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DOE OSTI2022

Investigating radiatively driven, magnetized plasmas with a university scale pulsed-power generator

We present first results from a novel experimental platform that is able to access physics relevant to topics including indirect-drive magnetized inertial confinement fusion, laser energy deposition, various topics in atomic physics, and laboratory astrophysics (for example, the penetration of B-fields into high energy density plasmas). This platform uses the x rays from a wire array Z-pinch to irradiate a silicon target, producing an outflow of ablated plasma. The ablated plasma expands into ambient, dynamically significant B-fields (∼5 T), which are supported by the current flowing through the Z-pinch. The outflows have a well-defined (quasi-1D) morphology, enabling the study of fundamental processes typically only available in more complex, integrated schemes. Experiments were fielded on the MAGPIE pulsed-power generator (1.4 MA, 240 ns rise time). On this machine, a wire array Z-pinch produces an x-ray pulse carrying a total energy of ∼15 kJ over ∼30 ns. This equates to an average brightness temperature of around 10 eV on-target.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Simulating the filamentation of smoothed laser beams with three-dimensional nonlinear dynamics

In a plasma, the ponderomotive force of an inhomogeneous electromagnetic field expels plasma from regions of high intensity. When a laser propagates through a plasma, this force creates density wells that subsequently modify the index of refraction. The beam refracts and focuses into these wells and may filament. In extreme cases, the laser beam will spray due to increasing angular divergence of the beam. The threshold for ponderomotive self-focusing is well established for isolated laser hotspots or speckles. Here, we define a practical threshold for characterizing the filamentation of thousands of speckles that are found in the focal plane of high-power laser beams spatially smoothed with random phase plates as used at high energy and power laser facilities studying inertial confinement fusion. This threshold is tested against three-dimensional simulations of speckled laser light propagating through plasma. Four metrics are applied to assess filamentation: the fraction of power above five times the average intensity, an effective f-number, the mean-squared perpendicular wavenumber, and the fraction of rarefied density with deviation from the initial density exceeding | δn/ n| = 0.1. The speckled beams studied are generated by random phase plates, both with and without additional polarization smoothing, in a parameter regime of relevance to indirect drive experiments. While filamentation has been discussed extensively in the literature, we believe this to be the first published simulation study with three-dimensional nonlinear hydrodynamics that addresses the onset threshold of ponderomotive filamentation and establishes the lengths and time scales necessary to reach a statistical steady state.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Reaching a burning plasma and ignition using smaller capsules/ Hohlraums , higher radiation temperatures, and thicker ablator/ice on the national ignition facility

In indirect-drive implosions, the final core hot spot energy and pressure and, hence, neutron yield attainable in 1D increase with increasing laser peak power and, hence, radiation drive temperature at the fixed capsule and Hohlraum size. Here we present simple analytic scalings validated by 1D simulations that quantify the improvement in performance and use this to explain existing data and simulation trends. Extrapolating to the 500 TW National Ignition Facility peak power limit in a low gas-fill 5.4 mm diameter Hohlraum based on existing high adiabat implosion data at 400 TW, 1.3 MJ and 1 × 10 16 yield, we find that a 2–3 × 10 17 yield (0.5–0.7 MJ) is plausible using only 1.8 MJ of laser energy. Based on existing data varying deuterium–tritium (DT) fuel thickness and dopant areal density, further improvements should be possible by increasing DT fuel areal density, and hence confinement time and yield amplification.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Time-dependent saturation and physics-based nonlinear model of cross-beam energy transfer

The nonlinear physics of cross-beam energy transfer (CBET) for multi-speckled laser beams is examined using large-scale particle-in-cell simulations for a range of laser and plasma conditions relevant to indirect-drive inertial confinement fusion (ICF) experiments. The time-dependent growth and saturation of CBET involve complex, nonlinear ion and electron dynamics, including ion trapping-induced enhancement and detuning, ion acoustic wave (IAW) nonlinearity, oblique forward stimulated Raman scattering (FSRS), and backward stimulated Brillouin scattering (BSBS) in a CBET-amplified seed beam. Ion-trapping-induced detuning of CBET is captured in the kinetic linear response by a new δf-Gaussian-mixture algorithm, enabling an accurate characterization of trapping-induced non-Maxwellian distributions. Ion trapping induces nonlinear processes, such as changes to the IAW dispersion and nonlinearities (e.g., bowing and self-focusing), which, together with pump depletion, FSRS, and BSBS, determine the time-dependent nature and level of CBET gain as the system approaches a steady state. Using VPIC simulations at intensities at and above the onset threshold for ion trapping and the insight from the time-dependent saturation analyses, we construct a nonlinear CBET model from local laser and plasma conditions that predicts the CBET gain and the energy deposition into the plasma. This model is intended to provide a more accurate, physics-based description of CBET saturation over a wide range of conditions encountered in ICF hohlraums compared with linear CBET gain models with ad hoc saturation clamps often used in laser ray-based methods in multi-physics codes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Alpha-heating analysis of burning plasma and ignition experiments on the National Ignition Facility

