Plasma viscosity in spherical ICF implosion simulations

The impact of capsule imperfections is one of the challenges in achieving reproducible, high-gain ignition of inertial confinement fusion (ICF). The nonuniformities of capsule imperfections, which create instability seeds during the shock propagation, may cause significant performance degradation. A systematic study of the propagation of collisional shock wave in highly nonuniform plasmas is carried out using a hybrid fluid-PIC code, which enables the analysis of electromagnetic fields, ion mixing, and plasma viscosity self-consistently. During shock propagation, it interacts with multiple bubbles and significant material mixing in the nonuniform plasmas are observed. Consequently, the average viscosity of the post-shock plasma in the nonuniform case increases to 1∼2 times that of the uniform case. These results provide a better understanding of the possible influence of capsule imperfections in ICF implosions.

We present the absolute calibration of the continuum x-ray spectrometer (ConSpec), designed to measure the hot-spot electron temperature of inertial confinement fusion (ICF) implosions at the National Ignition Facility (NIF). The spectrometer measures emission from photon energies of 20 to 30 keV where opacity effects in ICF implosions at the NIF are negligible and provides spatial resolution to separate the hot-spot emission from other x-ray sources, such as the gold emission from the hohlraum wall. Using a combination of x-ray ray tracing and calibration data taken using a well characterized x-ray source, we measure the dispersion, spatial resolution, and absolute sensitivity of the instrument. Finally, we present an example spectrum measured at the NIF and demonstrate the ability to measure the hot-spot electron temperature with uncertainty under 10%.

Building a sustainable burn platform in inertial confinement fusion (ICF) requires an understanding of the complex coupling of physical processes and the effects that key experimental design changes have on implosion performance. While simulation codes are used to model ICF implosions, incomplete physics and the need for approximations deteriorate their predictive capability. Identification of relationships between controllable design inputs and measurable outcomes can help guide the future design of experiments and development of simulation codes, which can potentially improve the accuracy of the computational models used to simulate ICF implosions. In this paper, we leverage developments in machine learning (ML) and methods for ML feature importance/sensitivity analysis to identify complex relationships in ways that are difficult to process using expert judgment alone. We present work using random forest (RF) regression for prediction of yield, velocity, and other experimental outcomes given a suite of design parameters, along with an assessment of important relationships and uncertainties in the prediction model. We show that RF models are capable of learning and predicting on ICF experimental data with high accuracy, and we extract feature importance metrics that provide insight into the physical significance of different controllable design inputs for various ICF design configurations. These results can be used to augment expert intuition and simulation results for optimal design of future ICF experiments.

Laser fusion, likely the ultimate solution to the crisis of human energy, is highly valued by the international community and has always been the focus of international research. It turns out that the biggest scientific obstacle of laser fusion is the effective control of the high-energy-density nonlinear flows during implosions. The research of high-energy-density nonlinear flows covers many different fields, such as high-energy-density physics, plasma physics, fluid mechanics, computing science, strong impact physics, and high pressure atomic physics. Meanwhile, the capability of multi-material and multi-scale numerical simulations as well as large laser facility with high output power is also needed. As an emerging research field, it is full of all kinds of novel phenomena to be explored. In addition, hydrodynamic instabilities and the subsequent turbulent mixing in high-energy-density flows, are also important processes in astrophysical phenomena (e.g., galaxy collision and merging, stellar evolution, formation of protostars and supernova explosion) and involve with the core content of astrophysics. This paper reviews, firstly the status and progress, as well as the challenges and opportunities of high-energy-density nonlinear flows research. Secondly, it introduces hydrodynamic instabilities during implosions in central ignition laser fusion, among which, key factors related to the bottleneck of implosion performance of the National Ignition Facility (NIF) in the United States are condensed. Next, it summarizes the development of hydrodynamic instability experiments in laser fusion abroad. Finally, it lists some key achievements on the fundamental issues of hydrodynamic instabilities by the laser fusion implosion physics team in China over the last three years. This team has been engaged in the research and control of nonlinear flows in laser fusion implosions, as well as the research and design of target physics. A lot of improvements have been made in recent years on the theoretical analysis and numerical simulation of outstanding issues for hydrodynamic instabilities in laser fusion implosions, and the design and analysis of experiments on large lasers, which greatly promoted the development of this research direction in China.

