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DOE OSTI2022

Frequency-domain vs time-domain SP{sub N} equations to simulate neutron noise

Inside the reactor core mechanical vibrations of fuel assemblies can produce high fluctuations around a steady-state configuration, known as neutron noise. This effect can cause the triggering of power reduction measures. Classically, diffusion theory has been used to simulate this behavior. However, this equation has some limitations if the materials of the reactor have strong variations. In this work, we use the diffusive time-dependent simplified spherical harmonics equations that improve the previous results without the necessity of using high computational requirements. In particular, two types of analyses with these equations (SP{sub 3}) are made: a frequency-domain and a time-domain. A numerical neutron noise benchmark tests the methodology and compare both formulations. First, numerical results show a good agreement between the amplitudes and phases of the SP3 equations computed with the frequency-domain and time-domain. Therefore, as the frequency-domain computation only requires to solve a linear system, it is a recommendable option for neutron noise computations. Second, one can conclude that for this type of nuclear systems, where the assemblies are not homogenized, the SP{sub 3} approximation results improve considerably the accuracy of the diffusion theory.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

FolpsD: combining EFT and phenomenological approaches for joint power spectrum and bispectrum analyses

We present a theoretical model for the power spectrum and bispectrum of galaxy clustering that exploits the complementarity between small-scale power spectrum information and large-scale bispectrum measurements. We extend the FOLPS code by combining its one-loop EFT galaxy power spectrum with a tree-level galaxy bispectrum projected onto the tripolar spherical harmonics (Sugiyama) basis. To access additional small-scale information, we also consider a line-of-sight damping factor in both statistics, mirroring approaches commonly used in studies of redshift-space distortions. We test the model using DESI DR2 galaxy mocks. Even without damping, the joint analysis of the EFT power spectrum and bispectrum significantly improves constraints and reduces parameter degeneracies relative to power spectrum analyses alone. For LRG-like samples, including the damping further extends the range beyond $k\sim 0.3 \,h \text{Mpc}^{-1}$ in the power spectrum and $k \sim 0.24 \,h \text{Mpc}^{-1}$ in the bispectrum without introducing statistically significant parameter biases. This leads to up to $\sim 30\%$ tighter constraints on $A_s$ and $ω_{cdm}$. For low signal-to-noise tracers such as QSOs, however, the damping parameters are weakly constrained and can absorb noise fluctuations, leading to shifts in inferred parameters. Similar limitations may arise in models where cosmological information is encoded in power-spectrum shape features degenerate with the damping, such as scenarios with massive neutrinos. In contrast, for $w_0w_a$CDM we obtain $15\%$ and $21\%$ tighter constraints on $w_0$ and $w_a$, respectively, yielding a deviation from constant dark energy at slightly more than the $1σ$ level using full-shape information alone. The code is publicly available at https://github.com/cosmodesi/FolpsD

Bansal, P. [Michigan U., MCTP; Michigan U.] (ORCID↗

DOE OSTI2021

GPU-accelerated multitiered iterative phasing algorithm for fluctuation X-ray scattering

The multitiered iterative phasing (MTIP) algorithm is used to determine the biological structures of macromolecules from fluctuation scattering data. It is an iterative algorithm that reconstructs the electron density of the sample by matching the computed fluctuation X-ray scattering data to the external observations, and by simultaneously enforcing constraints in real and Fourier space. This paper presents the first ever MTIP algorithm acceleration efforts on contemporary graphics processing units (GPUs). The Compute Unified Device Architecture (CUDA) programming model is used to accelerate the MTIP algorithm on NVIDIA GPUs. The computational performance of the CUDA-based MTIP algorithm implementation outperforms the CPU-based version by an order of magnitude. Furthermore, the Heterogeneous-Compute Interface for Portability (HIP) runtime APIs are used to demonstrate portability by accelerating the MTIP algorithm across NVIDIA and AMD GPUs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Efficient computation of N -point correlation functions in D dimensions

