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NASA NTRS2021

Transition Analysis for the CRM-NLF Wind Tunnel Configuration

This paper presents the results of an ongoing study into the linear stability characteristics of the boundary layer flow over the common research model with natural laminar flow (CRMNLF) aircraft configuration. The flow conditions match selected test conditions from a recent wind tunnel experiment in the National Transonic Facility at the NASA Langley Research Center. Previous work involving parallel stability computations of a boundary layer flow based on the conical flow approximation has shown that the measured onset of laminar-turbulent transition during the experiments can be correlated with the linear amplification of Tollmien- Schlichting (TS) and stationary crossflow (CF) instabilities in the swept wing boundary layer. Here, we examine the effects of the simplifying approximations in both basic state computation and the stability analysis, with the goal of quantifying the resulting changes in the N-factor correlations. Specifically, the basic states are computed by using full Navier-Stokes equations and the stability analysis is performed by using a nonorthogonal coordinate system that allows a clear distinction between planar TS and CF instabilities. Furthermore, the effects of curvature and nonparallel mean flow have been included in the stability computations based on the parabolized stability equations (PSE). The fully turbulent Reynolds-Averaged-Navier-Stokes (RANS) mean flow solutions show good agreement with the measured wall pressure distribution. Viscous-inviscid interactive effects are observed to be important because the shock fronts along the suction surface are influenced by the imposed transition front. The stability results confirm the previous findings related to TS amplification within the inboard region of the wing and the dominance of stationary CF modes in the outboard region. However, given the close proximity of the measured transition front and the dual shock system within the outer part of the wing, the onset of transition may well be shock limited within the outboard region. In general, the transition criterion based on the dual N-factor method with N TS = N CF = 6 is reasonably successful at correlating with the measured transition fronts at Re MAC = 15 million and AoA = 1.5, 2 degrees; however, the low values of the correlating N-factors at Re MAC = 17.5 million support the hypothesis that the measured transition at the higher Reynolds number may have been strongly influenced by the merging of turbulent wedges that originate from surface imperfections near the leading edge.

Boundary layer transition↗

NASA NTRS2021

Transition Analysis for the CRM-NLF Wind Tunnel Configuration

Boundary layer transition↗

DOE OSTI2021

A Multiport DC Transformer to Enable Flexible Scalable DC as a Service

The rapid adoption of new DC loads and sources, including photovoltaic arrays, DC fast charging of electric vehicle, battery energy storage and data centers, requires a large amount of DC power conversion. A majority of new deployments also necessitate the integration of multiple DC loads and sources at one site. The traditional approach to serve these new applications relies on multiple standard power converters, each dedicated to a source or load, and results in highly customized systems, with challenging control coordination, complex protection strategies, and poor scalability. Instead, this paper proposes the concept of a multiport DC transformer (MDCT) as a modular building block for realizing a flexible, scalable DC as a Service system and address this rapidly growing need. The MDCT uses the S4T to achieve very tight control of cycle-by-cycle energy exchange between multiple ports, with high efficiency. A single multiport converter replaces 4-6 distinct converters, integrates all energy flows and manages protection. As a result, a new layered control architecture is introduced to ensure stability and scalability of the MDCT, with multiple S4T power converter building blocks connected in parallel to realize a fully modular system and reach the target power levels.

30 DIRECT ENERGY CONVERSION↗

NASA NTRS1993

Comparative measurement of visual stability in Earth and cosmic space (L-4)

