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DOE OSTI2024

The Information Length Concept Applied to Plasma Turbulence

A methodology to study statistical properties of anomalous transport in fusion plasma is investigated. Three time traces generated by the full-f gyrokinetic code GKNET are analyzed for this purpose. The time traces consist of heat flux as a function of the radial position, which is studied in a novel manner using statistical methods. The simulation data exhibit transport processes with both medium and long correlation length along the radius. A typical example of a phenomenon with long correlation length is avalanches. In order to investigate the evolution of the turbulent state, two basic configurations are studied, one flux-driven and one gradient-driven with decaying turbulence. The information length concept in tandem with Boltzmann–Gibbs and Tsallis entropy is used in the investigation. It is found that the dynamical states in both flux-driven and gradient-driven cases are surprisingly similar, but the Tsallis entropy reveals differences between them. This indicates that the types of probability distribution function are nevertheless quite different since the higher moments are significantly different.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Thermal scattering law for structure-dependent-Doppler broadening in FLASSH

Traditional Doppler broadening methods assume that target nuclei velocities follow a Maxwell-Boltzmann distribution which inherently assumes that the atoms are a free gas or that their velocities are independent of each other. This approximation is reasonable at high target temperatures and high neutron energies. However, nuclei are not independent: the lattice temperature and chemical binding will define the atomic motion. The thermal scattering law (i.e., TSL or S(α,β)) is a material property which describes the chemical binding and temperature response in terms of available momentum and energy states. In the thermal energy range, this TSL will define the thermal scattering cross sections. In the resonance region, the TSL offers a first-principles description of the probability distribution function for the velocity of the target nuclei. Using the TSL in Doppler broadening captures the structure of the material consistently from the thermal range into the resonance cross sections. In this work, both traditional free-gas and precise TSL Doppler broadening methods for resonance cross section evaluation have been implemented within the Full Law Analysis Scattering System Hub (FLASSH). This framework provides a generalized formulation for evaluating low-lying resonance data and streamlines nuclear data processing methods. TSL data generated using ab initio lattice dynamics (AILD) can be used to broaden cross section libraries in ENDF format for high-fidelity input into reactor physics calculations. These capabilities are demonstrated for the lowest absorption resonances of {sup 238}U in UO{sub 2}, UC and UN. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

MARS-F/K modeling of plasma response and fast ion losses due to RMP in KSTAR

Abstract The toroidal single-fluid magnetohydrodynamic (MHD) code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) and the MHD-kinetic hybrid code MARS-K (Liu et al 2008 Phys. Plasmas 15 112503) are utilized to study the plasma response to the n = 1 ( n is the toroidal mode number) resonant magnetic perturbation (RMP), applied to suppress the type-I edge localized mode (ELM) in a KSTAR discharge. Both the resistive-rotating and ideal-static plasma models identify strong screening of the resonant radial field harmonics of the applied RMP due to the plasma response, and predict a strong edge-peeling response of the plasma which is consistent with the optimal ELM control coil current configuration adopted in experiment. The RMP-induced radial displacement of the plasma, computed by the resistive-rotating plasma model, agrees reasonably well with that reconstructed from the measured data in the plasma core. Taking into account the drift kinetic response of fast ions, MARS-K hybrid modeling also finds quantitative agreement of the plasma core fluid pressure perturbation with experiment. Based on the MARS-F computed plasma response, a guiding-center orbit-tracing simulation finds about 0.3% of fast ion losses due the n = 1 RMP in the KSTAR ELM control experiment considered. Most losses are associated with counter-current fast ions located near the plasma edge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Implementation and verification of a model linearized multi-species collision operator in the COGENT code

We implement the multi-species linearized model collision operator, based on the approach proposed by Kolesnikov, in the full-f continuum gyrokinetic code COGENT. We describe the operator and use it in several COGENT simulations of highly collisional plasmas. We analyze simulation results with the Braginskii fluid model to illustrate that COGENT recovers both friction and thermal forces. Finally, we simulate the neoclassical transport of heavy impurities with COGENT and illustrate agreement with previously published theoretical results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Neural network based fast prediction of β N limits in HL-2M