This manuscript examines the correlations between the hot-spot velocity (an observable signature of residual kinetic energy), low-mode implosion asymmetries, and burn amplification in inertial confinement fusion implosions on the National Ignition Facility (NIF). Using a combination of two-dimensional axis-symmetric and three-dimensional radiation-hydrodynamic simulations coupled to neutronics, we find that for typical NIF implosions, the stagnation asymmetry multiplies the observed hot-spot velocity anywhere from 80% to 120%, while burn amplification always increases it. Additionally, we find stagnation asymmetry typically deflects the observed hot-spot flow. The two mechanisms (low-mode implosion asymmetries and burn amplification) can be decoupled, and application of a simple model to a database of cryogenic implosions on the NIF infers the total hot-spot velocity amplification. This finding modifies the interpretation of data collected from inertial confinement fusion experiments and impacts the magnitude and origin of low-mode asymmetries.

Diffusion-dominated mix in inertial confinement fusion (ICF) is characterized where the majority of the mix occurs in the immediate fuel-shell interface while hydrodynamic-dominated mix pulls shell material from farther away into the central fuel. A thin (150nm) separated reactants ICF mix platform is highly sensitive to the amount of mix from the first micron of shell-fuel interface. This fine-spatial resolution platform has revealed that material mix in moderate convergence (CR∼12) ICF implosions is dominated by a diffusion mechanism. This technique has now been expanded across a set of OMEGA ICF implosions, observing an increase in mix width and mix amount for cooler, slower, and more compressive implosions. Hydrodynamic simulations require a buoyancy-drag mix model to capture the increasing mix width, suggesting a transition between these two mix mechanisms.

The electron thermal conduction strongly affects the hot-spot formation and the hydrodynamic instability growth in inertial confinement fusion implosions. A harmonic-mean flux-limited conductivity model has been widely used in implosion simulations. In this paper, using the high foot implosion N140520 as an example, we have performed a series of one-dimensional (1D) no-alpha simulations to quantify the impact of different conductivity models including the Spitzer–Harm model, the Lee–More model, and the recently proposed coupled Gericke-Murillo-Schlanges model [Ma et al., Phys. Rev. Lett. 122, 015001 (2019)] with the flux limiter fe ranging from 0.03 to 0.15 on the performance of cryogenic implosions. It is shown that varying fe has a bigger impact on the performance than changing conductivity models. Therefore, we have only performed two-dimensional (2D) no-alpha simulations using the Lee–More model with different flux limiters feLM to quantify the effect of the electron thermal conduction on the performance, with single-mode velocity perturbations with different mode numbers L seeded on the inner shell surface near the peak implosion velocity. We find that in both the 1D implosions and the 2D implosions with the same L, increasing fe leads to more hot-spot mass and lower hot-spot-averaged ion temperature, resulting in approximately constant hot-spot internal energy. In addition, the no-alpha yield Ynα is dominated by the neutron-averaged ion temperature Tn in these two cases. Increasing feLM from 0.0368 to 0.184 reduces Tn by ∼15% in 1D and by ∼20% for the 2D implosions with the same L, both leading to a ∼20% reduction in Ynα.

The alpha-particle energy deposition mechanism modifies the ignition conditions of the thermonuclear Deuterium-Tritium fusion reactions, and constitutes a key issue in achieving high gain in Inertial Confinement Fusion implosions. One-dimensional hydrodynamic calculations have been performed with the code Multi-IFE [R. Ramis and J. Meyer-ter-Vehn, Comp. Phys. Comm. 203, 226 (2016)] to simulate the implosion of a capsule directly irradiated by a laser beam. The diffusion approximation for the alpha energy deposition has been used to optimize three laser profiles corresponding to different implosion velocities. A Monte-Carlo package has been included in Multi-IFE to calculate the alpha energy transport, and in this case the energy deposition uses both the LP [C.K. Li and R.D. Petrasso, Phys. Rev. Lett. 70, 3059 (1993)] and the BPS [L.S. Brown, D.L. Preston, and R.L. Singleton Jr., Phys. Rep. 410, 237 (2005)] stopping power models. Homothetic transformations that maintain a constant implosion velocity have been used to map out the transition region between marginally-igniting and high-gain configurations. The results provided by the two models have been compared and it is found that - close to the ignition threshold - in order to produce the same fusion energy, the calculations performed with the BPS model require about 10% more invested energy with respect to the LP model.