We present efficient algorithms for computing the N-point correlation functions (NPCFs) of random fields in arbitrary D-dimensional homogeneous and isotropic spaces. Such statistics appear throughout the physical sciences and provide a natural tool to describe stochastic processes. Typically, algorithms for computing the NPCF components have $\mathscr O$(n N ) complexity (for a dataset containing n particles); their application is thus computationally infeasible unless N is small. By projecting the statistic onto a suitably defined angular basis, we show that the estimators can be written in a separable form, with complexity $\mathscr O$(n 2 ) or $\mathscr O$(n g log n g ) if evaluated using a Fast Fourier Transform on a grid of size n g . Our decomposition is built upon the D-dimensional hyperspherical harmonics; these form a complete basis on the (D – 1) sphere and are intrinsically related to angular momentum operators. Concatenation of (N – 1) such harmonics gives states of definite combined angular momentum, forming a natural separable basis for the NPCF. As N and D grow, the number of basis components quickly becomes large, providing a practical limitation to this (and all other) approaches: However, the dimensionality is greatly reduced in the presence of symmetries; for example, isotropic correlation functions require only states of zero combined angular momentum. We provide a Julia package implementing our estimators and show how they can be applied to a variety of scenarios within cosmology and fluid dynamics. The efficiency of such estimators will allow higher-order correlators to become a standard tool in the analysis of random fields.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Directional finite difference method for directly solving 3D gyrokinetic field equations with enhanced accuracy

The gyrokinetic (GK) field equation is a three-dimensional (3D) elliptic equation, but it is often simplified to a set of two-dimensional (2D) equations by assuming that the field does not vary along a specific direction. However, this simplification can introduce inevitable 0th-order numerical errors, as nonlinear mode coupling in toroidal geometry can produce undesirable harmonic modes that violate the assumption. In this work, we propose a novel directional finite difference method (FDM) with a local coordinate transformation to better resolve the target field of interest. The directional FDM can accurately solve 3D GK field equations without simplifications, which can overcome the limitations of conventional methods. The accuracy and efficiency of different FDMs are analyzed in great detail for a variety of geometries, from simple 2D Cartesian coordinates to realistic 3D curvilinear coordinates. The 0th-order numerical errors of simplified 2D GK equations were found to be more problematic for low-harmonic modes and low aspect ratio geometries such as spherical tokamaks. On the other hand, the directional 3D FDM can accurately resolve a much wider range of harmonic modes aligned to the direction of interest, including the low-harmonic modes. In conclusion, we demonstrate that the directional 3D FDM is a highly effective algorithm for solving the 3D GK field equations, achieving accuracy improvements of 10 to 100 times or more, particularly for low-harmonic modes in spherical tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Excitation of toroidally localized harmonics of global Alfvén eigenmodes

Abstract The spherical tokamak NSTX and the upgraded, higher toroidal field, NSTX-U, routinely create plasmas with large un-thermalized populations of super-Alfvénic fast ions. This population of non-thermal energetic ions excites a broad spectrum of Alfvénic waves, from the lower frequency (≈30 kHz–≈200 kHz) toroidal Alfvén eigenmodes (Cheng and Chance 1986 Phys. Fluids 29 3695), to the higher frequency (400 kHz–3 MHz) global Alfvén eigenmodes (GAEs) and compressional Alfvén eigenmodes (Goedbloed 1975 Phys. Fluids 18 1258). In this paper we present evidence that the GAE non-linearly excite modes, presumably GAE, at frequencies consistent with non-linear or 3-wave coupling. The observation of the excitation of 2 nd harmonic GAE through the intrinsic non-linearity of Global Alfvén modes demonstrates that the non-linear terms can act as an exciter-antenna inside the plasma, broadcasting at harmonics of the mode frequency and with concomitantly shorter wavelengths. As with experiments using external antenna to excite otherwise weakly stable Alfvénic modes, this data can provide information about the stability of modes at harmonics of the GAE. It may also provide information on the nature of the non-linearities in the wave dispersion equation or a direct measure of the mode amplitude (Smith et al 2006 Phys. Plasmas 13 042504). We also report that the short wavelength 2 nd harmonic GAE can be strongly toroidally localized. The observation that the shorter wavelength ( n ≈ 20) 2 nd harmonic modes can be toroidally localized potentially has implications for the impact of fast-ion driven instabilities on fast-ion confinement in ITER and future fusion reactors (Gorelenkov et al 2014 Nucl. Fusion 54 125001).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Nonlinear dynamics of quadratic gravity in spherical symmetry

