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Obtaining a burning plasma is a critical step towards self-sustaining fusion energy1. A burning plasma is one in which the fusion reactions themselves are the primary source of heating in the plasma, which is necessary to sustain and propagate the burn, enabling high energy gain. After decades of fusion research, here we achieve a burning-plasma state in the laboratory. These experiments were conducted at the US National Ignition Facility, a laser facility delivering up to 1.9 megajoules of energy in pulses with peak powers up to 500 terawatts. We use the lasers to generate X-rays in a radiation cavity to indirectly drive a fuel-containing capsule via the X-ray ablation pressure, which results in the implosion process compressing and heating the fuel via mechanical work. The burning-plasma state was created using a strategy to increase the spatial scale of the capsule2,3 through two different implosion concepts4–7. These experiments show fusion self-heating in excess of the mechanical work injected into the implosions, satisfying several burning-plasma metrics3,8. Additionally, we describe a subset of experiments that appear to have crossed the static self-heating boundary, where fusion heating surpasses the energy losses from radiation and conduction. These results provide an opportunity to study α-particle-dominated plasmas and burning-plasma physics in the laboratory.

In a burning plasma state1–7, alpha particles from deuterium–tritium fusion reactions redeposit their energy and are the dominant source of heating. This state has recently been achieved at the US National Ignition Facility8 using indirect-drive inertial-confinement fusion. Our experiments use a laser-generated radiation-filled cavity (a hohlraum) to spherically implode capsules containing deuterium and tritium fuel in a central hot spot where the fusion reactions occur. We have developed more efficient hohlraums to implode larger fusion targets compared with previous experiments9,10. This delivered more energy to the hot spot, whereas other parameters were optimized to maintain the high pressures required for inertial-confinement fusion. We also report improvements in implosion symmetry control by moving energy between the laser beams11–16 and designing advanced hohlraum geometry17 that allows for these larger implosions to be driven at the present laser energy and power capability of the National Ignition Facility. These design changes resulted in fusion powers of 1.5 petawatts, greater than the input power of the laser, and 170 kJ of fusion energy18,19. Radiation hydrodynamics simulations20,21 show energy deposition by alpha particles as the dominant term in the hot-spot energy balance, indicative of a burning plasma state.

Direct drive laser fusion ignition experiments rely on detailed understanding and control of irradiation uniformity, the Rayleigh-Taylor instability and target fabrication. The Laboratory for Laser Energetics (LLE) is investigating various theoretical aspects of a direct drive National Ignition Facility (NIF) ignition target based on an `all-DT' design: a spherical target of ~3.4 mm diameter, with a 1-2 μm CH wall thickness and a DT ice layer of ~340 μm near the triple point of DT (~19 K). OMEGA experiments are designed to address the critical issues related to direct drive laser fusion and to provide the necessary data to validate the predictive capability of LLE computer codes. The cryogenic targets to be used on OMEGA are hydrodynamically equivalent to those planned for the NIF. The current experimental studies on OMEGA address the essential components of direct drive laser fusion: irradiation uniformity and laser imprinting, Rayleigh-Taylor growth and saturation, compressed core performance and shell-fuel mixing, laser-plasma interactions and their effect on target performance, and cryogenic target fabrication and handling.

Direct-drive laser-fusion ignition experiments rely on detailed understanding and control of irradiation uniformity, Rayleigh–Taylor instability, and target fabrication. LLE is investigating various theoretical aspects of a direct-drive NIF ignition target based on an `all-DT' design: a spherical target of ∼3.5 mm diameter, 1 to 2 μ m of CH wall thickness, and a ∼350μ m DT-ice layer near the triple point of DT ( ∼19 K). OMEGA experiments are designed to address the critical issues related to direct-drive laser fusion and to provide the necessary data to validate the predictive capability of LLE computer codes. The future cryogenic targets used on OMEGA are hydrodynamically equivalent to those planned for the NIF. The current experimental studies on OMEGA address all of the essential components of direct-drive laser fusion: irradiation uniformity and laser imprinting, Rayleigh–Taylor growth and saturation, compressed core performance and shell–fuel mixing, laser–plasma interactions and their effect on target performance, and cryogenic target fabrication and handling.

Experiments to demonstrate the effects of various beam-smoothing techniques have been performed on the 60-beam, 30-kJ UV OMEGA laser system. These include direct measurements of the effect beam-smoothing techniques have on laser beam nonuniformity and on both planar and spherical targets. Demonstrated techniques include polarization smoothing and “dual-tripler” third-harmonic generation required for future broad bandwidth (∼1 THz) smoothing by spectral dispersion (SSD). The effects of improvements in single-beam uniformity are clearly seen in the target-physics experiments, which also show the effect of the laser pulse shape on the efficacy of SSD smoothing. Saturation of the Rayleigh-Taylor (RT) growth of the broad-bandwidth features, in agreement with the Haan model (Haan, 1989), produced by laser imprinting has also been observed.

