Session BO5: ICF: Analytical and Computational Techniques

Subgrid Model of Laser Propagation and Heating in a Foam

Foams are considered an attractive design option for inertial confinement fusion (ICF), because they have densities intermediate between those of a gas and a solid. However, large-scale ICF simulations cannot resolve the microstructure of a foam. The work done by the laser in burning down the foam microstructure slows down the ionization front. It also modifies the properties of the resulting plasma, resulting in a higher ion temperature. We have developed a subgrid foam model for use in plasma physics simulations. We treat the foam as a medium with an anomalous opacity due to the cross-sections of foam elements above critical density. We model the expansion of heated foam elements within a computational cell using a reduced set of equations. When neighboring foam elements overlap, the foam homogenizes and the kinetic energy of expansion is deposited into ion thermal energy. After this point, the cell evolves in the same manner as a homogeneous plasma. We present comparison of our model to experimental results. We show that laser propagation in a foam is slower than in a homogeneous gas with equivalent properties, consistent with experiments. The resulting high ion temperatures have implications for Laser Plasma Instabilities and can suppress Stimulated Brillouin Scattering.   

Benchmark Hohlraum Simulations Enabled by NLTE Kinetics on GPUs

Predicting the X-ray drive in hohlraums at the National Ignition Facility (NIF) has proven to be a challenge for radiation-hydrodynamics simulations. Uncertainties in modeling the non-local thermodynamic equilibrium (NLTE) state of the high-Z wall plasma could explain a significant fraction of the modeled drive discrepancy. Previously, we showed how improved hohlraum energetics predictions are achieved by performing inline atomic kinetics using more complete models for the underlying atomic structure and transitions. Because of their 100x computational expense (both in operations and memory), using our most complete atomic models for inline radiation hydrodynamics calculations had only been practical for 1D simulations. Using the GPU processing power on the latest generation of supercomputers (Sierra at LLNL), we have overcome this limitation and report the first set of highly resolved 2D hohlraum simulations using our most complete DCA atomic models. The improved near-LTE opacities allow for a physics-based, smoother transition from LTE to NLTE. These simulations also provide valuable benchmark data for complementary off-line approaches (e.g. steady-state NLTE tables).   

PIC Simulations of Laser-Irradiated Foam Filaments: Plasma Heating, Interpenetration, and Stagnation

We have been studying the early interpenetration and stagnation processes of laser-irradiated additive-manufactured foam materials with particle-in-cell simulations. Here we present 1D and 2D simulations of solid-density, pre-ionized foam filaments (slabs in 1D and cylinders in 2D) with and without an incident laser. The foam filaments consist of single or multiple ion species at temperatures ranging from 10 eV to 1 keV and separated from each other by vacuum regions ranging from 0.1 to 10 microns in width. We discuss the impact of an incident laser on heated filaments as they expand and fill space, as well as the range of effects that occur as plasma particles stream between filaments, spanning the range from relatively collisionless interpenetration to very collisional interpenetration giving rise to small shocks where the counter-streaming plasmas meet. We comment on the heating that occurs during stagnation, as well as on our diagnosis of quantities that can be compared with rad-hydro calculations in an attempt to bring together PIC and hydro modeling of realistic foams.   

Non-equilibrium electron distributions driven by inverse Bremsstrahlung heating and ionization: Langdon effect revisited

We utilize a computational model that self-consistently combines physics of kinetic electrons and atomic processes to study time evolution of the electron distribution driven by inverse Bremsstrahlung (IB) heating and ionization. The model consists of a kinetic Vlasov- Boltzmann-Fokker-Planck equation for free electrons and a non-Maxwellian collisional-radiative model for atomic state populations. The influence of atomic kinetics on inverse Bremsstrahlung (IB) heating is examined in detail. We show that atomic kinetics affects non-linear IB absorption rates by further modifying the electron distribution in addition to laser heating. Comparisons with experimental data from a laser-produced plasma experiment will be shown.   

Finding Correlations in Inertial Confinement Fusion Experimental Data Using Machine Learning

Here, we present results from a Machine Learning analysis of experimental data derived from Inertial Confinement Fusion (ICF) experiments performed at the \underline {National Ignition Facility (NIF)}. Neutron yield is the primary performance indicator of implosions, however, there is a suite of x-ray data such as images, broadband signals and spectroscopic data that provides additional information about the implosion. A machine learning model was developed where the program used the x-ray diagnostic results as the input parameters and the neutron yield and ion temperature as the output. The results of correlations inferred from the model will be presented. In addition, this model will help the ICF community determine which metrics are most important for achieving the highest energy gain.   

