Achievement of Target Gain Larger than Unity in an Inertial Fusion Experiment.

On December 5, 2022, an indirect drive fusion implosion on the National Ignition Facility (NIF) achieved a target gain G_{target} of 1.5. This is the first laboratory demonstration of exceeding "scientific breakeven" (or G_{target}>1) where 2.05 MJ of 351 nm laser light produced 3.1 MJ of total fusion yield, a result which significantly exceeds the Lawson criterion for fusion ignition as reported in a previous NIF implosion [H. Abu-Shawareb et al. (Indirect Drive ICF Collaboration), Phys. Rev. Lett. 129, 075001 (2022)PRLTAO0031-900710.1103/PhysRevLett.129.075001]. This achievement is the culmination of more than five decades of research and gives proof that laboratory fusion, based on fundamental physics principles, is possible. This Letter reports on the target, laser, design, and experimental advancements that led to this result.

Lawson Criterion for Ignition Exceeded in an Inertial Fusion Experiment.

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37 MJ of fusion for 1.92 MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion.

Cross-Beam Energy Transfer Saturation by Ion Heating.

We measure cross-beam energy transfer (CBET) saturation by ion heating in a gas-jet plasma characterized using Thomson scattering. A wavelength-tunable ultraviolet (UV) probe laser beam interacts with four intense UV pump beams to drive large-amplitude ion-acoustic waves. For the highest-intensity interactions, the power transfer to the probe laser drops, demonstrating ion-acoustic wave saturation. Over this time, the ion temperature is measured to increase by a factor of 7 during the 500-ps interaction. Particle-in-cell simulations show ion trapping and a subsequent ion heating consistent with measurements. Linear kinetic CBET models are found to agree well with the observed energy transfer when the measured plasma conditions are used.

Low Fuel Convergence Path to Direct-Drive Fusion Ignition.

A new class of inertial fusion capsules is presented that combines multishell targets with laser direct drive at low intensity (2.8×10^{14} W/cm^{2}) to achieve robust ignition. The targets consist of three concentric, heavy, metal shells, enclosing a volume of tens of µg of liquid deuterium-tritium fuel. Ignition is designed to occur well "upstream" from stagnation, with minimal pusher deceleration to mitigate interface Rayleigh-Taylor growth. Laser intensities below thresholds for laser plasma instability and cross beam energy transfer facilitate high hydrodynamic efficiency (∼10%).

Control of stimulated Raman scattering in the strongly nonlinear and kinetic regime using spike trains of uneven duration and delay.

Stimulated Raman scattering (SRS) in its strongly nonlinear, kinetic regime is controlled by a technique of deterministic, strong temporal modulation and spatial scrambling of laser speckle patterns, called spike trains of uneven duration and delay (STUD) pulses [B. Afeyan and S. Hüller (unpublished)]. Kinetic simulations show that the proper use of STUD pulses decreases SRS reflectivity by more than an order of magnitude over random-phase-plate or induced-spatial-incoherence beams of the same average intensity and comparable bandwidth.

Robust unfolding of MeV x-ray spectra from filter stack spectrometer data.

We present an inversion method capable of robustly unfolding MeV x-ray spectra from filter stack spectrometer (FSS) data without requiring an a priori specification of a spectral shape or arbitrary termination of the algorithm. Our inversion method is based upon the perturbative minimization (PM) algorithm, which has previously been shown to be capable of unfolding x-ray transmission data, albeit for a limited regime in which the x-ray mass attenuation coefficient of the filter material increases monotonically with x-ray energy. Our inversion method improves upon the PM algorithm through regular smoothing of the candidate spectrum and by adding stochasticity to the search. With these additions, the inversion method does not require a physics model for an initial guess, fitting, or user-selected termination of the search. Instead, the only assumption made by the inversion method is that the x-ray spectrum should be near a smooth curve. Testing with synthetic data shows that the inversion method can successfully recover the primary large-scale features of MeV x-ray spectra, including the number of x-rays in energy bins of several-MeV widths to within 10%. Fine-scale features, however, are more difficult to recover accurately. Examples of unfolding experimental FSS data obtained at the Texas Petawatt Laser Facility and the OMEGA EP laser facility are also presented.