The frequency and the intensity of space motion sickness was reviewed and investigated. Unusual induced-gravity situations, such as rotation, linear acceleration, parallel swinging etc. were investigated as well. Visually-induced motion sensation or distorted perception were evaluated with respect to visual stability by many investigators. These studies are all concerned with the effect of gravity and the induction of motion sickness through human visual perception. Direct investigation under the microgravity situation, such as parabolic flight, Skylab, and Spacelab, was carried out. These studies focused on how human visual stability is established through various sensory afferents in specific gravity conditions. Results from these investigations indicate that sensory mismatch probably plays an important role in space motion sickness. The interaction of visual, vestibular, and somatosensory perception is smoothly coordinated under normal gravitational conditions on the Earth in our daily life. When the cooperation is destroyed or a mismatch occurs among them, motion sickness may develop not only on the Earth but also in microgravity. The latter case may be the cause of space motion sickness or space adaption syndrome. How human beings obtain visual stability even with posture changes on the ground was investigated. Visual stability can be categorized as static or dynamic. Static visual stability is concerned with orientation and dynamic stability is concerned with object motion perception. The perception of visual stability is modified by many other sensations, such as somatosensory, vestibular, and muscle tension. We will mainly focus on modifications by vestibular inputs to visual perception produced by eye movements in microgravity. The Vestibular-Oscular Reflex (VOR) is a well-known characteristic which results from the relationship between eye mobility and vestibular afferent inputs. Eye movements also modify dynamic visual perception, such as perceived object motion velocity. The VOR is constantly simulated under 1-g conditions on Earth. In fact, human beings have been habituated and 'programmed' for orientation (visual stability) in their everyday, 1-g environment. When humans are exposed to a different gravity situation, this programmed behavior must change; that is, it is reprogrammed. This is called habituation or familiarization. We hope to examine how object motion perception is perturbed and subsequently adapted in the microgravity environment. This experiment is focused on the cooperation of visual, vestibular, and somatosensory perception coordination and how it is changed or reduced in space compared to 1-g environment. We will obtain information on the coordination between eye movement and neck muscle activity by using EOG and EMG. We will also collect data from Payload Specialists using a self-diagnostic questionnaire concerned with perceptual abnormality. When each sensory input function and its integration in the higher nervous system are well-characterized, then more effective techniques to control SAS may be developed.

Koga, Kazugo↗

NASA NTRS2010

Adaptive Numerical Algorithms in Space Weather Modeling

Space weather describes the various processes in the Sun-Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different physics in different domains. A multi-physics system can be modeled by a software framework comprising of several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models. Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solar wind Roe Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamics (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems. BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit numerical schemes. Depending on the application, we find that different time stepping methods are optimal. Several of the time integration schemes exploit the block-based granularity of the grid structure. The framework and the adaptive algorithms enable physics based space weather modeling and even forecasting.

Toth, Gabor↗

NASA NTRS2007

Receptivity of Hypersonic Boundary Layers Due to Acoustic Disturbances over Blunt Cone

The transition process induced by the interaction of acoustic disturbances in the free-stream with boundary layers over a 5-degree straight cone and a wedge with blunt tips is numerically investigated at a free-stream Mach number of 6.0. To compute the shock and the interaction of shock with the instability waves the Navier-Stokes equations are solved in axisymmetric coordinates. The governing equations are solved using the 5th -order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. After the mean flow field is computed, acoustic disturbances are introduced at the outer boundary of the computational domain and unsteady simulations are performed. Generation and evolution of instability waves and the receptivity of boundary layer to slow and fast acoustic waves are investigated. The mean flow data are compared with the experimental results. The results show that the instability waves are generated near the leading edge and the non-parallel effects are stronger near the nose region for the flow over the cone than that over a wedge. It is also found that the boundary layer is much more receptive to slow acoustic wave (by almost a factor of 67) as compared to the fast wave.

Kara, K.↗

NASA NTRS1980

An implicit algorithm for the transonic full-potential equation in conservative form

A fast, implicit approximate factorization algorithm for the solution of the conservative full-potential equation for transonic flow in two and three dimensions is presented. Stability in supersonic regions is maintained by the use of an upwind evaluation of the density coefficient along all coordinate directions, providing an effective upwind difference of the streamwise terms for any orientation of the velocity vector and thereby enhancing the reliability of the algorithm. The algorithm is shown to provide rapid convergence for the computation of certain difficult two-dimensional test cases, including cases with fishtail shock patterns, demonstrating the reliability and efficiency of the procedure. Surface pressure coefficient distributions obtained by the present method are also found to be in good agreement with those computed by successive-line overrelaxation and a hybrid direct-solver/successive-line overrelaxation scheme, with significant reductions in CPU time required. A three-dimensional solution for a swept wing mounted between parallel walls is also presented which demonstrates the high convergence rate of the algorithm in three dimensions as well as two.

