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NASA NTRS1995

A new criterion for bar-forming instability in rapidly rotating gaseous and stellar systems. 1: Axisymmetric form

We analyze previous results on the stability of uniformly and differentialy rotating, self-gravitating, gaseous and stellar, axisymmetric systems to derive a new stability criterion for the appearance of torodial, m = 2 intermediate or I-modes and bar modes. In the process, we demonstrate that the bar modes in stellar systems and the m = 2 I-modes in gaseous systems have many common physical characteristics and only one substantial difference: because of the anisotropy of the stress tensor, dynamical instability sets in at lower rotation in stellar systems. This difference is reflected also in the new stability criterion. The new stability parameter alpha equals (T(sub J))/(absolute value of W) is formulated first for uniformly rotating systems and is based on the angular momentum content rather than on the energy content of a system. (T(sub J) is defined as ((L)(Omega(sub J)))/2; L is the total angular momentum; Omega(sub J) is the Jeans frequency introduced by self-gravity; and W is the total gravitational potential energy.) For stability of stellar systems alpha less than or equal to 0.254-0.258 while alpha less than or equal to 0.341-0.354 for stability of gaseous systems. For uniform rotation, one can write alpha = ((ft)/2)(exp 1/2), where t is defined as T/(absolute value of W), T is the total kinetic energy due to rotation, and f is a function characteristic of the topology/connectedness and the geometric shape of a system. Equivalently, alpha equals t/(chi), where chi is defined as Omega/Omega(sub J) and Omega is the rotation frequency. Using these forms, alpha can be extended to and calculated for a variety of differentially rotating, gaseous and stellar, axisymmetric disk and spheroidal models whose equilibrium structures and stability characteristics are known. In this paper, we also estimate alpha for gaseous torodial models and for stellar disk systems embedded in an inert or responsive 'halo.' We find that the new stability criterion holds equally well for all these previously published axisymmetric models.

Christodoulou, Dimitris M.↗

DOE OSTI2024

Overview of recent turbulence studies across multiple confinement modes at the ASDEX Upgrade tokamak using the Correlation Electron Cyclotron Emission diagnostic

This work presents an overview of recent and ongoing experimental measurements of core and edge turbulence across multiple confinement regimes using the Correlation Electron Cyclotron Emission (CECE) diagnostic at the ASDEX Upgrade (AUG) tokamak. A common goal among these investigations is to identify how the properties of the turbulent electron temperature fluctuations measured by CECE influence and regulate the unique transport characteristics of each confinement regime, including L-mode, I-mode, ELMy H-mode, and ELM-free H-mode. Optics and signal processing methods to aid in the analysis and interpretation of experimental turbulence results are also presented. These methods, and particularly the down-sampling and ensemble averaging method, are relevant to a wide variety of fusion and non-fusion applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Plasma performance and operational space without ELMs in DIII-D

A database of DIII-D plasmas without ELMs compares the operating space and plasma performance of stationary no-ELM regimes: RMP-ELM suppression, QH-mode, I-mode, EDA H-mode, L-mode, and negative triangularity L-mode (Neg-D). Here, operational space is documented in terms of engineering and physics parameters, revealing divergent constraints. Some operational space discriminants (like pedestal collisionality) are well known, while others, such as low torque & safety factor, or high power & density, are less commonly emphasized. Normalized performance (H-factor and betan) also discriminate the no-ELM regimes and favor regimes tolerant to power in DIII-D: RMP, QH, and Neg-D.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Statistical inference of anomalous thermal transport with uncertainty quantification for interpretive 2D SOL models

The critical task of inferring anomalous cross-field transport coefficients is addressed in simulations of boundary plasmas with fluid models. A workflow for parameter inference in the UEDGE fluid code is developed using Bayesian optimization with parallelized sampling and integrated uncertainty quantification. In this workflow, transport coefficients are inferred by maximizing their posterior probability distribution, which is generally multidimensional and non-Gaussian. Uncertainty quantification is integrated throughout the optimization within the Bayesian framework that combines diagnostic uncertainties and model limitations. As a concrete example, we infer the anomalous electron thermal diffusivity $\chi_\perp$ from an interpretive 2D model describing electron heat transport in the conduction-limited region with radiative power loss. The workflow is first benchmarked against synthetic data and then tested on H-, L-, and I-mode discharges to match their midplane temperature and divertor heat flux profiles. We demonstrate that the workflow efficiently infers diffusivity and its associated uncertainty, generating 2D profiles that match 1D measurements. Future efforts will focus on incorporating more complicated fluid models and analyzing transport coefficients inferred from a large database of experimental results.

