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At least 325 records · Page 18

A reduced-order model for nonlinear radiative transfer problems based on moment equations and POD-Petrov-Galerkin projection of the normalized Boltzmann transport equation

A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor) equations for moments of the radiation intensity and (ii) the normalized Boltzmann transport equation (BTE). The multilevel system of moment equations is derived by projection of the BTE onto a sequence of subspaces which represent elements of the phase space of the problem. Exact closure for the moment equations is provided by the Eddington tensor. A Petrov-Galerkin (PG) projection of the normalized BTE is formulated using a proper orthogonal decomposition (POD) basis representing the normalized radiation intensity over the whole phase space and time. The Eddington tensor linearly depends on the solution of the normalized BTE. By linear superposition of the POD basis functions, a low-rank expansion of the Eddington tensor is constructed with coefficients defined by the PG projected normalized BTE. The material energy balance (MEB) equation is coupled with the effective gray low-order equations which exist on the same dimensional scale as the MEB equation. The resulting TRT ROM is structure and asymptotic preserving. A detailed analysis of the ROM is performed on the classical Fleck-Cummings (F-C) TRT multigroup test problem in 2D geometry. Numerical results are presented to demonstrate the ROM's effectiveness in the simulation of radiation wave phenomena. Importantly, the ROM is shown to produce solutions with sufficiently high accuracy while using low-rank approximation of the normalized BTE solution. Essential physical characteristics of supersonic radiation wave are preserved in the ROM solutions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Simultaneous enhancement of tritium burn efficiency and fusion power with low-tritium spin-polarized fuel

This study demonstrates that using spin-polarized deuterium-tritium (D-T) fuel with more deuterium than tritium can increase tritium burn efficiency (TBE) by at least an order of magnitude without compromising fusion power output, compared to unpolarized fuel. Although previous studies show that a low tritium fraction can enhance TBE, this strategy resulted in reduced fusion power density. The surprising improvement in TBE at fixed power reported here is due to the TBE increasing nonlinearly with decreasing tritium fraction but the fusion power density increasing roughly linearly with D-T cross section. A study is performed for an ARC-like tokamak producing 481 MW of fusion power with unpolarized 53:47 D-T fuel, finding the minimum startup tritium inventory (I startup,min ) is 0.69 kg. By spin-polarizing half of the fuel and using a 60:40 D-T mix, I startup,min is reduced to 0.08 kg, and fully spin-polarizing the fuel with a 63:37 D-T mix further reduces I startup,min to 0.03 kg. Some ARC-like scenarios are predicted to achieve plasma ignition with relatively modest spin polarization. These findings indicate that, with advancements in helium divertor pumping efficiency, TBE values of approximately 10%–40% could be achieved using low-tritium-fraction and spin-polarized fuel with minimal power loss. This would dramatically lower tritium startup inventory requirements and reduce the amount of on-site tritium. More generally than just for spin-polarized fuels, increased plasma performance can be used to increase TBE. This strongly motivates the development of spin-polarized fuels and low-tritium-fraction operation for burning plasmas.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Inertial collapse of a gas bubble in a shear flow near a rigid wall

Despite the extensive research on bubble collapse near rigid walls, the bubble collapse dynamics in the presence of shear flow near a rigid wall is poorly understood. We conduct direct simulations of the Navier–Stokes equations to explore the bubble dynamics and pressures during bubble collapse near a rigid, flat wall under linear shear flow conditions. We examine the dependence of the bubble collapse morphology and wall pressures on the initial bubble location and shear rate. We find that shear distorts the bubble, generating two re-entrant jets – one developing from the side opposite to the mean flow and the other from the far end toward the wall. Upon impact of the jet on the opposite side of the bubble, water-hammer shocks are produced, which propagate outward and interact with the convoluted bubble shape. The shock stretches the bubble towards the wall, resulting in a closer impact location for the jet originating from the far end compared with the case with no shear flow. The water-hammer pressure location can be approximated as the theoretical distance travelled by a particle initialised at the bubble centre with the corresponding constant shear flow velocity. The maximum wall pressures can thus be predicted by considering the distance between the far jet impingement location and the wall along the wall-normal direction. As the shear rate is increased, the maximum wall pressure increases, although only marginally. We determine the critical initial stand-off distance from the wall at which the bubble morphology is shear dominated, i.e. characterised by converging re-entrant jets.

