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At least 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Dissociative Recombination of Cold HeH + Ions

The HeH + cation is the simplest molecular prototype of the indirect dissociative recombination (DR) process that proceeds through electron capture into Rydberg states of the corresponding neutral molecule. This Letter develops the first application of our recently developed energy-dependent frame transformation theory to the indirect DR processes. The theoretical model is based on the multichannel quantum-defect theory with the vibrational basis states computed using exterior complex scaling of the nuclear Hamiltonian. The ab initio electronic R-matrix theory is adopted to compute quantum defects as functions of the collision energy and of the internuclear distance. The resulting DR rates are convolved over the beam energy distributions relevant to a recent experiment at the Cryogenic Storage Ring, giving good agreement between the experiment and the theory.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Hydroxyl radical yields in the heavy ion radiolysis of water

Scavenging experiments coupled with Monte Carlo track structure and kinetics simulations have been used to determining and understand the yields of hydroxyl radicals in the radiolysis of water with protons and carbon ions. Carbon dioxide production from aerated formic acid solutions with concentrations ranging from 10-3 to 1 mol./dm3 was used as a probe of the time dependence of the hydroxyl radical yield from about 5 ns to 1 ?s. Numerical extrapolation of the results at slightly different ion energies in combination with data from gamma radiolysis experiments allows a systematic analysis of both track average and track segment yields, with considerable track chemistry found to occur on the nanosecond to microsecond time scale. Track chemistry calculations utilizing Monte Carlo track structure simulations and nonhomogeneous independent reaction times diffusion-reaction modeling of product yields reproduce experimental observations. Subsequently, the track simulation methods were used to predict hydroxyl radical kinetics in deaerated and aerated water at neutral pH. Taken with literature data for helium ion beam studies, the results offer insight into the potential for indirect radiation induced damage to biological systems for light ions with very different track structures.

38 - RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCL↗
DOE OSTI2023

Multiple and nonlocal cation redox in Ca–Ce–Ti–Mn oxide perovskites for solar thermochemical applications

Modeling-driven design of redox-active off-stoichiometric oxides for solar thermochemical H 2 production (STCH) seldom has resulted in empirical demonstration of competitive materials. Here, we report the theoretical prediction and experimental evidence that the perovskite Ca 2/3 Ce 1/3 Ti 1/3 Mn 2/3 O 3 is synthesizable with high phase purity, stable, and has desirable redox thermodynamics for STCH, with a predicted average neutral oxygen vacancy (VO) formation energy, E v = 3.30 eV. Flow reactor experiments suggest potentially comparable or greater H 2 production capacity than recent promising Sr–La–Mn–Al and Ba–Ce–Mn metal oxide perovskites. Utilizing quantum-based modeling of a solid solution on both A and B sub-lattices, we predict the impact of nearest-neighbor composition on E v and determine that A-site Ce 4+ reduction dominates the redox-activity of Ca 2/3 Ce 1/3 Ti 1/3 Mn 2/3 O 3 . X-ray absorption spectroscopy measurements provide evidence that supports these predictions and reversible Ce 4+ -to-Ce 3+ reduction. Our models predict that Ce 4+ reduces even when it is not nearest-neighbor to the V O , suggesting that refinement of Ce stoichiometry has the possibility of further enhancing performance.

08 HYDROGEN↗
DOE OSTI2022

Corresponding Standard Reference Material Data used in Partial Least Squares Regression Models for Sugar Composition Estimates in Biomass in: Economic Impact of Yield and Composition Variation in Bioenergy Crops: Populus trichocarpa

