Physical Models and Mathematical Simulation of Laser-Driven Implosion and Their Relations with Experiments

Linear perturbation response of self-similar ablative flows relevant to inertial confinement fusion

“…Since Marshak (1958), similarity solutions of one-dimensional forms of (2.3), or of their two-temperature counterparts in the case of plasmas, have been investigated either by means of simulations of particular initial-and boundary-value problems (IBVPs) (Anisimov 1970;Brun et al 1977), either through asymptotic analysis (Barrero & Sanmartín 1977;Sanmartín & Barrero 1978a, b) or numerical integration (Reinicke & Meyer-ter-Vehn 1991) of similarity transformed equations. More recently, benefiting from an unpublished work of 1983 by Saillard (see Abéguilé et al 2006), the authors and co-workers (Boudesocque-Dubois 2000; Boudesocque-Dubois et al 2001;Gauthier et al 2005;Abéguilé et al 2006;Boudesocque-Dubois et al 2008) devised a numerical approach capable of computing self-similar ablative heat waves for quasi-non-isothermal leading shock waves, with a level of accuracy compatible with a hydrodynamic stability analysis.…”

“…see Zel'dovich & Raizer 1967;Landau & Lifshitz 1987), in addition to providing insights into complex hydrodynamic phenomena, through scaling relationships, and enabling qualitative and parametric studies in realistic configurations, have been profitably used in fluid mechanics as background states for performing hydrodynamic stability analyses beyond the assumptions of uniform or steady mean flows. Self-similar ablative heat waves have been known since Marshak (1958) and have been investigated by several authors in the context of ICF (Anisimov (1970); Brun et al 1977;Barrero & Sanmartín 1977;Sanmartín & Barrero 1978a, b;Reinicke & Meyer-ter-Vehn 1991;Sanz, Piriz & Tomasel 1992). Among the various configurations which have been studied, a particular family is most relevant for depicting the ablative heat wave during the early shell-irradiation stage (see Brun et al 1977) for which numerical simulations indicate that mean flow profiles are more akin to self-similar than to steady flows (Velikovich et al 1998).…”

“…Self-similar ablative heat waves have been known since Marshak (1958) and have been investigated by several authors in the context of ICF (Anisimov (1970); Brun et al 1977;Barrero & Sanmartín 1977;Sanmartín & Barrero 1978a, b;Reinicke & Meyer-ter-Vehn 1991;Sanz, Piriz & Tomasel 1992). Among the various configurations which have been studied, a particular family is most relevant for depicting the ablative heat wave during the early shell-irradiation stage (see Brun et al 1977) for which numerical simulations indicate that mean flow profiles are more akin to self-similar than to steady flows (Velikovich et al 1998). Hence such solutions present a genuine interest when investigating the stability of ablative heat waves found in ICF, including all the relevant effects of unsteadiness, compressibility and stratification.…”

Travaux Laser-Matière Au Centre d'ÉTUDES De Limeil

“…Des études [7] sont également faites sur Par exemple, le coefficient de conductibilité K, du mélange équimoléculaire de deutérium et de tritium est déterminé dans la plage de densités et de températures, balayée lors d'une implosion (Fig. 9), en particulier, dans la zone de transition entre les plasmas cinétiques classiques (K, de Spitzer) et les plasmas à forte dégénérescence électronique (K, de Hubbard) [16].…”

“…Les photographies intégrées dans le temps montrent que le dépôt d'énergie est isotrope et que l'implosion est sphérique. A l'aide de caméras à balayage de fente, on enregistre suivant un diamètre de la cible, le déplacement des zones émettant à 0,53 pm et dans le domaine X.Les résultats expérimentaux sont comparés à ceux d'un code de simulation numérique[7], monodimensionnel, lagrangien, à un fluide et deux températures, avec absorption du rayonnement laser par bremsstrahlung inverse et traitement du transfert du rayonnement produit dans la cible[8]. La figure 5 donne un exemple de comparaison dont les données expérimentales et numériques sont : une concordance assez satisfaipar ailleurs, les courbes donnant d'une part, la puissante entre les variations de la zone d'émission R,,, à sance de l'émission X intégrée sur la fente d'une caméra 0,53 pm et du rayon R, correspondant à la densité de X à balayage(Fig.…”