Planar, 20 and 40 μm thick CH targets have been accelerated by 351 nm laser beams of the OMEGA laser system [Opt. Commun. 133, 495 (1997)]. Different beam-smoothing techniques were employed including distributed phase plates, smoothing by spectral dispersion, and distributed polarization rotators. The Rayleigh–Taylor evolution of three-dimensional (3D) broadband planar-target perturbations seeded by laser nonuniformities was measured using x-ray radiography at ∼1.3 keV. Fourier analysis shows that the perturbations evolve to longer wavelengths and the shorter wavelengths saturate. The saturation amplitudes and rates of growth of these features are consistent with the predictions of Haan [Phys. Rev. A 39, 5812 (1989)].

Laser-plasma interaction experiments have been carried out on the OMEGA laser system [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)] under plasma conditions representative of the peak of a 1.5 MJ direct-drive laser pulse proposed for the National Ignition Facility (NIF). Plasmas have been formed by exploding 18–20 μm thick CH foils and by irradiating solid CH targets from one side, using up to 20 kJ of laser energy with phase plates installed on all beams. These plasmas and the NIF plasmas are predicted to have electron temperatures of 4 keV and density scale lengths close to 0.75 mm at the peak of the laser pulse. The electron temperature and density of the exploding-foil plasmas have been diagnosed using time-resolved x-ray spectroscopy and stimulated Raman scattering, respectively, and are consistent with predictions of the two-dimensional Eulerian hydrodynamics code SAGE [R. S. Craxton and R. L. McCrory, J. Appl. Phys. 56, 108 (1984)]. When the solid-target or exploding-foil plasmas were irradiate...

Time-resolved measurements of electron and ion temperatures using Thomson scattering have been combined with proton radiography data for comprehensive characterization of individual laser-produced plasma bubbles or the interaction of bubble pairs, where reconnection of azimuthal magnetic fields occurs. Measurements of ion and electron temperatures agree with lasnex simulations of single plasma bubbles, which include the physics of magnetic fields. There is negligible difference in temperatures between a single plasma bubble and the interaction region of bubble pairs, although the ion temperature may be slightly higher due to the collision of expanding plasmas. These results are consistent with reconnection in a $\ensuremath{\beta}\ensuremath{\sim}8$ plasma, where the release of magnetic energy ($l$5$%$ of the electron thermal energy) does not appreciably affect the hydrodynamics.

The National Ignition Facility has been used to compress deuterium-tritium to an average areal density of ~1.0±0.1 g cm(-2), which is 67% of the ignition requirement. These conditions were obtained using 192 laser beams with total energy of 1-1.6 MJ and peak power up to 420 TW to create a hohlraum drive with a shaped power profile, peaking at a soft x-ray radiation temperature of 275-300 eV. This pulse delivered a series of shocks that compressed a capsule containing cryogenic deuterium-tritium to a radius of 25-35 μm. Neutron images of the implosion were used to estimate a fuel density of 500-800 g cm(-3).

Recent experiments using proton backlighting of laser-foil interactions provide unique opportunities for studying magnetized plasma instabilities in laser-produced high-energy-density plasmas. Time-gated proton radiograph images indicate that the outer structure of a magnetic field entrained in a hemispherical plasma bubble becomes distinctly asymmetric after the laser turns off. It is shown that this asymmetry is a consequence of pressure-driven, resistive magnetohydrodynamic (MHD) interchange instabilities. In contrast to the predictions made by ideal MHD theory, the increasing plasma resistivity after laser turn-off allows for greater low-mode destabilization (m1) from reduced stabilization by field-line bending. For laser-generated plasmas presented herein, a mode-number cutoff for stabilization of perturbations with mapproximately [8pibeta(1+D_{m}k_{ perpendicular};{2}gamma_{max};{-1})];{1/2} is found in the linear growth regime. The growth is measured and is found to be in reasonable agreement with model predictions.

We report on the first proton radiography of laser-irradiated hohlraums. This experiment, with vacuum gold (Au) hohlraums, resulted in observations of self-generated magnetic fields with peak values approximately 10;{6} G. Time-gated radiographs of monoenergetic protons with discrete energies (15.0 and 3.3 MeV) reveal dynamic pictures of field structures and plasma flow. Near the end of the 1-ns laser drive, a stagnating Au plasma (approximately 10 mg cm;{-3}) forms at the center of the hohlraum. This is a consequence of supersonic, radially directed Au jets (approximately 1000 microm ns;{-1}, approximately Mach 4) that arise from the interaction of laser-driven plasma bubbles expanding into one another.

