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DOE OSTI2021

Ion-temperature-gradient stability near the magnetic axis of quasisymmetric stellarators

Abstract The stability of the ion-temperature gradient mode in quasisymmetric stellarators is assessed. This is performed using a set of analytical estimates together with linear gyrokinetic simulations. The peak growth rates, their corresponding real frequencies and wave-vectors are identified. A comparison is made between a first-order near-axis expansion model and eleven realistic designs obtained using numerical optimization methods. It is found that while the near-axis expansion is able to replicate the growth rates, real frequencies and perpendicular wave-vector at the inner core (both using simplified dispersion relations and first-principle gyrokinetic simulations), it leads to an overestimation of the growth rate at larger radii. An approximate analytic solution of the ITG dispersion relation for the non-resonant limit suggests growth rates could be systematically higher in quasi-axisymmetric (QA) configurations compared to quasi-helically (QH) symmetric ones. However except for very close to the axis, linear gyrokinetic simulations do not show systematic differences between QA and QH configurations.

Physics↗

DOE OSTI2017

The two-dimensional kinetic ballooning theory for ion temperature gradient mode in tokamak

The two-dimensional (2D) kinetic ballooning theory is developed for the ion temperature gradient mode in an up-down symmetric equilibrium (illustrated via concentric circular magnetic surfaces). The ballooning transform converts the basic 2D linear gyro-kinetic equation into two equations: (1) the lowest order equation (ballooning equation) is an integral equation essentially the same as that reported by Dong et al., [Phys. Fluids B 4, 1867 (1992)] but has an undetermined Floquet phase variable, (2) the higher order equation for the rapid phase envelope is an ordinary differential equation in the same form as the 2D ballooning theory in a fluid model [Xie et al., Phys. Plasmas 23, 042514 (2016)]. The system is numerically solved by an iterative approach to obtain the (phase independent) eigen-value. The new results are compared here to the two earlier theories. We find a strongly modified up-down asymmetric mode structure, and non-trivial modifications to the eigen-value.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Two-dimensional Thomson scattering measurements of misaligned electron density and temperature gradients and associated Biermann battery produced fields

We present optical Thomson scattering measurements of electron density and temperature in high Mach number laser-driven blast waves in homogeneous gases. Taylor–Sedov blast waves are launched in nitrogen (N2) or helium (He) at pressures between 0.4 mTorr and 10 Torr by ablating a solid plastic target with a high energy laser pulse (10 J, 1012 W/cm2). Experiments are performed at high repetition rate (1 Hz), which allows one-dimensional and two-dimensional Thomson scattering measurements over an area of several cm2 by automatically translating the scattering volume between shots. Electron temperature and density in the blast wave fronts were seen to increase with increasing background gas pressure. Measured electron density and temperature gradients were used to calculate ∂B/∂t∝∇Te×∇ne. The experimentally measured ∂B/∂t showed agreement with the magnetic field probe (B-dot) measurements, revealing that magnetic fields are generated in the observed blast waves via the Biermann battery effect. The results are compared to numerical three-dimensional collisional magnetohydrodynamic simulations performed with FLASH, and are discussed in the context of spontaneous magnetic field generation via the Biermann battery effect.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

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↗

DOE OSTI2015

Shear flow instabilities induced by trapped ion modes in collisionless temperature gradient turbulence

One important issue in turbulence self-organization is the interplay between the Kelvin–Helmholtz (KH) instability and streamers and/or zonal flows. This question has been debated for a long time. The effects of the KH instability and its position in the sequence of events between streamers, turbulence, and zonal flows have been investigated with a reduced gyro-bounce averaged kinetic code devoted to study the primary ion temperature gradient (ITG) instability linked to trapped ion modes (TIM). In toroidal geometry, the specific dynamics of TIM linked to trapped particles becomes important when the frequency of ITG modes falls below the ion bounce frequency, allowing one to average on both the cyclotron and bounce motion fast time scales. This reduction of the number of degrees of freedom leads to a strong reduction of computer resources (memory and computation time). Bounce-averaged gyrokinetic code can be considered as a toy model able to describe basic structures of turbulent transport in tokamak devices. In particular, by means of this code, we have observed that the energy injected in the system by the TIM instability is exchanged between streamers and zonal flows by means of KH vortices that grow along these structures in the nonlinear phase. The energy transfer occurs throughout the relaxation phase of the streamer growth leading to a modification of the KH modes and to the generation of the zonal flows.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Concentrating rare earth elements to phosphate in molten coal ash by a temperature gradient approach