Bayesian optimization↗

DOE OSTI2020

Inference of experimental radial impurity transport on Alcator C-Mod: Bayesian parameter estimation and model selection

We present a fully Bayesian approach for the inference of radial profiles of impurity transport coefficients and compare its results to neoclassical, gyrofluid and gyrokinetic modeling. Using nested sampling, the Bayesian Impurity Transport InferencE (BITE) framework can handle complex parameter spaces with multiple possible solutions, offering great advantages in interpretative power and reliability with respect to previously demonstrated methods. BITE employs a forward model based on the pySTRAHL package, built on the success of the well-known STRAHL code [Dux, IPP Report, 2004], to simulate impurity transport in magnetically-confined plasmas. In this paper, we focus on calcium (Ca, Z=20) Laser Blow-Off injections into Alcator C-Mod plasmas. Multiple Ca atomic lines are diagnosed via high-resolution X-ray Imaging Crystal Spectroscopy and Vacuum Ultra-Violet measurements. We analyze a sawtoothing I-mode discharge for which neoclassical and turbulent (quasilinear and nonlinear) predictions are also obtained. Here, we find good agreement in diffusion across the entire radial extent, while turbulent convection and density profile peaking are estimated to be larger in experiment than suggested by theory. Efforts and challenges associated with the inference of experimental pedestal impurity transport are discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Dimensionless parameter scaling of intrinsic torque in C-Mod enhanced confinement plasmas

A dimensionless parameter dependence study of intrinsic torque has been performed on a database of H- and I-mode plasmas from the Alcator C-Mod tokamak. Here, the torque was determined by comparing intrinsic angular momentum density profiles just before and just after L–H and L–I transitions. The intrinsic torque has been found to scale as ${\beta }_{N}^{ 1.5}\enspace {\rho }_{{\ast}}^{-1.0}\enspace {\nu }_{{\ast}}^{0.1}$, with the parameter ranges 0.3 $\leqslant$ β N $\leqslant$ 1.5, 0.004 $\leqslant$ ρ* $\leqslant$ 0.011 and 0.04 $\leqslant$ ν * $\leqslant$ 0.9. Comparison with results from JET and DIII-D suggests that the intrinsic torque should be normalized by some measure of the device size. Depending upon this normalization, the estimated total intrinsic torques for ITER, SPARC and ARC are ~20, ~4 and ~8 Nm, respectively.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Experimental inference of neutral and impurity transport in Alcator C-Mod using high-resolution x-ray and ultra-violet spectra

We present experimental inferences of cross-field impurity transport coefficients for AlcatorC-Mod plasmas without edge-localized modes, leveraging a novel forward model for the entire Ca Kα spectrum, including satellite lines within the spectral range, to compare to high-resolution x-ray imaging crystal spectroscopy (XICS). These measurements are complemented by extreme ultra-violet (EUV) spectroscopy that constrains transport closer to the edge. Using new atomic data sets for both XICS and EUV analysis has enabled consideration of line ratios across both spectral ranges and has increased the accuracy of inferred transport coefficients. Inclusion of charge exchange between edge thermal neutrals and impurities is shown to be extremely important in C-Mod pedestals. Atomic D neutral densities from experimental D Lyα measurements at the midplane are compared to SOLPS-ITER simulations, finding good agreement. Bayesian inferences of impurity transport coefficients are presented for L-, EDA H-, and I-mode discharges, making use of the Aurora package for forward modeling and combining our spectroscopic constraints. Experimentally inferred diffusion profiles are found to match turbulent transport models at midradius within uncertainties, using both quasilinear gyro-fluid TGLF SAT-1 and nonlinear ion-scale gyrokinetic CGYRO simulations. Furthermore, significant discrepancies in convection are observed in some cases, suggesting difficulties in predictions of flat or hollow impurity profiles.

neutrals↗

DOE OSTI2022

Dependence of the boundary heat flux width on core and edge profiles in Alcator C-Mod