A recent experiment conducted on the National Ignition Facility (NIF) described in the study by Abu-Shawareb et al. achieved a fusion yield output of 1.3 MJ from ~ 220 kJ of x-ray energy absorbed by the capsule, demonstrating remarkable progress in the field of laser driven inertial confinement fusion. In the study by A. R. Christopherson [“Effects of charged particle heating on the hydrodynamics of inertially confined plasmas,” Ph.D. thesis (2020)], the plasma conditions needed to claim the onset of ignition and burn propagation were outlined and multiple criterion were provided to assess progress in inertial fusion experiments. In this work, we modify the metrics from A. R. Christopherson to accurately calculate performance metrics for indirect-drive experiments on the NIF. We also show that performance metric trends observed in NIF data are consistent with theory and simulations. This analysis indicates that all the identified criterion for ignition and burn propagation have been exceeded by experiment 210 808.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Modeling stimulated Brillouin backscatter from outer-cone quads across multiple inertial confinement fusion hohlraum designs

Stimulated Brillouin scattering (SBS) is a potential risk for laser damage in the experiments carried out at the National Ignition Facility (NIF), and by altering the energy deposition pattern in hohlraums, it affects the symmetry of indirect-drive inertial confinement fusion implosions. We have surveyed backward SBS on outer-cone quads across NIF integrated hohlraums of various platforms numerically, using three-dimensional (3D) simulations with the backscatter code pF3D [Berger et al. Phys. Plasmas 5, 4337 (1998)] and ray-based gain calculations. Simulated reflected powers and energies, as well as the spectrum of reflected light all compare favorably with measurements. Ray-based calculations of exponential SBS amplification (“gain”), which assume a strongly damped plasma wave and steady-state response, are performed using a novel method that includes the 3D speckled field of the laser that drives SBS. This approach is useful for understanding qualitative differences between hohlraum designs and identifying regions susceptible to SBS within hohlraums. Quantitatively, gains are not found to correlate with SBS reflectivities in 3D, necessitating fully wave-based calculations that naturally include diffraction and various temporal dependencies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Directly driven magnetized fast-ignition targets with steep density gradients for inertial fusion energy

The development of advanced targets capable of achieving ignition with improved energy gain at lower driver energies is one of four key technical challenges to be solved in order to realize economical inertial fusion energy. We report the minimum energy necessary for a small hemispherical mass of fast-ignited high-density deuterium–tritium fuel to explosively ignite a significantly larger hemispherical mass of assembled cold fuel with much lower mass density, both with and without a flux-compressed magnetic field connecting the two regions. With the magnetic field, the burn rate improves, and lower energy states become more effective. The imploded fuel reservoir available in the lower-density, larger-mass region of the steep density gradient determines whether the fusion yield is several hundred MJ or up to a few GJ. We report a case wherein the cold reservoir ignited and produced high gain with the assistance of only ~700 kJ of hotspot yield, an amount that has already been demonstrated as feasible in laboratory experiments using indirect-drive targets.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Exact wave solver for nonparaxial laser beam propagation

Simulations of inertial confinement fusion (ICF) experiments require high-fidelity models for laser beam propagation in a nonuniform plasma with varying index of refraction. We describe a new numerical wave solver that is applicable to centimeter-scale length plasmas encountered in indirect drive ICF applications. The one-way Helmholtz equation (OHE) generalizes the time-harmonic paraxial wave equation to large angles. Here, we present a methodology to numerically evaluate the exact solution to the OHE. This solution is computed by analytically advancing eigenfunctions of the one-way Helmholtz operator along a propagation direction and is applicable to any given index of a refraction profile. We compare our exact method with a commonly used approximate split-step technique for solving the OHE. As a test problem, we consider nonparaxial propagation of Gaussian and speckled beams in a plasma density channel with internal reflection. We find that the split-step approach incurs significant errors compared to the exact solution computed using the novel algorithm.