Bhola, Sahil (ORCID:0000000236766302)↗

A Low-Rank QTT-based Finite Element Method for Elasticity Problems

We present an efficient and robust numerical algorithm for solving the linear elasticity problem that combines the Quantized Tensor Train format and a domain partitioning strategy. This approach makes it possible to solve the linear elasticity problem on a computational domain that is more general than a square. By integrating Z-ordering and subdomain concatenation, our method substantially decreases memory usage and achieves a notable reduction in rank compared to established Finite Element implementations like the FEniCS platform. This efficiency is maintained while still guaranteeing exponential convergence with respect to the number of degrees of freedom. This performance gain, however, requires a fundamental rethinking of how core finite element operations are implemented. This includes changes to mesh discretization, node and degree of freedom ordering, stiffness matrix and internal nodal force assembly, and the execution of algebraic matrix-vector operations. In this work, we discuss all these aspects in detail and assess the method’s performance in the numerical approximation of three representative test cases.

97 MATHEMATICS AND COMPUTING↗

Score-based deterministic density sampling

We propose a deterministic sampling framework using Score-Based Transport Modeling for sampling an unnormalized target density π given only its score ∇ log π. Our method approximates the Wasserstein gradient flow on KL($f_t$∥π) by learning the time-varying score ∇ log $f_t$ on the fly using score matching. While having the same marginal distribution as Langevin dynamics, our method produces smooth deterministic trajectories, resulting in monotone noise-free convergence. We prove that our method dissipates relative entropy at the same rate as the exact gradient flow, provided sufficient training. Numerical experiments validate our theoretical findings: our method converges at the optimal rate, has smooth trajectories, and is often more sample efficient than its stochastic counterpart. Experiments on high-dimensional image data show that our method produces high-quality generations in as few as 15 steps and exhibits natural exploratory behavior. The memory and runtime scale linearly in the sample size.

97 MATHEMATICS AND COMPUTING↗

Compensating slice emittance growth in high brightness photoinjectors using sacrificial charge

Achieving maximum electron beam brightness in photoinjectors requires detailed control of the 3D bunch shape and precise tuning of the beam focusing. Even in state-of-the-art designs, slice emittance growth due to nonlinear space charge forces and partial nonlaminarity often remains non-negligible. In this work, we introduce a new means to linearize the transverse slice phase space: a sacrificial portion of the bunch’s own charge distribution, formed into a wavebroken shock front by highly nonlinear space charge forces within the gun, whose downstream purpose is to dynamically linearize the desired bunch core. We show that linearization of an appropriately prepared bunch can be achieved via strongly nonlaminar focusing of the sacrificial shock front, while the inner core focuses laminarly. This leads to a natural spatial separation of the two distributions: a dense core surrounded by a diffuse halo of sacrificial charge that can be collimated. Multiobjective genetic algorithm optimizations of the ultracompact x-ray free electron laser injector employ this concept, and we interpret it with an analytic model that agrees well with the simulations. In simulation, we demonstrate a final bunch charge of 100 pC, peak current ∼ 30 A, and a sacrificial charge of 150 pC (250 pC total emitted from cathode) with normalized emittance growth of < 20 nm rad due to space charge. This implies a maximum achievable brightness approximately an order of magnitude greater than existing free electron laser injector designs. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗

Classical combinatorial optimization scaling for random Ising models on 2D heavy-hex graphs