Holst, T.↗

NASA NTRS1989

Compact finite volume methods for the diffusion equation

An approach to treating initial-boundary value problems by finite volume methods is described, in which the parallel between differential and difference arguments is closely maintained. By using intrinsic geometrical properties of the volume elements, it is possible to describe discrete versions of the div, curl, and grad operators which lead, using summation-by-parts techniques, to familiar energy equations as well as the div curl = 0 and curl grad = 0 identities. For the diffusion equation, these operators describe compact schemes whose convergence is assured by the energy equations and which yield both the potential and the flux vector with second order accuracy. A simplified potential form is especially useful for obtaining numerical results by multigrid and alternating direction implicit (ADI) methods. The treatment of general curvilinear coordinates is shown to result from a specialization of these general results.

Rose, Milton E.↗

NASA NTRS1997

A Cognitive System Model for Human/Automation Dynamics in Airspace Management

NASA has initiated a significant thrust of research and development focused on providing the flight crew and air traffic managers automation aids to increase capacity in en route and terminal area operations through the use of flexible, more fuel-efficient routing, while improving the level of safety in commercial carrier operations. In that system development, definition of cognitive requirements for integrated multi-operator dynamic aiding systems is fundamental. In order to support that cognitive function definition, we have extended the Man Machine Integrated Design and Analysis System (MIDAS) to include representation of multiple cognitive agents (both human operators and intelligent aiding systems) operating aircraft, airline operations centers and air traffic control centers in the evolving airspace. The demands of this application require representation of many intelligent agents sharing world-models, and coordinating action/intention with cooperative scheduling of goals and actions in a potentially unpredictable world of operations. The MIDAS operator models have undergone significant development in order to understand the requirements for operator aiding and the impact of that aiding in the complex nondeterminate system of national airspace operations. The operator model's structure has been modified to include attention functions, action priority, and situation assessment. The cognitive function model has been expanded to include working memory operations including retrieval from long-term store, interference, visual-motor and verbal articulatory loop functions, and time-based losses. The operator's activity structures have been developed to include prioritization and interruption of multiple parallel activities among multiple operators, to provide for anticipation (knowledge of the intention and action of remote operators), and to respond to failures of the system and other operators in the system in situation-specific paradigms. The model's internal representation has been be modified so that multiple, autonomous sets of equipment will function in a scenario as the single equipment sets do now. In order to support the analysis requirements with multiple items of equipment, it is necessary for equipment to access the state of other equipment objects at initialization time (a radar object may need to access the position and speed of aircraft in its area, for example), and as a function of perception and sensor system interaction. The model has been improved to include multiple world-states as a function of equipment am operator interaction. The model has been used -1o predict the impact of warning and alert zones in aircraft operation, and, more critic-ally, the interaction of flight-deck based warning mechanisms and air traffic controller action in response to ground-based conflict prediction and alerting systems. In this operation, two operating systems provide alerting to two autonomous, but linked sets of operators, whose view of the system and whose dynamics in response are radically different. System stability and operator action was predicted using the MIDAS model.