This work presents new evidence that the heat flux width, λ q , in the Alcator C-Mod tokamak scales with the edge electron pressure, as observed in the ASDEX Upgrade (AUG) tokamak, but the scaling with volume-averaged pressure, $\bar{p}$, from the plasma stored energy, is a better predictor of λ q in Alcator C-Mod than the edge electron pressure. These previous studies, which find that λ q decreases with increasing plasma pressure, imply that a high performance core at high pressure will lead to challenging heat and particle exhaust due to very small λ q . This concern has led to our significant enlargement of the C-Mod database with the electron density, temperature, and pressure profile data from the Thomson scattering and electron cyclotron emission diagnostics. Using the C-Mod database augmented with new profile data, we find that λ q decreases with increasing edge electron pressure as ${\lambda }_{q}\propto {p}_{\mathrm{e},95}^{-0.26}$, similar to results from AUG, and showing the strength of cross-machine comparisons. We also find that ${\lambda }_{q}\propto {p}_{\mathrm{e},\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}}^{-0.56}$, consistent with the original finding from C-Mod that the heat flux width scales as ${\bar{p}}^{-0.48}$. The scalings of λ q with separatrix pressure and gradient scale length are found to match the AUG results qualitatively. The C-Mod scalings with edge plasma quantities have more scatter than the $\bar{p}$ scaling, and, importantly, show different trends for H-modes relative to L- and I-mode. Furthermore, investigating the source of this discrepancy presents an opportunity for further study that may improve our ability to predict the heat flux width in different confinement scenarios in the pursuit of optimizing core-edge performance in future reactors.

Alcator C-Mod↗

DOE OSTI2023

Comparison of core Ar 17+ and Mo 32+ toroidal rotation in C-Mod plasmas

Abstract Core ( r / a < 0.5) toroidal rotation from argon (Ar 17+ , 40 AMU) and molybdenum (Mo 32+ , 96 AMU) ions has been compared in C-Mod tokamak plasmas over a wide range of operating conditions and confinement schemes, including Ohmic L-mode in the linear and saturated regimes, ion cyclotron range of frequencies heated I-mode and H-mode, as well as in discharges with induced locked modes and with external current and rotation drive. In all cases the velocities of the two impurities are identical within about 5%, for a range between −60 and +80 km s −1 . This is in general agreement with the predictions of neo-classical theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Edge radiated temperature fluctuations across confinement regime transitions in favorable and unfavorable drift configurations at ASDEX Upgrade

Abstract The physics behind the difference in heating power threshold for the low to high confinement (L–H) transition between favorable ion B × ∇ B drift (toward active X -point) and unfavorable ion B × ∇ B drift (away from active X -point) magnetic configurations is a longstanding open question. In this work we show differences in edge ( ρ p o l = 0.95 –1.0) turbulence in matched heating power favorable and unfavorable magnetic configuration discharges using a correlation electron cyclotron emission diagnostic to measure radiated temperature ( T r a d ) fluctuations. During power matched L-mode phases, the edge T r a d fluctuations have higher amplitude in the unfavorable configuration plasma as compared to the favorable configuration plasma. The lower fluctuation amplitude in favorable configuration is observed concomitant with increased E × B shear, as compared to the unfavorable case. Although this turbulence is different in amplitude, it is similar in radial and frequency structure between favorable and unfavorable configurations and grows to the weakly coherent mode during the I-mode phase of the unfavorable configuration discharge. A broadband pedestal fluctuation is seen during an inter-ELM H-mode period of the favorable configuration discharge.

Physics↗

DOE OSTI2025

Determination of confinement regime boundaries via separatrix parameters on Alcator C-Mod based on a model for interchange-drift-Alfvén turbulence

The separatrix operational space (SepOS) model (Eich and Manz 2021 Nucl. Fusion 61 086017) is shown to predict the L–H transition, the L-mode density limit, and the ideal magnetohydrodynamic ballooning limit in terms of separatrix parameters for a wide range of Alcator C-Mod plasmas. The model is tested using Thomson scattering measurements across a wide range of operating conditions on C-Mod, spanning $\overline{n}_{\mathrm{e}}$ = 0.3–5.5 $\times 10^{20}\,$m −3 , $B_{\mathrm{t}} = 2.5$–8.0 T, and $B_{\mathrm{p}}$= 0.1–1.2 T. An empirical regression for the electron pressure gradient scale length, $\lambda_{{p}_{\mathrm{e}}}$, against a turbulence control parameter, $\alpha_{\mathrm{t}}$, and the poloidal fluid gyroradius, $\rho_{\mathrm{s,p}}$, is constructed for H-modes and found to require positive exponents for both regression parameters, indicating turbulence widening of near-scrape-off layer widths at high $\alpha_{\mathrm{t}}$ and an inverse scaling with $B_{\mathrm{p}}$, consistent with results on ASDEX Upgrade. The SepOS model is also tested in the unfavorable drift direction and found to apply well to all three boundaries, including the L–H transition as long as a correction to the Reynolds energy transfer term, $\alpha_\mathrm{RS} \lt 1$ is applied. I-modes typically exist in the unfavorable drift direction for values of $\alpha_{\mathrm{t}} \lesssim 0.3$. Finally, an experiment studying the transition between the Type-I ELMy and EDA H-mode is analyzed using the same framework. It is found that a recently identified boundary $\alpha_{\mathrm{t}} = 0.55$ at excludes most EDA H-modes but that the balance of wavenumbers responsible for the L-mode density limit, namely $k_\mathrm{EM} = k_\mathrm{RBM}$, may better describe the transition on C-Mod. The ensemble of boundaries validated and explored is then applied to project regime access and limit avoidance for the SPARC primary reference discharge parameters.