Belyaev, Mikhail A. (ORCID:0000000224908887)↗
DOE OSTI2024

Modeling ablator defects as a source of mix in high-performance implosions at the National Ignition Facility

Recent indirect drive inertial confinement fusion implosions on the National Ignition Facility (NIF) [Spaeth et al., Fusion Sci. Technol. 69, 25 (2016)] have crossed the threshold of ignition. However, performance has been variable due to several factors. One of the leading sources of variability is the quality of the high-density carbon (HDC) shells used as ablators in these experiments. In particular, these shells can have a number of defects that have been found to correlate with the appearance of ablator mix into the hot spot and a degradation in nuclear yield. These defects include pits on the ablator surface, voids in the ablator bulk, high-Z debris from the Hohlraum wall that adheres to the capsule surface, and finally the inherent granular micro-structure of the crystalline HDC itself. This paper summarizes high-resolution modeling of each of these mix sources in two recent high-performance NIF implosion experiments. The simulated impact from a range of individual capsule defects is found to be broadly consistent with the trends seen in experiment, lending credence to the modeling results and the details of the mixing process that they reveal. Interestingly, modeling of the micro-structure inherent to HDC shows that this perturbation source results in considerable mixing of the deuterium–tritium fuel with ablator material during the implosion. The reduction in fuel compression from this mix results in an approximately factor of two reduction in neutron yield in current implosions and emphasizes the importance of mitigating this significant performance degradation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Reconciling calculations and measurements of inverse bremsstrahlung absorption

It was recently shown that the use of Coulomb logarithms appropriate for bremsstrahlung radiation (rather than transport processes) along with corrections for the Langdon effect and ion screening reproduced measurements of collisional absorption in well-characterized underdense plasmas [D. Turnbull et al., Phys. Rev. Lett. 130, 145103 (2023)]. However, it was recognized at the time that the use of the standard absorption-reduction factor from Langdon's seminal paper was inconsistent with the use of Coulomb logarithms that are thermally averaged over a Maxwellian electron-velocity distribution function. A more accurate approach would be to average over the expected super-Gaussian distribution function while accounting for the Gaunt factor's velocity dependence, which somewhat mitigates the Langdon effect; however, at that time, this theory matched the data less well. This conflict is now eliminated with the additional insight that the ionization state of our mid-Z ion species (when present) was lower than had been assumed, as evidenced by the Thomson-scattering data and time-dependent Cretin simulations. We are now able to show that an improved treatment of the Langdon effect provides the best match to data. Otherwise, the prior conclusions remain unchanged. We also show an example of the substantial expected impact to the absorption rate in calculations of indirect-drive hohlraums.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

What next: Further implosion space exploration on the path to NIF extended yield capability

We present quantitative motivations and assessments of various proposed and ongoing directions to further improving yields and target gain of igniting indirect-drive implosions at the National Ignition Facility (NIF). These include increasing compression and confinement time, improving hohlraum and ablator efficiency, and further increasing peak power and laser energy. 1D hydroscaled simulations, augmented by analytic 1D theory, have been used to project yield improvements for each of these implosion optimization tracks, normalized to the best current performing 4 MJ shot. At current NIF capabilities of 2.2 MJ, 450 TW, we project several paths could reach 15 MJ yield levels. We also expect several key implosion physics questions will be addressed in attempting to reach this yield level. These include demonstrating to what extent lower adiabat designs leading to higher compression will increase gain and efficiency, and whether we can reduce residual kinetic energy and ablator-fuel mix that is probably limiting the current burn-up fraction. For an envisaged NIF upgrade to EL = 3 MJ at fixed 450 TW peak power, scaling capsule size and fuel thicknesses faster than pure hydroscaling should allow for yields that could reach up to 60–80 MJ, depending on the efficiency gains realized in increasing deuterium-tritium fuel thickness, reducing hohlraum losses, and switching to lower Z ablators. The laser-plasma instability and beam transmission scaling in these larger hohlraums is shown to be favorable if the spot size is increased with hohlraum scale.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

The crucial role of diagnostics in achieving ignition on the National Ignition Facility (NIF)

