Ignition is needed to make fusion energy a viable alternative energy source, but has yet to be achieved. A key step on the way to ignition is to have the energy generated through fusion reactions in an inertially confined fusion plasma exceed the amount of energy deposited into the deuterium-tritium fusion fuel and hotspot during the implosion process, resulting in a fuel gain greater than unity. Here we report the achievement of fusion fuel gains exceeding unity on the US National Ignition Facility using a 'high-foot' implosion method, which is a manipulation of the laser pulse shape in a way that reduces instability in the implosion. These experiments show an order-of-magnitude improvement in yield performance over past deuterium-tritium implosion experiments. We also see a significant contribution to the yield from α-particle self-heating and evidence for the 'bootstrapping' required to accelerate the deuterium-tritium fusion burn to eventually 'run away' and ignite.

Point design targets have been specified for the initial ignition campaign on the National Ignition Facility [G. H. Miller, E. I. Moses, and C. R. Wuest, Opt. Eng. 443, 2841 (2004)]. The targets contain D-T fusion fuel in an ablator of either CH with Ge doping, or Be with Cu. These shells are imploded in a U or Au hohlraum with a peak radiation temperature set between 270 and 300 eV. Considerations determining the point design include laser-plasma interactions, hydrodynamic instabilities, laser operations, and target fabrication. Simulations were used to evaluate choices, and to define requirements and specifications. Simulation techniques and their experimental validation are summarized. Simulations were used to estimate the sensitivity of target performance to uncertainties and variations in experimental conditions. A formalism is described that evaluates margin for ignition, summarized in a parameter the Ignition Threshold Factor (ITF). Uncertainty and shot-to-shot variability in ITF are evaluated, and sensitivity of the margin to characteristics of the experiment. The formalism is used to estimate probability of ignition. The ignition experiment will be preceded with an experimental campaign that determines features of the design that cannot be defined with simulations alone. The requirements for this campaign are summarized. Requirements are summarized for the laser and target fabrication.

Indirect-drive hohlraum experiments at the National Ignition Facility have demonstrated symmetric capsule implosions at unprecedented laser drive energies of 0.7 MJ. 192 simultaneously fired laser beams heat ignition emulate hohlraums to radiation temperatures of 3.3 million Kelvin compressing 1.8-millimeter capsules by the soft x rays produced by the hohlraum. Self-generated plasma-optics gratings on either end of the hohlraum tune the laser power distribution in the hohlraum producing symmetric x-ray drive as inferred from the shape of the capsule self-emission. These experiments indicate conditions suitable for compressing deuterium-tritium filled capsules with the goal to achieve burning fusion plasmas and energy gain in the laboratory.With completion (1) and commissioning (2) of the National Ignition Facility (NIF) the quest for producing a burning fusion plasma has begun (3, 4). The goal of these experiments is to compress matter to densities and temperatures higher than the interior of the sun (5-7) which will initiate nuclear fusion and burn of hydrogen isotopes (8-10). This technique holds promise to demonstrate a highly efficient carbon-free process that will burn milligram quantities of nuclear fuel on each laser shot for producing energy gain in the laboratory.The NIF (11) consists of 192 laser beams that have been arranged into cones of beams to irradiate a target from the top and bottom hemispheres. This "indirect-drive" laser geometry has been chosen for the first experiments to heat the interior of centimeter-scale cylindrical gold hohlraums (8,(12)(13)(14)(15) through laser entrance holes (LEH) on the top and bottom end of the cylinder (Fig. 1). Hohlraums act as radiation enclosures that convert the optical laser light into soft x-rays that are characterized by the radiation temperature T RAD . Present ignition designs operate at temperatures of 270 to 305 eV or 3.1 to 3.5 million K. The radiation field compresses a spherical fusion capsule mounted in the center of the hohlraum by x-ray ablation of the outer shell. The ablation process compresses the cryogenically prepared solid deuterium-tritium fuel layer in a spherical rocket implosion. In the final stages, the fuel reaches densities 1000-times solid and the central hot spot temperatures will approach 100 million K to initiate the nuclear burn process.We have symmetrically imploded 1.8-mm diameter fusion capsules in cryogenically fielded centimeter-scale hohlraums at 20 K. These experiments show efficient hohlraum heating to radiation temperatures of 3.3 million K. In addition, the large scale-length plasmas encountered in these experiments have allowed us to use self-generated plasma optics gratings (16) to control the radiation symmetry (17) and to achieve symmetric fusion capsule implosions.Figure 2 A shows the laser power at the frequency-tripled wavelength of 351 nm versus time for two different pulse shapes. These 11-ns and 16-ns long pulses heat 8.4-mm long, 4.6-mm diameter hohlraums with 20% helium, 80% hydrogen (atomic) mixtures and ...

