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Final CRADA Report – NFE-21-08693

TAE Technologies is developing a magnetic fusion energy concept known as the beam-driven field-reversed configuration (FRC) with the ultimate goal of developing a reactor for commercial electricity production capable of burning aneutronic pB11 fuel. To achieve the high plasma temperatures this requires, auxiliary radiofrequency (RF) heating will likely be needed. High Harmonic Fast Wave (HHFW) heating has been identified as a candidate RF heating scheme to overcome the unique challenges posed to RF heating by the FRC, including the large distance from the plasma edge to the last closed flux surface and a magnetic field profile with strength decreasing from edge to core and reversing sign at a null point inside the plasma. The purpose of this project was to develop the experimental capabilities to test HHFW on TAE’s C-2W device through the design of a phased array antenna and accompanying matching network. The design was performed by ORNL and informed by experiments with a prototype four-strap phased antenna-array that was manufactured and installed on the LArge Plasma Device (LAPD) at UCLA and simulations conducted with the Petra-M code under the purview of a previous INFUSE grant. The ORNL team completed the conceptual design of the antenna and matching network which was then handed off to the TAE Mechanical Design team. The design was then iterated on to ensure changes to the mechanical design did not interfere with the RF performance. This process is now complete, and, with mechanical design in hand, TAE is proceeding with plans for final integration.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A conservative implicit-PIC scheme for the hybrid kinetic-ion fluid-electron plasma model on curvilinear meshes

We report that the hybrid kinetic-ion fluid-electron plasma model is widely used to study challenging multi-scale problems in space and laboratory plasma physics. Here, a novel conservative scheme for this model employing implicit particle-in-cell techniques is extended to arbitrary coordinate systems via curvilinear maps from logical to physical space. The scheme features a fully non-linear electromagnetic formulation with a multi-rate time advance - including sub-cycling and orbit-averaging for the kinetic ions. By careful choice of compatible particle-based kinetic-ion and mesh-based fluid-electron discretizations in curvilinear coordinates, as well as particle-mesh interpolations and implicit midpoint time advance, the scheme is proven to conserve total energy for arbitrary curvilinear meshes. In the electrostatic limit, the method is also proven to conserve total momentum for arbitrary curvilinear meshes. Although momentum is not conserved for arbitrary curvilinear meshes in the electromagnetic case, it is for an important subset of Cartesian tensor-packed meshes. The scheme and its novel conservation properties are demonstrated for several challenging numerical problems using different curvilinear meshes, including a merging flux-rope simulation for a space weather application, and a helical m = 1 mode simulation for magnetic fusion energy application.

97 MATHEMATICS AND COMPUTING↗

Doppler Backscattering Data Analysis and Integrated Modeling with OMFIT

One Modeling Framework for Integrated Tasks (OMFIT) is a widely used software tool in the magnetic fusion research community. OMFIT provides magnetic fusion energy researchers with a framework for the development of special-purpose physics modules. This paper describes an OMFIT physics module pertaining to the Doppler Backscattering (DBS) fusion plasma diagnostic. DBS measures density fluctuations and flow velocity through plasma scattering of electromagnetic waves. The OMFIT DBS module was developed to analyze experimental DBS data and facilitate modeling of DBS systems installed on multiple tokamak devices. The OMFIT DBS module is designed to support several analysis workflows: detailed analysis of experimental data, experimental planning, and theory-based synthetic diagnostic modeling. The DBS module uses integrated modeling by leveraging other OMFIT physics modules to perform tasks related to DBS, e.g. ray/beam–tracing simulations, edge-localized mode–synchronized data analysis, magnetic equilibrium reconstruction, and fitting kinetic profile data. Furthermore, this paper describes several supported workflows and serves a reference for the OMFIT DBS module.