Knudsen layer reduction of fusion reactivity.

Knudsen layer losses of tail fuel ions can significantly reduce the fusion reactivity of multi-keV DT in capsules with small fuel ρr; sizable yield reduction can result for small inertial confinement fusion (ICF) capsules. This effect is most pronounced when the distance from a burning DT gas region to a nonreacting or cold wall is comparable to the mean free path of reacting fuel ions. A simplified asymptotic theory of Knudsen layer tail depletion is presented and a nonlocal reduced fusion reactivity model is obtained. Application of the model in simulations of ICF capsule implosion experiments gives calculated yields and ion temperatures that are in much closer agreement with observations than are the results of "nominal" or mixed simulations omitting the model.

Self-organized bursts of coherent stimulated Raman scattering and hot electron transport in speckled laser plasma media.

Nonlinear electron trapping physics governs the onset and saturation of stimulated Raman scattering (SRS) in laser beams with many speckles. Hot electrons from intense speckles, produced during SRS daughter electron-plasma-wave bowing and filamentation, seed and enhance the growth of SRS in neighboring speckles by reducing Landau damping. Trapping-induced nonlinearity and speckle interaction through transport of hot electrons and back- and sidescattered SRS waves enable the system of speckles to self-organize and exhibit coherent, sub-ps SRS bursts with more than 100% instantaneous reflectivity, consistent with a SRS transverse coherence width much larger than a speckle width.

Laser acceleration of quasi-monoenergetic MeV ion beams.

Acceleration of particles by intense laser-plasma interactions represents a rapidly evolving field of interest, as highlighted by the recent demonstration of laser-driven relativistic beams of monoenergetic electrons. Ultrahigh-intensity lasers can produce accelerating fields of 10 TV m(-1) (1 TV = 10(12) V), surpassing those in conventional accelerators by six orders of magnitude. Laser-driven ions with energies of several MeV per nucleon have also been produced. Such ion beams exhibit unprecedented characteristics--short pulse lengths, high currents and low transverse emittance--but their exponential energy spectra have almost 100% energy spread. This large energy spread, which is a consequence of the experimental conditions used to date, remains the biggest impediment to the wider use of this technology. Here we report the production of quasi-monoenergetic laser-driven C5+ ions with a vastly reduced energy spread of 17%. The ions have a mean energy of 3 MeV per nucleon (full-width at half-maximum approximately 0.5 MeV per nucleon) and a longitudinal emittance of less than 2 x 10(-6) eV s for pulse durations shorter than 1 ps. Such laser-driven, high-current, quasi-monoenergetic ion sources may enable significant advances in the development of compact MeV ion accelerators, new diagnostics, medical physics, inertial confinement fusion and fast ignition.

Three-dimensional dynamics of breakout afterburner ion acceleration using high-contrast short-pulse laser and nanoscale targets.

Breakout afterburner (BOA) laser-ion acceleration has been demonstrated for the first time in the laboratory. In the BOA, an initially solid-density target undergoes relativistically induced transparency, initiating a period of enhanced ion acceleration. First-ever kinetic simulations of the BOA in three dimensions show that the ion beam forms lobes in the direction orthogonal to laser polarization and propagation. Analytic theory presented for the electron dynamics in the laser ponderomotive field explains how azimuthal symmetry breaks even for a symmetric laser intensity profile; these results are consistent with recent experiments at the Trident laser facility.

Monoenergetic ion beam generation by driving ion solitary waves with circularly polarized laser light.

