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DOE OSTI2022

Tritium Transport Modeling at the Pore Scale in Ceramic Breeder Materials Using TMAP8

Fusion reactors depend on the blanket material to breed and release tritium at the same rate or faster than it is consumed by the fusion reaction. Cellular ceramic breeders (CCBs) are dense materials that can maintain a high tritium breeding ratio while promoting tritium release because of highly connected pores. Assessing the tritium breeding capabilities of these materials requires a combination of extensive experimental and modeling efforts. In this work, we develop and calibrate a multiphysics model of tritium transport. This novel model accounts for ceramic and pore diffusion, trapping and detrapping, and several surface reactions at the pore surface. We perform a sensitivity analysis and calibrate the model by comparing its predictions against experimental measurements of deuterium absorption. The calibrated model is then used to model tritium absorption in samples with different pore microstructures to investigate the effect of pore interconnectivity on tritium absorption. The model is part of the development of the multiscale, multiphysics framework for tritium transport [i.e., the Tritium Migration Analysis Program (TMAP8)], which is itself built on top of the finite-element multiphysics framework multiphysics object-oriented simulation environment (MOOSE). This study demonstrates some of TMAP8’s capabilities and is the first step toward assessing the tritium breeding capabilities of ceramic breeder material designs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Steepest-descent algorithm for simulating plasma-wave caustics via metaplectic geometrical optics

The design and optimization of radiofrequency-wave systems for fusion applications is often performed using ray-tracing codes, which rely on the geometrical-optics (GO) approximation. However, GO fails at wave cutoffs and caustics. To accurately model the wave behavior in these regions, more advanced and computationally expensive “full-wave” simulations are typically used, but this is not strictly necessary. A new generalized formulation called metaplectic geometrical optics (MGO) has been proposed that reinstates GO near caustics. The MGO framework yields an integral representation of the wavefield that must be evaluated numerically in general. We present an algorithm for computing these integrals using Gauss-Freud quadrature along the steepest-descent contours. Benchmarking is performed on the standard Airy problem, for which the exact solution is known analytically. Furthermore, the numerical MGO solution provided by the new algorithm agrees remarkably well with the exact solution and significantly improves on previously derived analytical approximations of the MGO integral.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Final Report: Performance-structure characterization to improve REBCO Fusion conductor production at SuperPower

Several companies have used ReBCO tapes to make magnets operating at 20 K, at magnetic fields up to 20T suitable for plasma confining for controlled fusion applications. The transport properties of ReBCO conductors should be optimized for such conditions. NHMFL is one of the few laboratories where such tests can be accomplished. Recently, SuperPower Inc. came up with a new product, REBCO MOCVD HM tape, optimized for plasma confining applications. These HM tapes are designed to have increased critical currents at intermediate temperatures of 4.2K

36 MATERIALS SCIENCE↗

DOE OSTI2021

Load dynamics of double planar foil liners and double planar wire arrays on the UM MAIZE LTD generator

In previous studies using the University of Nevada, Reno's (UNR's) high-impedance Zebra Marx generator (1.9 Ω, 1.7 MA, 100 ns), Double Planar Wire Arrays (DPWAs) proved to be excellent radiators, and Double Planar Foil Liners (DPFLs) proved useful for future inertial confinement fusion applications. This article presents the results of joint UNR/UM (University of Michigan) experiments with aluminum (Al) DPWAs, Al DPFLs, and tungsten (W) DPWAs using UM's Michigan Accelerator for Inductive Z-Pinch Experiments (MAIZE) generator, a low-impedance Linear Transformer Driver (LTD) (0.1 Ω, 0.5–1 MA, and 100–250 ns). The main goals of this study were twofold: the first was a pioneering effort to test whether a relatively heavy Al DPFL could successfully be imploded on a low-impedance university-scale LTD like the MAIZE generator, and, if so, to analyze the results and make comparisons to the optimized, lighter DPWA configurations that have been previously studied. The DPWAs consisted of two planes of micrometer-scale diameter Al or W wires, while the DPFLs consisted of two planes of micrometer-scale thickness Al foils. Diagnostics include filtered Si-diodes, an absolutely calibrated filtered PCD, x-ray pinhole cameras, spectrometers, and gated optical self-emission imaging. The implosion dynamics and radiative properties of Al DPWAs and DPFLs and W DPWAs on the MAIZE LTD are discussed and compared. Time-dependent load inductance calculations derived from measurements of the load current and a MAIZE circuit model provide a relative measurement of pinch strength. In experiments on MAIZE, W planar wire arrays exhibited a higher peak load inductance throughout the pinch than Al DPWAs and DPFLs, while x-ray pulses from Al DPFLs had the longest emission duration.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

