Session UO09: High Energy Density Science: Modeling Methodologies

A 3D Model of Directly-Driven Cylindrical Implosions for Bayesian Analysis

Directly-driven cylindrical implosion experiments conducted at the Omega Laser Facility are used to study the effects of converging hydrodynamic instabilities in the high energy density (HED) regime. A sinusoidal perturbation seeded along a cylindrical tracer shell results in instability growth driven by a combination of Rayleigh-Taylor, Richtmyer-Meshkov, and Bell-Plesset effects. By imaging down the axis of the cylinder and radially from the side simultaneously, we obtain crucial information as to how these systems decelerate, stagnate, and evolve. Proper understanding of these instabilities at HED conditions can inform the design of platforms like the Los Alamos Double Shell program [1,2]. We are developing a tool to generate synthetic radiographs of a parameterized 3D model of the driven cylinder, which are compared against the data. A parameter space is found via Bayesian inference and Markov Chain Monte Carlo (MCMC) methods [3,4], providing statistical metrics on features in the data. These results can then be used to inform both hydrodynamic simulations as well as experimental design.

[1] P. Amendt et al. PoP 9 (5): 2221–2233 (2002)

[2] D. S. Montgomery et al. PoP 25 (9): 092706

[3] P. F. Knapp and W. E. Lewis. RSI 94 061103 (2023)

[4] M. F. Kasim et al. PoP 26 (11): 112706 (2019)   

A novel Bayesian approach to PDV analysis

Photon Doppler Velocimetry (PDV) is an established technique for measuring the velocities of fast-moving surfaces in high-energy-density experiments. In the classical approach to PDV analysis, a short-time Fourier transform is used to generate a spectrogram from which the velocity history of the target is inferred. Issues with this method include choices made by the user (such as the window function), which are prone to human biases, and difficulty in quantifying uncertainties. We present a novel Bayesian method to infer the velocity, with uncertainty, directly from the PDV oscilloscope trace, negating the need to use a spectrogram for analysis. We forward-model the velocity history using a parametrized time-series, from which a synthetic PDV signal is then generated. The noise is modelled using a covariance matrix, where the standard deviation and correlations are estimated from Monte-Carlo simulations of bandpass filtered Gaussian noise. Due to the inherently periodic nature of the data this is clearly a difficult inference problem, but we find that with carefully chosen prior distributions for the model parameters we can accurately recover an injected velocity history. We validate this method using PDV data from the STAR two-stage light gas gun (Skidmore et al., submitted to PRL), recovering shock-front velocity histories in quartz that are consistent with those inferred using the classical approach, and importantly, are interpolated at early times and across regions of missing or noisy data.   

Quantum Accurate Machine Learning Interatomic Potential for Large-scale Simulations of Deuterium Under Shock

Large-scale molecular dynamics (MD) simulations of inertial confinement fusion (ICF) experiments naturally include atomistic level microscopic physics missing from traditional radiation-hydrodynamic codes, and thus can model kinetic processes such as species separation in CH plastic ablators and the subsequent hydrogen streaming and mixing into the deuterium-tritium (DT) fuel.

To directly simulate a shock transiting through the ablator-fuel interface, we require interatomic potentials that accurately describe the interactions between the different species from ambient to the eV temperatures and multi-megabar pressures encountered in experiments. We will present work on developing a broadly transferrable quantum-accurate machine learning potential for deuterium gas using the Chebyshev Interaction Model for Efficient Simulations (ChIMES) framework. We show that this model is able to reproduce the equation of state, radial distribution functions, and Hugoniot relations predicted from density functional theory for densities up to ~0.8 g/cm^3 and temperatures up to ~60,000 K.

We will also discuss ideas for improving the potential model via the inclusion of a temperature-dependent force correction term to include the effects of ionization at high temperatures. These ideas will be employed in a future work to generate potentials for CH-DT compounds to allow for simulations of the ablator-fuel interface with ab initio levels of accuracy.   

Kinetic modeling of ion acceleration in laser-driven tin plasma EUV sources

Laser-produced tin plasmas are enabling the continuation of Moore's law through the use of 13.5 nm narrow-band EUV radiation for next generation lithography. A major challenge for their industrial application is damage to the sensitive optics from energetic ions produced during the laser-plasma interaction. In this work we use fully kinetic PIC simulations to study the ion acceleration mechanisms in tin plasma EUV sources, utilizing an inverse-bremsstrahlung heating operator to model the interaction of a tin target with an Nd:YAG laser and a Monte-Carlo Coulomb collision operator to model thermal conduction. These simulations capture the global source evolution while allowing for detailed analysis of energetic ion trajectories. Benchmarking tests against analogous single-fluid radiation hydrodynamics simulations show qualitative agreement in most of the domain. However, the long timescales for thermal equilibration in the ablated plasma allow for the development of two-temperature features in the PIC simulation. A collimated population of energetic ions is produced in the PIC simulation with a significant enhancement at the highest energies compared to the fluid simulations. The dominant acceleration mechanism is a large-scale electric field supported by the electron pressure gradient, which becomes stronger in the kinetic simulations due to the increased electron temperature. We discuss the implications for advancing the modeling of these sources and developing debris mitigation schemes.   

