which are however computationally more demanding [3].…”