High Radiation Resistance in the Binary W‐Ta System Through Small V Additions: A New Paradigm for Nuclear Fusion Materials

Abstract Refractory High‐Entropy Alloys (RHEAs) are promising candidates for structural materials in nuclear fusion reactors, where W‐based alloys are currently leading. Fusion materials must withstand extreme conditions, including i) severe radiation damage from energetic neutrons, ii) embrittlement due to H and He ion implantation, and iii) exposure to high temperatures and thermal gradients. Recent RHEAs, such as WTaCrV and WTaCrVHf, have shown superior radiation tolerance and microstructural stability compared to pure W, but their multi‐element compositions complicate bulk fabrication and limit practical use. In this study, it is demonstrated that reducing alloying elements in RHEAs is feasible without compromising radiation tolerance. Herein, two Highly Concentrated Refractory Alloys (HCRAs) − W 53 Ta 44 V 3 and W 53 Ta 42 V 5 (at.%) − were synthesized and investigated. We found that small V additions significantly influence the radiation response of the binary W–Ta system. Experimental results, supported by ab‐initio Monte Carlo simulations and machine‐learning‐driven molecular dynamics, reveal that minor variations in V content enhance Ta–V chemical short‐range order (CSRO), improving radiation resistance in the W 53 Ta 42 V 5 HCRA. By focusing on reducing chemical complexity and the number of alloying elements, the conventional high‐entropy alloy paradigm is challenged, suggesting a new approach to designing simplified multi‐component alloys with refractory properties for thermonuclear fusion applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

An efficient high-order numerical solver for diffusion equations with strong anisotropy

In this paper, we present an interior penalty discontinuous Galerkin finite element scheme for solving diffusion problems with strong anisotropy arising in magnetized plasmas for fusion applications. Additionally, we demonstrate the accuracy produced by the high-order scheme and develop an efficient preconditioning technique to solve the corresponding linear system, which is robust to the mesh size and anisotropy of the problem. Several numerical tests are provided to validate the accuracy and efficiency of the proposed algorithm.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

A process optimization framework for laser direct energy deposition: Densification, microstructure, and mechanical properties of an Fe-Cr alloy

Laser Direct Energy Deposition (DED) is a metal additive manufacturing technique with the ability to fabricate large and complex parts through deposition of metal powders. However, achieving high-density parts and targeted build heights using DED can be challenging due to the large number of highly sensitive process variables. This work proposes a robust fabrication parameter optimization framework to generate process maps for primary parameters in DED, including laser power, scan speed, mass flow rate, hatch spacing, and layer height. Simple single-track experiments were utilized to map out the parameter space, and a combination of geometric criteria for hatch spacing and layer height were proposed to determine parameter sets that achieve both targeted build heights and mitigate porosity formation. Using this framework, specimens with >99 % density and consistent mechanical properties were successfully fabricated over a wide range of process parameters for an Fe-9wt.%Cr (Fe9Cr) alloy, a surrogate for radiation damage-resistant reduced activation ferritic/martensitic (RAFM) steels. Processing these materials using DED is of particular interest in the development of plasma facing components for nuclear fusion applications. The microstructure and mechanical properties of as-printed Fe9Cr were characterized using optical and electron microscopy, X-ray diffraction, and uniaxial tensile tests. As-printed Fe9Cr displayed ~25 % elongation and ultimate tensile strengths of up to 475 MPa which is comparable to similar wrought alloys. Finally, the proposed framework will allow for accelerated DED parameter optimization for novel alloy systems, as well as open the possibility for local microstructure control while simultaneously mitigating defect formation.

