Design of the first fusion experiment to achieve target energy gain G>1.

In this work we present the design of the first controlled fusion laboratory experiment to reach target gain G>1 N221204 (5 December 2022) [Phys. Rev. Lett. 132, 065102 (2024)10.1103/PhysRevLett.132.065102], performed at the National Ignition Facility, where the fusion energy produced (3.15 MJ) exceeded the amount of laser energy required to drive the target (2.05 MJ). Following the demonstration of ignition according to the Lawson criterion N210808, experiments were impacted by nonideal experimental fielding conditions, such as increased (known) target defects that seeded hydrodynamic instabilities or unintentional low-mode asymmetries from nonuniformities in the target or laser delivery, which led to reduced fusion yields less than 1 MJ. This Letter details design changes, including using an extended higher-energy laser pulse to drive a thicker high-density carbon (also known as diamond) capsule, that led to increased fusion energy output compared to N210808 as well as improved robustness for achieving high fusion energies (greater than 1 MJ) in the presence of significant low-mode asymmetries. For this design, the burnup fraction of the deuterium and tritium (DT) fuel was increased (approximately 4% fuel burnup and a target gain of approximately 1.5 compared to approximately 2% fuel burnup and target gain approximately 0.7 for N210808) as a result of increased total (DT plus capsule) areal density at maximum compression compared to N210808. Radiation-hydrodynamic simulations of this design predicted achieving target gain greater than 1 and also the magnitude of increase in fusion energy produced compared to N210808. The plasma conditions and hotspot power balance (fusion power produced vs input power and power losses) using these simulations are presented. Since the drafting of this manuscript, the results of this paper have been replicated and exceeded (N230729) in this design, together with a higher-quality diamond capsule, setting a new record of approximately 3.88MJ of fusion energy and fusion energy target gain of approximately 1.9.

Intensity of focused waves near turning points.

A wave near an isolated turning point is typically assumed to have an Airy function profile with respect to the separation distance. This description is incomplete, however, and is insufficient to describe the behavior of more realistic wave fields that are not simple plane waves. Asymptotic matching to a prescribed incoming wave field generically introduces a phase front curvature term that changes the characteristic wave behavior from the Airy function to that of the hyperbolic umbilic function. This function, which is one of the seven classic "elementary" functions from catastrophe theory along with the Airy function, can be understood intuitively as the solution for a linearly focused Gaussian beam propagating in a linearly varying density profile, as we show. The morphology of the caustic lines that govern the intensity maxima of the diffraction pattern as one alters the density length scale of the plasma, the focal length of the incident beam, and also the injection angle of the incident beam are presented in detail. This morphology includes a Goos-Hänchen shift and focal shift at oblique incidence that do not appear in a reduced ray-based description of the caustic. The enhancement of the intensity swelling factor for a focused wave compared to the typical Airy solution is highlighted, and the impact of a finite lens aperture is discussed. Collisional damping and finite beam waist are included in the model and appear as complex components to the arguments of the hyperbolic umbilic function. The observations presented here on the behavior of waves near turning points should aid the development of improved reduced wave models to be used, for example, in designing modern nuclear fusion experiments.

Inverse Bremsstrahlung Absorption.

Inverse bremsstrahlung absorption was measured based on transmission through a finite-length plasma that was thoroughly characterized using spatially resolved Thomson scattering. Expected absorption was then calculated using the diagnosed plasma conditions while varying the absorption model components. To match data, it is necessary to account for (i) the Langdon effect; (ii) laser-frequency (rather than plasma-frequency) dependence in the Coulomb logarithm, as is typical of bremsstrahlung theories but not transport theories; and (iii) a correction due to ion screening. Radiation-hydrodynamic simulations of inertial confinement fusion implosions have to date used a Coulomb logarithm from the transport literature and no screening correction. We anticipate that updating the model for collisional absorption will substantially revise our understanding of laser-target coupling for such implosions.