Artificial neural networks (NNs) are trained, based on the numerical database, to predict the no-wall and ideal-wall β N limits, due to onset of the n = 1 ( n is the toroidal mode number) ideal external kink instability, for the HL-2M tokamak. The database is constructed by toroidal computations utilizing both the equilibrium code CHEASE (Lütjens et al 1992 Comput. Phys. Commun. 69 287) and the stability code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681). The stability results show that (1) the plasma elongation generally enhances both β N limits, for either positive or negative triangularity plasmas; (2) the effect is more pronounced for positive triangularity plasmas; (3) the computed no-wall β N limit linearly scales with the plasma internal inductance, with the proportionality coefficient ranging between 1 and 5 for HL-2M; (4) the no-wall limit substantially decreases with increasing pressure peaking factor. Furthermore, both the NN model and the convolutional neural network (CNN) model are trained and tested, producing consistent results. The trained NNs predict both the no-wall and ideal-wall limits with as high as 95% accuracy, compared to those directly computed by the stability code. Additional test cases, produced by the Tokamak Simulation Code (Jardin et al 1993 Nucl. Fusion 33 371), also show reasonable performance of the trained NNs, with the relative error being within 10%. The constructed database provides effective references for the future HL-2M operations. The trained NNs can be used as a real-time monitor for disruption prevention in the HL-2M experiments, or serve as part of the integrated modeling tools for ideal kink stability analysis.

Physics↗

DOE OSTI2025

Modeling fast ion losses due to tearing and internal kink perturbations in MAST-U

Fast ion (FI) loss properties in the presence of tearing mode and internal kink perturbations are numerically investigated for discharges in the MAST-U spherical tokamak, utilizing the MARS-F magnetohydrodynamic stability code and the REORBIT test particle guiding-center orbit-following module. Here, tracing about 100 000 particle markers sampled from the equilibrium distribution of the neutral-beam injection induced FIs, it is found that about 10% out of the total strike the limiting surface (including the divertor surface) in MAST-U discharge 46943, assuming a maximum perturbation of 100 G inside the plasma (corresponding to ~6 G at the Mirnov probe location at the outboard mid-plane). Detailed particle tracing, assuming a uniform initial distribution in the 2D phase space (at given radial locations), reveals that initially counter-current FIs launched near the plasma edge are subject to significant prompt losses, while almost all initially co-current ions remain well confined at the assumed perturbation level. Most lost FIs strike the lower-half of the limiting surface. Finite gyro-radius effects prevent lost ions from striking the top-outer corner of the super-X divertor chamber. A scan of the perturbation level (based on discharge 45163) reveals, not surprisingly, an approximately linear scaling of the particle loss fraction (for counter-current FIs) with respect to the perturbation amplitude.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Conceptual design of ELM control coils for the TCABR tokamak

An upgrade of the Tokamak à Chauffage Alfvén Brésilien (TCABR) is being designed to make it capable of creating a well controlled environment where the impact of resonant magnetic perturbation (RMP) fields on edge localised modes can be addressed over a wide range of (i) plasma shapes, (ii) divertor configurations, (iii) RMP coil geometries and (iv) perturbed magnetic field spectra. To this end, a unique set of in-vessel RMP coils is being designed and, in this work, their conceptual design is presented. This unique set of coils is composed of three toroidal arrays of coils on the low field side and three toroidal arrays of coils on the high field side. Each of these six toroidal arrays is composed of 18 coils thus allowing for the creation of RMP fields with toroidal mode numbers n ≤ 9 and with increased control of the poloidal mode number spectrum. To study dynamical effects of RMP fields of different toroidal mode numbers, all rotating simultaneously with different velocities, each of the 108 RMP coils will be powered independently by power supplies that can provide voltages of up to 4 kV and electric currents of up to 2 kA, with frequencies varying continuously from 0Hz up to 10kHz. A set of physical criteria were used to determine the optimal coil geometry and their respective number of turns to reduce the coil currents and voltages during operation with alternate current. Further, the conceptual design was carried out using both the vacuum approach (no plasma response) and the single-fluid response approach, which accounts for the response of a linear, single-fluid, visco-resistive plasma calculated using the M3D-C 1 code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Chasing the multi-modal plasma response in MAST-U

