The 1990 National Academy of Science final report of its review of the Inertial Confinement Fusion Program recommended completion of a series of target physics objectives on the 10-beam Nova laser at the Lawrence Livermore National Laboratory as the highest-priority prerequisite for proceeding with construction of an ignition-scale laser facility, now called the National Ignition Facility ͑NIF͒. These objectives were chosen to demonstrate that there was sufficient understanding of the physics of ignition targets that the laser requirements for laboratory ignition could be accurately specified. This research on Nova, as well as additional research on the Omega laser at the University of Rochester, is the subject of this review. The objectives of the U.S. indirect-drive target physics program have been to experimentally demonstrate and predictively model hohlraum characteristics, as well as capsule performance in targets that have been scaled in key physics variables from NIF targets. To address the hohlraum and hydrodynamic constraints on indirect-drive ignition, the target physics program was divided into the Hohlraum and Laser-Plasma Physics ͑HLP͒ program and the Hydrodynamically Equivalent Physics ͑HEP͒ program. The HLP program addresses laser-plasma coupling, x-ray generation and transport, and the development of energy-efficient hohlraums that provide the appropriate spectral, temporal, and spatial x-ray drive. The HEP experiments address the issues of hydrodynamic instability and mix, as well as the effects of flux asymmetry on capsules that are scaled as closely as possible to ignition capsules ͑hydrodynamic equivalence͒. The HEP program also addresses other capsule physics issues associated with ignition, such as energy gain and energy loss to the fuel during implosion in the absence of alpha-particle deposition. The results from the Nova and Omega experiments approach the NIF requirements for most of the important ignition capsule parameters, including drive temperature, drive symmetry, and hydrodynamic instability. This paper starts with a review of the NIF target designs that have formed the motivation for the goals of the target physics program. Following that are theoretical and experimental results from Nova and Omega relevant to the requirements of those targets. Some elements of this work were covered in a 1995 review of indirect-drive ͓J. D. Lindl, ''Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain,'' Phys. Plasmas 2, 3933 ͑1995͔͒. In order to present as complete a picture as possible of the research that has been carried out on indirect drive, key elements of that earlier review are also covered here, along with a review of work carried out since 1995.

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.

For many cases of interest to inertial fusion, growth of Rayleigh–Taylor and other hydrodynamic instabilities is such that the perturbations remain linear or weakly nonlinear. The transition to nonlinearity is studied via a second-order solution for multimode classical Rayleigh–Taylor growth. The second-order solution shows how classical Rayleigh–Taylor systems forget initial amplitude information in the weakly nonlinear phase. Stabilized growth relevant to inertial fusion is qualitatively different, and initial amplitudes are not dominated by nonlinear effects. In all systems with a full spectrum of modes, nonlinear effects begin when mode amplitudes reach about 1/Lk2, for modes of wave number k and system size L.

It is generally recognized that a single Rayleigh-Taylor unstable mode grows exponentially, proportional to the initial amplitude, until the amplitude is about ]p to -, ' of the wavelength. The growth then becomes nonlinear, and the mode evolves into spikes and bubbles. This paper considers how this picture of the transition to nonlinearity changes when, instead of there being a single mode, there is a full spectrum of modes. We argue that nonlinear behavior begins whenever the sum of modes over a specified small region of k space becomes comparable to the wavelength. In the case of a single mode, this reduces to the usual comparison of the mode's amplitude with its wavelength A, . But if the modal amplitudes are smooth functions of k, the modes begin to saturate when their amplitude is comparable to A, /R times a dimensionless scale factor; here, 8 is the radius in spherical geometry, or the length of the surface in planar geometry. Given this new notion of the amplitude at which nonlinear saturation begins, we construct a simple model to estimate the net perturbation resulting from a broadband initial spectrum. We assume that modes grow exponentially until saturation occurs, and then the growth of the individual modes becomes linear in time.The model predictions in two and three dimensions are compared with Read and Young's experiments [Atomic Weapons Research Establishment Report No. 011/83, Aldermasten, 1983 (unpublished)], and to Youngs's calculations [Physica 12D, 32 (1984)]. The experimental results are used to set the single parameter characterizing the onset of nonlinearity. The model provides a complete description of a weak dependence on initial amplitude. The model can be easily extended to any situation for which one can estimate single-mode growths; results are presented regarding effects on multirnode growth of spherical geometry, ablation stabilization, and interface coupling.

Several targets are described that in simulations give yields of 1–30 MJ when indirectly driven by 0.9–2 MJ of 0.35 μm laser light. The article describes the targets, the modeling that was used to design them, and the modeling done to set specifications for the laser system in the proposed National Ignition Facility. Capsules with beryllium or polystyrene ablators are enclosed in gold hohlraums. All the designs utilize a cryogenic fuel layer; it is very difficult to achieve ignition at this scale with a noncryogenic capsule. It is necessary to use multiple bands of illumination in the hohlraum to achieve sufficiently uniform x-ray irradiation, and to use a low-Z gas fill in the hohlraum to reduce filling of the hohlraum with gold plasma. Critical issues are hohlraum design and optimization, Rayleigh–Taylor instability modeling, and laser–plasma interactions.