Motivated by near term quantum computing hardware limitations, combinatorial optimization problems that can be addressed by current quantum algorithms and noisy hardware with little or no overhead are used to probe capabilities of quantum algorithms such as the quantum approximate optimization algorithm. In this study, a specific class of near term quantum computing hardware defined combinatorial optimization problems, Ising models on heavy-hex graphs both with and without geometrically local cubic terms, are examined for their classical computational hardness via empirical computation time scaling quantification. Specifically the time-to-solution (TTS) metric using the classical heuristic simulated annealing is measured for finding optimal variable assignments (ground states), as well as the time required for the optimization software Gurobi to find an optimal variable assignment. Because of the sparsity of these Ising models, the classical algorithms are able to find optimal solutions efficiently even for large instances (i.e. 100 000 spin variables). The Ising models both with and without geometrically local cubic terms exhibit average-case linear-time or weakly quadratic scaling when solved exactly using Gurobi, and the Ising models with no cubic terms show evidence of exponential-time TTS scaling when sampled using simulated annealing. These findings point to the necessity of developing and testing more complex, namely more densely connected, optimization problems in order for quantum computing to ever have a practical advantage over classical computing. Our results are another illustration that different classical algorithms can indeed have exponentially different running times, thus making the identification of the best practical classical technique important in any quantum computing vs. classical computing comparison.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Multi-parametric analysis for mixed integer linear programming: An application to transmission upgrade and congestion management

Upgrading the capacity of existing transmission lines is essential for meeting the growing energy demands, facilitating the integration of renewable energy, and ensuring the security of the transmission system. This study focuses on the selection of lines whose capacities and by how much should be expanded from the perspective of the Independent System Operators (ISOs) to minimize the total system cost. We employ advanced multi-parametric programming and an enhanced branch-and-bound algorithm to address complex mixed-integer linear programming (MILP) problems, considering multi-period time constraints and physical limitations of generators and transmission lines. To characterize the various decisions in transmission expansion, we model the increased capacity of existing lines as parameters within a specified range. This study first relaxes the binary variables to continuous variables and applies the Lagrange method and Karush-Kuhn-Tucker (KKT) conditions to obtain optimal solutions and identify critical regions associated with active and inactive constraints. Moreover, we extend the traditional branch-and-bound (B&B) method by determining the problem’s upper and lower bounds at each node of the B&B decision tree, helping to manage computational challenges in large-scale MILP problems. Here, we compare the difference between the upper and lower bounds to obtain an approximate optimal solution within the decision-makers’ tolerable error range. In addition, the first derivative of the objective function on the parameters of each line is used to inform the selection of lines for easing congestion and maximizing social welfare. Finally, the capacity upgrades are selected by weighing the reductions in system costs against the expense of upgrading line capacities. The findings are supported by numerical simulations and provide transmission-line planners with decision-making guidance.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Denoising of imaginary time response functions with Hankel projections

Imaginary-time response functions of finite-temperature quantum systems are often obtained with methods that exhibit stochastic or systematic errors. Reducing these errors comes at a large computational cost—in quantum Monte Carlo simulations, the reduction of noise by a factor of two incurs a simulation cost of a factor of four. In this paper, we relate certain imaginary-time response functions to an inner product on the space of linear operators on Fock space. We then show that data with noise typically does not respect the positive definiteness of its associated Gramian. The Gramian has the structure of a Hankel matrix. As a method for denoising noisy data, we introduce an alternating projection algorithm that finds the closest positive definite Hankel matrix consistent with noisy data. We test our methodology at the example of fermion Green's functions for continuous-time quantum Monte Carlo data and show remarkable improvements of the error, reducing noise by a factor of up to 20 in practical examples. We argue that Hankel projections should be used whenever finite-temperature imaginary-time data of response functions with errors is analyzed, be it in the context of quantum Monte Carlo, quantum computing, or in approximate semianalytic methodologies. Published by the American Physical Society 2024

Yu, Yang (ORCID:0000000186178878)↗

Degradation of Poly- and Perfluoroalkyl Substances (PFAS) in Water via High Power, Energy-Efficient Electron Beam Accelerator