Abstract Achieving edge localized modes (ELMs) suppression in spherical tokamaks by applying resonant magnetic perturbations (RMPs) has proven challenging. The poloidal spectrum of the applied RMP is a key parameter that has an impact on the capability to mitigate and eventually suppress ELMs. In this work the resistive magnetohydrodynamic code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) is used to evaluate the possibility of directly measuring the plasma response in MAST-U, and particularly its variation as function of the applied poloidal spectrum, in order to guide the experimental validation of the predicted best RMP configuration for ELM suppression. Toroidal mode number n = 2 RMP is considered to minimize the presence of sidebands, and to avoid the deleterious core coupling of n = 1. Singular Value Decomposition is used to highlight linearly independent structures in the simulated magnetic 3D fields and how those structures can be measured at the wall where the magnetic sensors are located. Alternative ways to measure the multimodal plasma response and how they can be used to infer the best RMP configuration to achieve ELM suppression are also presented, including the plasma displacement and the 3D footprints at the divertor plates.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Global gyro-kinetic ion temperature gradient and trapped electron mode turbulence modelling in X -point geometry in negative and positive triangularity

Comparative modelling of ion temperature gradient (ITG)/trapped electron mode (TEM) turbulence in negative (NT) and positive (PT) triangularity plasma shapes was done using the nonlinear global full-f gyrokinetic particle code JOREK-GK in the realistic X-point tokamak geometry including the Scrape Off Layer (SOL) for TCV and DIII-D parameters. A comparison of JOREK-GK code with the gyrokinetic codes GS2 and GENE was done using NT/PT triangularity TCV L-modes parameters showing good agreement between codes in linear growth rates and clear beneficial effect of NT as compared to PT. Global non-linear modelling of the ITG/TEM saturated turbulence for realistic DIII-D NT pulses was done and compared with numerically constructed PT equilibrium with the same plasma profiles. Existence of longer correlation length of density fluctuations in PT compared to NT was demonstrated. Stronger and more sheared zonal flows are generated via Reynolds stress in NT compared to PT. These factors are stabilizing for TEM/ITG turbulence in NT and lead to smaller heat fluxes and heat conductivities in NT compared to PT configuration. Weak dependence of plasma confinement on collisionality and plasma rotation was found in modelling of DIII-D NT shots similar to the experiment. The confinement scaling with normalized ion gyro-radius ρ* was estimated both for NT and PT. Bohm-like scaling was obtained in both configurations, however with better confinement for NT compared to PT which could be favourable factor for reactor size machines.

ITG↗

DOE OSTI2022

Toroidal modeling of 3D perturbations generated by current filaments in scrape-off layer in tokamak with biased divertor targets

The divertor biasing technique offers a promising alternative to control the edge localized mode (ELM) as well as the divertor heat load in tokamaks, as compared to the resonant magnetic perturbation (RMP) generated by magnetic coils. The linear resistive MHD code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) is employed to study the plasma response to the n = 2 (n is the toroidal mode number) field perturbation in HL-2A, produced by the divertor biasing current filaments flowing in the scrape-off layer region. The response field due to biasing currents is compared with the RMP field utilized for ELM control in HL-2A. The strength of the radial resonant field perturbation, produced by the biasing currents of 100 A level, is found to be comparable with RMP generated by several kA of ELM control coil currents for the reference plasma. The plasma normal displacement near the X-point and the associated neoclassical toroidal viscosity torque are also computed to be similar between these two techniques. The modeling results thus strongly suggest that the biasing technique can be applied to control ELMs. Moreover, the biasing currents produce field perturbations, including the plasma response, that are localized more near the plasma edge (compared to the RMP counterpart), thus reducing the chance of mode locking associated with core perturbations. Particle orbit tracing also reveals that the biasing current produced magnetic perturbation tends to widen the heat deposition region and induce the strike point splitting of the ion saturation flow on the outer divertor surface, consistent with experimental observations in HL-2A. These toroidal modeling results confirm the possibility of ELM control and plasma exhaust solution by the divertor biasing technique.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

On the uncertainties in helium generation predictions for fission and fusion alloys

With ongoing advances in fusion and advanced fission reactors, quantifying irradiation effects in materials is critical. Transmutation-induced helium in cladding and structural materials can drive swelling and embrittlement, thereby reducing these components’ lifespans. Yet most studies ignore the considerable uncertainties in predicting helium generation rates. In this work, we created a code wrapper, F-SCATTER, that automatically performs simulations in FISPACT-II. We used this tool to investigate potential variance in helium generation rate, or He/dpa, calculations based on deviations in alloy composition, irradiating neutron flux spectrum, computational methodology, and nuclear data sources. We used 12 wt% Cr HT9 steel as the reference case and observed a 6.5%–98.3% He/dpa spread based on compositional variation within a single chemical specification, a 1.8%–11.5% He/dpa variation upon the incorporation of a 15% artificial uncertainty in flux at each energy, and a He/dpa difference as high as 231% when using ENDF/B-VIII.0 versus TENDL-2021 data libraries. Similar results were found for other prominent iron-based alloys, including Grade 91, castable nano-structured alloy, and 316H—where additional variations exist based on reactor type (e.g. thermal, fast, or fusion) and alloying elements such as carbon, nitrogen, and nickel. Based on the simulated results, we conclude that a significant part of the heat-to-heat variability in swelling responses of Fe-based alloys can be driven by impurity content in alloy compositions, and, therefore, chemical control should be a key element in supply chain design for advanced nuclear energy systems. Furthermore, we provide critical recommendations on best practices for evaluating and reporting helium production and lattice damage rates when computing predictions with multiphysics programs such as FISPACT-II.