Radiative hydrodynamics simulations of ignition experiments show that energy transfer between crossing laser beams allows tuning of the implosion symmetry. A new full-scale, three-dimensional quantitative model has been developed for crossed-beam energy transfer, allowing calculations of the propagation and coupling of multiple laser beams and their associated plasma waves in ignition hohlraums. This model has been implemented in a radiative-hydrodynamics code, demonstrating control of the implosion symmetry by a wavelength separation between cones of laser beams.

The Hohlraum energetics experimental campaign started in the summer of 2009 on the National Ignition Facility (NIF) [E. I. Moses et al., Phys. Plasmas 16, 041006 (2009)]. These experiments showed good coupling of the laser energy into the targets [N. Meezan et al., Phys. Plasmas 17, 056304 (2010)]. They have also demonstrated controlled crossed-beam energy transfer between laser beams as an efficient and robust tool to tune the implosion symmetry of ignition capsules, as predicted by earlier calculations [P. Michel et al., Phys. Rev. Lett. 102, 025004 (2009)]. A new linear model calculating crossed-beam energy transfer between cones of beams on the NIF has been developed. The model has been applied to the subscale Hohlraum targets shot during the National Ignition Campaign in 2009. A good agreement can be found between the calculations and the experiments when the impaired propagation of the laser beams due to backscatter is accounted for.

A series of cryogenic, layered deuterium-tritium (DT) implosions have produced, for the first time, fusion energy output twice the peak kinetic energy of the imploding shell. These experiments at the National Ignition Facility utilized high density carbon ablators with a three-shock laser pulse (1.5 MJ in 7.5 ns) to irradiate low gas-filled (0.3  mg/cc of helium) bare depleted uranium hohlraums, resulting in a peak hohlraum radiative temperature ∼290  eV. The imploding shell, composed of the nonablated high density carbon and the DT cryogenic layer, is, thus, driven to velocity on the order of 380  km/s resulting in a peak kinetic energy of ∼21  kJ, which once stagnated produced a total DT neutron yield of 1.9×10^{16} (shot N170827) corresponding to an output fusion energy of 54 kJ. Time dependent low mode asymmetries that limited further progress of implosions have now been controlled, leading to an increased compression of the hot spot. It resulted in hot spot areal density (ρr∼0.3  g/cm^{2}) and stagnation pressure (∼360  Gbar) never before achieved in a laboratory experiment.

The “High-Foot” platform manipulates the laser pulse-shape coming from the National Ignition Facility laser to create an indirect drive 3-shock implosion that is significantly more robust against instability growth involving the ablator and also modestly reduces implosion convergence ratio. This strategy gives up on theoretical high-gain in an inertial confinement fusion implosion in order to obtain better control of the implosion and bring experimental performance in-line with calculated performance, yet keeps the absolute capsule performance relatively high. In this paper, we will cover the various experimental and theoretical motivations for the high-foot drive as well as cover the experimental results that have come out of the high-foot experimental campaign. At the time of this writing, the high-foot implosion has demonstrated record total deuterium-tritium yields (9.3×1015) with low levels of inferred mix, excellent agreement with implosion simulations, fuel energy gains exceeding unity, and evidence for the “bootstrapping” associated with alpha-particle self-heating.

No abstract