Corresponding Standard Reference Material Data used in Partial Least Squares Regression Models for Sugar Composition Estimates in Biomass in: Economic Impact of Yield and Composition Variation in Bioenergy Crops: Populus trichocarpa (for corresponding manuscript: DOI: 10.1002/bbb.2148) PDF Files: Images of 1H NMR spectra for neutralized 2-stage acid hydrolysates of 4 NIST Standard Reference Material biomass samples (Monterey Pine 8493, Sugarcane Bagasse 8491, Wheat Straw 8494, and Eastern Cottonwood/Poplar 8492) and 2 Center for Bioenergy Innovation reference biomass samples (Poplar - Populus trichocarpa and Switchgrass - Panicum Virgatum). Suppression of the water peak was achieved using a NOESY-1D with presaturation, a recycle delay of 5 s, and a total of 64 scans. Spectra were acquired at 298 K and processed with automatic phase correction, baseline correction, and chemical shift referencing to TSP-d4. Images show all 1H data from 10 to 1ppm with inset spectra of region of interest (4.0 to 3.1 ppm). Text Files: Spectra for neutralized 2-stage acid hydrolysates of 4 NIST Standard Reference Material biomass samples (Monterey Pine 8493, Sugarcane Bagasse 8491, Wheat Straw 8494, and Eastern Cottonwood/Poplar 8492) and 2 Center for Bioenergy Innovation reference biomass samples (Poplar - Populus trichocarpa and Switchgrass - Panicum Virgatum) were converted into text files for plotting. Files contain 8192 points of raw spectral data from 12.23 to -2.78 ppm. The text file contains 4 columns of data and includes: Point number, Intensity, Hz, and ppm. Xcel Spreadsheet: HPLC measured monomeric sugar concentrations and bucketed 1H NMR data used to build monomeric sugar composition prediction models. Sugar composition in biomass determined from HPLC analyses are given in mg sugar/mg of biomass. Spectral bucketing was performed using Bruker’s AMIX software. Spectra were divided into 0.005 ppm buckets in the region of 3.10– 4.15 ppm for a total of 210 buckets. Headers for the bucketed data are the chemical shift in ppm of the center of the bucket. Bucketed data was used to build partial least squares models for subsequent predictions in The Unscrambler v. 10.5(CAMO A/S, Trondheim, Norway). The formation of methanol during hydrolysis interferes with the quantitative NMR analysis of sugars, so the methanol peak centered at 3.37 ppm and spanning four buckets (3.2925 – 3.2775 ppm) was set to zero for all spectra.

09 BIOMASS FUELS↗
DOE OSTI2021

The effect of hydrogen-bonding on flavin’s infrared absorption spectrum

Cluster and continuum solvation computational models are employed to model the effect of hydrogen bonding interactions on the vibrational modes of lumiflavin. Calculated spectra were compared to experimental Fourier-transform infrared (FTIR) spectra in the diagnostic 1450–1800 cm –1 range, where intense V C=C , V C=N , V C 2 =O , and V C 4 =O stretching modes of flavin’s isoalloxazine ring are found. Local mode analysis is used to describe the strength of hydrogen-bonding in cluster models. The computations indicate that V C=C and V C=N mode frequencies are relatively insensitive to intermolecular interactions while the V C 2 =O and V C 4 =O modes are sensitive to direct (and also indirect for V C 2 =O ) hydrogen-bonding interactions. Although flavin is neutral, basis sets without the diffuse functions provide incorrect relative frequencies and intensities. The 6-31+G* basis set is found to be adequate for this system, and there is limited benefit to considering larger basis sets. Calculated vibrational mode frequencies agree with experimentally determined frequencies in solution when cluster models with multiple water molecules are used. Accurate simulation of relative FTIR band intensities, on the other hand, requires a continuum (or possibly quantum mechanical/molecular mechanical) model that accounts for long-range electrostatic effects. Lastly, an experimental peak at ca. 1624 cm –1 that is typically assigned to the V C 2 =O vibrational stretching mode has a complicated shape that suggests multiple underlying contributions. Our calculations show that this band has contributions from both the C 6 –C 7 and C 2 = O stretching vibrations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Pulsed photoemission induced plasma breakdown

