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Investigation of linear gyrokinetic ion-scale modes ([Formula: see text]) finds that a transition from ion temperature gradient to microtearing mode (MTM) dominance occurs as the density is increased near the pedestal region of a parameterized DIII-D sized tokamak. H-modes profile densities, temperatures, and equilibria are parameterized utilizing the OMFIT PRO_create module. With these profiles, linear gyrokinetic ion-scale instabilities are predicted with CGYRO. This transition ( nMTM) has a weak dependence on radial location in the region near the top of the pedestal ([Formula: see text]), which allows simulating single radii to examine the approximate scaling of nMTM with global parameters. The critical nMTM is found to scale with plasma current. Additionally, increasing the minor radius by decreasing the aspect ratio and increasing the major radius are found to reduce nMTM. However, any relationship between nMTM and density limit physics remains unclear as nMTM increases relative to the Greenwald density with larger minor radius and with larger magnetic field, suggesting that the transport due to MTM may be less important for a reactor. Additionally, nMTM is sensitive to the pedestal temperature, the local electron and ion gradients, the ratio of ion to electron temperature [Formula: see text], and the current profile. MTMs are predicted to be the dominant instability in the core at similar Greenwald fractions for DIII-D, NSTX, and NSTX-U H-mode experiments, supporting the results of the parameterized study. Additionally, MTMs continue to be the dominant linear instability in a DIII-D L-mode after an H–L transition as the plasma approaches a density limit disruption despite the large change in plasma profiles.

The successful validation of theory-based models of transport, magnetohydrodynamic stability, heating and current drive, with tokamak measurements over the last 20 years, has laid the foundation for a new era where these models can be routinely used in a ‘predict first’ approach to design and predict the outcomes of experiments on tokamaks today. The capability to predict the plasma confinement and core profiles with a quantified uncertainty, based on a multi-machine, international, database of experience, will provide confidence that a proposed discharge will remain within the operational limits of the tokamak. Developing this predictive capability for the first generation of burning plasma devices, beginning with ITER, and progressing to tokamak demonstration reactors, is a critical mission of fusion energy research. Major advances have been made implementing this predict first methodology on today’s tokamaks. An overview of several of these recent advances will be presented, providing the integrated modeling foundations of the experimental successes. The first steps to include boundary plasmas, and tokamak control systems, have been made. A commitment to predicting experiments as part of the planning process is needed in order to collect predictive accuracy data and evolve the models and software into a robust whole discharge pulse design simulator.

New workflows have been developed for predictive modeling of magnetohydrodynamic (MHD) equilibrium in tokamak plasmas. The goal of this work is to predict the MHD equilibrium in tokamak discharges without having measurements of the kinetic profiles. The workflows include a cold start tool, which constructs all the profiles and power flows needed by transport codes; a Grad–Shafranov equilibrium solver; and various codes for the sources and sinks. For validation purposes, a database of DIII-D tokamak discharges has been constructed that is comprised of scans in the plasma current, toroidal magnetic field, and triangularity. Initial efforts focused on developing a workflow utilizing an empirically derived pressure model tuned to DIII-D discharges with monotonic safety factor profiles. This workflow shows good agreement with experimental kinetic equilibrium calculations, but is limited in that it is a single fluid (equal ion and electron temperatures) model and lacks H-mode pedestal predictions. The best agreement with the H-mode database is obtained using a theory-based workflow utilizing pressure profile predictions from a coupled TGLF turbulent transport and EPED pedestal models together with external magnetics and Motional Stark Effect (MSE) data to construct the equilibrium. Here, we obtain an average root mean square error of 5.1% in the safety factor profile when comparing the predicted and experimental kinetic equilibrium. We also find good agreement with the plasma stored energy, internal inductance, and pressure profiles. Including MSE data in the theory-based workflow results in noticeably improved agreement with the q-profiles in high triangularity discharges in comparison with the results obtained with magnetic data only. The predictive equilibrium workflow is expected to have wide applications in experimental planning, between-shot analysis, and reactor studies.