Well over 100 diagnostics can operate on the National Ignition Facility (NIF) as a result of several decades of development on NIF, and before that on Nova, OMEGA, and earlier LLNL lasers. A subset of these have guided the approach to achieving ignition on the NIF in 2022 [H. Abu-Shawareb et al. (Indirect Drive ICF Collaboration), Phys. Rev. Lett. 129(7), 075001 (2022)]. Achieving ignition on NIF has required many types of experiments with this core set of diagnostics, some constraining known unknowns and some revealing surprises—arguably unknown unknowns. Early design work realized that the extreme precision required for ignition on NIF would require fine-tuning by experiment, that is, measuring and adjusting known unknowns. Many examples are given where the use of the core set of ignition diagnostics in experimental arrangements called platforms demonstrated control of the key theoretical parameters defined as shape, adiabat, velocity, and mix. The direction of the adjustments to input conditions is found either by trend analysis or, in many cases, by observing from the diagnostic data the direction to make an adjustment. In addition, diagnostics have revealed some unexpected or neglected known issues, which degrade performance, or unexpected issues, unknown unknowns. Some of these factors had been previously considered, but underestimated or difficult to calculate at the time. The overall methodology can be described as a variant of Popper's falsifiability philosophy [K. Popper, The Logic of Scientific Discovery (Hutchinson, 1974)]. This paper summarizes the role of ignition diagnostics in terms of falsification or validation of theory or experimental setup as well as uncovering unexpected issues. The journey to ignition started in the seventies with a 1-µm wavelength laser producing disastrous results. Diagnostics have guided us to the recent multi-decadal goal of demonstrating ignition and burn in the laboratory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Ex situ calibration of the scattered-light time-history diagnostic on the National Ignition Facility

The scattered-light time-history diagnostic (SLTD) suite measures time-resolved scattered light in three wavelength bands: stimulated Brillouin scattering (350–352 nm), stimulated Raman scattering (430–760 nm), and plasma emission at half the laser frequency (695–735 nm), at 15 locations around the National Ignition Facility (NIF) target chamber. The SLTD, along with the full-aperture backscatter station (FABS), collects scattered light from direct- and indirect-drive inertial confinement fusion experiments. The SLTD calibration was revisited after a discrepancy between FABS and SLTD measurements was observed on NIF polar direct-drive experiments. An integrated calibration of the SLTD was performed for the first time, and individual components were also calibrated for the wavelengths of 351, 527, and 532 nm. The optical transmission of the instrument was measured to be (1.12 ± 0.04) × 10 –7 and (1.96 ± 0.11) × 10 –7 for the wavelengths of 351 and 532 nm, respectively. The revised calibration at 351 nm brings the SLTD measured scattered energy in agreement with the FABS measured scattered energy after additionally accounting for the degradation of an optical element in FABS. Furthermore, this decreased the inferred absorption by 7% for a representative experiment. However, discrepancies remain between FABS and SLTD measurements in the SRS band (532 nm).

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

The long road to ignition: An eyewitness account

This paper reviews the many twists and turns in the long journey that culminated in ignition in late 2022 using the laser heated indirect-drive approach to imploding DT filled targets at the National Ignition Facility (NIF), located at the Lawrence Livermore National Laboratory (LLNL). We describe the early origins of the Laser Program at LLNL and key developments such as the paradigm shifting birth of high energy density physics (HEDP) studies with lasers, changes in choice of laser wavelength, and the development of key diagnostics and computer codes. Fulfilling the requirements of the multi-faceted Nova Technical Contract was a necessary condition for the approval of the NIF, but more importantly, the end of the Cold War and the cessation of nuclear testing were key catalysts in that approval, along with the ready-and-waiting field of HEDP. The inherent flexibility of the field of laser driven inertial confinement fusion played a fundamental role in achieving success at the NIF. We describe how the ultimately successful ignition target design evolved from the original “point design” target, through the lessons of experiment. All key aspects of that original design changed: The capsule's materials and size were changed; the hohlraum's materials, size, laser entrance hole size, and gas fills were also all changed, as were the laser pulse shapes that go along with all those changes. The philosophy to globally optimize performance for stability (by raising the adiabat and thus lowering the implosion convergence) was also key, as was progress in target fabrication, and in increasing NIF's energy output. The persistence of the research staff and the steadfast backing of our supporters were also necessary elements in this success. We gratefully acknowledge seven decades of researcher endeavors and four decades of the dedicated efforts of many hundreds of personnel across the globe who have participated in NIF construction, operation, target fabrication, diagnostic, and theoretical advances that have culminated in ignition.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Toward an improved nonlocal thermodynamic equilibrium model for more predictive simulations of ignition scale hohlraums

