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DOE OSTI2023

Interpretable inverse-designed cavity for on-chip nonlinear photon pair generation

Inverse design is a powerful tool in wave physics for compact, high-performance devices. To date, applications in photonics have mostly been limited to linear systems and it has rarely been investigated or demonstrated in the nonlinear regime. In addition, the “black box” nature of inverse design techniques has hindered the understanding of optimized inverse-designed structures. We propose an inverse design method with interpretable results to enhance the efficiency of on-chip photon generation rate through nonlinear processes by controlling the effective phase-matching conditions. We fabricate and characterize a compact, inverse-designed device using a silicon-on-insulator platform that allows a spontaneous four-wave mixing process to generate photon pairs at a rate of 1.1 MHz with a coincidence to accidental ratio of 162. Our design method accounts for fabrication constraints and can be used for scalable quantum light sources in large-scale communication and computing applications.

42 ENGINEERING↗

DOE OSTI2024

Experimental measurements for extracting nonlinear invariants

Nonlinear integrable optics are a promising alternative approach to lattice design. The integrable optics test accelerator (IOTA) at Fermilab has been constructed for dedicated studies of magnetostatic elliptical elements as described by Danilov and Nagaitsev. The most compelling verification of correct implementation of the NIO lattice is direct observation of the analytically expected invariants. This report outlines the experimental and analytical methods for extracting the nonlinear invariants of motion from data gathered in the last IOTA run.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Measured dynamic aperture and detuning of nonlinear integrable optics

One of the most promising advantages of nonlinear integrable optics is strong amplitude dependent tune shift without degrading the dynamic aperture. The integrable optics test accelerator (IOTA) at Fermilab is constructed around nonlinear lattice elements of the elliptical type as described by Danilov and Nagaitsev. Detuning and dynamic aperture scans in IOTA were performed using a fast dipole kicker and a low emittance electron beam. The evolution of the dynamic aperture and detuning for different configurations of the integrable optics lattice are presented.

43 PARTICLE ACCELERATORS↗

DOE OSTI2020

Online Modelling and Optimization of Nonlinear Integrable Systems

Nonlinear integrable optics was recently proposed as a design approach to increase the limits on beam brightness and intensity imposed by fast collective instabilities. To study these systems experimentally, a new research electron and proton storage ring, the Integrable Optics Test Accelerator, was constructed and recently commissioned at Fermilab. Beam-based diagnostics and online modelling of nonlinear systems presents unique challenges - in this paper, we report on our efforts to develop optimization methods suited for such lattices. We explore the effectiveness of neural networks as fast online surrogate estimators, and integrate them into a beam-based tuning algorithm. We also develop a method of knob dimensionality reduction and subsequent robust multivariate optimization for maximizing key performance metrics under complicated lattice optics constraints.

43 PARTICLE ACCELERATORS↗

DOE OSTI2020

Hot Electron Scaling and Energy Coupling In Nonlinear Laser Plasma Interactions

Energy conversion from high power lasers to energetic hot electrons is a fundamental phenomenon in laser-plasma interactions. At laser intensities above a few times 10 14 W/cm 2 , nonlinear laser-plasma interactions lead to the generation of hot electrons with a broad energy distribution at typical temperatures of 10’s – 100’s kilo-electron-volt (keV). The fraction of laser energy transferred to hot electrons, their energy distribution and energy coupling efficiency to the targets are strongly affected by the laser intensity, wavelength and the plasma condition. Most investigations to date that are related to the fusion of high-energy-density laboratory plasmas (HEDLP) are carried out with relatively moderate laser intensity and lower laser wavelength to minimize hot electron generation, as electron preheating can degrade the fuel assembly. An alternative fusion scheme known as shock ignition (SI) has been proposed, requiring a high intensity spike pulse at the end of a fuel assembly phase to generate a strong shock to ignite the fuel. An initial shock pressure of 0.3 Gbar is required for ignition-scale targets using the SI scheme, requiring a relatively high on-target laser intensity of 5-10X10 15 W/cm 2 for the spike pulse. At such intensities, copious hot electrons can be produced by laser-plasma-instabilities (LPI), e.g., Stimulated Raman Scattering (SRS) and Two-Plasmon Decay (TPD). While very energetic electrons (>200 keV) could preheat the fuel, electrons with moderate energies may actually be beneficial for the SI scheme. Electrons in the 50-100 keV range can be stopped in the compressed high-density outer ablator layer leading to an increase in the ignitor shock strength and therefore enhancing overall efficiency in the SI scheme. Considering this importance of total energy and temperature of hot electrons, it is necessary to understand the LPI in the SI high intensity regime. Characterizing the hot electron source and energy coupling is key to investigating the viability of the SI concept. The overall goal of the HEDLP award was to perform a detailed study of the scaling of hot electron generation and energy coupling on high power laser systems, with intensity, wavelength, and target ablator material relevant to the nonlinear laser-plasma interaction at SI relevant conditions. This was a collaborative project between the Center for Energy Research at the University of California, San Diego (UCSD) and General Atomics. The experiment was performed at the Omega Laser Facility at the Laboratory for Laser Energetics (LLE) in the University of Rochester. Specific objectives of the work were to: understand the basic physics of laser-plasma interactions and instabilities at high laser intensities (up to 10 17 W/cm 2 ) and the effects of low-Z ablator materials and laser wavelengths (IR pulse at 1.054 µm versus UV pulse at 0.351 µm) and intensity scaling, fully characterize the resultant hot electron energy distribution, validate hot electron energy deposition via collisional and kinetic processes in the target and the induced shocks in support of electron-assisted SI concept.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Nonlinear manifold-based reduced order model