Experimental data from the Trident Laser facility is presented showing quasimonoenergetic carbon ions from nm-scaled foil targets with an energy spread of as low as ±15% at 35 MeV. These results and high-resolution kinetic simulations show laser acceleration of quasimonoenergetic ion beams by the generation of ion solitons with circularly polarized laser pulses (500 fs, λ=1054 nm). The conversion efficiency into monoenergetic ions is increased by an order of magnitude compared with previous experimental results, representing an important step towards applications such as ion fast ignition.

Observation of persistent species temperature separation in inertial confinement fusion mixtures.

The injection and mixing of contaminant mass into the fuel in inertial confinement fusion (ICF) implosions is a primary factor preventing ignition. ICF experiments have recently achieved an alpha-heating regime, in which fusion self-heating is the dominant source of yield, by reducing the susceptibility of implosions to instabilities that inject this mass. We report the results of unique separated reactants implosion experiments studying pre-mixed contaminant as well as detailed high-resolution three-dimensional simulations that are in good agreement with experiments. At conditions relevant to mixing regions in high-yield implosions, we observe persistent chunks of contaminant that do not achieve thermal equilibrium with the fuel throughout the burn phase. The assumption of thermal equilibrium is made in nearly all computational ICF modeling and methods used to infer levels of contaminant from experiments. We estimate that these methods may underestimate the amount of contaminant by a factor of two or more.

Nonlinear development of stimulated Raman scattering from electrostatic modes excited by self-consistent non-Maxwellian velocity distributions.

The parametric coupling involving backward stimulated scattering of a laser and electron beam acoustic modes (BAM) is described as observed in particle-in-cell (PIC) simulations. The BAM modes evolve from Langmuir waves (LW) as the electron velocity distribution is nonlinearly modified to be non-Maxwellian by backward stimulated Raman scattering (BSRS). With a marginal damping rate, BAM can be easily excited and allow an extended chirping in frequency to occur as later SRS pulses encounter modified distributions. Coincident with the emergence of this non-Maxwellian distribution is a rapid increase in BSRS reflectivities with laser intensities. Both the reflectivity scaling with laser intensity and the observed spectral features from PIC simulations are consistent with recent Trident experiments.

Linear dependence of surface expansion speed on initial plasma temperature in warm dense matter.

Recent progress in laser-driven quasi-monoenergetic ion beams enabled the production of uniformly heated warm dense matter. Matter heated rapidly with this technique is under extreme temperatures and pressures, and promptly expands outward. While the expansion speed of an ideal plasma is known to have a square-root dependence on temperature, computer simulations presented here show a linear dependence of expansion speed on initial plasma temperature in the warm dense matter regime. The expansion of uniformly heated 1-100 eV solid density gold foils was modeled with the RAGE radiation-hydrodynamics code, and the average surface expansion speed was found to increase linearly with temperature. The origin of this linear dependence is explained by comparing predictions from the SESAME equation-of-state tables with those from the ideal gas equation-of-state. These simulations offer useful insight into the expansion of warm dense matter and motivate the application of optical shadowgraphy for temperature measurement.

Hot-electron surface retention in intense short-pulse laser-matter interactions.

Implicit hybrid plasma simulations predict that a significant fraction of the energy deposited into hot electrons can be retained near the surface of targets with steep density gradients illuminated by intense short-pulse lasers. This retention derives from the lateral transport of heated electrons randomly emitted in the presence of spontaneous magnetic fields arising near the laser spot, from geometric effects associated with a small hot-electron source, and from E fields arising in reaction to the ponderomotive force. Below the laser spot hot electrons are axially focused into a target by the B fields, and can filament in moderate Z targets by resistive Weibel-like instability, if the effective background electron temperature remains sufficiently low. Carefully engineered use of such retention in conjunction with ponderomotive density profile steepening could result in a reduced hot-electron range that aids fast ignition. Alternatively, such retention may disturb a deeper deposition needed for efficient radiography and backside fast ion generation.

Visualization of expanding warm dense gold and diamond heated rapidly by laser-generated ion beams.