ELM suppression↗

DOE OSTI2021

Impurity screening behavior of the high-field side scrape-off layer in near-double-null configurations: prospect for mitigating plasma-material interactions on RF actuators and first-wall components

The impurity screening response of the high-field side (HFS) scrape-off layer (SOL) to localized nitrogen injection is investigated on Alcator C-Mod for magnetic equilibria spanning lower-single null, double-null and upper single null configurations under otherwise identical plasma conditions. L-mode, EDA H-mode and I-mode discharges are investigated. HFS impurity screening is found to depend on magnetic flux balance and the direction of B×?B relative to the most active divertor. Impurity ‘plume’ emission patterns indicate that both parallel and perpendicular (E×B) flows in the SOL contribute to the ‘flushing’ of impurities towards the active divertor, thereby affecting the overall impurity screening behavior. Despite the fact that the HFS scrape-off layer is extremely narrow in near-double-null configurations, this SOL is able to screen locally injected nitrogen at least as effectively as the low-field side (LFS) SOL – up to a factor of 10 more effective, depending on specific plasma conditions and whether the magnetic geometry produces parallel flows that work with or against E×B flows. For situations in which the E×B drift of the impurity ions opposes parallel flow toward the primary divertor, HFS impurity screening is found to be least effective. When E×B drifts assist parallel flow toward the primary divertor, HFS impurity screening is found to be very effective. These data support the idea of placing RF actuators and close-fitting wall components on the high-field side of the tokamak. With this configuration, near-double-null magnetic topologies may be used for active control of plasma parameters at the antenna/plasma interface for optimal RF coupling, mitigate the generation of local impurities from plasma-material interactions and, taking advantage of favorable plasma flows and good screening properties of the HFS SOL, further minimize the impact of wall-born impurity sources on the plasma core.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Dimensionless Parameter Scaling of Intrinsic Torque in C-Mod Enhanced Confinement Plasmas

A dimensionless parameter dependence study of intrinsic torque has been performed on a database of H- and I-mode plasmas from the Alcator C-Mod tokamak. The torque was determined by comparing intrinsic angular momentum density profiles just before and just after L-H and L-I transitions. The intrinsic torque has been found to scale as beta_N^1.5 rho_*^-1.0 nu_$^0.1, with the parameter ranges 0.3 < beta_N <1.5, 0.004 < rho_* < 0.011 and 0.04 < nu_* < 0.9. Comparison with results from other tokamaks suggests that the intrinsic torque should be normalized by some measure of the device size.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Inference of Experimental Radial Impurity Transport on Alcator C-Mod: Bayesian Parameter Estimation and Model Selection.

We present a fully Bayesian approach for the inference of radial profiles of impurity transport coefficients and compare its results to neoclassical, gyrofluid and gyrokinetic modeling. Using nested sampling, the Bayesian Impurity Transport InferencE (BITE) framework can handle complex parameter spaces with multiple possible solutions, offering great advantages in interpretative power and reliability with respect to previously demonstrated methods. BITE employs a forward model based on the pySTRAHL package, built on the success of the well-known STRAHL code [Dux, IPP Report, 2004], to simulate impurity transport in magnetically-confined plasmas. In this paper, we focus on calcium (Ca, Z=20) Laser Blow-Off injections into Alcator C-Mod plasmas. Multiple Ca atomic lines are diagnosed via high-resolution X-ray Imaging Crystal Spectroscopy and Vacuum Ultra-Violet measurements. We analyze a sawtoothing I-mode discharge for which neoclassical and turbulent (quasilinear and nonlinear) predictions are also obtained. We find good agreement in diffusion across the entire radial extent, while turbulent convection and density profile peaking are estimated to be larger in experiment than suggested by theory. Efforts and challenges associated with the inference of experimental pedestal impurity transport are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1990