Synthetic coal ash bearing 560 ppm europium oxide, blended with aluminum phosphate, was heat treated above its melting temperature and crystal evolutions with respect to europium concentration under controlled cooling were studied. The sample in a boat crucible was subjected to a temperature gradient of 100 °C across it to cause zone refining effects on crystallization behaviors in the melt (slag). Post analysis found six mineral phases formed from the melt while europium was only present in calcium phosphate, implying the majority of europium was segregated to the calcium phosphate. Europium concentrations in the calcium phosphate phase tended to be higher at zones with higher temperatures: as high as 7200 ppm, a 13-fold increase from the initial concentration.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2020

Comparative Analysis of Microbial Diversity Across Temperature Gradients in Hot Springs From Yellowstone and Iceland

Geothermal hot springs are a natural setting to study microbial adaptation to a wide range of temperatures reaching up to boiling. Temperature gradients lead to distinct microbial communities that inhabit their optimum niches. We sampled three alkaline, high temperature (80–100°C) hot springs in Yellowstone and Iceland that had cooling outflows and whose microbial communities had not been studied previously. The microbial composition in sediments and mats was determined by DNA sequencing of rRNA gene amplicons. Over three dozen phyla of Archaea and Bacteria were identified, representing over 1700 distinct organisms. We observed a significant non-linear reduction in the number of microbial taxa as the temperature increased from warm (38°C) to boiling. At high taxonomic levels, the community structure was similar between the Yellowstone and Iceland hot springs. We identified potential endemism at the genus level, especially in thermophilic phototrophs, which may have been potentially driven by distinct environmental conditions and dispersal limitations.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Effects of zonal flows on ion temperature gradient instability in the scrape-off layer of a field-reversed configuration

Gyrokinetic simulations of long wavelength ion temperature gradient (ITG) turbulence in the scrape-off layer (SOL) of a field-reversed configuration (FRC) find that zonal flows are nonlinearly generated and are the dominant mechanism for the nonlinear saturation of the ITG instability. After the ITG saturation, zonal flows remain undamped and gradually suppress the turbulent transport to a very low level. In the simulations with collisions, collisional damping gradually reduces zonal flow amplitude to a lower level, which allows finite ITG turbulence intensity and ion heat transport in the SOL. The steady state turbulence intensity and ion heat transport are found to be proportional to the collision frequency. Furthermore, this favorable scaling suggests that minimizing collisions (e.g. increasing temperature, reducing impurity content, etc) and preserving toroidal symmetry could improve plasma confinement in the FRC.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Electron temperature gradient instability and transport analysis in NSTX and NSTX-U plasmas

Extensive linear and nonlinear simulations to study electron temperature gradient (ETG) stability and thermal transport in National Spherical Torus Experiment (NSTX) and NSTX-U plasmas were performed using the fully electromagnetic gyrokinetic code CGYRO. Linear simulations were performed to determine ETG thresholds in different discharges, showing that ETG modes in spherical tokamaks can present different scalings compared to conventional aspect-ratio tokamaks. Nonlinear gyrokinetic simulations were conducted for selected cases to calculate electron thermal transport and compare to experimental values. Results are also compared with those of ETG modes in the multi-mode model and the Trapped-Gyro-Landau-Fluid reduced model codes, to better understand their applicability in spherical tokamaks.