Corker, Kevin M.↗

NASA NTRS2008

Analysis of a Dynamic Multi-Track Airway Concept for Air Traffic Management

The Dynamic Multi-track Airways (DMA) Concept for Air Traffic Management (ATM) proposes a network of high-altitude airways constructed of multiple, closely spaced, parallel tracks designed to increase en-route capacity in high-demand airspace corridors. Segregated from non-airway operations, these multi-track airways establish high-priority traffic flow corridors along optimal routes between major terminal areas throughout the National Airspace System (NAS). Air traffic controllers transition aircraft equipped for DMA operations to DMA entry points, the aircraft use autonomous control of airspeed to fly the continuous-airspace airway and achieve an economic benefit, and controllers then transition the aircraft from the DMA exit to the terminal area. Aircraft authority within the DMA includes responsibility for spacing and/or separation from other DMA aircraft. The DMA controller is responsible for coordinating the entry and exit of traffic to and from the DMA and for traffic flow management (TFM), including adjusting DMA routing on a daily basis to account for predicted weather and wind patterns and re-routing DMAs in real time to accommodate unpredicted weather changes. However, the DMA controller is not responsible for monitoring the DMA for traffic separation. This report defines the mature state concept, explores its feasibility and performance, and identifies potential benefits. The report also discusses (a) an analysis of a single DMA, which was modeled within the NAS to assess capacity and determine the impact of a single DMA on regional sector loads and conflict potential; (b) a demand analysis, which was conducted to determine likely city-pair candidates for a nationwide DMA network and to determine the expected demand fraction; (c) two track configurations, which were modeled and analyzed for their operational characteristic; (d) software-prototype airborne capabilities developed for DMA operations research; (e) a feasibility analysis of key attributes in the concept design; (f) a near-term, transitional application of the DMA concept as a proving ground for new airborne technologies; and (g) conclusions. The analysis indicates that the operational feasibility of a national DMA network faces significant challenges, especially for interactions between DMAs and between DMA and non-DMA traffic. Provided these issues are resolved, sectors near DMAs could experience significant local capacity benefits.

Wing, David J.↗

DOE OSTI2024

Spinbox: tools for many-body quantum systems in a Monte Carlo context

Spinbox is a piece of software that facilitates quantum mechanical calculations relevant to Monte Carlo simulation of atomic nuclei. At the front lines of research on the nuclear many-body problem are a large number of supercomputer-scale simulation codes. These codes produce valuable results but can be hard to understand, especially for those without intimate knowledge of the relevant theoretical methods. Thus, tools that fill pedagogical roles are extremely valuable. Spinbox makes it easy for one to replicate and analyze the computational processes relevant to a Quantum Monte Carlo (QMC) simulation that may be difficult to understand/debug/analyze due to the scale of the corresponding simulation software. Spinbox is written in Python using other state-of-the-art Python modules for numerical calculations. While a number of Python libraries exist that are suited to general quantum many-body calculations, the motivation of Spinbox is quite particular. In Diffusion Monte Carlo methods (DMC, GFMC, AFDMC), the central calculation is the imaginary-time propagation of individual samples of the many-body wavefunction. Although quantum wavefunctions generally must be described by a probability distribution over a basis, DMC imbues particles (within one sample) with classical spatial coordinates. This method is unusual, so other Python packages are typically not set up to do this easily. Furthermore, the software has built-in options for nuclear systems assuming isospin symmetry, which can be set up with other libraries but is a nontrivial process to do so. Features: - numerical representation of samples of the many-body wavefunctions, including tensor-product states (used in AFDMC) - numerical representation of many-body operators, including tensor-product operators: general, spin, imaginary-time propagation, etc. - the correct associated arithmetic and algebra, implemented as class methods - classes for representing realistic nuclear two- and three-body Hamiltonians (e.g. Argonne V18, Illinois NNN) - large-scale parallel integration over random variables, crucial for the AFDMC method My goal is to make this package open source so that anyone may use it and contribute to it, particularly other researchers doing AFDMC calculations

Fox, Jordan↗

DOE OSTI2023

Photon Detection System for DUNE Low-Energy Physics Study and the Demonstration of a Timing Resolution of a Few Nanoseconds Using ProtoDUNE-SP PDS

Photon detection systems (PDS) are an integral part of liquid-argon neutrino detectors. Besides providing the timing information for an event, which is necessary for reconstructing the drift coordinates of ionizing particle tracks, photon detectors can be effectively used for other purposes, including triggering events, background rejection, and calorimetric energy estimation. PDS in particular for the DUNE Far Detector Module 2 is designed to achieve a more extended optical coverage (→4 ) with new-generation large-size PD modules based on the ARAPUCA technology. This will provide enhanced opportunities for the study of low-energy neutrino physics using PDS. The ARAPUCA technology was extensively tested within the ProtoDUNE-SP detector operated at the CERN neutrino platform. Here, we present a study of the timing resolution of ARAPUCA detectors using light emitted from a sample of energetic cosmic ray muons traveling parallel to the PDS. An intrinsic timing resolution in the order of 3 ns is observed for the ARAPUCA detectors. The excellent timing resolution ability of PDS can be exploited for further enhancing physics studies using the DUNE far detectors.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