Nonuniformities present in the laser illumination and target in laser-driven inertial confinement fusion experiments lead to an asymmetric compression of the target, resulting in an inefficient conversion of shell kinetic energy to thermal energy of the hot-spot plasma. In this paper, the effects of asymmetric compression of cryogenic deuterium tritium laser-direct-drive implosions are examined using a suite of nuclear and x-ray diagnostics on the OMEGA laser. The neutron-averaged hot-spot velocity (u→hs) and apparent ion temperature (Ti) asymmetry are determined from neutron time-of-flight measurements of the primary deuterium tritium fusion neutron energy spectrum, while the areal density (ρR) of the compressed fuel surrounding the hot spot is inferred from measurements of the scattered neutron energy spectrum. The low-mode perturbations of the hot-spot shape are characterized from x-ray self-emission images recorded along three quasi-orthogonal lines of sight. Implosions with significant mode-1 laser-drive asymmetries show large hot-spot velocities (>100 km/s) in a direction consistent with the hot-spot elongation observed in x-ray images, measured Ti asymmetry, and ρR asymmetry. Laser-drive corrections have been applied through shifting the initial target location in order to mitigate the observed asymmetry. With the asymmetry corrected, a more-symmetric hot spot is observed with reduced u→hs, Ti asymmetry, ρR asymmetry, and a 30% increase in the fusion yield.

High-mode perturbations and low-mode asymmetries were measured in the deceleration phase of indirectly driven, deuterium gas filled inertial confinement fusion capsule implosions at convergence ratios of 10 to 15, using a new “enhanced emission” technique at the National Ignition Facility [E. M. Campbell et al., AIP Conf. Proc. 429, 3 (1998)]. In these experiments, a high spatial resolution Kirkpatrick-Baez microscope was used to image the x-ray emission from the inner surface of a high-density-carbon capsule's shell. The use of a high atomic number dopant in the shell enabled time-resolved observations of shell perturbations penetrating into the hot spot. This allowed the effects of the perturbations and asymmetries on degrading neutron yield to be directly measured. In particular, mix induced radiation losses of ∼400 J from the hot spot resulted in a neutron yield reduction of a factor of ∼2. In a subsequent experiment with a significantly increased level of short-mode initial perturbations, shown through the enhanced imaging technique to be highly organized radially, the neutron yield dropped an additional factor of ∼2.

Ion temperatures serve as an important diagnostic for inertial confinement fusion (ICF) implosions. In direct-drive ICF experiments on OMEGA, neutron-time-of-flight (nTOF) data are used to infer the ion temperature of the fusing plasma produced in the implosion experiment. The analysis of the nTOF data requires an assumption about the shape of the underlying source signal. Since the source nTOF signal is a near-replica of the neutron energy spectrum, an ideal Gaussian shape, corresponding to the neutron energy spectrum of a uniform temperature plasma, is routinely employed. However, spatial and temporal variations of the ion temperature in the plasma give rise to higher-order moments, which were first described by Munro [Nucl. Fusion 56, 036001 (2016)]. In this work, we show a simpler alternative analysis to derive moments of the neutron energy spectrum for a plasma with variations in ion temperature. We also present a revised analysis of measured nTOF signals that uses a model with an additional degree of freedom to take into account the effect of ion temperature variations on the shape of the spectrum. Compared to presently used nTOF analysis, the revised analysis yields on average ≈2× more accurate fits to the data and up to 15% higher ion temperatures for cryogenic experiments. Furthermore, we quantify the ion temperature inflation caused by radially symmetric fluid flows, which are present even in a symmetric implosion, and which serve as a lower bound on the ion temperature inflation in real implosions.