Analysis of NIF scaling using physics informed machine learning

Hundreds of thermonuclear (TN) ignition experiments in inertial confinement fusion (ICF) were conducted on the National Ignition Facility (NIF). None of the experiments achieved ignition. Although experiments to fine-tune the target designs are the focus of the national ICF program, insightful analysis of the vast amount of existing data is a pressing need. In highly integrated ignition experiments, it is impossible to vary only one design parameter without perturbing all other implosion variables. Thus, to determine the nonlinear relationships between the design parameters and performance from the data, a multivariate analysis based on physics model is necessary. We apply machine learning methods to the existing NIF data to uncover patterns and physics scaling laws in TN ignition. We focus on the scaling laws between the implosion parameters and neutron yield by using different supervised machine learning methods including: Polynomial Regression, Connected Neural Network, and Deep Jointly-Informed Neural Network (LLNL). Our results show that these models could predict the outcomes reasonably from the trained experimental data and agree with the theory. This exploratory study will help build new capability to evaluate capsule designs and provide inputs for new designs.   

Analysis and Extrapolation of Highest{\-}Performing OMEGA DT Layered Implosions to National Ignition Facility Energy

OMEGA optimization campaigns produced both highest neutron yields 1.51~\texttimes ~10$^{\mathrm{14}}$ and areal densities of 160 mg/cm$^{\mathrm{2}}$. The 2-D deceleration hydrodynamic code \textit{DEC2D} was used to reproduce experimental observables (yield, areal density, hot-spot size, neutron-averaged ion temperature, burnwidth, and bang time). This was done by extracting hydrodynamic profiles at peak velocity from a 1-D \textit{LILAC} simulation and by simulating the deceleration phase in \textit{DEC2D} with imposed low mode and mid-mode of arbitrary amplitude to match all the observables. Then the extrapolation to the National Ignition Facility (NIF) energy of 1.9 MJ and 2.5 MJ was carried by simulating the deceleration phase of a NIF-scaled target with scaled perturbations. In addition, the performance for NIF{\-}scaled implosions were projected with corrected (removed) individual modes to assess the highest possible performance. Performance degradation caused by hot-electron preheat was also assessed by including a hot-electron source in the simulations to match the measured hard x-ray signal. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0003856.   

Area-Based Image Metrics Elucidate Differences Between Radiation-Hydrodynamics Simulations and NIF Experimental X-ray Images

X-ray images at the National Ignition Facility (NIF) provide important metrics regarding the shape of the hotspot along a given line-of-sight. The 17% contour from peak brightness is usually used to infer the size of the hotspot as well as determine shape perturbations quantified through the Legendre coefficients P2 and P4. Unfortunately features that lie inside the contour such as those that could arise from tent or fill-tube perturbations are not easily captured. Here we present the use of a two-dimensional orthonormal basis of Laguerre-Gaussian modes (LGM) to accurately represent an image with about 100 coefficients. The LGM basis is able to describe both low- and high-frequency components of the entire image unlike the Legendre decomposition which is limited to the 17% contour. The decomposition of the image into LGM modes reduces the image storage requirements by about 100x; an important consideration for doing an ensemble of 50K rad-hydro simulations. LGM image coefficients from NIF hGXD images can be directly compared to post-shot rad-hydro simulations. We demonstrate how the LGM coefficients from simulations centered around the BigFoot N180128 shot can be used to better constrain the evolution of ICF implosions. LLNL-ABS-780323   

Deep Learning for Non-Local Thermodynamic Equilibrium in hydrocodes for ICF.

We are developing new techniques to accelerate radiation hydrodynamics simulations. A deep neural network can be called in place of a traditional physics package to obtain absorption coefficients and emissivities. The neural network is not only dramatically faster, but uses substantially less memory. We examined the NLTE physics of mid-Z materials for ICF simulations as a test application. This entails great numbers of ion quantum states that set the computational size of the resolved linear system used in the collisional-radiative model. We used CRETIN for in-line collisional-radiative computations in the radhydro code HYDRA. We then trained a deep neural network on a set of CRETIN data under a broad set of plasma conditions. This is a hard regression problem: computing spectra with high-dimensional inputs and outputs (both are around 100). We attacked the dimensionality issue using auto-encoders to reduce the dimensionality and DJINN (random-forest based neural networks) to link latent spaces. Finally, we replaced the in-line atomic physics computation in HYDRA with the well-trained neural network accelerator. We address both the accuracy of the results and the feasibility for implementation in high-precision predictive simulation.   