We present the first numerically stable nonlinear evolution for the leading-order gravitational effective field theory (quadratic gravity) in the spherically-symmetric sector. The formulation relies on (i) the harmonic gauge to cast the evolution system into quasilinear form (ii) the Cartoon method to reduce to spherical symmetry in keeping with the harmonic gauge, and (iii) order reduction to first order (in time) by means of introducing auxiliary variables. The well posedness of the respective initial-value problem is numerically confirmed by evolving randomly perturbed flat-space and black-hole initial data. In conclusion, our study serves as a proof-of-principle for the possibility of stable numerical evolution in the presence of higher derivatives.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Engineering and revealing Dirac strings in spinor condensates

Artificial monopoles have been engineered in various systems, yet there has been no systematic study of the singular vector potentials associated with the monopole field. We show that the Dirac string, the line singularity of the vector potential, can be engineered, manipulated, and made manifest in a spinor atomic condensate. We elucidate the connection among spin, orbital degrees of freedom, and the artificial gauge, and show that there exists a mapping between the vortex filament and the Dirac string. We also devise a proposal where preparing initial spin states with relevant symmetries can result in different vortex patterns, revealing an underlying correspondence between the internal spin states and the spherical vortex structures. Such a mapping also leads to a new way of constructing spherical Landau levels, and monopole harmonics. Our observation provides insights into the behavior of quantum matter possessing internal symmetries in curved spaces. Published by the American Physical Society 2024

Xu, Gui-Sheng↗

DOE OSTI2021

Scoping study of detecting high harmonic fast waves in NSTX-U hot core plasma directly using beam emission spectroscopy

In this paper, we used radio frequency (RF) full wave simulation to explore the feasibility of generating a density beat oscillation formed by high harmonic fast waves (HHFWs) in the National Spherical Tokamak Experiment-Upgrade (NSTX-U) and of measuring it numerically with 2D beam emission spectroscopy (BES). This oscillation is of interest as it can be used to determine the injected RF fields. We began by computing HHFW fields in NSTX-U under a variety of experimental conditions and antenna configurations with Petra-M, a 3D RF wavefield solver. These fields were then used to evaluate the amplitude of δne,beat/ne0 in the volume of measurement, which we predict to be between 5 × 10−10 and 10−9, although it is highly dependent on plasma parameters. Trends in magnetic field, core temperature, core density, and antenna phasing are presented, and the parameters most suitable to this measurement are identified. Finally, we developed a synthetic BES diagnostic to compare the experimental BES signal against.

Rutherford, Grant (ORCID:0000000163620037)↗

DOE OSTI2021

Ball transfer mechanism with polycrystalline diamond bearing support

A ball transfer mechanism for a harmonic drive and linear piston motor is disclosed. The ball transfer mechanism includes a spherical ball and a cylindrical seat portion. The seat portion defines a hemispherical shaped recess with a contour for receiving the ball. The ball transfer mechanism is in an exterior wall of a housing for converting rotary motion to linear motion, driving a linear piston motor. The harmonic drive drives a rotor of the linear piston motor. The harmonic drive includes a hollow cylindrical coupler portion engaging a rotor portion for transferring torque to the rotor portion. Transfer mechanisms disposed along a housing wall of the linear piston motor engage the coupler portion. The coupler portion includes harmonic cam grooves for receiving spherical balls in the ball transfer mechanism that drives rotational motion in the rotor in response to axially linear movement of the piston assembly.