Doppler backscattering↗

A robust fourth-order finite-difference discretization for the strongly anisotropic transport equation in magnetized plasmas

We propose a second-order temporally implicit, fourth-order-accurate spatial discretization scheme for the strongly anisotropic heat transport equation characteristic of hot, fusion-grade plasmas. Following Du Toit et al. (2018), the scheme transforms mixed-derivative diffusion fluxes (which are responsible for the lack of a discrete maximum principle) into nonlinear advective fluxes, amenable to nonlinear-solver-friendly monotonicity-preserving limiters. The scheme enables accurate multi-dimensional heat transport simulations with up to seven orders of magnitude of heat-transport-coefficient anisotropies with low cross-field numerical error pollution and excellent algorithmic performance, with the number of linear iterations scaling very weakly with grid resolution and grid anisotropy, and scaling with the square-root of the implicit timestep. We propose a multigrid preconditioning strategy based on a lower-order approximation that renders the scheme efficient and scalable under grid refinement. Several numerical tests are presented that display the expected spatial convergence rates and strong algorithmic performance, including fully nonlinear magnetohydrodynamics simulations of kink instabilities in a Bennett pinch in 2D helical geometry and of ITER in 3D toroidal geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Experimental evaluation of thermal-fluids performance of Helium-Cooled Flat Plate (HCFP) divertor

Various helium (He)-cooled solid-tungsten (W) divertor concepts have been proposed for long-pulse magnetic fusion energy reactors. Among these concepts, the He-cooled flat plate divertor (HCFP) modules have the largest plasma-facing surface area of ~0.2 m 2 . Simulations have shown that the most recent version of the design can withstand heat fluxes as great as 8 MW/m 2 . Earlier experimental studies of a single shortened HCFP cooling unit with a slot length of 7.6 cm used air at ambient temperature and pressures below 0.6 MPa. Here, we present initial experimental studies of a copper alloy and steel test section modeling a shortened HCFP cooling unit using He at prototypical pressure of 10 MPa, inlet temperatures T i ≤ 200 °C and steady-state incident heat fluxes q" ≤ 1.2 MW/m 2 . Results for Nusselt number Nu as a function of Reynolds number Re were obtained for Re = 1.2×10 4 –3.4×10 4 , and used to develop a Nu(Re) correlation and validate numerical models of the test section using commercial computational fluid dynamics (CFD) software. Simulations with this model are performed to evaluate the effect of the shortened slot. Furthermore, these analyses are used to estimate the thermal-fluids performance of the HCFP under prototypical conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Estimation of the Thermal-Fluids and Thermal-Structural Performance of Helium-Cooled Modular Finger-Type Divertors

Over the past decade, our group has investigated the thermal-fluid performance of the helium-cooled modular divertor with multiple jets (HEMJ) and a simplified “flat” design of the HEMJ for long-pulse magnetic fusion energy (MFE) reactors. Experimental studies were performed in a helium (He) loop at the prototypical pressure of 10 MPa, nearly prototypical He temperatures and incident heat fluxes using test sections made from stainless steel and tungsten alloys. Correlations for average Nusselt numbers and pressure loss coefficients were developed from the data and are used to validate computational fluid dynamics (CFD) models. Here, this work presents updated thermal-fluids performance curves based on these correlations that estimate the maximum heat flux that can be accommodated by the plasma-facing surface and coolant pumping power requirements at prototypical operating conditions. Thermal-structural performance curves developed from ITER structural design criteria are introduced, which include protection against ductile and non-ductile failure, ratcheting fatigue, and creep fatigue. The performance design curves for these finger-type divertors demonstrate that the “flat” design, with a significantly less complicated geometry than the HEMJ, has thermal-fluid and thermal-structural performance comparable to the original HEMJ concept, and may be superior in terms of non-ductile failure criteria.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Data-driven model for divertor plasma detachment prediction

We present a fast and accurate data-driven surrogate model for divertor plasma detachment prediction leveraging the latent feature space concept in machine learning research. Our approach involves constructing and training two neural networks: an autoencoder that finds a proper latent space representation (LSR) of plasma state by compressing the multi-modal diagnostic measurements and a forward model using multi-layer perception (MLP) that projects a set of plasma control parameters to its corresponding LSR. By combining the forward model and the decoder network from autoencoder, this new data-driven surrogate model is able to predict a consistent set of diagnostic measurements based on a few plasma control parameters. In order to ensure that the crucial detachment physics is correctly captured, highly efficient 1D UEDGE model is used to generate training and validation data in this study. The benchmark between the data-driven surrogate model and UEDGE simulations shows that our surrogate model is capable of providing accurate detachment prediction (usually within a few per cent relative error margin) but with at least four orders of magnitude speed-up, indicating that performance-wise, it has the potential to facilitate integrated tokamak design and plasma control. Comparing with the widely used two-point model and/or two-point model formatting, the new data-driven model features additional detachment front prediction and can be easily extended to incorporate richer physics. This study demonstrates that the complicated divertor and scrape-off-layer plasma state has a low-dimensional representation in latent space. Understanding plasma dynamics in latent space and utilising this knowledge could open a new path for plasma control in magnetic fusion energy research.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Collisionless cooling of perpendicular electron temperature in the thermal quench of a magnetized plasma