An integrated modeling workflow capable of finding the steady-state plasma solution with self-consistent core transport, pedestal structure, current profile, and plasma equilibrium physics has been developed and tested against a DIII-D discharge. Key features of the achieved core-pedestal coupled workflow are its ability to account for the transport of impurities in the plasma self-consistently, as well as its use of machine learning accelerated models for the pedestal structure and for the turbulent transport physics. Notably, the coupled workflow is implemented within the One Modeling Framework for Integrated Tasks (OMFIT) framework, and makes use of the ITER integrated modeling and analysis suite data structure for exchanging data among the physics codes that are involved in the simulations. Such technical advance has been facilitated by the development of a new numerical library named ordered multidimensional arrays structure.

Dedicated electron heat transport experiments have been carried out in L- and H-mode Deuterium plasmas of the JET-ILWtokamak to identify the amount of electron heat carried by electron-scale electron temperature gradient (ETG) modes. Ion cyclotron resonance heating at different positions has been used to probe the response of the electron temperature inverse gradient length R/LTe to changes in electron heat flux qe, while different amounts of neutral beam heating allowed to scan the ratio of ion to electron temperature Te/Ti, which is a key parameter for the onset of ETGs. Results indicate a steepening of the normalized qe vs R/LTe curve above R/LTe ~ 8 for Te/Ti _ 1, suggestive of the ETG onset. Ion-scale gyro-kinetic (GK) simulations match the ion heat flux and the low-R/LTe part of the qe curve, but do not reproduce such steepening at high R/LTe. Multi-scale GK simulations covering both ion and electron scales and including one impurity bundling light and heavy species indicate an ETG contribution only for R/LTe values larger than the experimental ones. Sensitivity studies of such result are difficult to achieve due to limitation in numerical resources. The quasi-linear TGLF model has been used for sensitivity studies. With the same bundled impurity as the GK multi-scale, TGLF shows the qe steepening at much larger R/LTe values than in experiment, but when using the real mix of light impurities neglecting the heavy impurities, TGLF gets closer to the experimental results. Profile simulations with TGLF including both light and heavy impurities show over-prediction of Te profiles and in some cases also of density, but good Ti predictions, confirming issues with the model electron stiffness for these plasmas EURATOM 2021.

We review progress made on the advanced tokamak path to fusion energy by the DIII-D National Fusion Facility (Luxon et al. in Nucl Fusion 42:614, 2002). The advanced tokamak represents a highly attractive approach for a future steady state fusion power plant. In this concept, there is a natural alignment between high pressure operation, favorable stability and transport properties, and a highly self-driven (‘bootstrap’) plasma current to sustain operation efficiently and without disruptions. Research on DIII-D has identified several promising plasma configurations for fully non-inductive operation with potential applications to a range of future devices, from ITER to nuclear science facilities, to compact or large scale fusion power plants. Significant progress has been made toward realizing these scenarios, with the demonstration of high β access, off-axis current drive techniques, model based profile control, and stability and ELM control in reactor relevant physics regimes. Radiative techniques have also been pioneered to develop improved compatibility with divertor requirements, and simultaneous access to high performance pedestals. Research has also developed major advances in physics understanding, validating concepts of kinetic damping of ideal MHD instabilities that enable high β operation, identifying how current profile and β influence plasma turbulence in order to validate and improve turbulent transport models, and understanding the physics of energetic particle redistribution due to Alfvenic and other instabilities. These advances have been partnered with development of a rigorous integrated modeling framework used to interpret and validate individual physics models of the various aspects of plasma behavior, and to guide development of improved regimes and upgrades. These tools are also being used to develop and validate concepts for future reactors directly. Having established these foundations, DIII-D is now undergoing a substantial upgrade to raise power, current drive, electron heating and 3-D field capabilities in order to validate this physics and test conceptual solutions in reactor-relevant physics regimes, with a goal to resolve the key scientific and technology questions to enable a decision on a future steady state fusion power plant.