Subcritical crack growth in soda-lime glass in combined mode I and mode II loading

Subcritical crack growth under mixed-mode loading was studied in soda-lime glass. Pure mode I, combined mode I and mode II, and pure mode II loadings were achieved in precracked disk specimens by loading in diametral compression at selected angles with respect to the symmetric radial crack. Crack growth was monitored by measuring the resistance changes in a microcircuit grid consisting of parallel, electrically conducting grid lines deposited on the surface of the disk specimens by photolithography. Subcritical crack growth rates in pure mode I, pure mode II, and combined mode I and mode II loading could be described by an exponential relationship between crack growth rate and an effective crack driving force derived from a mode I-mode II fracture toughness envelope. The effective crack driving force was based on an empirical representation of the noncoplanar strain energy release rate. Stress intensities for kinked cracks were assessed using the method of caustics and an initial decrease and a subsequent increase in the subcritical crack growth rates of kinked cracks were shown to correlate with the variations of the mode I and the mode II stress intensities.

Singh, Dileep↗

NASA NTRS1993

Combined mode I and mode II fracture of monolithic ceramics

The mode I, mode II, and combined mode I-mode II fracture behaviors of a coarse-grained silicon nitride, a fine-grained silicon nitride, and an alumina were investigated. These ceramics were fractured from two types of fracture initiating flaws: small surface flaws and large single edge precracks. The small surface flaws were introduced by Knoop indentation in flexural samples at various angles to the tensile stress direction and fractured in four-point bending. The samples with large precracks were fractured in the asymmetric four-point-bend geometry. The mixed-mode fracture toughness values obtained from the two flaw configurations were in good agreement with each other. All three ceramics displayed very similar mixed-mode fracture behavior, although their microstructures were not similar. Comparison of experimental data to mixed-mode fracture theories revealed that the minimum strain energy density theory best described the mixed-mode fracture behavior of all three ceramics.

Tikare, Veena↗

NASA NTRS2003

Combined Mode I and Mode II Fracture of Plasma-Sprayed Thermal Barrier Coatings at Ambient and Elevated Temperatures

The mode I, mode II, and combined mode I-mode II fracture behavior of ZrO2- 8wt%Y2O3 thermal barrier coatings was determined in asymmetric flexure loading at both ambient and elevated temperatures. Precracks were introduced in test specimens using the single-edge-v-notched beam (SEVNB) method incorporated with final diamond polishing to achieve sharp crack tips. A fracture envelope of KI versus KII was determined for the coating material at ambient and elevated temperatures. Propagation angles of fracture as a function of K(sub I)/K(sub II) were also determined. The mixed-mode fracture behaviors of the coating material were compared with those of monolithic advanced ceramics determined previously. The mixed-mode fracture behavior of the plasma-sprayed thermal barrier coating material was predicted in terms of fracture envelope and propagation angle using mixed-mode fracture theories.

Choi, Sung R.↗

NASA NTRS2004

Sintering and Fracture Behavior of Plasma-sprayed Thermal Barrier Coatings

Thermal barrier coatings will be more aggressively designed to protect gas turbine engine hot-section components in order to meet future engine higher fuel efficiency and lower emission goals. There is a need to characterize the fundamental sintering and fracture behavior of the current ZrO2-(7 to 8)wt%Y2O3 coating, in order to fully take advantage of the coating capability. In addition, a thorough evaluation of the coating behavior and temperature limits will be useful for more accurately assessing the benefit gained from future advanced coating systems. In this study, the sintering behavior of plasma-sprayed ZrO2-8wt%Y2O3 coatings was systematically investigated as a function of temperature and time using a dilatometer in the temperature range of 1200-1500 C. The coating sintering kinetics obtained by dilatometry were compared with the coating thermal conductivity increase kinetics, determined by a steady-state laser heat-flux testing approach, under high temperature and thermal gradient sintering conditions. The mode I, mode II, and mixed mode I-mode II fracture behavior of as-processed and sintering-annealed coatings was determined in asymmetric flexure loading at ambient and elevated temperatures in order to evaluate the coating sintering effects on the fracture envelope of K(sub I) versus K(sub II). The coating thermal conductivity cyclic response associated with the interface delamination of the coating systems under simulated engine heat-flux conditions will be discussed in conjunction with the sintering and fracture testing results.

Zhu, Dongming↗