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations, in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov n-width. However, for physical phenomena not of this type, e.g., any advection-dominated flow phenomena such as in traffic flow, atmospheric flows, and air flow over vehicles, a low-dimensional linear subspace poorly approximates the solution. To address cases such as these, we have developed a fast and accurate physicsinformed neural network ROM, namely nonlinear manifold ROM (NM-ROM), which can better approximate high-fidelity model solutions with a smaller latent space dimension than the LSROMs. Our method takes advantage of the existing numerical methods that are used to solve the corresponding full order models. The efficiency is achieved by developing a hyper-reduction technique in the context of the NM-ROM. Numerical results show that neural networks can learn a more efficient latent space representation on advection-dominated data from 1D and 2D Burgers’ equations. A speedup of up to 2.6 for 1D Burgers’ and a speedup of 11.7 for 2D Burgers’ equations are achieved with an appropriate treatment of the nonlinear terms through a hyper-reduction technique. Finally, a posteriori error bounds for the NM-ROMs are derived that take account of the hyper-reduced operators.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Evaluating Novel Polymer-Composite Resins for the Ability to Derive Elastic Properties for Explicit Formulations, or to Develop Nonlinear Models Thereof

This project evaluates the ability to derive elastic material properties for novel additively manufactured carbon-polymer matrix materials. Initially stress-strain equilibrium equations were thought to be sufficient to characterize the elastic region of material performance. However, initial test data shows the cured material behaves nonlinearly in the elastic region. To properly determine the elastic performance, additional strain data must be collected in future testing. This paper discusses the initial test data, methods and models used to describe nonlinear elasticity, and the determination of mean elastic material properties, such as Lame’s constants, using the stress-strain equilibrium equations.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Laboratory Study of Nonlinear QED in Intense Laser-Matter Interactions

The goal of the project was to investigate the interaction of powerful laser light with matter, which is of fundamental interest to electrodynamics, thermonuclear fusion plasmas, and high-energy-density physics for DOE. Experiments on highly nonlinear relativistic interactions were performed using the state-of-the-art DIOCLES laser at the Extreme Light Laboratory of the University of Nebraska–Lincoln (UNL). We have demonstrated a novel testbed for laser-plasma interactions in which laser pulses collided in plasma with femtosecond and micron-scale accuracy under extreme experiment conditions. This capability is crucial for future radiation reaction experiments and nonlinear QED studies. Moreover, this is also a milestone towards the efficient generation of GeV electron beams via travelling wave laser wakefield accelerator. We proposed a novel idea for measuring the radiation reaction process using travelling wave Thomson scattering, which was studied in numerical simulations. This method allows unambiguous measurement of radiation reaction in a single shot, therefore, surpassing the conventional methods, which suffer severely from the shot-to-shot fluctuations, due to the instability of laser wavefield acceleration.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2021

Nonlinear Characterization of a Joint Exhibiting a Reduction in Damping at High Energy