LDRD conclusion poster - Synthesizing Heterometallic Uranium Single Crystals to Understand the Influence of the Secondary Metals on Uranyl Axial Bond Strength

Understanding how transition metals influenced the chemistry of lanthanide and actinide (f-element) materials is critical for advancing separation technologies, materials design, and coordination chemistry. This project examined how incorporating first-row transition metals affected the structural and spectroscopic properties of f-element coordination polymers. In uranium(VI)-based systems synthesized with 2,6-pyridinedicarboxylic acid (PDC) ligands, single-crystal X-ray diffraction and Raman spectroscopy revealed that the presence of transition metals shortened the uranyl axial bond and induced a blue shift in its symmetric stretching vibration—evidence of increased bond strength. Electronic structure analysis, including Density of States (DOS) calculations using density functional theory (DFT), revealed altered orbital overlaps and highlighted the role of transition metal d-orbitals in modulating bonding. Raman modes were modeled using truncated structural fragments in collaboration with the University of Notre Dame, and although the predicted frequencies were lower than experimental values, they remained within expected ranges. In parallel, similar experiments with cerium (Ce) in the presence of cobalt (Co) and PDC demonstrated multi-step single-crystal-to-single-crystal transformations—behavior not observed in the uranium systems. Initial products included light yellow, orange, and polycrystalline materials. Single-crystal X-ray diffraction studies, conducted in collaboration with the Colorado School of Mines, identified the yellow phase as monometallic Ce(PDC)2(H2O)2·4H2O and the orange phase as heterometallic Ce2Co(PDC)4(H2O)6. After standing in solution for one week, both phases fully transformed into a dark yellow crystalline phase, [Ce3(PDC)5(H2O)8].6(H2O). Remarkably, this transformation was reversible—disturbing the equilibrium by removing some crystals caused reversion to the initial Ce(PDC)2(H2O)2·4H2O phase, highlighting dynamic behavior. All three structures were previously unreported. Solid-state UV-visible and Raman spectroscopy further distinguished these phases, revealing ligand-to-metal charge transfer involving Ce and characteristic d–d transitions from Co(II). The precise mechanism driving these transformations remained unclear; however, pH-dependent experiments confirmed that the transformation did not occur when the pH decreased. Overall, the project demonstrated that transition metals could be employed to tune bonding interactions, structural dimensionality, and optical properties in f-element materials, establishing new pathways for designing functional heterometallic systems. The work resulted in several novel structural discoveries and fostered productive collaborations with the University of Notre Dame and the Colorado School of Mines.

37 - INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL C↗

NASA NTRS1989

Transputer parallel processing at NASA Lewis Research Center

The transputer parallel processing lab at NASA Lewis Research Center (LeRC) consists of 69 processors (transputers) that can be connected into various networks for use in general purpose concurrent processing applications. The main goal of the lab is to develop concurrent scientific and engineering application programs that will take advantage of the computational speed increases available on a parallel processor over the traditional sequential processor. Current research involves the development of basic programming tools. These tools will help standardize program interfaces to specific hardware by providing a set of common libraries for applications programmers. The thrust of the current effort is in developing a set of tools for graphics rendering/animation. The applications programmer currently has two options for on-screen plotting. One option can be used for static graphics displays and the other can be used for animated motion. The option for static display involves the use of 2-D graphics primitives that can be called from within an application program. These routines perform the standard 2-D geometric graphics operations in real-coordinate space as well as allowing multiple windows on a single screen.