The goal of the 2-year workplan was to see if electron beam (EB) could be used to break down a sub-set of the larger chemical family of per and polyfluoroalkylated substances (PFAS) in an energy efficient and economical manner when compared to conventional water treatment technologies. Year one (Y1) work focused on sample EB treatment work in the Fermi National Accelerator Laboratory’s (FNALs) Accelerator Applications Demonstration and Development (A2D2) EB accelerator. While there are reportedly thousands of types of PFAS, for the point of most of the work herein, a small subset was examined, typically perfluorooctane sulfonate (PFOS) and perfluorooctanoate (PFOA). PFOA and PFOS are two of the most well studied PFAS and are studied for baseline evaluations and are considered most useful. The work from Y1 provided information about the optimal operating parameters and additives to use when treating PFOS and PFOA via EB. The data were then used to see where in a water treatment system an EB accelerator would be best suited to treat PFAS. A conventional water treatment technology, GAC, was then compared to e-beam treatment technology with respect to energy and costs for treatment. In year two (Y2), several conventional e-beam accelerator designs, and FNAL’s developmental compact SRF accelerator design, were evaluated for their suitability in PFAS treatment, from an energy efficiency and cost standpoint. Several EB parameters were evaluated and optimized for the removal of PFOA and PFOS from water at normal pressure and temperature, measured as total PFAS removal. Under the optimized test conditions both PFOA showed complete destruction to inorganic fluoride, and PFOS to inorganic fluoride and sulfate, with mass balance. The effect on PFAS removal relative to solution pH, total EB dose, EB dose rate, dissolved oxygen concentration (DO), temperature, and initial PFAS concentration were evaluated. In general, PFOA was easier to destroy than PFOS. Degradation products, typically observed under less-than-optimal EB conditions, provided insight to degradation mechanisms. Products were identified to rule out possible deleterious biproduct formation. The water radiolysis radical reaction kinetics with PFOS and PFOA were not dependent on the initial concentration over 5-orders of magnitude from 2 μg/L to 20 mg/L. This is thought to be because there was an overabundance of the reactive water radiolysis radicals relative to PFAS molecules and largely attributed to aqueous electrons. The reaction rates appeared to be diffusion limited. Testing at higher concentrations (100-200 mg/L) showed a decrease in removal efficiency, suggesting alternative kinetics, possibly second order rates, at higher concentrations. In all, we successfully defined a set of optimal EB parameters to treat PFOA and PFOS at concentrations of 20 mg/L in water with destruction efficiencies near 100%. We further tested the optimized EB parameters with other types of PFAS, including shorter and longer fluorocarbon chain homologs of PFOA and PFOS, and PFAS with alternative functional groups such as sulfonamides. Based on our results EB can be optimized as an effective destructive technology for removing PFAS from water. The conditions optimized for PFOA and PFOS were less effective with ultra-short fluorocarbon compounds like TFMS, PFES, PFPS and PFBS, and likely require re-optimization of parameters to them. In all, it was determined that from a cost and energy efficiency standpoint, EB would be best applied to waste streams with relatively high concentrations of PFOS and PFOA and is not as cost effective as GAC treatment for removing low concentrations of PFAS from water. Higher concentrations of PFAS can be found in the wastewater of conventional treatment processes such as RO and IE and therefore EB may be used to supplement such treatment technologies. Some real-world IE regeneration wash water and RO reject water containing higher concentrations of PFAS and obtained from pilot scale industrial wastewater treatment system at a fluorochemical manufacturing facility, showed that EB could remove PFAS from such types of wastewaters. The IE regenerant wash water appeared to be the most efficient of the two types of wastewaters tested. However, some further optimization of the EB parameters for the specific PFAS types present in those wastewaters may be required. Also, the effects of co-present TOC and mineral salts should be considered during such optimization efforts. From the experimental Y1 results it was seen that the aqueous electron drives degradation of the PFAS. In a hypothetical water treatment skid using EB for PFAS destruction the parameters of the system should be optimized to promote aqueous electron production. Before EB treatment, the PFAS should be preconcentrated when possible, the pH should be raised to pH 10 or higher to enhance aqueous electron production, and the water should be nitrogen purged to remove dissolved oxygen to minimize aqueous electron scavenging. An excel spreadsheet was created that calculates optimal conditions based on inlet PFAS concentration and desired outlet concentration, by optimizing the accelerator power, dose rate, water treatment rate, pH and dissolved oxygen levels to reach the desired endpoint. Given this information on accelerator operating conditions five different EB accelerator systems were compared. One EB system was a continuous-wave, linear superconducting accelerator being designed at Fermilab. Three other EB systems (IMPELA at 5% and 25% duty factor and the ILU-14) were normal conducting pulsed linear accelerators. The fifth system was an IBA Rhodotron which is a normal conducting, circular, continuous-wave accelerator. The accelerator efficiency (% of the incoming power that is used in water treatment) was the dominating factor in accelerator choice. The radio frequency (RF) power supply and the accelerator design (superconducting versus warm technology) drive the accelerator efficiency. The IBA Rhodotron was seen to be the most energy efficient commercially available technology with a wall-plug (total) power efficiency of 43% at 400 kW. The Fermilab design, with a prototype for a different application currently being fabricated, was the most energy efficient at 55% when driven by a Klystron RF power supply and as high as 77% when powered by a magnetron. As the Fermilab design was the most energy efficient by approximately 10-30%, further design work was done on the accelerator and beam delivery system specific to the destruction of PFAS in water. The Fermilab design is unique from industrial accelerators in that is superconducting. Superconducting technology allows for the acceleration of electrons without losses. The accelerator must be cooled to below the point where it is superconducting and is operated around 4 degrees Kelvin. The bulk of the design work for the accelerator is on making the accelerator as energy efficient as possible so that it does not require liquid helium and can be cooled with conduction cooling via cryocoolers. Final design work resulted in an EB accelerator that would operate at minimally 200 kW and 10 MeV. Prototype construction would cost $\$ $7.8 million dollars when driven by a Klystron power supply. A second version of the same accelerator would cost $\$ $5.5 million dollars when driven by a magnetron that is still under development. The commercially available 300 kW IBA Rhodotron cost was estimated at approximately $\$ $9 million. While it is hard to directly compare, an operational GAC system used by 3M for groundwater treatment capital cost (2022 dollars) was estimated to cost $\$ $3.3 million. While the capital expense of the EB accelerator systems was higher than GAC, the accelerator EB treatment would result in destruction of the PFAS and not just sequestration of PFAS to form a new waste stream that requires further treatment or disposal. The operating cost to destroy the PFAS via 400 kw EB system was less than $\$ $1000/kg of PFAS destroyed when treating at a 20 mg/L PFAS concentration, compared to GAC with operating costs that calculated at $\$ $27,530 per kg of PFAS sequestered when treating 100 μg/L PFOA and PFOS combined concentration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Distribution of centrality measures on undirected random networks via the cavity method