Even with the advent of additive manufacturing, the vast majority of complex structures are comprised of individual components held together with bolted joints. However, bolted joints present a challenge for mechanical design as they are a source of nonlinearity and increase the uncertainty in the overall behavior of the system in a dynamic environment. While many advances have been made in the ability to accurately model and test bolted joints, it is still an open area of research. Modes of vibration that exercise bolted joints typically exhibit nonlinear behavior where, with increased excitation level, the natural frequency decreases (i.e. softens) and the damping increases. However, the system under study for this work has an axial mode which does not follow this trend; it does soften as expected, but, after an initial increase, the apparent damping decreases with excitation amplitude. At the highest excitation level, the frequency of the mode decreases to that of a nearby bending mode and the response is amplified nearly 500% above that at lower levels. It is unclear whether the decrease in damping is due to the coupling of the two modes or if it is a characteristic of the axial mode. Therefore, the objective of this project is to investigate the coupling between the axial and bending modes and the dynamics leading to the decrease in damping.

42 ENGINEERING↗

DOE OSTI2021

Optimization-based algorithms for nonlinear mechanics and frictional contact

An optimization-based strategy for solving nonlinear mechanics problems is proposed. In contrast to typical nonlinear equation solver algorithms that aim to find zeros in the residual force function, we minimize an energy (or energy-like) function to encourage solutions which are locally stable equilibria. These smooth and potentially non-convex objective functions are minimized using a preconditioned conjugate-gradient trust-region algorithm. Contact is formulated as an inequality constrained minimization problem, and is solved with an augmented Lagrangian algorithm. Friction is included in the approach via a regularized quasi-potential energy, and other dissipative behavior is included through the use of variational constitutive updates. Finally, to accelerate convergence rates for the Lagrange multipliers, we propose a novel multiplier update algorithm utilizing the Fischer-Burmeister function, and demonstrate super-linear solver convergence for some applications.

42 ENGINEERING↗

DOE OSTI2022

Linear Seismic Source Equivalents in 3D Nonlinear Models: Effects of Embedded Small-Scale, Near-Source Structures

Gaining a proper understanding of how Earth structure and other near-source properties affect estimates of explosion yield is important to the nonproliferation mission. The yields of explosion sources are often based on seismic moment or waveform amplitudes. Quantifying how the seismic waveforms or estimates of the source characteristics derived from those waveforms are influenced by natural or man-made structures within the near-source region, where the wavefield behaves nonlinearly, is required to understand the full range of uncertainty in those yield estimates. We simulate tamped chemical explosions using a nonlinear, shock physics code and couple the ground motions beyond the elastic radius to a linear elastic, full waveform seismic simulation algorithm through 3D media. In order to isolate the effects of simple small-scale 3D structures on the seismic wavefield and linear seismic source estimates, we embed spheres and cylinders close to the fully- tamped source location within an otherwise homogenous half-space. The 3 m diameters spheres, given their small size compared to the predominate wavelengths investigated, not surprisingly are virtually invisible with only negligible perturbations to the far-field waveforms and resultant seismic source time functions. Similarly, the 11 m diameter basalt sphere has a larger, but still relatively minor impact on the wavefield. However, the 11 m diameter air-filled sphere has the largest impact on both waveforms and the estimated seismic moment of any of the investigated cases with a reduction of ~25% compared to the tamped moment. This significant reduction is likely due in large part to the cavity collapsing from the shock instead of being solely due to diffraction effects . Although the cylinders have the same diameters as the 3 m spheres, their length of interaction with the wavefield produces noticeable changes to the seismic waveforms and estimated source terms with reductions in the peak seismic moment on the order of 10%. Both the cylinders and 11 m diameter spheres generate strong shear waves that appear to emanate from body force sources.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2023

Energy conserving quadrature based dimensionality reduction for nonlinear hydrodynamics problems

Projection based dimensionality reduction is used to approximate the full discretiza tion of a PDE problem in order to reduce the cost of its numerical simulation while staying faithful to the full dynamics. For nonlinear problems, hyperreduction methods are additionally needed to remove the dependence of the nonlinear terms on the full problem’s size. In this project, we develop an energy conserving hyperreduction method and apply it to Eulerian-Lagrangian hydrodynamics problems, demonstrating that the reduced model successfully accelerates the numerical simulations while conserving the problem’s total energy with high accuracy.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Measured Dynamic Aperture and Detuning of Nonlinear Integrable Optics

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

Theory and Implementation of the Spectacular Nonlinear Viscoelastic Constitutive Model