Increased Ion Temperature and Neutron Yield Observed in Magnetized Indirectly Driven D_{2}-Filled Capsule Implosions on the National Ignition Facility.

The application of an external 26 Tesla axial magnetic field to a D_{2} gas-filled capsule indirectly driven on the National Ignition Facility is observed to increase the ion temperature by 40% and the neutron yield by a factor of 3.2 in a hot spot with areal density and temperature approaching what is required for fusion ignition [1]. The improvements are determined from energy spectral measurements of the 2.45 MeV neutrons from the D(d,n)^{3}He reaction, and the compressed central core B field is estimated to be ∼4.9 kT using the 14.1 MeV secondary neutrons from the D(T,n)^{4}He reactions. The experiments use a 30 kV pulsed-power system to deliver a ∼3 µs current pulse to a solenoidal coil wrapped around a novel high-electrical-resistivity AuTa_{4} hohlraum. Radiation magnetohydrodynamic simulations are consistent with the experiment.

Stopping-power enhancement from discrete particle-wake correlations in high-energy-density plasmas.

Three-dimensional (3D) simulations of electron beams propagating in high-energy-density plasmas using the quasistatic Particle-in-Cell (PIC) code QuickPIC demonstrate a significant increase in stopping power when beam electrons mutually interact via their wakes. Each beam electron excites a plasma wave wake of wavelength ∼2πc/ω_{pe}, where c is the speed of light and ω_{pe} is the background plasma frequency. We show that a discrete collection of electrons undergoes a beam-plasma-like instability caused by mutual particle-wake interactions that causes electrons to bunch in the beam, even for beam densities n_{b} for which fluid theory breaks down. This bunching enhances the beam's stopping power, which we call "correlated stopping," and the effect increases with the "correlation number" N_{b}≡n_{b}(c/ω_{pe})^{3}. For example, a beam of monoenergetic 9.7 MeV electrons with N_{b}=1/8, in a cold background plasma with n_{e}=10^{26}cm^{-3} (450 g cm^{-3} DT), has a stopping power of 2.28±0.04 times the single-electron value, which increases to 1220±5 for N_{b}=64. The beam also experiences transverse filamentation, which eventually limits the stopping enhancement.

Diagnosing plasma magnetization in inertial confinement fusion implosions using secondary deuterium-tritium reactions.

Diagnosing plasma magnetization in inertial confinement fusion implosions is important for understanding how magnetic fields affect implosion dynamics and to assess plasma conditions in magnetized implosion experiments. Secondary deuterium-tritium (DT) reactions provide two diagnostic signatures to infer neutron-averaged magnetization. Magnetically confining fusion tritons from deuterium-deuterium (DD) reactions in the hot spot increases their path lengths and energy loss, leading to an increase in the secondary DT reaction yield. In addition, the distribution of magnetically confined DD-triton is anisotropic, and this drives anisotropy in the secondary DT neutron spectra along different lines of sight. Implosion parameter space as well as sensitivity to the applied B-field, fuel ρR, temperature, and hot-spot shape will be examined using Monte Carlo and 2D radiation-magnetohydrodynamic simulations.

Progress towards a more predictive model for hohlraum radiation drive and symmetry.

For several years, we have been calculating the radiation drive in laser-heated gold hohlraums using flux-limited heat transport with a limiter of 0.15, tabulated values of local thermodynamic equilibrium gold opacity, and an approximate model for not in a local thermodynamic equilibrium (NLTE) gold emissivity (DCA_2010). This model has been successful in predicting the radiation drive in vacuum hohlraums, but for gas-filled hohlraums used to drive capsule implosions, the model consistently predicts too much drive and capsule bang times earlier than measured. In this work, we introduce a new model that brings the calculated bang time into better agreement with the measured bang time. The new model employs (1) a numerical grid that is fully converged in space, energy, and time, (2) a modified approximate NLTE model that includes more physics and is in better agreement with more detailed offline emissivity models, and (3) a reduced flux limiter value of 0.03. We applied this model to gas-filled hohlraum experiments using high density carbon and plastic ablator capsules that had hohlraum He fill gas densities ranging from 0.06 to 1.6 mg/cc and hohlraum diameters of 5.75 or 6.72 mm. The new model predicts bang times to within ±100 ps for most experiments with low to intermediate fill densities (up to 0.85 mg/cc). This model predicts higher temperatures in the plasma than the old model and also predicts that at higher gas fill densities, a significant amount of inner beam laser energy escapes the hohlraum through the opposite laser entrance hole.