The Katz centrality of a node in a complex network is a measure of the node’s importance as far as the flow of information across the network is concerned. For ensembles of locally tree-like undirected random graphs, this observable is a random variable. Its full probability distribution is of interest but difficult to handle analytically because of its “global” character and its definition in terms of a matrix inverse. Leveraging a fast Gaussian Belief Propagation-Cavity algorithm to solve linear systems on tree-like structures, we show that i) the Katz centrality of a single instance can be computed recursively in a very fast way, and ii) the probability P ( K ) that a random node in the ensemble of undirected random graphs has centrality K satisfies a set of recursive distributional equations, which can be analytically characterized and efficiently solved using a population dynamics algorithm. We test our solution on ensembles of Erdős-Rényi and Scale Free networks in the locally tree-like regime, with excellent agreement. The analytical distribution of centrality for the configuration model conditioned on the degree of each node can be employed as a benchmark to identify nodes of empirical networks with over- and underexpressed centrality relative to a null baseline. We also provide an approximate formula based on a rank- 1 projection that works well if the network is not too sparse, and we argue that an extension of our method could be efficiently extended to tackle analytical distributions of other centrality measures such as PageRank for directed networks in a transparent and user-friendly way.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

End-to-end protocol for high-quality quantum approximate optimization algorithm parameters with few shots

The quantum approximate optimization algorithm (QAOA) is a quantum heuristic for combinatorial optimization that has been demonstrated to scale better than state-of-the-art classical solvers for some problems. For a given problem instance, QAOA performance depends crucially on the choice of the parameters. While average-case optimal parameters are available in many cases, meaningful performance gains can be obtained by fine-tuning these parameters for a given instance. This task is especially challenging, however, when the number of circuit executions (shots) is limited. In this work, we develop an end-to-end protocol that combines multiple parameter settings and fine-tuning techniques. We use large-scale numerical experiments to optimize the protocol for the shot-limited setting and observe that optimizers with the simplest internal model (linear) perform best. We implement the optimized pipeline on a trapped-ion processor using up to 32 qubits and 5 QAOA layers, and we demonstrate that the pipeline is robust to small amounts of hardware noise. To the best of our knowledge, these are the largest demonstrations of QAOA parameter fine-tuning on a trapped-ion processor in terms of two-qubit gate count.