This report is a comprehensive guide to the nonlinear viscoelastic Spectacular model, which is an isotropic, thermo-rheologically simple constitutive model for glass-forming materials, such as amorphous polymers. Spectacular is intermediate in complexity to the previous PEC and SPEC models (Potential Energy Clock and Simplified Potential Energy Clock models, respectively). The model form consists of two parts: a Helmholtz free energy functional and a nonlinear material clock that controls the rate of viscoelastic relaxation. The Helmholtz free energy is derived from a series expansion about a reference state. Expressions for the stress and entropy functionals are derived from the Helmholtz free energy following the Rational Mechanics approach. The material clock depends on a simplified expression for the potential energy, which itself is a functional of the temperature and strain histories. This report describes the thermo-mechanical theory of Spectacular, the numerical methods for time-integrating the model, model verification for its implementation in LAMÉ, a user guide for its implementation in LAMÉ, and ideas for future work. A number of appendices provide supplementary mathematical details and a description of the procedure used to derive the simplified potential energy from the full expression for the potential energy. The goal of this report is create a convenient point-of-entry for engineers who wish to learn more about Spectacular, but also to serve as a reference manual for advanced users of the model.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Grain2Mesh: Mesh Generation for Grain-Scale Nonlinear Elasticity Modeling

The nonlinear hysteretic behavior of rocks under cyclic loading is a crucial area of study in geomechanics. The macroscopic response of a variety of materials has been found to be contingent upon the behavior of the micro-scale structure. This project aims to develop a functional and maintainable software package for generating a multi-phase numerical mesh and accompanying simulation files for finite element modeling used in computational mechanics solvers. Meshes generated from images often lack key preprocessing that reduces noise and prevents mesh element distortion that can increase computational cost. By incorporating user feedback throughout, grain2mesh ensures a high-fidelity mesh that can be used to model grain-scale interactions such as shearing, crack propagation, and interfacial material contrast. Scientific applications of this software include material fracturing, stress-strain analysis for natural and engineered materials, and nonlinear meso-scale analysis.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Lattice Refinements for Nonlinear Integrable Optics in IOTA

Nonlinear integrable optics of the type proposed by Danilov and Nagaitsev place strict constraints on the lattice parameters in the matching section outside of the nonlinear insert. In particular, the effects of energy spread in the beam have significant effects on the stability of the system. Typical chromatic compensation using sextupoles has significant perturbative effects on the dynamics but is operationally necessary to suppress fast losses. Fast decoherence of kicked beam measurements limits the available signal for studies. Refinements to the IOTA lattice parameters based on this experience with electron beam operation are presented.

Wieland, John [Fermilab] (ORCID:0000000289718523)↗

DOE OSTI2022

Neural Ordinary Differential Equations for Nonlinear System Identification

Neural ordinary differential equations (NODE) have been recently proposed as a promising approach for nonlinear system identification tasks. In this work, we systematically compare their predictive performance with current state-of-the-art nonlinear and classical linear methods. In particular, we present a quantitative study comparing NODE's performance against neural state-space models and classical linear system identification methods and evaluate their inference speed and prediction performance on open-loop errors across eight different dynamical systems. The experiments show that NODEs can consistently improve the prediction accuracy by order of magnitude compared to benchmark methods. Besides improved accuracy, we also observed that NODEs are less sensitive to hyperparameters compared to neural state-space models by paying the cost of increased computation at the inference time.

machine leaning, system identification, physics in↗

DOE OSTI2022

Analysis of Compressibility Effects and Nonlinear Property Variations in a Supercritical CO2 Mixing Layer

Calculations are performed using the large eddy simulation technique to qualitatively assess the effects of fluid compressibility and thermodynamic nonlinearities on the dynamics of a supercritical flow field. Resulting data are also used to interrogate instantaneous subfilter-scale fields, as modeled by the mixed-dynamic Smagorinsky closure and gradient diffusion model. A three-dimensional wall-resolved calculation of a spatially evolving mixing layer composed solely of carbon dioxide is performed. This is followed by a coarse grid calculation to examine model performance as a function of resolution. Theoretical analysis indicates that the partial derivatives of density with respect to pressure and temperature are important modulators of the temperature and pressure field evolution, respectively. Results pertaining to subfilter velocity-velocity and velocity-temperature fields indicate that the models are most stressed in the regions where compressibility and thermo-fluid nonlinearities dominate the physics.

42 ENGINEERING↗