Abstract This article characterises the effects of cathode photoemission leading to electrical discharges in an argon gas. We perform breakdown experiments under pulsed laser illumination of a flat cathode and observe Townsend to glow discharge transitions. The breakdown process is recorded by high-speed imaging, and time-dependent voltage and current across the electrode gap are measured for different reduced electric fields and laser intensities. We employ a 0D transient discharge model to interpret the experimental measurements. The fitted values of transferred photoelectron charge are compared with calculations from a quantum model of photoemission. The breakdown voltage is found to be lower with photoemission than without. When the applied voltage is insufficient for ion-induced secondary electron emission to sustain the plasma, laser driven photoemission can still create a breakdown where a sheath (i.e. a region near the electrode surfaces consisting of positive ions and neutrals) is formed. This photoemission induced plasma persists and decays on a much longer time scale ( ∼ 10 s μ s) than the laser pulse length ( 30 ps). The effects of different applied voltages and laser energies on the breakdown voltage and current waveforms are investigated. The discharge model can accurately predict the measured breakdown voltage curves, despite the existence of discrepancy in quantitatively describing the transient discharge current and voltage waveforms.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Time-Dependent Boundary Modeling to Inform Design of SPARC Diagnostic and Actuators

The purpose of this work was to inform the design of diagnostic and actuator systems for a new experimental facility for Commonwealth Fusion Systems (CFS), called SPARC [Creely2020], using time-dependent plasma boundary simulations with the Scrape Off Layer Plasma Simulator (SOLPS) code [Wiesen2015]. The SPARC tokamak is a device that aims to demonstrate fusion energy production and high-field plasma operating scenarios. The developed technologies will be incorporated into a net-electricity pilot that will demonstrate approximately 200MW of electric power. A major difference from other private industry fusion companies is the use of a standard aspect ratio, but at a high magnetic field strength, which provides a well-established physics basis and a modest extrapolation to reactor operation. Time-dependent simulations were used to inform the design of main-chamber plasma facing components, which are protected by feedback control of the heat and particle loads during high power operation. The simulations provide the timescales and magnitudes of plasma and neutral particle response useful for determining the position and operation of diagnostics and actuators that will enable control. The plasma response and phase-space diagrams also provide input into advanced model-based control schemes, which are envisioned for later SPARC operation. Model-based control can reduce the risk of component failure, which would require expensive in-situ repairs and the associated delays, by predicting the system response to actuators over a short time-horizon.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Dual-Baseline Search for Active-to-Sterile Neutrino Oscillations in NOvA

We report a search for neutrino oscillations to sterile neutrinos under a model with three active and one sterile neutrinos (3+1 model). This analysis uses the NOvA detectors exposed to the NuMI beam, running in neutrino mode. The data exposure, 13.6 × 10 20 protons on target, doubles that previously analyzed by NOvA, and the analysis is the first to use 𝜈 𝜇 charged-current interactions in conjunction with neutral-current interactions. Neutrino samples in the near and far detectors are fitted simultaneously, enabling the search to be carried out over a Δ⁢𝑚$^{2}_{41}$ range extending 2 (3) orders of magnitude above (below) 1 eV 2 . NOvA finds no evidence for active-to-sterile neutrino oscillations under the 3+1 model at 90% confidence level. New limits are reported in multiple regions of parameter space, excluding some regions currently allowed by IceCube at 90% confidence level. We additionally set the most stringent limits for anomalous 𝜈 𝜏 appearance for Δ⁢𝑚$^{2}_{41}$ ≤ 3 eV 2 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

A theoretical model for sheath dynamics in the two-plasma mode of a cylindrical filament discharge

We present a refined understanding of cylindrical plasma-facing emitter cathodes by examining the limitations of the conventional space charge limited model, which overlooks ion trapping dynamics within the virtual cathode. While conventional theory distinguishes between temperature-limited and space charge limited regimes based on electron current constraints, our findings reveal that trapped ions can form a quasi-neutral “second plasma,” expanding upstream and interacting with the primary plasma. In cylindrical and other non-planar geometries, an expanding trapped-ions layer produces current enhancement by converting more of the emitted electron flux to passing flux. The current enhancement leads to a complex coupling between the trapped-ions plasma and upstream plasma through ionizing collisions in the upstream region and charge exchange collisions in the virtual cathode. The coupling results in mutual density enhancement and at the same time, antagonistic expansion dynamics between the two plasma layers. The process is understood using a new “aid-compete” model. Numerical solutions, validated against simulations, reveal the model's capacity to predict system evolution and complex discharge behaviors, albeit with qualitative approximations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Carbon‐Neutral Pathways for the United States