quantum algorithms & computation↗

Benchmarking Optimizers for Qumode State Preparation with Variational Quantum Algorithms

Quantum state preparation involves preparing a target state from an initial system, a process integral to applications such as quantum machine learning and solving systems of linear equations. Recently, there has been a growing interest in qumodes due to advancements in the field and their potential applications. However there is a notable gap in the literature specifically addressing this area. This paper aims to bridge this gap by providing performance benchmarks of various optimizers used in state preparation with Variational Quantum Algorithms. We conducted extensive testing across multiple scenarios, including different target states, both ideal and sampling simulations, and varying numbers of basis gate layers. Our evaluations offer insights into the complexity of learning each type of target state and demonstrate that some optimizers perform better than others in this context. Notably, the Powell optimizer was found to be exceptionally robust against sampling errors, making it a preferred choice in scenarios prone to such inaccuracies. Additionally, the Simultaneous Perturbation Stochastic Approximation optimizer was distinguished for its efficiency and ability to handle increased parameter dimensionality effectively.

Kan, Shuwen [Fordham University]↗

Variability of MHD instabilities in benign termination of high-current runaway electron beams in the JET and DIII-D tokamaks

Benign termination, in which magnetohydrodynamic (MHD) instabilities deconfine runaway electrons (REs) following hydrogenic injections, is a promising strategy for mitigating dangerous RE loads after disruptions. Recent experiments on the Joint European Torus (JET) have explored this scenario at higher pre-disruptive plasma currents than are achievable on other devices, revealing challenges in obtaining benign terminations at I p ≥2.5 MA. This work analyzes the evolution of these high-current RE beams and their terminating MHD events using fast magnetic sensor measurements and EFIT equilibrium reconstructions for approximately 40 JET and 20 DIII-D tokamak discharges. On JET, unsuccessful non-benign terminations occur at low edge safety factor (q edge ≈ 2), and are preceded by intermittent, non-terminating MHD events at higher rational qedge. Trends in the internal inductance I i indicate more peaked RE current profiles in the high-I p non-benign population, which may hinder successful recombination through re-ionization of the companion plasma. In contrast, benign terminations on JET typically occur at higher q edge ≥3 and exhibit less peaked RE current profiles. DIII-D displays a broader range of terminating edge safety factors, again correlated with the measured values. Across both tokamaks, the RE current peaking is therefore found to determine which MHD instability boundary is encountered, a result confirmed by linear resistive MHD modeling with the CASTOR3D code. Measured growth rates are similar for benign and non-benign cases, indicating that ideal MHD timescales at low density after hydrogenic injection do not alone explain efficient RE deconfinement. Instead, non-benign cases are most readily characterized by their comparably lower overall MHD perturbation amplitudes δB. These observations suggest that the interplay between ideal and resistive dynamics governs the termination process, with implications for extrapolating benign RE termination to high-I p reactor scenarios.

MHD instabilities↗

Thermo-hydraulic steam pipe models for district heating simulations: Simplifications to balance accuracy and simulation speed

Steam piping networks are essential for optimizing performance in industrial processes and district heating systems. However, dynamic models that balance thermo-hydraulic accuracy with computational efficiency remain limited. In response, this paper presents a new discretized steam pipe model based on the plug flow approach, capturing key thermo-hydraulic behaviors while simplifying steam phase change processes. Implemented in Modelica, the model accurately calculates temperature and pressure distributions along steam pipelines. To improve computational efficiency for district-scale simulations, five model simplifications are introduced: lumped thermo-hydraulic functions, empirical correlations, fluid state approximations, steady-state dynamics and inclusion of flow derivatives. These simplified models achieve 85%-98% accuracy in predicting pressure drop and condensation losses, including dynamic condensate behavior during pipe warm-up—a factor often overlooked in existing models. The models support diverse network configurations, scaling effectively to systems with multiple distribution pipes and connected building loads. Discrete models provide detailed insights but exhibit a cubic increase in simulation time as the network scales by N connected building O(N 2.42 ). In contrast, lumped models simulate 10–28 times faster than discrete, offering quadratic scaling of simulation time O(N 1.73 ). However, they still require 6 times more computation time than a lossless network, highlighting the inherent computational challenges of modeling compressible fluid flow. In conclusion, the steady-state lumped variant, with its near-linear scalability in computational time O(N 1.01 ), emerges as an efficient solution for preliminary design evaluations and extensive parametric studies.