Interplay of Laser-Plasma Interactions and Inertial Fusion Hydrodynamics.

The effects of laser-plasma interactions (LPI) on the dynamics of inertial confinement fusion hohlraums are investigated via a new approach that self-consistently couples reduced LPI models into radiation-hydrodynamics numerical codes. The interplay between hydrodynamics and LPI-specifically stimulated Raman scatter and crossed-beam energy transfer (CBET)-mostly occurs via momentum and energy deposition into Langmuir and ion acoustic waves. This spatially redistributes energy coupling to the target, which affects the background plasma conditions and thus, modifies laser propagation. This model shows reduced CBET and significant laser energy depletion by Langmuir waves, which reduce the discrepancy between modeling and data from hohlraum experiments on wall x-ray emission and capsule implosion shape.

Measurement of high-pressure shock waves in cryogenic deuterium-tritium ice layered capsule implosions on NIF.

The first measurements of multiple, high-pressure shock waves in cryogenic deuterium-tritium (DT) ice layered capsule implosions on the National Ignition Facility have been performed. The strength and relative timing of these shocks must be adjusted to very high precision in order to keep the DT fuel entropy low and compressibility high. All previous measurements of shock timing in inertial confinement fusion implosions [T. R. Boehly et al., Phys. Rev. Lett. 106, 195005 (2011), H. F. Robey et al., Phys. Rev. Lett. 108, 215004 (2012)] have been performed in surrogate targets, where the solid DT ice shell and central DT gas regions were replaced with a continuous liquid deuterium (D2) fill. This report presents the first experimental validation of the assumptions underlying this surrogate technique.

Raman backscatter as a remote laser power sensor in high-energy-density plasmas.

Stimulated Raman backscatter is used as a remote sensor to quantify the instantaneous laser power after transfer from outer to inner cones that cross in a National Ignition Facility (NIF) gas-filled hohlraum plasma. By matching stimulated Raman backscatter between a shot reducing outer versus a shot reducing inner power we infer that about half of the incident outer-cone power is transferred to inner cones, for the specific time and wavelength configuration studied. This is the first instantaneous nondisruptive measure of power transfer in an indirect drive NIF experiment using optical measurements.

Experimental evidence of predominantly transverse electron plasma waves driven by stimulated Raman scattering of picosecond laser pulses.

We report on highly time- and space-resolved measurements of the evolution of electron plasma waves driven by stimulated Raman scattering of a picosecond, single laser speckle propagating through a preformed underdense plasma. Two-dimensional Thomson scatter spectra indicate that the dominant waves have significant transverse components. These results are supported by particle-in-cell simulations which pinpoint the dominant role of the wave front bowing and of secondary nonlinear electrostatic instabilities in the evolution of the plasma waves.

Direct measurements of an increased threshold for stimulated brillouin scattering with polarization smoothing in ignition hohlraum plasmas.

We demonstrate a significant reduction of stimulated Brillouin scattering by polarization smoothing in large-scale high-temperature hohlraum plasma conditions where filamentation is measured to be negligible. The stimulated Brillouin scattering experimental threshold (defined as the intensity at which 5% of the incident light is backscattered) is measured to increase by a factor of 1.7+/-0.2 when polarization smoothing is applied. An analytical model relevant to inertial confinement fusion plasma conditions shows that the measured reduction in backscatter with polarization smoothing results from the random spatial variation in polarization of the laser beam, not from the reduction in beam contrast.