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.
This paper considers the hydrodynamic equations with nonlinear conduction when the internal energy and the opacity have power-law dependences in the density and in the temperature. This system models the situation in which a dense solid is brought into contact with a thermal bath. It supports self-similar solutions that depend on the surface temperature. The self-similar solution can exhibit a shock wave followed by an ablation front if the surface temperature does not increase too fast in time, but it can exhibit a heat front followed by an isothermal shock otherwise. These flows are carefully studied in order to clarify the role of the initial solid density in the energy absorption and the ablation process. Comparisons with numerical simulations show excellent agreement.
In inertial confinement fusion experiments, a cold target material is accelerated by a hot, low-density plasma. The interface between the heavy and light materials is Rayleigh–Taylor (RT) unstable. To estimate the perturbation growth in accelerated targets, a postprocessor to the results of one-dimensional codes is developed. The postprocessor is based on the sharp-boundary model that takes into account time variation in the unperturbed state, mode interaction of neighboring interfaces in the target, effects of spherical convergence, and the mass ablation. The model reveals a new stabilizing effect of ablation for modes with wavelengths longer than the shell thickness. For such modes with γcl>Va/d, the perturbation growth is reduced to η∼m(t)/m(0)e∫dt′γcl2−kVblVa/(2d), where γcl=kg is the classical RT growth rate of interface perturbations in the semi-infinite slab subject to gravitational field g, k is the wave number, d and m(t) are the slab thickness and mass, and Va and Vbl are the ablation and blowoff velocities, respectively. The perturbation evolution calculated by using the developed postprocessor is shown to be in good agreement with the results of two-dimensional hydrodynamic simulations.
A weakly nonlinear model is proposed for the Rayleigh-Taylor instability in the presence of ablation and thermal transport. The second harmonic generation efficiency of a single-mode disturbance is computed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. Mode coupling in the spectrum of a multimode disturbance is thoroughly analyzed. The ablative stabilization can be clearly discussed because the derived formulas for the evanescent ablation rate are in agreement with previously known results for incompressible, inviscid, irrotational, and immiscible fluids [S. W. Haan, Phys. Fluids B 3, 2349 (1991)]; M. Berning and A. M. Rubenchik, Phys. Fluids 10, 1564 (1998)]].
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