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 OSTI2023

Global gyrokinetic simulations of the impact of magnetic island on ion temperature gradient driven turbulence

The effect of island width on the multi-scale interactions between magnetic island (MI) and ion temperature gradient (ITG) turbulence has been investigated based on the global gyrokinetic approach. It is found that the coupling between the island and turbulence is enhanced when the MI width (w) becomes larger. A vortex flow that is highly sensitive to the width of the MI can be triggered, ultimately resulting in a potent E × B shear flow and a consequent reduction in turbulent transport. The shearing rate induced by the vortex flow is minimum at the O-point while it is maximum at both of the two reconnection points of the island, i.e. the X-points, regardless of the island width. There exists a nonmonotonic relationship between zonal flow (ZF) amplitude and island width, showing that the ZF is partially suppressed by medium-sized MIs whereas enhanced in the case of large island. A larger MI can tremendously damage the ITG mode structure, resulting in higher turbulent transport at the X-point whereas a lower one at the O-point, respectively. Such phenomenon will be less distinct at very small island widths below w/a ~ 8% ≈ 12ρ i (a is the minor radius and ρ i the ion gyroradius), where it shows that turbulence near the X-point is hardly affected although it is still suppressed inside the island. Furthermore, the influence of different island sizes on turbulence transport level is also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Suppression of ion temperature gradient modes by Alfvén activity above a drive threshold in DIII-D

A recent study demonstrates that the suppression of ion temperature gradient (ITG) modes can occur during the nonlinear evolution of toroidicity-induced Alfvén eigenmodes (TAEs) in the DIII-D tokamak [Du et al., Phys. Rev. Lett. 135, 265101 (2025)]. In that work, ITG was suppressed by the formation of a narrow, TAE-induced shear flow layer, whose shearing rate exceeded the ITG decorrelation rate. Here, the shear flow arises from an imbalance between Reynolds and Maxwell stress forces, as the TAE departs from the conventional shear Alfvén wave polarization. This follow-up paper systematically identifies the plasma conditions required for robust ITG suppression through a series of comparative experiments. The results show that TAEs routinely suppress ITG turbulence in plasmas with higher local safety factor (q), elevated fast-ion beta, and larger populations of fast ions on passing orbits, i.e., conditions consistent with the substantial TAE drive. Database analysis further reveals the existence of a threshold in TAE drive for ITG suppression. That is, once the drive exceeds a critical value within a favorable q window, the system undergoes the nonlinear bifurcation process, characterized by a sharp increase in TAE saturated amplitudes at a nearly fixed fast ion drive, suppression of ITG turbulence, and the formation of an internal thermal transport barrier at the localized radii.

Du, X. D. [General Atomics, San Diego, CA (United ↗

DOE OSTI2020

Apparatus, methods and system for temperature gradient aging with in-situ electrical monitoring

An apparatus for making in-situ electrical measurements of a sample while the sample is subjected to a temperature gradient between a first side of the sample and a second side of the sample. The apparatus comprises a first heater and a second heater that are positioned in contact with the first side of the sample and the second side of the sample, respectively. The first heater and the second heater comprise respective faces that each have electrical contacts embedded therein. Electrical measurements pertaining to the sample can be made by way of the electrical contacts embedded in the faces. A temperature at either side of the sample can be monitored by way of thermocouples positioned inside the heaters in proximity to the faces of the heaters.

Reyes, Karla Rosa↗

DOE OSTI2023

On the effect of negative triangularity on ion temperature gradient turbulence in tokamaks

Considering the same magnetic equilibrium and plasma conditions as in Duff et al., we perform linear and nonlinear simulations of electrostatic ion temperature gradient turbulence investigating the role of triangularity δ. Differently from what was previously reported, we find that triangularity increases the transport level regardless of its sign, but more strongly when δ is positive. Here, for the case analyzed, we identify the shear of triangularity as the critical parameter determining the transport level, indicating that even in the local limit negative triangularity can reduce the transport efficiently, suggesting that confinement improvement can also be expected for larger devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2019

