Early stage of implosion in inertial confinement fusion: Shock timing and perturbation evolution

Abstract

Excessive increase in the shell entropy and degradation from spherical symmetry in inertial confinement fusion implosions limit shell compression and could impede ignition. The entropy is controlled by accurately timing shock waves launched into the shell at an early stage of an implosion. The seeding of the Rayleigh-Taylor instability, the main source of the asymmetry growth, is also set at early times during the shock transit across the shell. In this paper we model the shock timing and early perturbation growth of directly driven targets measured on the OMEGA laser system [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)]. By analyzing the distortion evolution, it is shown that one of the main parameters characterizing the growth is the size of the conduction zone Dc, defined as a distance between the ablation front and the laser deposition region. Modes with kDc>1 are stable and experience oscillatory behavior [V. N. Goncharov, Phys. Rev. Lett. 82, 2091 (1999)]. The model shows that the main stabilizing mechanism is the dynamic overpressure due to modulations in the blow-off velocity inside the conduction zone. The long wavelengths with kDc<1 experience growth because of coupled Richtmyer-Meshkov-like and Landau-Darrieus instabilities [L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, New York, 1982)]. To match the simulation results with both the shock timing and perturbation growth measurements a new nonlocal thermal transport model is developed and used in hydrocodes.

Cryogenic-target performance and implosion physics studies on OMEGA

“…It gives an effective time-dependent flux limiter, defined as the ratio of nonlocal heat flux to the freestream heat flux. 11 The measured target trajectory ͓Fig. 1͑a͔͒ is in good agreement with the simulated trajectory using the effective time-dependent flux limiter shown in Fig.…”

“…6 The simulations used a local model for electron transport 10 with a time-dependent flux limiter derived from a one-dimensional ͑1D͒ nonlocal thermal-electron-transport model. 11 The nonlocal model solves the Boltzmann equation with Krook's collision operator and an appropriate electrondeposition length. It gives an effective time-dependent flux limiter, defined as the ratio of nonlocal heat flux to the freestream heat flux.…”

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

“…Finite length effects of the thermal conduction region on the ablative RMI have been recently considered in detail (Abéguilé et al 2006;Goncharov et al 2006;Gotchev et al 2006;Clarisse et al 2008). Goncharov had pointed out that long-wavelength modes with kD c < 1 grow because of the combined effect of the RM-like and Landau-Darrieus instabilities (Landau & Lifshitz 1987), although the modes with kD c > 1 are stable and experience oscillatory behaviour by the dynamic overpressure, where D c is the length of the thermal conduction region.…”

Capsule modeling of high foot implosion experiments on the National Ignition Facility

“…In progressing from N130812 to N140819, the maximum ablation front growth factor more than doubles from ∼170 to ∼430. Also evident in these spectra is the importance of the ablative Richtmyer-Meshkov (RM) oscillation [25] in setting the node in the growth factor spectrum [22,23,[26][27][28][29][30]: as the ablator was thinned in N140520 and N140819, and the pulse length consequently shortened, the time for this RM oscillation was reduced and the location of the growth factor node moved froml 80 to ∼120, resulting in enhanced growth of shorter wavelength features. Figure 2 plots the maximum of each growth factor spectrum from figure 1 versus simulated peak implosion velocity.…”