The widely differing spatial, temporal, and density scales needed to accurately model the fast ignition process and other short-pulse laser-plasma interactions leads to a computationally challenging project that is difficult to solve using a single code. This report summarizes the work performed on a three year LDRD to couple together three independent codes using PYTHON to build a new integrated computational tool. An example calculation using this new model is described.

Electromagnetic (E/B) fields generated by the interaction with plasmas of long-pulse, low-intensity laser beams relevant to inertial confinement fusion have been measured for the first time using novel monoenergetic proton radiography methods. High-resolution, time-gated radiography images of a plastic foil driven by a 10(14) W/cm(2) laser implied B fields of approximately 0.5 MG and E fields of approximately 1.5 x 10(8) V/m. Simulations of these experiments with LASNEX+LSP have been performed and are in overall (though not exact) agreement with the data both for field strengths and for spatial distributions; this is the first direct experimental test of the laser-generated B-field package in LASNEX. The experiments also demonstrated that laser phase plates substantially reduce medium-scale chaotic field structure.

A fully nonlinear sharp-boundary model of the ablative Rayleigh-Taylor instability is derived and closed in a similar way to the self-consistent closure of the linear theory. It contains the stabilizing effect of ablation and accurately reproduces the results of 2D DRACO simulations. The single-mode saturation amplitude, bubble and spike evolutions in the nonlinear regimes, and the seeding of long-wavelength modes via mode coupling are determined and compared with the classical theory without ablation. Nonlinear stability above the linear cutoff is also predicted.

The Rayleigh-Taylor instability in its highly nonlinear, turbulent stage causes atomic-scale mixing of the shell material with the fuel in the compressed core of inertial-confinement fusion targets. The density of shell material mixed into the outer core of direct-drive plastic-shell spherical-target implosions on the 60-beam, OMEGA laser system is estimated to be 3.4(+/-1.2) g/cm(3) from time-resolved x-ray spectroscopy, charged-particle spectroscopy, and core x-ray images. The estimated fuel density, 3.6(+/-1) g/cm(3), accounts for only approximately 50% of the neutron-burn-averaged electron density, n(e)=2.2(+/-0.4)x10(24) cm(-3).

A wide variety of diagnostics have been deployed to study direct-drive spherical implosions of gas-filled, plastic shells on the 60-beam OMEGA laser system at the Laboratory for Laser Energetics. Neutron detectors using plastic scintillators measure primary yield, ion temperature, secondary neutron yield, and burn history. Charged- particle detectors record, on CR-39 samples, the secondary protons in pure D2 implosions and elastically scattered protons, deuterons, and tritons in DT implosions to measure the shell and fuel areal densities. Primary D3He protons from plastic shells with a CD layer at the shell-gas interface and a 3He fill provide a significant signal only if the shell and fuel regions are mixed. Shells with an Ar-doped fill are used to infer the emissivity- averaged core electron temperatures and densities from the measured time-dependent Ar K-shell spectra. The level of nonuniformity in the shell areal density at stagnation is measured using gated x-ray images of Ti-doped shells.

High Density Carbon (HDC) is a leading candidate as an ablator material for Inertial Confinement Fusion (ICF) capsules in x-ray (indirect) drive implosions. HDC has a higher density (3.5 g/cc) than plastic (CH, 1 g/cc), which results in a thinner ablator with a larger inner radius for a given capsule scale. This leads to higher x-ray absorption and shorter laser pulses compared to equivalent CH designs. This paper will describe a series of experiments carried out to examine the feasibility of using HDC as an ablator using both gas filled hohlraums and lower density, near vacuum hohlraums. These experiments have shown that deuterium (DD) and deuterium-tritium gas filled HDC capsules driven by a hohlraum filled with 1.2 mg/cc He gas, produce neutron yields a factor of 2× higher than equivalent CH implosions, representing better than 50% Yield-over-Clean (YoC). In a near vacuum hohlraum (He = 0.03 mg/cc) with 98% laser-to-hohlraum coupling, such a DD gas-filled capsule performed near 1D expectations. A cryogenic layered implosion version was consistent with a fuel velocity = 410 ± 20 km/s with no observed ablator mixing into the hot spot.

The shock heating of a laser-driven, direct-drive target can determine its stability by affecting Rayleigh-Taylor growth rates through target decompression and ablative stabilization. Measurements indicate that pulses that rise rapidly to 10(14) W/cm(2) produce shock-induced temperatures of approximately 25 eV, whereas more slowly rising pulses show less heating. Analysis of the observed target behavior produced by these two pulses demonstrates that shock heating improves hydrodynamic stability because ablative stabilization increases when the targets are preheated by shocks.