Ion temperature gradient turbulence modification in quasi-axisymmetry

The large flexibility of the proposed QUASAR facility is leveraged in order to explore the effect of magnetic shear on adiabatic Ion Temperature Gradient (ITG) turbulence. The QUASAR facility is a reimagining of the National Compact Stellarator Experiment utilizing and expanding upon the already constructed coil set. Recent work using fixed boundary optimization of the LI383 equilibrium (upon which QUASAR is based) has suggested possible improvements to ITG turbulence. In this work, a different approach is taken, wherein a series of self-consistent free boundary VMEC equilibria are developed for QUASAR. These equilibria assume temperature and density profiles consistent with 2% beta and ohmic current drive. In each configuration, the toroidal field coils are energized to different values and the STELLOPT code is used to vary the modular coil current and net toroidal current. The edge value of rotational transform is targeted in the optimization, producing a magnetic shear scan. All these configurations share similar neoclassical transport levels, while nonlinear GENE flux tube simulations show up to a factor of four change in adiabatic ITG turbulence at various radii. Comparisons of proxy functions and linear flux tube runs are also made. This work highlights the capability of the QUASAR experiment as a tool to explore transport in 3D magnetic fields and the possibility of the further improvements to stellarators through optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2018

Saturation scalings of toroidal ion temperature gradient turbulence

The emerging understanding of instability-driven plasma-turbulence saturation in terms of energy transfer to stable modes in the same scale range as the instability is employed to derive a saturation theory for the toroidal branch of ion temperature gradient turbulence that provides the scaling of turbulence and zonal flow levels for all physical parameters. The theory is based on the eigenmode decomposition of a nonlinear fluid model, which is subjected to a statistical closure and simplified via an ordering expansion consistent with zonal-flow catalyzed energy transfer from the unstable mode to the stable mode at large scale. Solution of the closed energy balance equations yields a turbulence level that is proportional to the ratio of the zonal flow damping rate and the inverse of the triplet correlation time of the zonal-flow catalyzed wavenumber triplet interaction. The zonal flow energy is proportional to the ratio of the growth rate and the inverse triplet correlation time. The saturation scalings are applied to the ion heat flux, showing that it has a factor proportional to the quasilinear heat flux and a correction factor that includes the inverse of the triplet correlation time and a reduction due to the stable mode.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Linear gyrokinetic simulations of reversed shear Alfvén eigenmodes and ion temperature gradient modes in DIII-D tokamak

Abstract Global linear gyrokinetic simulations using realistic DIII-D tokamak geometry and plasma profiles find co-existence of unstable reversed shear Alfvén eigenmodes (RSAE) with low toroidal mode number n and electromagnetic ion temperature gradient (ITG) instabilities with higher toroidal mode number n . For intermediate n = [10, 12], RSAE and ITG co-exist and overlap weakly in the radial domain with similar growth rates but different real frequencies. Both RSAE and ITG growth rates decrease less than 5% when compressible magnetic perturbations are neglected in the simulations. The ITG growth rates increase less than 7% when fast ions are not included in the simulations. Finally, the effects of trapped electrons on the RSAE are negligible.

Physics↗

DOE OSTI2021

Separate-Effects Tests for Studying Temperature-Gradient-Driven Cracking in UO 2 Pellets

We report a variety of normal operation and accident scenarios can generate thermal stresses large enough to cause cracking in light-water reactor (LWR) fuel pellets. Cracking of fuel pellets can lead to reduced heat removal, higher centerline temperatures, and localized stress in cladding, all of which impact fuel performance. It is important to experimentally characterize the thermal and mechanical behavior in the pellet before and after cracking to improve cracking models in fuel performance codes. However, in-reactor observation and measurement of cracking is very challenging due to the harsh environment and logistics. Recently, an experimental pellet cracking test stand was developed for separate effects testing of normal operations and accident temperature conditions, using thermal imaging to capture the pellet surface temperature for evaluation of thermal stresses and optical imaging to capture the evolution of cracking in real time. Experiments were performed using depleted uranium dioxide (UO 2 ) pellets, which are useful for collecting data valuable for development and validation of cracking models. A combination of induction and resistance heating was used to create an average temperature gradient of 236°C/cm and 193°C/cm before and after cracking respectively. Characterization of the pellets were done before as well as after cracking. The cracking patterns are somewhat different than those expected in a typical reactor because of the differences in thermal conditions and pellet microstructure. However, if the actual conditions of these experiments are reproduced in computational models, these out-of-pile tests on UO 2 pellets provide relevant data for modeling purposes.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