15 GEOTHERMAL ENERGY↗

Design and Materials of Reference Electrodes for Radioactive Waste Tank Service – A Literature Review

The Hanford site stores approximately 55 million gallons of radioactive and chemically hazardous wastes from the production of weapons materials. The wastes are stored in 177 underground, carbon steel storage tanks, 149 of these are single shell tanks (SSTs) and 28 of these are double shell tanks (DSTs). The DSTs provide critical retrieval and interim storage before the waste is vitrified in the Waste Treatment and Isolation Plant (WTP). The DSTs have been in service for 38 to 56 years and current plans indicate that WTP operations will be completed in 2075. Thus, the tanks will need to remain in service far beyond the initial 40-year life expectancy. For life extension of the tanks, effective corrosion control practices must remain in force. This effort includes direct measurements of the extent of corrosion (e.g., ultrasonic measurements and corrosion coupons) and electrochemical processes (e.g., linear polarization measurements).

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

High-Fidelity and High-Performance Computational Simulations for Rapid Design Optimization of Sulfur Thermal Energy Storage (CRADA Report)

NREL and Element 16 collaborated on sulfur thermal energy storage modeling using NREL’s high performance computing (HPC) resources to assist its application in industrial processes. Industrial process heat (IPH) accounts for ~70% of US manufacturing energy use and is primarily produced by fossil fuel combustion. Approximately, 1500 TWht (~60% Terawatt hour thermal) of IPH demand is in the temperature range of 100-300°C. Industrial applications in this temperature range include drying, hydrothermal processing, thermal enhanced oil recovery, food and beverage, bioethanol production, etc. Cost-effective thermal energy storage (TES) that increases the utilization of waste and renewable heat (solar, geothermal, etc.) could provide significant energy savings and reliable heat sources, decrease emissions, and increase US manufacturing competitiveness through reductions in fuel consumption. This HPC4EI project facilitated Element 16’s development of low-cost and high-impact molten sulfur TES for dispatchable IPH. The development of a high-fidelity model validated by experimental data and HPC simulations enabled the successful resolution of the complex interplay between fluid dynamics and heat transfer processes during transient operation of sulfur TES, overcoming the numerical challenges posed by the non-linear temperature-dependent physical properties of sulfur. The project helped accelerate Element 16’s molten sulfur TES product design and support its broad applications.

25 ENERGY STORAGE↗

Estimating Residual Gas Beam Loss in the BNL AGS Booster:Model, Numerical Tools, and Implications for a Polarimeter Chamber

Beamloss from residual gas scattering is calculated for a storage ring of circumference C = 200m, covering a linear magnetic rigidity ramp from B ρ inj = 1.25Tm to B ρ ext = 9.50Tm over tramp = 1.00s. Three loss mechanisms are considered: nuclear inelastic reactions, single Coulomb scattering beyond the acceptance angle of the machine, and charge-state exchange for heavy ions. Calculations are performed for protons and Au 32+ ions, the latter being the charge state delivered by the EBIS pre-injector into the BNL AGS Booster. At a baseline vacuum of P 0 = 5 × 10 −11 mbar the integrated fractional beam loss over the full ramp is negligible for protons (< 0.001%) and 33.1% for Au 32+ . The impact of a 1m polarimeter section at elevated pressure P s = 5 × 10 −9 mbar is evaluated: the proton loss remains negligible, while the Au 32+ loss rises to 45.1%, establishing the vacuum requirement for the polarimeter chamber. In the present compact approximate model, Au 32+ losses are dominated by charge exchange at injection, while proton losses are dominated by single Coulomb scattering. The design, outgassing budget, pumping strategy, and commissioning sequence for a UHV polarimeter chamber housing silicon detectors and ASICs are described in detail.

43 PARTICLE ACCELERATORS↗