With the development of several novel heating sources, scientists can now heat a small sample isochorically above 10,000 K. Although matter at such an extreme state, known as warm dense matter, is commonly found in astrophysics (e.g., in planetary cores) as well as in high energy density physics experiments, its properties are not well understood and are difficult to predict theoretically. This is because the approximations made to describe condensed matter or high-temperature plasmas are invalid in this intermediate regime. A sufficiently large warm dense matter sample that is uniformly heated would be ideal for these studies, but has been unavailable to date. Here we have used a beam of quasi-monoenergetic aluminum ions to heat gold and diamond foils uniformly and isochorically. For the first time, we visualized directly the expanding warm dense gold and diamond with an optical streak camera. Furthermore, we present a new technique to determine the initial temperature of these heated samples from the measured expansion speeds of gold and diamond into vacuum. We anticipate the uniformly heated solid density target will allow for direct quantitative measurements of equation-of-state, conductivity, opacity, and stopping power of warm dense matter, benefiting plasma physics, astrophysics, and nuclear physics.

Uniform heating of materials into the warm dense matter regime with laser-driven quasimonoenergetic ion beams.

In a recent experiment at the Trident laser facility, a laser-driven beam of quasimonoenergetic aluminum ions was used to heat solid gold and diamond foils isochorically to 5.5 and 1.7 eV, respectively. Here theoretical calculations are presented that suggest the gold and diamond were heated uniformly by these laser-driven ion beams. According to calculations and SESAME equation-of-state tables, laser-driven aluminum ion beams achievable at Trident, with a finite energy spread of ΔE/E∼20%, are expected to heat the targets more uniformly than a beam of 140-MeV aluminum ions with zero energy spread. The robustness of the expected heating uniformity relative to the changes in the incident ion energy spectra is evaluated, and expected plasma temperatures of various target materials achievable with the current experimental platform are presented.

On the analysis of inhomogeneous magnetic field spectrometer for laser-driven ion acceleration.

We present a detailed study of the use of a non-parallel, inhomogeneous magnetic field spectrometer for the investigation of laser-accelerated ion beams. Employing a wedged yoke design, we demonstrate the feasibility of an in-situ self-calibration technique of the non-uniform magnetic field and show that high-precision measurements of ion energies are possible in a wide-angle configuration. We also discuss the implications of a stacked detector system for unambiguous identification of different ion species present in the ion beam and explore the feasibility of detection of high energy particles beyond 100 MeV/amu in radiation harsh environments.

Quiet direct simulation of Eulerian fluids.

The direct simulation Monte Carlo method of modeling fluids requires sampling one or more random variables every time step for each particle. In this paper a "quiet Monte Carlo" technique is proposed that eliminates the random sampling and the noise it produces by deterministically generating a small number of computational particles. The technique is applied to particle equations of motion appropriate for modeling an Eulerian fluid. Results indicate that strong one- and two-dimensional shocks with large dynamic ranges are accurately represented with only a few particles per cell.

Characterization of deuterium clusters mixed with helium gas for an application in beam-target-fusion experiments.

We measured the average deuterium cluster size within a mixture of deuterium clusters and helium gas by detecting Rayleigh scattering signals. The average cluster size from the gas mixture was comparable to that from a pure deuterium gas when the total backing pressure and temperature of the gas mixture were the same as those of the pure deuterium gas. According to these measurements, the average size of deuterium clusters depends on the total pressure and not the partial pressure of deuterium in the gas mixture. To characterize the cluster source size further, a Faraday cup was used to measure the average kinetic energy of the ions resulting from Coulomb explosion of deuterium clusters upon irradiation by an intense ultrashort pulse. The deuterium ions indeed acquired a similar amount of energy from the mixture target, corroborating our measurements of the average cluster size. As the addition of helium atoms did not reduce the resulting ion kinetic energies, the reported results confirm the utility of using a known cluster source for beam-target-fusion experiments by introducing a secondary target gas.