Photon scattering contribution in plasma transmission experiments

The photon scattering contribution in recent transmission experiments at the Sandia Z-Facility [1] is examined using several approaches. First, spectral lines from single photon absorption are compared to resonant scattering estimates at line centers where photon scattering makes the largest contribution. Second, the full Waller-Kramers-Heisenberg expression [2] is applied to a few initial levels producing spectral lines prominent in the experimental spectrum. Finally, a dispersion-type relation [3] is used to compute the total plasma photon scattering cross-section. This last method accounts for all initial levels included in the photon absorption calculation. The numerical results show that photon scattering by bound electrons fails to resolve the extant discrepancies between transmission measurements of Fe and plasma radiation models.

[1] J.E. Bailey, T. Nagayama, G.P. Loisel, G.A. Rochau et al., Nature 517 (2015) 56-59, doi:10.1038/nature14048. T. Nagayama, J. E. Bailey et al, PRL 122, 235001 (2019), https://doi.org/10.1103/PhysRevLett.122.235001

[2] J. J. Sakurai, Advanced Quantum Mechanics, Addison-Wesley: Reading, MA, (1967)

[3] W.D. Barfield, W.F. Huebner, J. Quant. Spectrosc. Radiat. Transfer 16 (1976) 27-34.   

Vlasov-Fokker-Planck Simulation of a Laser-Plasma Interaction for Inertial Confinement Fusion

Most laser-plasma interactions are in the kinetic regime, but kinetic simulations of realistic systems are rare and limited to one dimension, without magnetic field. We have coupled a new electron Vlasov-Fokker-Planck code to the Chimera radiation-magnetohydrodynamics code, which allows us to perform two-dimensional kinetic simulations of a laser-target interaction, including magnetic field, over long timescales. All of the relevant physics of laser absorption, equation of state, radiative cooling etc is included via the hydrodynamics, but with the addition of a kinetic solution for the electron thermal transport and the associated electromagnetic fields. We describe how the codes are coupled and the approach to solving for the fields via generalized Ohm’s Laws. We use the code to simulate a laser interacting with a solid, high-Z target, and choose conditions relevant to Inertial Confinement Fusion (ICF). Comparisons are then made to traditional flux-limited rad-hydro and extended-MHD models, highlighting the differences in the heat flow, absorption, generation and transport of magnetic field, and instabilities. This model complements recent advances in computational modeling of ICF plasmas [1].

[1] A.R. Bell and M. Sherlock, Plasma Phys. Control. Fusion 66, 035014 (2024).   

Quantifying Hall Conductivity using Data-Driven Model Identification

Particle simulations are an effective tool for modeling loss mechanisms in the magnetically insulated transmission lines (MITL) on Sandia National Laboratories' Z machine. Previous work has shown that Hall conductivity plays a significant role in time-dependent current loss in this region. In this work we use WSINDy, a data-driven model identification method, as an alternative approach to demonstrate the significance of the Hall-driven effects arising in particle simulations of the inner MITL. The weak formulation used in WSINDy allows us to perform this analysis without a smoothing or averaging step and work directly with fluid quantities calculated from the particle data. Regions of space and time are examined to highlight where the Hall conductivity has the greatest effect. The end goal is a parameterization to represent how the Hall coefficient corresponds to the geometry of the inner MITL.   

Reconstructing the dynamics of non-linear, kinetic plasma dynamics from partial measurements using physics-informed machine learning

Accurately diagnosing and characterizing plasma dynamics in laboratory experiments is essential for advancing basic plasma science and technology. Modern plasma physics experiments that leverage high repetition-rate lasers and pulsed power systems are providing unprecedented amounts of highly-resolved spatiotemporal plasma measurements, but the development of computational tools that can harness the full potential of such data are still lacking. In this work, we show that physics-informed neural networks (PINNs) can be used to combine partial spatiotemporal measurements of plasma dynamics with fundamental plasma physics equations to reconstruct physically-consistent plasma quantities that were not measured in experiment. We illustrate this approach on PIC simulation data of the nonlinear and kinetic dynamics of electrostatic streaming instabilities. We show that PINNs can reconstruct nonlinear kinetic plasma dynamics from sparse measurement data, and we characterize how the reconstruction accuracy depends on the amount of measurement data and noise level. Finally, we discuss how PINNs can be used to guide and optimize data collection in experiments.   