Direct-drive laser-fusion ignition experiments rely on detailed understanding and control of irradiation uniformity, the Rayleigh-Taylor instability, and target fabrication. LLE is investigating various theoretical aspects of a direct-drive NIF ignition target based on an 'all-DT' design: a spherical target of approximately 3.5-mm diameter, 1 to 2 micrometers of CH wall thickness, and an approximately 350-micrometers DT-ice layer near the triple point of DT. OMEGA experiments are designed to address the critical issues related to direct-drive laser fusion and to provide the necessary data to validate the predictive capability of LLE computer codes. The cryogenic targets planned for OMEGA are hydrodynamically equivalent to those planned for the NIF. The current experimental studies on OMEGA address all of the essential components of direct- drive laser fusion: irradiation uniformity and laser imprinting, Rayleigh-Taylor growth and saturation, compressed core performance and shell-fuel mixing, laser- plasma interactions and their effect on target performance, and cryogenic target fabrication and handling.

Using EXAFS to characterize metals shocked to -Mbar pressures by a laser has been studied. High-contrast modulations were obtained using a laser-imploded spherical target as the source. EXAFS visibility as function of shock pressure was calculated.

Indirect drive experiments have now been carried out with laser powers and energies up to 520 TW and 1.9 MJ. These experiments show that the energy coupling to the target is nearly constant at 84% ± 3% over a wide range of laser parameters from 350 to 520 TW and 1.2 to 1.9 MJ. Experiments at 520 TW with depleted uranium hohlraums achieve radiation temperatures of ∼330 ± 4 eV, enough to drive capsules 20 μm thicker than the ignition point design to velocities near the ignition goal of 370 km/s. A series of three symcap implosion experiments with nearly identical target, laser, and diagnostics configurations show the symmetry and drive are reproducible at the level of ±8.5% absolute and ±2% relative, respectively.

A one-dimensional Fokker-Planck code coupled to a non-local-thermodynamic-equilibrium ionization dynamics model is described. Simulations are presented of the interaction of a short-pulse laser with a solid target which show that the variable ionization state distorts the distribution function. This distortion modifies the temperature and heat flow profiles. The heat front penetration is found to be different from fixed ionization simulation.

The first inertial confinement fusion implosion experiments with equimolar deuterium-tritium thermonuclear fuel have been performed on the National Ignition Facility. These experiments use 0.17 mg of fuel with the potential for ignition and significant fusion yield conditions. The thermonuclear fuel has been fielded as a cryogenic layer on the inside of a spherical plastic capsule that is mounted in the center of a cylindrical gold hohlraum. Heating the hohlraum with 192 laser beams for a total laser energy of 1.6 MJ produces a soft x-ray field with 300 eV temperature. The ablation pressure produced by the radiation field compresses the initially 2.2-mm diameter capsule by a factor of 30 to a spherical dense fuel shell that surrounds a central hot-spot plasma of 50 μm diameter. While an extensive set of x-ray and neutron diagnostics has been applied to characterize hot spot formation from the x-ray emission and 14.1 MeV deuterium-tritium primary fusion neutrons, thermonuclear fuel assembly is studied by m...

This paper describes simulations of short-pulse-laser\char21{}solid experiments using a one-dimensional Fokker-Planck code. Results are presented which show that the Spitzer theory of heat flow is inapplicable for these experiments. The ionization dynamics have been investigated by postprocessing using an average atom model. It is found that the dominant processes are collisional ionization and three-body recombination and that full ionization takes a signficant fraction of the rise time of the laser pulse. The collisional ionization rates obtained from a Maxwellian distribution are found to be in good agreement with those obtained from convolving the cross sections with the actual distribution.

The viability of inertial confinement fusion depends crucially on implosion symmetry. A spherical three-dimensional hydrocode called plato has been developed to model the growth in asymmetries during an implosion. Results are presented in the deceleration phase which show indistinguishable linear growth rates, but greater nonlinear growth of the Rayleigh-Taylor instability than is found in two-dimensional cylindrical simulations. The three-dimensional enhancement of the nonlinear growth is much smaller than that found by Sakagami and Nishihara.

Proton generation from the interaction of an intense, short pulse laser with a foil target is simulated using the particle-in-cell hybrid code LSP. The efficiencies for proton production are compared for foils having thin coatings of CH, CH2, CH4, and LiH, as well as heavy hydrides such as ErH3. Enhanced efficiencies are found for both light hydrogen-rich compounds and for heavy hydrides, which in the latter case approach the pure H result. A simple model reproduces these results over a wide range of materials.

Multidimensional hydrodynamic properties of high-adiabat direct-drive plastic-shell implosions on the OMEGA laser system [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)] are investigated using the multidimensional hydrodynamic code, DRACO [D. Keller et al., Bull. Am. Phys. Soc. 44, 37 (1999)]. Multimode simulations including the effects of nonuniform illumination and target roughness indicate that shell stability during the acceleration phase plays a critical role in determining target performance. For thick shells that remain integral during the acceleration phase, target yields are significantly reduced by the combination of the long-wavelength (l