42 ENGINEERING↗

DOE OSTI2026

Geometrical optics without singularities: using the ray time as the coordinate space

Geometrical optics (GO) is widely used for reduced modelling of waves in plasmas, but it fails near reflection points, where it predicts a spurious singularity of the wave amplitude. We show how to avoid this singularity by adopting a different representation of the wave equation. Instead of the physical coordinate 𝑥 and the wavevector 𝑘, we use the ray time 𝜏 as the new canonical coordinate and the ray energy ℎ as the associated canonical momentum. To derive the envelope equation in the 𝜏-representation, we construct the Weyl symbol calculus on the (𝜏,ℎ) space and show that the corresponding Weyl symbols are related to their (𝑥,𝑘) counterparts by the Airy transform. This allows us to express the coefficients in the envelope equation through the known properties of the original dispersion operator. When necessary, solutions of this equation can be mapped to the 𝑥-space using a generalised metaplectic transform. However, the field per se might not even be needed in practice. Instead, knowing the corresponding Wigner function usually suffices for linear and quasilinear calculations. As a Weyl symbol itself, the Wigner function can be mapped analytically, using the aforementioned Airy transform. We show that the standard Airy patterns that form in regions where conventional GO fails are successfully reproduced within metaplectic GO (MGO) simply by remapping the field from the 𝜏-space to the 𝑥-space. An extension to mode-converting waves is also presented. This formulation, which we call generalised MGO, can be particularly useful, for example, for reduced modelling of the O–X conversion in inhomogeneous plasma near the critical density, an effect that is important for fusion applications and also occurs in the ionosphere. Overall, MGO can replace GO for any practical purposes, because it better handles cutoffs and is similar otherwise.

plasma waves↗

DOE OSTI2021

Gold-tantalum alloy films deposited by high-density-plasma magnetron sputtering

Gold-tantalum alloy films are of interest for biomedical and magnetically-assisted inertial confinement fusion applications. Here, we systematically study the effects of substrate tilt (0°–80°) and negative substrate bias (0–100 V) on properties of ≲3-μm-thick films deposited by high-power impulse magnetron sputtering (HiPIMS) from a Au–Ta alloy target (with 80 at. % of Ta). Results reveal that, for all the substrate bias values studied, an increase in substrate tilt leads to a monotonic decrease in film thickness, density, residual compressive stress, and electrical conductivity. Larger substrate bias favors the formation of a body-centered cubic phase, with films exhibiting lower column tilt and higher density, electrical conductivity, and residual compressive stress. Furthermore, these changes are attributed to metal atom ionization effects, based on the lack of correlation with distributions of landing energies and incident angles of depositing species as calculated by Monte Carlo simulations of ballistic collisions and gas phase atomic transport. By varying substrate tilt and bias in HiPIMS deposition, properties of Au–Ta alloy films can be controlled in a very wide range, including residual stress from –2 to +0.5 GPa, density from 12 to 17 g/cm 3 , and the electrical resistivity from 50 to 4500 μΩ cm, enabling optimum deposition conditions to be selected for specific applications.

36 MATERIALS SCIENCE↗

DOE OSTI2024

A Survey of Multimaterial Treatments for Thermal Radiative Transfer

Arbitrary Lagrangian-Eulerian methods are a popular choice for hydrodynamic modeling in radiation (rad-hydro) simulations. Because these methods involve a relaxation step that moves the mesh relative to material boundaries, multimaterial spatial zones are generally present. Accurate treatments of these zones are needed to resolve various physical phenomena of interest for inertial confinement fusion applications. However, these codes are often paired with single-material, deterministic thermal radiative transfer (TRT) codes that are oblivious to the material compositions of each zone. These single-material TRT codes can only accept homogenized material properties (opacities, specific heats, etc.) from the hydrodynamic code and output homogenized solutions. After each TRT time step, the multimaterial hydrodynamic code must dehomogenize the quantities computed by the TRT package in order to update subzonal material temperatures. The process by which hydrodynamic codes perform this dehomogenization has not been well documented in previous literature, and the methods can vary significantly from code to code. The purpose of this paper is to document, study, and compare existing techniques used for rad-hydro simulations as well as present a new method with potentially promising results. We summarize several methods and give comparisons on infinite-medium problems as well a finite-medium problem for two of the methods.