FISPACT-II↗

DOE OSTI2025

Magic State Distillation using Asymptotically Good Codes on Qudits

Qudits offer the potential for low-overhead magic state distillation, although previous results for asymptotically good codes have required qudit dimension $q\gg 100$ or code length $\mathcal{N}\gg 100$. These parameters far exceed experimental demonstrations of qudit platforms, and thus motivate the search for better codes. Using a novel lifting procedure, we construct the first family of good triorthogonal codes on the $\mathbb{F}_{2^{2m}}$ alphabet with $m \geq 3$ that lies above the Tsfasman-Vladut-Zink bound. These codes yield a family of asymptotically good quantum codes with transversal CCZ gates, enabling constant space overhead magic state distillation with qudit dimension as small as $q=64$. Further, we identify a promising code with parameters $[[42,14,6]]_{64}$. Finally, we show that a distilled $|{CCZ}\rangle_{2^{2m}}$ can be reduced to a $|{CCZ}\rangle_{2^n}$ state for arbitrary $n$ with a constant-depth Clifford circuit of at most 9 computational basis measurements, 12 single-qudit and 9 two-qudit Clifford gates.

Cervia, Michael J. [Washington U., Seattle] (ORCID↗

DOE OSTI2025

Validation of Numerical Tools for Calculating Reactivity Feedback in Sodium Fast Reactors Using SEFOR Experimental Data

The Southwest Experimental Fast Oxide Reactor (SEFOR) was an experimental sodium-cooled fast breeder reactor operated from 1969 to 1972 with experiments designed to measure Doppler reactivity feedback in a wide temperature range from around 350 °F to temperatures approaching the melting point of mixed oxide fuel of around 5000 °F, providing valuable data for code validations. Co-supported by the Department of Energy (DOE) Fast Reactor Program (FRP) and the DOE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, the SEFOR benchmark project focused on using the experimental data to validate numerical tools that are used in industry and academia to design and license sodium-cooled fast reactors (SFRs). By the end of FY-25, substantial progress was achieved in the SEFOR benchmark study. A variety of numerical tools commonly used for modeling SFRs were applied to develop models for SEFOR core configurations I-D, I-E, I-I, and I-J. These included Monte Carlo codes such as MCNP, Serpent, and Shift; deterministic codes such as the legacy Argonne Reactor Computation (ARC) suite and the high-fidelity NEAMS code Griffin; and the system analysis code SAS4A/SASSYS-1 (SAS). Using these models, both SEFOR zero-power experiments and power-ascending tests were successfully simulated. Comparisons were performed against experimental measurements of core criticalities, reflector worth, kinetics parameters (Λ/βeff), isothermal reactivity feedback (from 350 °F to 760 °F at zero power), and power-ascending reactivity feedback (as power increased from 0.4 MW to 17 MW). In general, these comparisons demonstrated very good agreement between numerical results and experimental data. In Fiscal Year 26 (FY-26), the SEFOR benchmark project will continue to address the modeling issues identified in FY-25. Effort will focus on the simulation of reactivity insertion transients in SEFOR core II using the ARC/SAS model. Future work will also focus on incorporating BISON into the SEFOR core modeling process to enable the first Multiphysics simulations of the isothermal tests based on the MOOSE framework.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2022

Verification and Validation of a Modified Numerical Algorithm for Simulation of Transient Unconfined Groundwater Flow