Abstract The Intergovernmental Panel on Climate Change (IPCC) Special Report on Global Warming of 1.5°C points to the need for carbon neutrality by mid‐century. Achieving this in the United States in only 30 years will be challenging, and practical pathways detailing the technologies, infrastructure, costs, and tradeoffs involved are needed. Modeling the entire U.S. energy and industrial system with new analysis tools that capture synergies not represented in sector‐specific or integrated assessment models, we created multiple pathways to net zero and net negative CO 2 emissions by 2050. They met all forecast U.S. energy needs at a net cost of 0.2–1.2% of GDP in 2050, using only commercial or near‐commercial technologies, and requiring no early retirement of existing infrastructure. Pathways with constraints on consumer behavior, land use, biomass use, and technology choices (e.g., no nuclear) met the target but at higher cost. All pathways employed four basic strategies: energy efficiency, decarbonized electricity, electrification, and carbon capture. Least‐cost pathways were based on >80% wind and solar electricity plus thermal generation for reliability. A 100% renewable primary energy system was feasible but had higher cost and land use. We found multiple feasible options for supplying low‐carbon fuels for non‐electrifiable end uses in industry, freight, and aviation, which were not required in bulk until after 2035. In the next decade, the actions required in all pathways were similar: expand renewable capacity 3.5 fold, retire coal, maintain existing gas generating capacity, and increase electric vehicle and heat pump sales to >50% of market share. This study provides a playbook for carbon neutrality policy with concrete near‐term priorities.

Williams, James H.↗
DOE OSTI2023

Significance of Energy Conservation in Coupled-Trajectory Approaches to Nonadiabatic Dynamics

Practical methods for simulating photo-induced dynamics of molecules often rely on a trajectory-description of the nuclear dynamics, incorporating approximate electron-nuclear feedback. Through approximating electron–nuclear correlation terms in the exact factorization approach, trajectory-based methods have been derived and successfully applied to the dynamics of a variety of light-induced molecular processes, capturing quantum (de)coherence effects rigorously. These terms account for the coupling among the trajectories, recovering the nonlocal nature of quantum nuclear dynamics that is completely overlooked in traditional independent-trajectory algorithms. Nevertheless, some of the approximations introduced in the derivation of some of these methods do not conserve the total energy. We analyze energy conservation in the coupled trajectory mixed quantum-classical (CTMQC) algorithm and explore the performance of a modified algorithm, CTMQC-E, where some of the terms are redefined to restore energy conservation. Here, a set of molecular models is used as a test, namely, 2-cis-penta-2,4-dienimium cation, bis(methylene) adamantyl radical cation, butatriene cation, uracil radical cation, and neutral pyrazine.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Performance prediction applying different reduced turbulence models to the SMART tokamak

The SMall Aspect Ratio Tokamak (SMART) is currently being commissioned at the University of Seville and will be able to compare the performance of positive and negative triangularity plasmas at low aspect ratio. Predictive simulations have been performed for different machine scenarios and heating schemes using the TRANSP code. The objectives of these simulations are to predict the parameters expected in positive triangularity plasmas, to guide diagnostic development, and to validate transport models. Several reduced turbulence models have been used to predict electron and ion temperatures for the operational phase 2. All models provide similar results from approximately mid-radius to the separatrix but important discrepancies are found in the core region. These positive triangularity results are compared with experiments from a similar size machine like GLOBUS-M2. The multi-mode model (MMM) shows the best agreement. Simulations with different boundary conditions have been performed and no strong differences have been observed between them. The impact of neutral beam injection (NBI) on the predicted profiles has also been addressed. Rotation reduces turbulence levels so higher temperatures are achieved when included in the simulations. Studying the different contributions to the thermal diffusivities, it is observed that electron temperature gradient (ETG) turbulence dominates at the plasma core while micro-tearing modes (MTM) dominate at the edge in the electron channel. In the ion channel, the neoclassical contribution is dominant at the core and at the very edge while the Weiland component, which includes ion temperature gradient mode (ITG), trapped electron mode (TEM), kinetic ballooning mode (KBM), peeling mode (PM) and collisionless and collision dominated magnetohydrodynamic (MHD) modes governs the mid-radius region. For phase 3, two plasmas with different electron densities have been studied. The case with lower density matches well a specific discharge of GLOBUS-M2. The higher density plasma shows high performance with β N ≈ 3.8.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Theory of In-Cloud Activation of Aerosols and Microphysical Quasi-Equilibrium in a Deep Updraft