42 ENGINEERING↗

DOE OSTI2025

Calibration of RAFM Micromechanical Model for Creep Using Bayesian Optimization for Functional Output

A Bayesian optimization procedure is presented for calibrating a multimechanism micromechanical model for creep to experimental data of F82H steel. Reduced activation ferritic martensitic (RAFM) steels based on Fe(8–9)%Cr are the most promising candidates for some fusion reactor structures. Although there are indications that RAFM steel could be viable for fusion applications at temperatures up to 600°C, the maximum operating temperature will be determined by the creep properties of the structural material and the breeder material compatibility with the structural material. Due to the relative paucity of available creep data on F82H steel compared to other alloys such as Grade 91 steel, micromechanical models are sought for simulating creep based on relevant deformation mechanisms. As a point of departure, this work recalibrates a model form that was previously proposed for Grade 91 steel to match creep curves for F82H steel. Due to the large number of parameters (9) and cost of the nonlinear simulations, an automated approach for tuning the parameters is pursued using a recently developed Bayesian optimization for functional output (BOFO) framework (Huang et al., 2021, “Bayesian optimization of functional output in inverse problems,” Optim. Eng., 22, pp. 2553–2574). Incorporating extensions such as batch sequencing and weighted experimental load cases into BOFO, a reasonably small error between experimental and simulated creep curves at two load levels is achieved in a reasonable number of iterations. In conclusion, validation with an additional creep curve provides confidence in the fitted parameters obtained from the automated calibration procedure to describe the creep behavior of F82H steel.

42 ENGINEERING↗

DOE OSTI2024

Berkeley Lab Finite Element Framework (BELFEM) v0.1

The software program, referred to as BELFEM, is a specialized finite element code designed for the magnetodynamic modeling of high-temperature superconducting (HTS) tapes. It incorporates novel mixed finite element formulations, particularly the h-ϕ-formulation with thin-shell simplification, to efficiently simulate larger geometries. This methodology is extremely promising for predicting the electrodynamic performance of HTS tapes used in superconducting cables and magnets, offering the benefit of reduced computational cost. Compared to similar technologies like COMSOL Multiphysics and GetDP, BELFEM's performance benchmarking indicates superior efficiency in its thin-shell implementation. In the future, it will also support features like thermal coupling and inter-tape current sharing, enhancing its utility in research and development, particularly in nuclear fusion applications. The intent is to develop BELFEM as a robust and efficient tool for the HTS community, contributing to the analysis and design of superconducting cables and magnets.

Messe, Christian↗

DOE OSTI2022

Characterization of Disconnection Content Associated with Grain Boundary Motion in Tungsten

The objective of this study is to develop a new computational methodology to predict the motion of grain boundaries in tungsten associated with recrystallization. This approach accounts recently discovered high-temperature grain boundary phases in tungsten and other metals and alloys. This paper reports the initial work in the project that developed a novel technique for molecular dynamics to characterize disconnections, dislocation-like defects in grain boundaries that mediate grain boundary motion. Grain boundary properties are needed for a thermomechanical model of recrystallization of tungsten for magnetic fusion applications.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Fabrication of the HFVMTF Double-Bath Cryostat

The High Field Vertical Magnet Test Facility (HFVMTF) at Fermilab is designed to test superconducting magnets up to 20 tons and 1.3 meters in diameter. Central to the facility is a double-bath superfluid helium cryostat reaching 1.8 K at 1.2 bar. Integrated with a 15 T superconducting dipole from LBNL, HFVMTF supports HTS cable testing for fusion applications. This paper presents the design and fabrication of the cryostat, with a focus on two complex components: the 2 K heat exchanger and the lambda plate. The heat exchanger thermally links sub-atmospheric and pressurized helium baths. The 1.4-meter lambda plate provides thermal isolation and structural support for over 20 tons under 1.3 bar pressure differential. Finite Element Analysis validated the vessel’s integrity under maximum load conditions.