Raymond, David W.↗

DOE OSTI2023

Ball transfer mechanism with polycrystalline diamond bearing support

Raymond, David W.↗

DOE OSTI2022

On the origin of high harmonic fast wave edge losses in NSTX

Many mechanisms have been proposed to explain the high harmonic fast wave edge losses in the National Spherical Torus Experiment (NSTX) (Perkins et al 2012 Phys. Rev. Lett. 109 045001). Here, we discuss a newly discovered edge loss mechanism (Tierens et al 2021 Plasma Phys. Control. Fusion 64 035001) which involves the resonant excitation of surface waves on filaments. We show that this edge loss mechanism can explain the main parameter dependencies observed in NSTX experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Multi-harmonic electron cyclotron heating and current drive scenarios for non-inductive start-up and ramp-up in high field ST-40 spherical tokamak

We report non-inductive start-up and ramp-up is an important topic for spherical tokamak reactor design as the central solenoid implementation is highly restrictive particularly for the low-aspect-ratio tokamak configuration. In the high field spherical tokamak (ST), ST-40 with B T0 ≤ 3 T, a preparation is underway for high power ECH and ECCD current start-up/ramp-up experiments utilizing two MW-class 140/105 GHz gyrotrons. Here, we explored various ECH/ECCD scenarios for a low-field-side (LFS) launch-angle steerable waveguide launcher placed near the mid-plane region. Due to the large toroidal field variation of ST configuration, multiple cyclotron harmonic resonance layers could exist within the plasma. In this start-up and ramp-up regime, both fundamental and second harmonic ECH resonances must be considered. We find that even with the presence of X-II resonance layer in the plasma, an efficient X-I ECH and ECCD regime can be accessed for the low electron temperature T e0 as low as 200 eV which is a typical starting temperature of ECH heated plasmas in an open-field-line configuration. The presence of X-II resonance could become significant at higher T e0 as X-II absorption increases with T e0 which could reduce the current ramp-up efficiency as the power reaching X-I is reduced. Finally for the pure X-I regime where the 2Ω e resonance is moved outside the plasma with B T0 ~ 3.4 T, we find that it is possible to reach the full current of I p ~ 1 MA fully non-inductively with the ECH power of ~1 MW at n e0 ~ 1.0 × 10 19 m -3 using 105 GHz frequency gyrotron. By reducing the outer limiter position R L ~ 78 cm to 70 cm, the pure X-I regime is recovered at the rated ST-40 magnetic field of B T0 ~ 3.0 T. This X-I regime is accessible with a relatively broad range of launched n II or the launching angles. A survey of X-mode X-II ECH and ECCD at higher density regimes is also shown for completeness.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Energy Exascale Earth System Model v2.0.1