Recently, nonlocal thermodynamic equilibrium (NLTE) modeling has been identified as the primary reason for discrepant predictions of the peak neutron production time in indirectly driven inertial confinement fusion (ICF) platforms. It has also been observed that predictions of collisional excitation rates differ by as much as 50% from measurements. Theoretical uncertainties in dielectronic recombination rates have also been posited as possibly contributing to errors in NLTE predictions. This work examines the impact of multipliers on collisional excitation and dielectronic recombination rates on simulations of a directly driven gold sphere and an indirect drive ICF implosion. It is found that multipliers on the collisional excitation rates have a strong impact on radiant intensity and electron temperature and a weaker impact on ionization state, whereas multipliers on dielectronic recombinations rates strongly impact ionization state with a smaller impact on radiant intensity and electron temperature. A self-consistent NLTE model which places multipliers on differing transitions, as motivated by experimental measurements and more detailed atomic physics predictions, improves agreement but does not completely eliminate discrepancies with measurements of the radiant intensity within the 2–4 keV spectral range.

Farmer, W. A. [Lawrence Livermore National Laborat↗
DOE OSTI2025

Hot-spot model for inertial confinement fusion implosions with an applied magnetic field

Imposing a magnetic field on inertial confinement fusion implosions magnetizes the electrons in the compressed fuel; this suppresses thermal losses, which increases temperature and fusion yield. Indirect-drive experiments at the National Ignition Facility with 12 and 26 T applied magnetic fields demonstrate up to 40% increase in temperature, 3× increase in fusion yield, and indicate that magnetization alters the radial temperature profile [Moody et al., Phys. Rev. Lett. 129, 195002 (2022); Lahmann et al., APS DPP (2022)]. In this work, we develop a semi-analytic hot-spot model, which accounts for the two-dimensional (2D) Braginskii anisotropic heat flow due to an applied axial magnetic field. First, we show that hot-spot magnetization alters the radial temperature profile, increasing the central peakedness, which is most pronounced for moderately magnetized implosions (with 8–14 T applied field), compared to both unmagnetized (with no applied field) and highly magnetized (with 26 T or higher applied field) implosions. This model explains the trend in the experimental data, which finds a similarly altered temperature profile in the 12 T experiment. Next, we derive the hot-spot model for gas-filled (Symcap) implosions, accounting for the effects of magnetization on the thermal conduction and in changing the radial temperature (and density) profiles. Using this model, we compute predicted central temperature amplification and yield enhancement scaling with the applied magnetic field. The central temperature fits the experimental data accurately, and the discrepancy in the yield suggests a systematic (independent of applied field) degradation, such as mix, and additional degradation in the reference unmagnetized shot, such as reduced laser drive, increased implosion asymmetry, or the magnetic field suppressing ablator mixing into the hot-spot.

Alpha particles↗
DOE OSTI2025

First demonstration of improved yield with reduced adiabat in inertial confinement fusion implosions on the National Ignition Facility

Laser-driven, indirect-drive inertial confinement fusion (ICF) experiments at the National Ignition Facility (NIF) recently achieved a target gain greater than one, where fusion energy output exceeds input laser energy [Abu-Shawareb et al., Phys. Rev. Lett. 132, 065102 (2024)]. Despite this milestone, gain levels remain insufficient for practical applications such as inertial fusion energy, making performance improvement critical. One promising approach is increasing fuel compression by lowering the implosion adiabat. To explore reduced adiabat, experiments were conducted modifying the laser pulse shape and shock timing of an existing 1.9-MJ-drive implosion design performing near the ignition cliff [Abu-Shawareb et al., Phys. Rev. Lett. 129, 075001 (2022)]. These experiments demonstrated increased compression and fusion yield in ICF implosions at the NIF by using a lower fuel adiabat, and increased compression with a reduced adiabat in high-density carbon ablators. The updated design achieved up to 80% higher fusion yield and 14% greater fuel compression compared to the previous best-performing 1.9-MJ experiment, with repeatable performance, and is the only implosion design to achieve a target gain exceeding one with < 2.04 MJ laser energy. Notably, this work was made possible because of recent advances in target quality and pulse shape control allowing experimental access to the ignition regime, and thereby increased sensitivity to adiabat. This work addresses a long-standing question in ICF research and lays the foundation for higher target gains through optimized implosion strategies. It underscores the potential of reduced adiabat designs to enhance compression and fusion yields for future ICF applications.

Hohenberger, M. [Lawrence Livermore National Labor↗