Thermal quench of a nearly collisionless plasma against an isolated cooling boundary or region is an undesirable off-normal event in magnetic fusion experiments, but an ubiquitous process of cosmological importance in astrophysical plasmas. Parallel transport theory of ambipolar-constrained tail electron loss is known to predict rapid cooling of the parallel electron temperature $T_{e\Vert}$ although $T_{e\Vert}$ is difficult to diagnose in actual experiments. Instead direct experimental measurements can readily track the perpendicular electron temperature $T_{e\bot}$ via electron cyclotron emission. The physics underlying the observed fast drop in $T_{e\bot}$ requires a resolution. Here two collisionless mechanisms, dilutional cooling by infalling cold electrons and wave-particle interaction by two families of whistler instabilities, are shown to enable fast $T_{e\bot}$ cooling that closely tracks the mostly collisionless crash of $T_{e\Vert}$. These findings motivate both experimental validation and reexamination of a broad class of plasma cooling problems in laboratory, space, and astrophysical settings.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Dependence of Heat Removal Rate of Pebble-Based Rods on Inter-Pebble Matrix Fill Fraction

Carbon pebble rods are a promising candidate for use in high heat flux regions of magnetic fusion energy reactor walls. Under high (10 – 50 MW/m 2 ) heat loads, carbon pebble rods release hot pebbles from the exposed surface, carrying away heat as the pebble rod surface recedes. In this work, we show that the surface recession rate during heating can be adjusted by changing the mechanical strength of the extruded rods, modifying the heat removal rate; this is accomplished here by varying the fill fraction of the inter-pebble matrix. A three-dimensional finite element model is presented that captures many experimental observations, including the sphere temperature and the surface recession rate. The model predicts that pebble release is caused by thermally driven crack propagation through the matrix and that the matrix strength against breaking is the single most important material parameter setting the pebble release rate; this prediction is supported by experimental results.

36 MATERIALS SCIENCE↗

Toward Verification of RANS Simulations of the T-Tube Modular Divertor Using Large Eddy Simulations of Impinging Turbulent Plane Jets

Turbulent impinging jets have been proposed to cool high heat flux plasma-facing components such as the solid tungsten target plates of the divertor in long-pulse magnetic fusion energy reactors. In particular, the T-tube modular divertor, originally developed by the ARIES Team, consists of two concentric cylindrical tubes where helium flows through a slot in the inner tube, forming an approximately planar jet that impinges upon and cools the inner surface of the pressure boundary (namely, the outer tube) and the ~15-cm 2 plasma-facing W target. The objective of this work is to demonstrate that large eddy simulations (LESs) accurately simulate the thermal transport in canonical flows that comprise the cooling flow in the T-tube, as well as validate temperatures from LES with experimental measurements in a simplified T-tube geometry. Wall‑resolved LESs, validated by experimental data and verified by direct numerical simulations (DNSs), provide benchmark data for two canonical flows in the T‑tube, namely, planar impinging and wall jets, for Reynolds numbers Re B = 4 × 10 3 to 2 × 10 4 . Our LES results are within 4% to 12% root-mean-square error (RMSE) of surface Nusselt number distributions (Nu) from experiments and DNSs. The validated LES results are then used as the ground truth to evaluate four Reynolds‑averaged Navier-Stokes (RANS) turbulence closures, namely, the k‑ω SST, realizable k‑ε, GEKO, and γ‑SST models. The k‑ω SST model has the best overall performance in terms of heat transfer, giving surface Nu within 12% RMSE of the LES results for high‑ReB impinging jets and reduced overprediction in the wall‑jet region. The GEKO model with default constants has the next best performance, providing slightly better Nu predictions for low ReB impinging jets (versus k-ω SST) but worse overall performance over the full range of ReB studied here. The realizable k‑ε turbulence model significantly overestimates turbulence near the stagnation point, while the γ‑SST model suppresses near‑wall production, biasing the simulations toward simulating laminar surface heat transfer. Simulations of the simplified T‑tube show that LES and RANS simulations with the k‑ω SST model give nearly identical average heat transfer coefficients (HTCs) over the impingement surface. The realizable k‑ε model predicts significantly lower wall temperatures due to overestimation of HTC in the outlet flow.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Bayesian parameter estimation and evaluation of the K -ω shear stress transport model for plane impinging jets