Ellis, Graham K.↗

DOE OSTI2021

A Non-cooperative Game-based Approach to Distributed Beam Scheduling in Millimeter-Wave Networks

We consider the distributed beam scheduling problem in mm-Wave networks where the base stations may belong to different operators and there is no centralized coordination among them. Our goal is to design distributed beam scheduling algorithms such that the network utility, which is defined as a logarithm function of the average throughput of the user equipment, can be maximized. We propose a non-cooperative game-based scheduling approach where the base stations are modeled as players that greedily maximize their own utilities. The Nash Equilibrium (NE) then provides a distributed solution to the network utility maximization problem. By employing the Lyapunov optimization, the asymptotic optimality of the proposed scheduling can be guaranteed. We prove the existence and provide sufficient conditions which guarantee the uniqueness of the NE by establishing an equivalence to the Variational Inequality (VI) problem. We also propose a parallel power adaptation algorithm which is proved to converge to the NE. Numerical results show the superiority of the proposed scheduling over several distributed baseline schemes.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2021

Simulations of future particle accelerators: issues and mitigations

The ever increasing demands placed upon machine performance have resulted in the need for more comprehensive particle accelerator modeling. Computer simulations are key to the success of particle accelerators. Many aspects of particle accelerators rely on computer modeling at some point, sometimes requiring complex simulation tools and massively parallel supercomputing. Examples include the modeling of beams at extreme intensities and densities (toward the quantum degeneracy limit), and with ultra-fine control (down to the level of individual particles). In the future, adaptively tuned models might also be relied upon to provide beam measurements beyond the resolution of existing diagnostics. Much time and effort has been put into creating accelerator software tools, some of which are highly successful. However, there are also shortcomings such as the general inability of existing software to be easily modified to meet changing simulation needs. In this paper possible mitigating strategies are discussed for issues faced by the accelerator community as it endeavors to produce better and more comprehensive modeling tools. This includes lack of coordination between code developers, lack of standards to make codes portable and/or reusable, lack of documentation, among others.

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

Backbonding in Thorium(IV) and Uranium(IV) Diarsenido Complexes with t BuNC and CO

The coordination of tBuNC and CO with the diarsenido complexes (C 5 Me 5 ) 2 An(η 2 -As 2 Mes 2 ), An=Th, U, has been investigated. For the first time, a comparison between isostructural complexes of Th IV and U IV has been possible with CO; density functional calculations indicated an appreciable amount of π backbonding that originates from charge transfer from an actinide-arsenic sigma bond. The calculated CO stretching frequencies in the Th IV and U IV diarsenido complexes are consistent with the experimental measurements, both show large shifts to lower frequency. We demonstrate that the π backbonding is crucial to explaining the red shifts of CO frequency upon An IV complex formation. Interestingly, this interaction essentially correlates to the parallel orientation of π*(C-O) orbitals relative to the An-As bond.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

An E and B gyrokinetic simulation model for kinetic Alfvén waves in tokamak plasmas

The gyrokinetic particle simulation is a powerful tool for studies of transport, nonlinear phenomenon, and energetic particle physics in tokamak plasmas. While most gyrokinetic simulations make use of the scalar and vector potentials, a new model (GK-E&B) has been developed by using the E and B field in a general form and has been implemented in simulating kinetic Alfvén waves in uniform plasma. In our work, the Chen et al. GK-E&B model has been expressed, in general, tokamak geometry using the local orthogonal coordinates and general tokamak coordinates. Its reduction for uniform plasma is verified, and the numerical results show good agreement with the original work. The theoretical dispersion relation and numerical results in the local model in screw pinch geometry are also in excellent agreement. Numerical results show excellent performance in a realistic parameter regime of burning plasmas with high values of β/(M e k$^{2}_{⊥}$ρ$^{2}_{i}$), which is a challenge for traditional methods due to the “cancellation” problem. As one application, the GK-E&B model is implemented with kinetic electrons in the local single flux surface limit. With the matched International Tokamak Physics Activity-Toroidicity-induced Alfvén Eigenmodes parameters adopted, numerical results show the capability of the GK-E&B in treating the parallel electron Landau damping for realistic tokamak plasma parameters. As another application, the global GK-E&B model has been implemented with the dominant electron contribution in the cold electron limit. Its capability in simulating the finite E || due to the finite electron mass is demonstrated.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