Data-driven discovery of reduced plasma physics models from high-fidelity simulations

Computationally efficient reduced plasma models that accurately capture the essential physics of Inertial Confinement Fusion (ICF) and High-Energy-Density (HED) plasmas are highly desirable to bridge the range of spatial and temporal scales of many of the problems of interest, from laser-plasma interactions to hydrodynamic instabilities. In this work, we explore the use of modern sparse-learning techniques to uncover reduced plasma physics models directly from the data of high-fidelity fully kinetic particle-in-cell (PIC) simulations. We demonstrate the methodology through the robust recovery of the fundamental hierarchy of plasma physics equations, from the kinetic Vlasov equation to magnetohydrodynamics, based solely on spatial and temporal data of plasma dynamics from first-principles PIC simulations. We discuss how such data-driven reduced models can overcome the limitations of traditional analytically derived reduced models, and contribute to the discovery of improved kinetic-fluid closure models for ICF and HED simulations.   

Can reinforced learning be used to design ICF experiments?

Machine learning technology continues to grow in expectations for solving a wide range of problems. Basic neural networks and ML techniques have been applied to a small number of plasma physics problems for a couple decades, but more recently are moving to the forefront for optimization problems. The approaches being employed for fusion require either large data sets or tens of thousands of simulations. However, techniques such as reinforced learning for optimization are not being exploited. Unlike optimization problems using machine learning that analyzes a given set of data, reinforced learning searches for a solution based on a reward/penalty system using the given state, a simple set of instructions called actions, and policies governing these actions. Thus, the algorithm autonomously searches the space based on the policy to reach the end state. For example, the algorithm can search a space to maximize quantities such as yield or find robust regimes maximizing the distance in parameter space away from degradation cliffs using the value of the yield as a reward or the distance from a cliff as a reward. In this presentation, we will show proof of principle examples and discuss the potential of such technology for fusion science. This work was supported by the US Department of Energy through the Los Alamos National Laboratory. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract No. 89233218CNA000001)   

Building physics into neural networks to improve predictions and reduce uncertainty

Comparison of precision experiments and numerical simulations, like those at the National Ignition Facility (NIF), are increasingly reliant on statistical analyses to quantify uncertainty and to explore correlations among key diagnostic signatures. These methods typically rely on a high-fidelity surrogate model, for example a deep neural network, that can emulate the simulation output. However, for physics applications, we demand that these emulated outputs respect key physical laws. We demonstrate in this talk multiple new methods to force neural network surrogates to respect physics-based constraints. These include demanding that the surrogate model be consistent with its own inverse and adjusting regularizing terms in loss functions to drive solutions to physical consistency. We apply our techniques to ICF simulations based on BigFoot and HDC implosion campaigns at the NIF. We will show, absent these physics enforcements, correlations among multiple physics outputs are broken and physics analyses can break down. With the physics enforcements, analyses obey physics principles and lead to more robust inferences with reduced uncertainty.   

Analytic insights into non-local electron energy transport: Steady state Krook and Fokker Planck theory in spherical geometry

This work develops a Krook and Fokker Planck theory of non-local electron energy transport in a laser fusion target. There have been two basic theories, which we call the NRL (1) and SNB (2) models, both of which have been worked out in planar geometry, In planar geometry, there are differences between them, but the theories are basically the same. However in spherical geometry, the NRL model is much closer to the spherically correct model, in fact the SNB model as formulated does not allow preheat in the fuel portion of a laser target. This is consistent with the results of numerical implosion models based on this model (3), where they saw no preheat. Using the NRL Krook model, there is a great deal of preheat. However using a Fokker Planck, rather than a Krook model, does greatly reduces the fuel preheat. 1. W. Manheimer, D. Colombant, and A Schmitt, Phys. Plasmas 25, 082711, 2018 2. G. Schurtz, P. Nicolai and M. Busquet, Phys Plasmas, 7 (10) 4238, 2000 3. A Marocchino, S. Atzeni, and A. Schiavi, Phys Phys. Plasmas 21, 012710, 2014