Effects of temporal density variation and spherical convergence on the nonlinear bubble evolution of single-mode, classical Rayleigh-Taylor instability are studied using an analytical model based on Layzer's theory [Astrophys. J. 122, 1 (1955)]. When the temporal density variation is included, the bubble amplitude in planar geometry is shown to asymptote to integral(t)U(L)(t')rho(t')dt'/rho(t), where U(L) = square root of (g/(C(g)k)) is the Layzer bubble velocity, rho is the fluid density, and C(g) = 3 and C(g) = 1 for the two- and three-dimensional geometries, respectively. The asymptotic bubble amplitude in a converging spherical shell is predicted to evolve as eta approximately etam(-/r0//(lU(L)sp-eta/r0), where r0 is the outer shell radius, eta(t) = integral(t)U(L)sp(t')rho(t') r(0)2(t')dt'/rho(t)r(0)2(t), U(L)(sp) = square root of (-r0(t)r0(t)/l), m(t) = rho(t)r(0)3(t), and l is the mode number.

Direct-drive laser absorption, mass ablation rate, and shock heating are experimentally studied on the OMEGA Laser System [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)] to validate hydrodynamics simulations. High-gain, direct-drive inertial confinement fusion target implosions require accurate predictions of the shell adiabat α (entropy), defined as the pressure in the main fuel layer to the Fermi-degenerate pressure, and the implosion velocity of the shell. The laser pulse shape determines the shell adiabat and the hydrodynamic efficiency determines the implosion velocity. A comprehensive set of measurements tracking the flow of energy from the laser to the target was conducted. Time-resolved measurements of laser absorption in the corona are performed on spherical implosion experiments. The mass ablation rate is inferred from time-resolved Ti K-shell spectroscopic measurements of nonaccelerating, solid CH spherical targets with a buried tracer layer of Ti. Shock heating is diagnosed in planar-CH-foil targets using time-resolved x-ray absorption spectroscopy and noncollective spectrally resolved x-ray scattering. The highly reproducible experimental results achieved with a high level of laser drive uniformity [S. P. Regan et al., J. Opt. Soc. Am. B 22, 998 (2005)] constrain the modeling of direct-drive energy coupling. A detailed comparison of the experimental results and the simulations reveals that a single-value flux limiter in the thermal transport model cannot explain all of the experimental observables. Simulations of laser absorption measurements need a time-dependent flux limiter to match the data. Modeling of both resonance absorption and nonlocal effects in the electron thermal conduction from the critical density to the ablation front are underway to resolve the observed discrepancies.

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