The microphysical quasi-equilibrium in an ascending adiabatic parcel is elucidated by an analytical theory in 0D with drastic simplifications. The theory predicts how in-cloud activation is most likely to be triggered by the onset of precipitation during sufficient ascent, with the ascent only needing to approach almost twice the cloud-base updraft speed aloft. The precipitation and cloud condensate mass fields are coupled in a closed system in a simplified version of the model. The initial state of no precipitation is unstable with respect to a perturbation. In the 2D phase space of both mass fields, there is a neutral line. Unstable growth of precipitation mass drives the system to cross the line into a regime of stability. An attractor is then approached consisting of precipitation mass balanced by accretion of cloud mass and fallout. The cloud-particle number concentration also approaches a stable equilibrium governed by the balance between in-cloud activation aloft from the inexorably increasing supersaturation during vertical acceleration and accretion of cloud droplets by precipitation. Dimensionless numbers characterizing the microphysical equilibria and their stability are derived mathematically, including a condensation–precipitation efficiency and an in-cloud activation efficiency. The theory explains common observations of the orders of magnitude of liquid water content in convective and stratiform clouds. Finally, sensitivity tests of the numerically integrated theoretical equations are documented with respect to variations in cloud condensation nucleus (CCN) aerosols and updraft speed. In conclusion, it is shown that this theory of in-cloud activation, with an increasing supersaturation during ascent, applies to both ice-only and liquid-only cloud.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Green Methanol via an Integrated Direct Air Capture, CO 2 Electrolyzer, and Hydrogenation Reactor

This project pioneered a groundbreaking reactor design to produce green methanol by harnessing the electrochemical CO 2 reduction reaction (eCO 2 RR), a cornerstone of power-to-fuels technology. The effort integrated three innovative technologies to achieve carbon-neutral methanol production at a target cost of under $\$$800/ton: 1. Direct Air Capture (DAC): Using a cutting-edge sorbent material developed at Holocene, scalable models were developed to integrate captured atmospheric CO₂ into the reactor system. 2. Intermediate-Temperature CO 2 Electrolyzer: Developed by the University of Tennessee (UTK), this electrolyzer utilizes a cost-effective, proton-conducting solid acid electrolyte (CsH 2 PO 4 , CDP) and a mixed-metal oxide cathode. It achieves high faradaic efficiencies (>98%) by effectively suppressing hydrogen evolution at high current densities, converting CO 2 to CO with remarkable selectivity. 3. Catalysis and Reactor Engineering: Oak Ridge National Laboratory (ORNL) contributed world-class expertise in heterogeneous catalysis and reactor design. Their advanced ASPEN modeling drove systems integration and supported techno-economic and life cycle analyses. This effort was further bolstered by partnerships with industry leaders Air Company and Plug Power, who provided critical guidance on scaling, systems engineering, and the integration of water electrolyzers into large-scale operations. During Phase 1, the team focused on modeling and validating a lab-scale reactor demonstrating the feasibility of the integrated approach. Key accomplishments include a 52% increase in current density at 0.8 V while maintaining >98% CO faradaic efficiency, successful 10× scale-up of the electrolyzer with performance within 5% of coin-cell results, best-in-class durability (168-hour test at 0.6 V with 0.14 mA/cm 2 -h degradation), validated TEA confirming the $\$$800/ton methanol target, and completed preliminary LCA showing potential for net-negative GHG emissions under renewable energy scenarios.