First patch release of v2.0.0 Changes since v2.0.0 [Important change] Fix ocean threading bug seen in debug cases on Chrysalis with Intel 20.0.4. Was introduced around time of v2.0.0 tag. Does not change v2.0.0 answers on Chrysalis because those didn't use threading or debugging. [EAM] Add semi-lagrangian tracer transport for theta-l (F90 and C++), add new algorithm for finding tropopause, add DSCREAM to allow v2 and SCREAM settings in same code such as adjust_ps [EAM-MMF] 60L default, allow C++ back end of RRTMGP (EAM too). [EAMxx] add nu-top functionality, fix forcing functor, add ttype9 and dcmip2012 tests 2.1, 2.2, and 3 HOMME: remove obsolete remap algs, option to specify dynamics alg indep of tracer, new sponge layer, add imex tests [ELM] Add topography-based subgrid (topounits), add FATES-ELM Nitro., Phos. and CH4 coupling, add land-use ts for NARRM, add lulc for SSP3 RCP7, Fix nutrient fertilization exp test and carbon isotope flux, Fix xactive lnd dry deposition, add lake water storage option, fix plant hydraulics 2d params, fix carbon budget calc, fix soil nutrient conc. bug, fix mosart dam bug, add test for new ELM, MOSART features, fix bug in O3 dry dep stomatal resistances, fix plant hydraulics restart BFB error, update mkmapdata. [MOSART] fix bug for reading the latitude from an unstructured input file, fix oversat in bubble test. [MPAS-ocean] Add CFC11, CFC12 tracers, add 2D spherical transport tests, fix del4 tracer mixing, add MARBL ocean tracer mixing, modify harmonic analysis options, add GPU port of vmix routines, fix calc of ML-averaged BV freq. [MPAS-seaice] Change extents of initial polar disks for oRRS18to6v3 grid, fix ice BGC with MARBL, update spherical test cases, fix DON coupling, Remove Cf from sea ice constants. [MPAS-landice] add CRYO1850-4xCO2 compset [CIME] add GCP, ANL GCE, Spock, Perlmutter, deprecate config_compilers.xml, fix and clean-up cmake macros, fix slurm bindings, refactor CIME internal testing, cleanup SCORPIO perf data, allow position independent compset naming, [also] update v2 benchmarking suite, extend e3sm_prod with throughput and memory checks

E3SM Project, DOE↗

DOE OSTI2022

Resonant wave–filament interactions as a loss mechanism for HHFW heating and current drive

Abstract Perkins et al (2012 Phys. Rev. Lett. 109 045001) reported unexpected power losses during high harmonic fast wave (HHFW) heating and current drive in the National Spherical Torus Experiment (NSTX). Recently, Tierens et al (2020 Phys. Plasmas 27 010702) proposed that these losses may be attributable to surface waves on field-aligned plasma filaments, which carry power along the filaments, to be lost at the endpoints where the filaments intersect the limiters. In this work, we show that there is indeed a resonant loss mechanism associated with the excitation of these surface waves, and derive an analytic expression for the power lost to surface wave modes at each filament.

Tierens, W. (ORCID:0000000269798140)↗

DOE OSTI2022

Multiview Incomplete Knowledge Graph Integration with application to cross-institutional EHR data harmonization

Objective: The growing availability of electronic health records (EHR) data opens opportunities for integrative analysis of multi-institutional EHR to produce generalizable knowledge. A key barrier to such integrative analyses is the lack of semantic interoperability across different institutions due to coding differences. We propose a Multiview Incomplete Knowledge Graph Integration (MIKGI) algorithm to integrate information from multiple sources with partially overlapping EHR concept codes to enable translations between healthcare systems. Methods: The MIKGI algorithm combines knowledge graph information from (i) embeddings trained from the co-occurrence patterns of medical codes within each EHR system and (ii) semantic embeddings of the textual strings of all medical codes obtained from the Self-Aligning Pretrained BERT (SAPBERT) algorithm. Due to the heterogeneity in the coding across healthcare systems, each EHR source provides partial coverage of the available codes. MIKGI synthesizes the incomplete knowledge graphs derived from these multi-source embeddings by minimizing a spherical loss function that combines the pairwise directional similarities of embeddings computed from all available sources. MIKGI outputs harmonized semantic embedding vectors for all EHR codes, which improves the quality of the embeddings and enables direct assessment of both similarity and relatedness between any pair of codes from multiple healthcare systems. Results: With EHR co-occurrence data from Veteran Affairs (VA) healthcare and Mass General Brigham (MGB), MIKGI algorithm produces high quality embeddings for a variety of downstream tasks including detecting known similar or related entity pairs and mapping VA local codes to the relevant EHR codes used at MGB. Based on the cosine similarity of the MIKGI trained embeddings, the AUC was 0.918 for detecting similar entity pairs and 0.809 for detecting related pairs. For cross-institutional medical code mapping, the top 1 and top 5 accuracy were 91.0% and 97.5% when mapping medication codes at VA to RxNorm medication codes at MGB; 59.1% and 75.8% when mapping VA local laboratory codes to LOINC hierarchy. When trained with 500 labels, the lab code mapping attained top 1 and 5 accuracy at 77.7% and 87.9%. MIKGI also attained best performance in selecting VA local lab codes for desired laboratory tests and COVID-19 related features for COVID EHR studies. Compared to existing methods, MIKGI attained the most robust performance with accuracy the highest or near the highest across all tasks. Conclusions: The proposed MIKGI algorithm can effectively integrate incomplete summary data from biomedical text and EHR data to generate harmonized embeddings for EHR codes for knowledge graph modeling and cross-institutional translation of EHR codes.