Numerical simulations with semi-empirical turbulence models are commonly used to model impinging jets, often used for cooling solid surfaces. In this work, the constants in the k-ω shear stress transport model in ANSYS FLUENT are calibrated to experimental velocity and heat transfer data for a plane turbulent impinging air jet to determine if Kennedy-O'Hagan calibration (Kennedy and O'Hagan 2001 J. R. Stat. Soc. B 63 425–64) can improve predictions of near-surface velocities and surface Nusselt numbers for similar flows. Impinging jets have been proposed to cool the target plates of the divertor in future magnetic fusion energy reactors, where simulations are used to estimate divertor performance. The flat-plate divertor (Wang et al 2009 Fusion Sci. Technol .56 1023–7) uses a plane jet of helium issuing from a B = 0.5 mm slot to cool a surface with radius of curvature of 44 B at a distance 4 B from the slot. Predictions from the calibrated numerical model are compared with independent experimental data at different flow conditions, as well as surface temperature data for a flat plate divertor test section. The contribution of this work is evaluation of the accuracy of a calibrated turbulence model for modest extrapolations in flow geometry and flow conditions for a plane impinging jet.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Support of US Burning Plasma Organization (Final Technical Report)

The objective of the project described here was to support and increase the effectiveness of the US Burning Plasma Organization. This a national organization of scientists and engineers in magnetic fusion energy, established in 2005 at the request of the DOE Office of Fusion Energy Sciences, which serves to “Advance the scientific understanding of burning plasmas and ensure the greatest benefit from a burning plasma experiment by coordinating relevant U.S. fusion research with broad community participation.” It has grown to over 420 members from over 70 institutions, primarily across the US but with some associate members from other countries. The project was divided into two tasks. The first supported leadership activities in the USBPO by the Deputy Director, Dr. Amanda Hubbard. Responsibilities included chairing regular meetings of the USBPO Research Committee, communicating with the USBPO membership via emails and web seminars, forming and overseeing activities of Task Groups, and ensuring good communication about activities of the International Tokamak Physics Activity. A task group report on ‘Recommendations for ITER Experimental Operation, U.S. Team Formation and Participation’ was completed. Hubbard organized a series of highly popular web seminars for the burning plasma community, on a range of topics attracting a large number of participants from diverse institutions. Hubbard ended her term as Deputy Director in May, 2020. She subsequently received the Secretary of Energy’s Appreciation award for her service to USBPO. The second task supported the communications functions of the USBPO, led by Communications Coordinator, Mark London. Communications are critical for the effective operation of the USBPO, given it consists of members at many widely scattered institutions, and conducts its business almost entirely using remote tools. MIT has hosted and maintained the USBPO website, mailing lists, and discussion forums and provided member support, and videoconferencing support. MIT has continued this support following this grant, with funding incorporated into a broader Cooperative Agreement.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Upgrade of the Materials Analysis Particle Probe (MAPP-U) to decipher the impact of lithium-based surfaces on NSTX-U plasma behavior