Bruce, Romain [Fermilab] (ORCID:0000000234200612)↗

DOE OSTI2025

Modeling of Stress and Temperature Effects on Creep of Reduced Activation Ferritic-Martensitic Steel Alloy F82H (Tertiary Creep Modeling of RAFM Steel)

A Bayesian optimization procedure is presented for calibrating a multi-mechanism micromechanical model for creep to experimental data of F82H steel. Reduced activation ferritic martensitic (RAFM) steels based on are the most promising candidates for some fusion reactor structures. Although there are indications that RAFM steel could be viable for fusion applications at temperatures up to 600 °C, the maximum operating temperature will be determined by the creep properties of the structural material and the breeder material compatibility with the structural material. Due to the relative paucity of available creep data on F82H steel compared to other alloys such as Grade 91 steel, micromechanical models are sought for simulating creep based on relevant deformation mechanisms. As a point of departure, this work recalibrates a model form that was previously proposed for Grade 91 steel to match creep curves for F82H steel. Due to the large number of parameters (9) and cost of the nonlinear simulations, an automated approach for tuning the parameters is pursued using a recently developed Bayesian optimization for functional output (BOFO) framework [1]. Incorporating extensions such as batch sequencing and weighted experimental load cases into BOFO, a reasonably small error between experimental and simulated creep curves at two load levels is achieved in a reasonable number of iterations. Validation with an additional creep curve provides confidence in the fitted parameters obtained from the automated calibration procedure to describe the creep behavior of F82H steel at 600 °C. The model is further extended using a temperature dependent scaling law approach to simulate creep response between 550 °C and 650 °C. The efficacy of this extension is compared with the previously used scaling law approach for Grade 91 steel.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Improving the Fracture Toughness and Ductility of Liquid-Phase Sintered WNiFe Tungsten Heavy Alloys by High-Temperature Annealing

Tungsten heavy alloys (WHAs) are candidates for use in fusion reactor divertors. Here, we characterize liquid-phase sintered WHAs with 90, 92.5, 95, and 97 (wt.%) tungsten (W), with a balance of a 0.7Ni–0.3Fe ductile phase. These WHAs show remarkable room temperature (RT) fracture toughness at the maximum load, K Jm , ranging from ≈ 38 to 107 MPa√m, compared to a monolithic W toughness of ≈ 8 MPa√m. In most cases, the fracture of WHAs occurs through stable crack tearing. However, the 97W WHA has the lowest toughness and fracture elastically in all but the smallest specimens. As lower Ni contents are desirable for fusion application, we explore the potential for improving the ductility and K Jm of WHAs using vacuum annealing at 1300 °C for 24 h. The microstructural observations reveal negligible changes in the WHA microstructure and constituent compositions. While annealing reduces the Vickers microhardness (HV), it does not significantly change the RT yield (σ y ) and ultimate (σ u ) strengths but results in beneficial increases in total elongation in the 95 and 97W WHAs by a factor of 2. RT tests on the precracked three-point-bend (3PB) bars show that annealing increases the K Jm of these WHAs, and in the case of the 97W WHA, the increase is from 42 to 92%, depending on the size of the specimen. Toughening is due to enhanced crack tip process zone microcracking and dilatation.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Fabrication of the HFVMTF Double-Bath Cryostat

Bruce, R. [Fermilab] (ORCID:0000000234200612)↗

DOE OSTI2023

Quantum computing for fusion energy science applications

This is a review of recent research exploring and extending present-day quantum computing capabilities for fusion energy science applications. We begin with a brief tutorial on both ideal and open quantum dynamics, universal quantum computation, and quantum algorithms. Then, we explore the topic of using quantum computers to simulate both linear and nonlinear dynamics in greater detail. Because quantum computers can only efficiently perform linear operations on the quantum state, it is challenging to perform nonlinear operations that are generically required to describe the nonlinear differential equations of interest. In this work, we extend previous results on embedding nonlinear systems within linear systems by explicitly deriving the connection between the Koopman evolution operator, the Perron–Frobenius evolution operator, and the Koopman–von Neumann evolution (KvN) operator. We also explicitly derive the connection between the Koopman and Carleman approaches to embedding. Extension of the KvN framework to the complex-analytic setting relevant to Carleman embedding, and the proof that different choices of complex analytic reproducing kernel Hilbert spaces depend on the choice of Hilbert space metric are covered in the appendixes. Finally, we conclude with a review of recent quantum hardware implementations of algorithms on present-day quantum hardware platforms that may one day be accelerated through Hamiltonian simulation. We discuss the simulation of toy models of wave–particle interactions through the simulation of quantum maps and of wave–wave interactions important in nonlinear plasma dynamics.

Joseph, I. (ORCID:0000000255400840)↗