This report extends verification and validation testing of the NUFT package of codes (Nitao 2000a,b) to the US1P module of code designed for simulation of single-phase mixed or “coupled” saturated and unsaturated (or “variably saturated”) groundwater flow. Importantly, the verification and validation testing of US1P in this report includes performance evaluation of a modified numerical algorithm that was not included in prior quality assurance (QA) of the NUFT package by Carle et al. (2014) for Underground Test Area (UGTA) project activities, which are directed at assessment of radionuclide contamination in groundwater sourced from underground nuclear test locations at the Nevada National Security Site (NNSS). An immediate purpose of this report is to provide QA for ongoing large-scale, three-dimensional (3-D) groundwater flow modeling of transient water levels associated with longterm water supply pumping and underground nuclear testing at the NNSS (Jackson and Fenelon, 2018; Jackson et al., 2021). For UGTA activities, the QA refers to the standards of ASTM (1996) for verification and validation testing of groundwater modeling codes.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Draft ASME Boiler and Pressure Vessel Code Cases and Technical Bases for Use of Alloy 617 for Constructions of Nuclear Component Under Section III, Division 5

The American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code currently only allows five materials for use in construction of nuclear components for high temperature service. These are: 2.25Cr-1Mo and V-modified 9Cr-1Mo steels, Types 304 and 316 stainless steels and the high nickel Alloy 800H. Since 2005, the US high temperature gas-cooled reactor program has been characterizing elevated temperature mechanical properties of Alloy 617 as the leading candidate construction material for the intermediate heat exchanger. After analysis of these experimental results, along with historical data and additional results available through the Generation IV International Forum, Very High Temperature Reactor, Materials Program Management Board Materials Handbook, a draft ASME Code Case to allow nuclear construction with Alloy 617 for temperatures up to 1750°F (954°C) has been developed. This report contains the Code Case for Low Temperature Service Construction of Section III, Division 5, Subsection HB, Subpart A, Class A and Subsection HC, Subpart A, Class B components, which has been approved in Section II, Materials, and Section III, Rules for Construction of Nuclear Facility Components. Supporting technical justification for the low temperature Code Case is also included. This Code Case allows use of Alloy 617 up to 800°F (425°C). This report also contains an updated draft of a Section III, Division 5, Subsection HB, Subpart B, Class A Code Case for Alloy 617 to qualify it for use in construction of nuclear components up to 1750°F (954°C) for service life up to 100,000 hours. The draft contained in Appendix 4, subject to editorial revision and approval by the ASME Special Task Group on Alloy 617 Code Qualification, will be submitted for approval by letter ballot by the appropriate ASME Committees. The technical justification supporting the Code Case is presented in Appendix 5 of this report. This background document is part of the information package that will be submitted with the Code Case for ballot.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

XGC-6D

XGC-6D is a geometric full-f Particle-In-Cell code on unstructured meshes including XGC-like unstructured mesh, tetrahedral mesh, etc. The code is particularly suitable to study boundary plasma with steep gradient and frequency higher than ion gyro-frequency. References: Wang Z, Qin H, Sturdevant B, Chang CS. Geometric electrostatic particle-in-cell algorithm on unstructured meshes. Journal of Plasma Physics. 2021;87(4):905870406.

Wang, Zhenyu [Princeton Plasma Physics Laboratory ↗

DOE OSTI2023

XGC-6D

Wang, Zhenyu [Princeton Plasma Physics Laboratory ↗

DOE OSTI2022

SAM-ML: Integrating data-driven closure with nuclear system code SAM for improved modeling capability

Advanced reactors often involve complicated thermal-fluid (T-F) phenomena. Modeling such phenomena with the traditional one-dimensional (1-D) system code is a challenging task. The System Analysis Module (SAM), a modern nuclear system code, has developed a coarse mesh multi-dimensional (multi-D) flow model to capture the spatial effect of T-F phenomena in advanced reactors. As a coarse mesh solver, constitutive relations are required for SAM's multi-D model for unresolved fine-scale physics, such as turbulence. Here this work presents a novel approach that integrates neural networks as data-driven closure for SAM's multi-D flow model. The data-driven closure is trained with fine-resolution data to ensure its accuracy while maintaining a coarse mesh setup to ensure its efficiency and consistency with SAM. We demonstrate the applicability of this SAM-ML capability in an open volume thermal stratification problem, where a neural network model serves as the eddy viscosity closure. A customized interface between the neural network and SAM is developed to ensure flexible and efficient data exchange. The SAM-ML results demonstrate superior performance compared to SAM's built-in zero-equation eddy viscosity closure. The case study shows that although the generalization capability of the data-driven closure still needs to be improved for different transient case or different geometric setup, SAM -ML demonstrates good potential for challenging simulation problems with improved accuracy and computational efficiency.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