Understanding the plasma wall interaction (PWI) remains a critical issue for the feasibility of thermonuclear magnetic fusion energy solutions. Key issues with PWI mechanisms in fusion tokamak reactors include: evolution of surface chemistry and its role on hydrogen retention. In particular how low-Z coatings such as lithium can impact the behavior of plasma at the edge and in the core. PMI (plasma-material interactions) are particularly important for strategies that involve low-recycling regimes and the use of lithium PFS (plasma-facing surfaces) to attain them, as in the case of NSTX-U. Recent reports have indicated the importance of access to the evolving plasma-facing surface during and in-between plasma discharges. Changes in surface chemistry and morphology due to ion bombardment and the difficulty of diagnosing plasma-facing surfaces, especially reactive surfaces, complicate the development of a predictive understanding of the wall and its interaction with the plasma. Consequently, this impairs the ability to design advanced PFC materials for future plasma-burning fusion reactors and appropriate PMI code validation. The Materials Analysis Particle Probe (MAPP) is an established and on-going PMI probe diagnostic system compatible with the highly chemically reactive system of lithium and boron coatings adopted by the NSTX-U research program. MAPP is the first PMI diagnostic to capture the surface physics and chemistry in-vacuo in a fusion tokamak system and correlate this data to controlled plasma shots. Currently MAPP captures this information at a fixed radial location at the NSTX-U outboard divertor region. The MAPP diagnostic has enabled understanding of the near-surface and surface chemistry of complex evolving lithiated and borated carbon-based PFC surfaces retention and transport of hydrogen. Coupled to atomistic simulations in collaboration with P. Krstic of Stony Brook U. MAPP has been very successful in achieving high-impact scientific research in its current grant period evidenced by two invited review articles and over 20 peer-reviewed manuscripts and over 40 contributed and invited presentations at both national and international conferences.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Species mix & distribution function dependence of energetic-ion driven magnetospheric instabilities on DIII-D (Final Report)

Energetic ions drive a rich variety of instabilities in the complex multi-species plasma of Earth’s magnetosphere. This experiment exploited the highly flexible, high power particle beam injection capability and sophisticated diagnostic suite of the DIII-D tokamak to advance understanding of two particular instabilities of significant interest to the magnetospheric research community that have closely-related counterparts in beam-heated tokamak plasmas: electromagnetic ion cyclotron waves (EMIC) [1], observed at frequencies somewhat below the ion cyclotron frequencies of bulk ion species, and equatorial noise [2], observed at energetic-ion cyclotron harmonics. In the magnetic fusion energy domain, such waves are called ICE (Ion Cyclotron Emission). Recent substantial advances in diagnostic capability in the ion cyclotron range of frequencies in DIII-D, including measurement of wave polarization, spa)al structure and amplitude created an exciting opportunity to challenge and drive advances in theoretical understanding of these phenomena.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Plasma Surface Interactions: Predicting the Performance and Impact of Dynamic PFC Surfaces

The objective of this project is to develop, and integrate, high-performance simulation tools capable of predicting plasma-facing component (PFC) operating lifetime and the impact of the evolving surface morphology of tungsten-based PFCs on plasma contamination, including the dynamic recycling of fuel species and tritium retention, in future magnetic fusion devices. Establishing a fundamental physical understanding and developing predictive capabilities of plasma-surface interactions (PSI) requires simultaneously addressing complex and diverse physics occurring over a wide range of length (Angstroms to meters) and time (femtoseconds to years) scales, as well as integrating extensive physical processes across the plasma–surface interface. This requires development of not only detailed physics models and computational strategies at each scale, but also algorithms and methods to couple them effectively in a way that can be robustly validated. Deploying these tools requires the continued development and coupling of leadership-scale computational codes to describe the boundary plasma and the evolving PFC surface, as well as a host of simulations that bridge disparate scales to address complex physical and computational issues at the plasma–surface interface in multi-component materials systems for magnetic fusion energy development beyond ITER.

36 MATERIALS SCIENCE↗

Adapting High-Resolution X-Ray Microcalorimeter Spectrometers to Transform MFE Plasma Diagnostics

The aim of this project was to begin the transformation of magnetic fusion energy (MFE) X-ray diagnostics by applying detector technology developed over the past several decades by the astrophysics community. We installed and operated an X-ray microcalorimeter detector system under fusion-relevant plasma conditions at the Madison Symmetric Torus (MST). X-ray microcalorimeter spectrometers combine the best characteristics of instrumentation currently available on fusion devices: the high spectral resolution of crystal spectrometers (2 eV) and broadband coverage provided by pulse-height analysis systems. These spectrometers have small port-access requirements, a key advantage for future MFE experiments. This new plasma diagnostic technique will satisfy the need for multispecies impurity ion data by providing absolute measurements of impurity core accumulation, and it will provide the core impurity ion temperature. This project was a joint effort between Lawrence Livermore National Laboratory (LLNL) and researchers at the Wisconsin Plasma Physics Laboratory (WiPPl) at the University of Wisconsin–Madison (UW–Madison). Megan E. Eckart is the principal investigator at LLNL, which is funded separately from UW–Madison. This final report fulfills the reporting obligation of the UW–Madison effort.

Den Hartog, Daniel J. [Department of Physics, Univ↗