10 SYNTHETIC FUELS↗
DOE OSTI2026

Building a Trusted Roaming Hub [Slides]

The Trusted Roaming Hub is a U.S. Department of Energy-backed initiative led by the National Laboratory of the Rockies (NLR) to address one of the most persistent challenges in electric vehicle (EV) charging: fragmented roaming, inconsistent interoperability, and insufficient digital trust across charging networks. As EV adoption accelerates and charging infrastructure scales nationwide, today's many-to-many integration model between eMobility Service Providers (eMSPs) and Charge Point Operators (CPOs) has become increasingly brittle, costly, and difficult to secure. The Trusted Roaming Hub introduces a neutral, cybersecurity-forward "switchboard" architecture that enables standardized, secure, and scalable roaming interactions across the EV charging ecosystem. Rather than replacing existing networks or commercial relationships, the hub acts as a trusted intermediary that enforces consistent identity, authentication, authorization, and routing across participants improving reliability for drivers, lowering integration burden for industry, and creating a foundation for future grid-interactive charging services. This read-ahead provides an overview of the problem the hub is designed to solve, the core functional and security concepts behind the architecture, the value proposition to key stakeholders, and the near-term trajectory of the work.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2021

Designed, highly expressing, thermostable dengue virus 2 envelope protein dimers elicit quaternary epitope antibodies

Dengue virus (DENV) is a worldwide health burden, and a safe vaccine is needed. Neutralizing antibodies bind to quaternary epitopes on DENV envelope (E) protein homodimers. However, recombinantly expressed soluble E proteins are monomers under vaccination conditions and do not present these quaternary epitopes, partly explaining their limited success as vaccine antigens. Using molecular modeling, we found DENV2 E protein mutations that induce dimerization at low concentrations (<100 pM) and enhance production yield by more than 50-fold. Cross-dimer epitope antibodies bind to the stabilized dimers, and a crystal structure resembles the wild-type (WT) E protein bound to a dimer epitope antibody. Mice immunized with the stabilized dimers developed antibodies that bind to E dimers and not monomers and elicited higher levels of DENV2-neutralizing antibodies compared to mice immunized with WT E antigen. Our findings demonstrate the feasibility of using structure-based design to produce subunit vaccines for dengue and other flaviviruses.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Examination of stiff ion temperature gradient mode physics in simulations of DIII-D H-mode transport

A systematic evaluation of gyrokinetic and gyrofluid model predictions of ion temperature gradient (ITG) stability and transport using parameters from DIII-D high confinement mode (H-mode) plasmas has been performed. The nonlinear CGYRO code is used to make the gyrokinetic predictions, and the quasilinear TGLF model for the corresponding gyrofluid predictions. The assessments are made at three radii (normalized toroidal flux ρtor = 0.4, 0.55, and 0.7) in three different plasma scenarios with varying levels of neutral beam heating and torque. For each of the nine cases (3 radii × 3 scenarios) considered, ITG turbulence is found to be the dominant long-wavelength instability and transport mechanism. The inclusions of both transverse magnetic fluctuations and dynamic fast beam ions are stabilizing for all cases considered, with strongest effects seen at ρor = 0.4 where the fast ion population and normalized plasma pressure β = 2μ0nT/B2 are highest. The further inclusion of parallel magnetic fluctuations does not have a meaningful impact on the ITG turbulence in these scenarios, but does destabilize (in combination with fast ions) new high-frequency instabilities at ρtor = 0.4 in the high power scenarios. In each case the linear and nonlinear ITG critical gradients are predicted to be lower than the measured ITG scale lengths and their associated uncertainties. Inclusion of equilibrium flow shear in the transport predictions generally leads to an upshift in effective critical gradient rather than a qualitative change in the predicted stiffness, with stronger responses typically seen in the gyrokinetic predictions than in the gyrofluid results. However, in most cases these upshifted gradients still remain below the measured values and their uncertainties. Although the predicted critical gradients are below the measured gradients, both models predicted flux-matching gradients consistent with measured values in six of the nine cases considered, with no clear systematic over- or underprediction. Thus, while the experimental ion temperature profiles do not appear to be closely pinned to the ITG critical gradient, both gyrokinetic and gyrofluid models are able to accurately match the measured gradients reasonably well in most cases.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