Zhou, Doudou↗

DOE OSTI2026

Interpretation of high-harmonic fast-wave propagation in the scrape-off layer of NSTX-U as a geometrically bounded-waveguide mode

This paper revisits the onset of high-harmonic fast-wave (HHFW) propagation in the scrape-off layer (SOL) plasma of the NSTX/NSTX-U spherical tokamak, motivated by past HHFW heating and current drive experiments and modelling. Previously, the fast-wave propagation in the SOL was correlated with the opening (suppression) of the fast-wave right-hand cutoff layer in front of the antenna. In this work, the SOL propagation is interpreted as a geometric waveguide mode guided by the SOL geometry, whose radial width can be comparable to the wave’s perpendicular wavelength in the HHFW regime. A two-dimensional circular model is first employed using full-wave solvers to characterise the poloidal eigenmode structures and to clarify their relationship to annulus resonance. By progressively adding a tokamak-like magnetic-field configuration, starting from a uniform axial field, the effects of magnetic-field gradients and pitch on the SOL waveguide mode are characterised. The poloidal mode numbers supported by the SOL plasma agree well with analytic estimates, indicating that an anisotropic plasma in a bounded geometry selectively supports and amplifies the resonant poloidal mode number. Additionally, two-dimensional axisymmetric NSTX-U simulations demonstrate that the SOL eigenmode features identified in the circular model persist in the experimentally relevant configurations. A control approach based on lengthening the wave perpendicular wavelength relative to the SOL width, including a higher magnetic (B)-field operation, is discussed. The analysis here shows the key role of a bounded geometry in interpreting HHFW eigenmode coupling and propagation in the NSTX-U SOL plasma.

plasma heating↗

DOE OSTI2021

Observation of second harmonic electron cyclotron resonance heating and current-drive transition during non-inductive plasma start-up experiment in QUEST

Here, noninductive plasma current start-up using 2nd harmonic electron cyclotron resonance heating (ECRH) with oblique radio frequency (RF) injection is demonstrated in a Q-shu University experiment with steady-state spherical tokamak. A strong transition was observed in the heating and plasma current ramp-up. The initial bulk electron heating regime exhibits T ebulk ~ 140 eV and no hard x-ray (HXR) emission with a low I p of ~15 kA; it abruptly transitions to a regime that exhibits a low T ebulk of ~10 eV and a strong HXR emission with a high I p of ~50 kA. This behavior is distinctly different from that observed in previous fundamental ECRH experiments. The mechanism of the heating and current drive transition are investigated considering wave power absorption and plasma power balance. The results indicate that the transition is caused by the favorable heating of tail electrons where the RF power absorption at the 2nd harmonic increases nearly linearly with T etail , while the power transfer from the tail electrons to the bulk electrons decreases with 1/T etail 0.5 . This causes a rapid transition to a state with high T etail while reducing T ebulk towards colder ion temperature. The understanding of the transition mechanism helps to consider plasma current start-up using 2nd harmonic ECRH for tokamak reactors such as JT-60 SA and ITER.

QUEST↗