We use a second-order three-dimensional hydrodynamics code with self-gravity to investigate the role that thermal energetics plays in the development of nonaxisymmetric instabilities in protostellar disks. The initial axisymmetric equilibrium state is a continuous, fluid star/disk system, in which the star, the disk, and the star/disk boundary are resolved in 3D in our hydrodynamics code. An adiabatic evolution is compared to two previous simulations of the same model in which either local isentropy or local isothermality is maintained in the disk throughout the calculation. In all three cases, the model is highly unstable to multiple low-order nonaxisymmetric disturbances which induce significant mass and angular momentum transport in a few dynamical times. The star and star/disk boundary are dominated by three- and four-armed disturbances, whereas the disk is susceptible to a two-armed spiral. These disturbances saturate at moderate nonlinear amplitude in the adiabatic and isentropic evolutions; the same instabilities in the isothermal evolution lead to the disruption of the disk and concentration of material into several dense, thin arcs and arclets. Figures, tables and animations are included in the CD-ROM supplement.Much numerical work has shown that protostellar objects are subject to nonaxisymmetric instabilities, generally due to a combination of rapid rotation, self-gravity, and thermal pressure. In this presentation, we investigate how different assumptions about thermal energetics affect the origin and maintenance of nonaxisymmetric structure in three dimensions.Our initial, continuous, axisymmetric equilibrium state is a cooled version of a model in the isentropic, polytropic sequence of star/disk models (the “I” models) studied in our previous work (Pickett et al. 1997, 1998; see also Imamura et al. in this volume). The equilibrium configuration represents an early stage in the axisymmetric collapse of a uniformly rotating singular isothermal sphere. The model is small in radial extent (R eq ∼ 0.10 AU), with the mass roughly evenly divided between star and rotationally supported disk. The minimum Toomre Q in the disk is 1.5. The model is shown in Figure 1; Table 1 lists physical properties.Three simulations with our 3D hydrodynamics code (Pickett et al. 1996, 1998) were conducted: 1) a locally isothermal evolution, in which the disk temperature was held at its initial, axisymmetric value; 2) a locally isentropic evolution, in which the disk entropy is held fixed; and 3) an adiabatic evolution, in which artificial viscosity was used to treat shocks. The star was treated adiabatically in all cases. Each run begins with a random density perturbation throughout the disk; grid resolution is (128,64,16) in (r,ϕ,z).Table 2 describes the simulations. We find: 1. The early growth of nonaxisymmetric modes is similar in all cases. The star and inner disk are subject to three- and four-armed Kelvin-like modes; the disk is unstable to a two-armed spiral. 2. The nonlinear development of the modes varies greatly. In the isothermal evolution, relative density amplitudes reach highly nonlinear levels (δρ/ρ ∼ 80% and above). The same instabilities in the isentropic evolution saturate at moderately nonlinear amplitudes, apparently from effective mode interaction (Laughlin & Rózyczka 1996). In the adiabatic evolution, the amplitudes fall to the percent level or less due to heating from shocks (Figure 2). 3. Copious mass and angular momentum transport occurs (Figure 3). 4. The effects of the instabilities vary drastically. The two-armed spiral in the isothermal evolution disrupts the disk, concentrating most of the material outside the star in thin, dense arms. In the isentropic and adiabatic evolutions, the disk remains, although a strong two-armed spiral is embedded inside it. Further, heating of the low density regions in the adiabatic calculation leads to their expansion (Figures 4 and 5). KeywordsArtificial ViscosityAdiabatic EvolutionDisk TemperatureAngular Momentum TransportProtostellar DiskThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In ablator shell fabrication, trace elements and impurities are introduced in the deposition and the pyrolysis process, which must be controlled below a critical level. However, it is the opacity, not the individual elements, which matters in an Inertial Confinement Fusion (ICF) implosion. Radiography measures the opacity, allowing the accurate determination of the total impurity effect in a lump sum. Furthermore, by using the sputter target trace element information, we can determine the radial profile of oxygen to ±0.4 at. %. Oxygen is very difficult to measure by any other method, but is critically important for beryllium process development such as mandrel removal. To ensure measurement accuracy, we use a local standard to remove fluctuation in film developing and a step wedge to calibrate the film model.

Indirect drive inertial confinement fusion experiments with convergence ratios below 17 have been previously shown to be less susceptible to Rayleigh–Taylor hydrodynamic instabilities, making this regime highly interesting for fusion science. Additional limitations imposed on the implosion velocity, in-flight aspect ratio and applied laser power aim to further reduce instability growth, resulting in a new regime where performance can be well represented by one-dimensional (1D) hydrodynamic simulations. A simulation campaign was performed using the 1D radiation-hydrodynamics code HYADES to investigate the performance that could be achieved using direct-drive implosions of liquid layer capsules, over a range of relevant energies. Results include potential gains of 0.19 on LMJ-scale systems and 0.75 on NIF-scale systems, and a reactor-level gain of 54 for an 8.5 MJ implosion. While the use of 1D simulations limits the accuracy of these results, they indicate a sufficiently high level of performance to warrant further investigations and verification of this new low-instability regime. This potentially suggests an attractive new approach to fusion energy.This article is part of a discussion meeting issue ‘Prospects for high gain inertial fusion energy (part 2)’.

We perform two-dimensional simulations of strongly–driven compressible Rayleigh–Taylor and Kelvin–Helmholtz instabilities with and without plasma transport phenomena, modeling plasma species diffusion, and plasma viscosity in order to determine their effects on the growth of the hydrodynamic instabilities. Simulations are performed in hydrodynamically similar boxes of varying sizes, ranging from 1 μm to 1 cm in order to determine the scale at which plasma effects become important. Our results suggest that these plasma effects become noticeable when the box size is approximately 100 μm, they become significant in the 10 μm box, and dominate when the box size is 1 μm. Results suggest that plasma transport may be important at scales and conditions relevant to inertial confinement fusion, and that a plasma fluid model is capable of representing some of the kinetic transport effects.