The turbulent Rayleigh-Taylor instability is investigated in the limit of strong mode-coupling using a variety of high-resolution, multimode, three dimensional numerical simulations ͑NS͒. The perturbations are initialized with only short wavelength modes so that the self-similar evolution ͑i.e., bubble diameter D b ϰamplitude h b) occurs solely by the nonlinear coupling ͑merger͒ of saturated modes. After an initial transient, it is found that h b ϳ␣ b Agt 2 , where AϭAtwood number, gϭacceleration, and tϭtime. The NS yield D b ϳh b /3 in agreement with experiment but the simulation value ␣ b ϳ0.025Ϯ0.003 is smaller than the experimental value ␣ b ϳ0.057Ϯ0.008. By analyzing the dominant bubbles, it is found that the small value of ␣ b can be attributed to a density dilution due to fine-scale mixing in our NS without interface reconstruction ͑IR͒ or an equivalent entrainment in our NS with IR. This may be characteristic of the mode coupling limit studied here and the associated ␣ b may represent a lower bound that is insensitive to the initial amplitude. Larger values of ␣ b can be obtained in the presence of additional long wavelength perturbations and this may be more characteristic of experiments. Here, the simulation data are also analyzed in terms of bubble dynamics, energy balance and the density fluctuation spectra.

The performance of a targets designed for the National Ignition Facility ͑NIF͒ are simulated in three dimensions using the HYDRA multiphysics radiation hydrodynamics code. ͓M. Marinak et al., Phys. Plasmas 5, 1125 ͑1998͔͒ In simulations of a cylindrical NIF hohlraum that include an imploding capsule, all relevant hohlraum features and the detailed laser illumination pattern, the motion of the wall material inside the hohlraum shows a high degree of axisymmetry. Laser light is able to propagate through the entrance hole for the required duration of the pulse. Gross hohlraum energetics mirror the results from an axisymmetric simulation. A NIF capsule simulation resolved the full spectrum of the most dangerous modes that grow from surface roughness. Hydrodynamic instabilities evolve into the weakly nonlinear regime. There is no evidence of anomalous low mode growth driven by nonlinear mode coupling.

Transport modeling of idealized, cone-guided fast ignition targets indicates the severe challenge posed by fast-electron source divergence. The hybrid particle-in-cell [PIC] code Zuma is run in tandem with the radiation-hydrodynamics code Hydra to model fast-electron propagation, fuel heating, and thermonuclear burn. The fast electron source is based on a 3D explicit-PIC laser-plasma simulation with the PSC code. This shows a quasi two-temperature energy spectrum, and a divergent angle spectrum (average velocityspace polar angle of 52 • ). Transport simulations with the PIC-based divergence do not ignite for > 1 MJ of fast-electron energy, for a modest (70 µm) standoff distance from fast-electron injection to the dense fuel. However, artificially collimating the source gives an ignition energy of 132 kJ. To mitigate the divergence, we consider imposed axial magnetic fields. Uniform fields ∼50 MG are sufficient to recover the artificially collimated ignition energy. Experiments at the Omega laser facility have generated fields of this magnitude by imploding a capsule in seed fields of 50-100 kG. Such imploded fields are however more compressed in the transport region than in the laser absorption region. When fast electrons encounter increasing field strength, magnetic mirroring can reflect a substantial fraction of them and reduce coupling to the fuel. A hollow magnetic pipe, which peaks at a finite radius, is presented as one field configuration which circumvents mirroring.

Rayleigh–Taylor (RT) experiments have been conducted with planar CH(Br) foils accelerated by x-ray ablation from a shaped, low adiabat drive. The surface perturbations investigated consisted of single-mode, two-mode, and eight-mode sinusoids. The perturbation evolution begins during the shock transit phase, when perturbations show gradual growth due to Richtmyer–Meshkov-like dynamics. After shock breakout, the compressed foils accelerate and perturbation growth continues due to the Rayleigh–Taylor instability. Detailed comparisons with simulations indicate that in the linear Rayleigh–Taylor regime, the single-mode perturbations grow exponentially in time. In the nonlinear regime, the growth slows and the perturbation shape changes from sinusoidal to ‘‘bubble and spike’’ with the appearance of higher Fourier harmonics. In the multimode perturbations, the individual modes grow independently in the linear regime, but become coupled in the nonlinear regime. In addition to the higher harmonics of the individual modes, coupling leads to the appearance of ki±kj ‘‘beat’’ modes. This results in a redistribution of the perturbation into a broader Fourier spectrum causing a change of shape: bubbles become broader and flatter and spikes narrower, in agreement with simulations and multimode theory.

Three similar cryogenic ignition capsule designs for the National Ignition Facility [J. Lindl, Phys. Plasmas 2, 3933 (1995)] are analyzed to determine surface roughness specifications required to mitigate the growth of hydrodynamic instabilities. These capsule utilize brominated plastic, polyimid and copper-doped beryllium ablator materials respectively. Direct three-dimensional numerical simulations with the HYDRA radiation hydrodynamic code [M. M. Marinak et al., Phys. Plasmas 3, 2070 (1996)] examine the growth of multimode perturbations seeded by roughness on the outer ablator and inner ice surfaces. The simulations, which showed weakly nonlinear behavior for optimized surfaces, were carried through ignition and burn. A three-dimensional multimode perturbation achieves somewhat larger amplitudes in the nonlinear regime than a corresponding two-dimensional simulation of the same rms amplitude. The beryllium and polyimid capsules exhibit enhanced tolerance of roughness on both the ice and ablator surfaces.