Developing a generalized NLTE spectral ML model for HED applications

Non-local thermodynamic equilibrium (NLTE) physics are important in high energy density (HED) plasmas. These effects must be included in simulations and analyses of HED systems to obtain accurate results. However, calculating the needed NLTE data is computationally expensive. Machine learning (ML) based NLTE models have been developed to address these inefficiencies, but published methods are generally trained on small plasma parameter spaces and low-resolution spectra. In this talk, we present an approach to develop a generalized, high-resolution NLTE ML spectral model that covers 0.01–10 keV in temperature and 10¹⁹–10²² cm^-3 in ion density. The ML model is therefore applicable to nearly every HED experiment. Initial tests show that the ML model is faster, more memory efficient, and more accurate than tabular spectral interpolators. The ML training process reveals the need for multiple models to cover the entire plasma parameter space. Dividing along average plasma ion charge bounds has shown promising results. We also discuss incorporating non-Planckian radiation fields into the training set. Once fully developed, our ML model can be applied to simulations and analyses of HED experiments and significantly enhance scientific understanding of these systems.   

Determination of Plasma Density and Temperature Gradients through the X-ray Spectroscopy with Deep Learning

Short-pulse, laser-solid interactions provide a unique platform to develop well-characterized laboratory high-energy density (HED) matter conditions to diagnose fundamental properties such as opacity and equations of state. These measurements are needed to benchmark atomic physics models and simulations tools. However, analysis of such plasmas remains challenging due to the rapid temporal and spatial evolution of the emitting plasma. Recent work has shown that the use of deep learning can provide enhanced analysis of hard X-ray spectra relevant to HED plasmas in both speed and complexity. Here, we present the model development of a neural network trained on the collisional-radiative modeling code SCRAM that is capable of extracting the temperature and density profiles, and hot electron fraction. This model is applied to experimental data performed at Colorado State University’s ALEPH laser where high-resolution (E/ΔE > 7500) X-ray spectroscopy of copper K-shell emission was used to generate micron-scale, near solid-density plasmas with electron densities exceeding 1024 cm-3 and temperatures exceeding 3 keV.

Citations: 

[1] Mariscal, D. A. et al., Enhanced analysis of experimental x-ray spectra through deep learning. Phys. Plasmas 1 September 2022; 29 (9): 093901. https://doi.org/10.1063/5.0097777   

Simulating Radiation Flow through Lattices

Recent experimental breakthroughs, such as LANL’s COAX platform, have advanced our ability to explore radiation flow dynamics through unconventional targets. Of particular interest is radiation through heterogeneous media such as lattices, consisting of optically thick struts in an optically thin background. Such heterogeneous targets introduce intricate interactions between radiation and hydrodynamics. Simulations using LANL’s xRage/Cassio code are constrained using diagnostic images from these indirectly driven lattice experiments.

Simulating lattices with precision remains computationally daunting. Significant scale differences between regions necessitate an impractically large number of computational cells to properly resolve features. To address this, we focus on developing simplified models, ranging from a laterally infinite 3D domain to a fully homogenized 2D representation. Each model undergoes detailed analysis of radiation front position, energy and opacity spectra, angular radiation profile, and mean and directional chord length. This approach aims to evaluate how different geometries influence radiation flow propagation within simulations.   

Parametric Study of Ultrashort Pulse Laser-Driven Neutron Production with Particle-In-Cell Simulations

Recent experimental advances in tabletop laser-driven neutron generation raise a number of questions regarding how the neutron yield can be further improved by novel target configurations and increased laser intensity. This work uses the WarpX Particle-In-Cell (PIC) code to model high-intensity ultrashort laser pulses interacting with thin deuterated targets in bulk and 'pitcher-catcher' configurations. A pairwise fusion algorithm [Higginson et al. Journal of Computational Physics 388 (2019)] directly calculates neutron generation and standard PIC algorithms model the subsequent motion of the new fusion products within the simulation. We evaluate this method by systematically exploring how predicted neutron yield depends on laser intensity and target thickness. Additional parameters tested include the separation between the 'pitcher' and 'catcher' and the influence of initial target heating on neutron production. We also highlight important convergence considerations and effects of simulation dimensionality. In conjunction with experimental efforts, PIC simulations provide a pathway for evaluating the viability of laser-driven neutron sources for applications including neutron imaging, radiation hardening, and fusion energy.   

Integrated Analysis of X-ray Self-Emission Data for Diagnosing Thermodynamic Conditions in Implosion Experiments

The extreme conditions reached in laser-driven implosion experiments have made them a popular platform to study high-energy-density plasmas such as those that occur in the interiors of stars and other astrophysical bodies. However, the quantitative study of these systems often hinges on the accurate determination of the plasma conditions achieved in the implosion, which is challenging given the highly integrated nature of measurements in convergent geometries. We present a data-driven, Bayesian analysis that leverages measurements of x-ray self-emission from multiple diagnostics to enable statistically rigorous inference of the thermodynamic conditions reached in these implosion experiments. This analysis is applied to implosions of D₂-filled glass (SiO₂) exploding pusher type targets on the OMEGA laser system to simultaneously infer the pressure, temperature, and density histories in the SiO₂ at multi-gigabar conditions. Implications and future extensions of this platform are discussed.