The verification and calibration of a new quasi-linear transport model with a large database of gyrokinetic turbulence simulations is presented in this paper. In a previous paper \cite{staebler:2020}, a model for the saturated spectrum of electric potential fluctuations was developed based on the properties of the non-linear 3D spectrum. In this paper, a modification to the overall multiplicative factor in this model is found to be necessary to improve the fit to scans of the temperature and density gradients and safety factor. The error in the fit of the quasi-linear fluxes of electron and ion energy fluxes is significantly better than for previous saturation models. The spectral shift model for the impact of equilibrium $E\times B$ velocity shear \cite{staebler:2013a} and the zonal flow mixing model for electron-scale turbulence \cite{staebler:2016} are both revised to be compatible with this new model. The models for the loss of bounce averaging and electron collisions in the TGLF reduced linear equations \cite{staebler:2005} are also changed to improve the linear eigenmodes.

Perturbative transport experiments in magnetically confined plasmas have shown, for more than 20 years, that the injection of cold pulses at the plasma edge can trigger the increase of core temperature. Predictive heat transport simulations with the trapped gyro Landau fluid (TGLF) quasilinear transport model demonstrate that the increase of core temperature in some regimes, and lack thereof in other regimes, can be explained by a change in dominant linear micro-instability in Alcator C-Mod. The effect of density and plasma current on the cold pulse are well captured by TGLF, including the relative change in position of the temperature flex point as current density changes. Linear stability analysis of simulated density and current scans reveals a competition between trapped electron and ion temperature gradient modes as the main driver of the core transient response. These results further demonstrate that cold-pulse propagation and associated phenomenology in the cases studied are well explained within the local transport paradigm, without resorting to non-local effects.

DIII-D research is addressing critical challenges in preparation for ITER and the next generation of fusion devices through focusing on plasma physics fundamentals that underpin key fusion goals, understanding the interaction of disparate core and boundary plasma physics, and developing integrated scenarios for achieving high performance fusion regimes. Fundamental investigations into fusion energy science find that anomalous dissipation of runaway electrons (RE) that arise following a disruption is likely due to interactions with RE-driven kinetic instabilities, some of which have been directly observed, opening a new avenue for RE energy dissipation using naturally excited waves. Dimensionless parameter scaling of intrinsic rotation and gyrokinetic simulations give a predicted ITER rotation profile with significant turbulence stabilization. Coherence imaging spectroscopy confirms near sonic flow throughout the divertor towards the target, which may account for the convection-dominated parallel heat flux. Core-boundary integration studies show that the small angle slot divertor achieves detachment at lower density and extends plasma cooling across the divertor target plate, which is essential for controlling heat flux and erosion. The Super H-mode regime has been extended to high plasma current (2.0 MA) and density to achieve very high pedestal pressures (~30 kPa) and stored energy (3.2 MJ) with H 98y2 ≈ 1.6–2.4. In scenario work, the ITER baseline Q = 10 scenario with zero injected torque is found to have a fusion gain metric independent of current between q 95 = 2.8–3.7, and a lower limit of pedestal rotation for RMP ELM suppression has been found. In the wide pedestal QH-mode regime that exhibits improved performance and no ELMs, the start-up counter torque has been eliminated so that the entire discharge uses ≈0 injected torque and the operating space is more ITER-relevant. Finally, the high- (⩽3.8) hybrid scenario has been extended to the high-density levels necessary for radiating divertor operation, achieving ~40% divertor heat flux reduction using either argon or neon with P tot up to 15 MW.

A benchmark of the reduced quasi-linear models QuaLiKiz and TGLF with GENE gyrokinetic simulations has been performed for parameters corresponding to a JET high performance hybrid pulse in deuterium. Given the importance of the study of such advanced scenarios in view of ITER and DEMO operations, the dependence of the transport on the ion isotope mass has also been assessed, by repeating the benchmark changing the ion isotope to tritium. TGLF agrees better with GENE on the linear spectra and the flux levels. However, concerning the isotope dependence, only QuaLiKiz reproduces the GENE radial trend of a basically gyro-Bohm (gB) scaling at inner radii and instead anti-gB at outer radii. The physics effects which are responsible of the antigB effect in GENE simulations have been singled out.

Experimental and modeling investigations of high βp scenarios on DIII-D and EAST tokamaks show advantages in high energy confinement, avoidance of n = 1 MHD, and core-edge integration with reduced heat flux, making this scenario an attractive option for China Fusion Engineering Test Reactor steady-state operation. Experiments show that plasmas with high confinement and high density can be achieved with neutral beam injection on DIII-D (βp ∼ 2.2, βN ∼ 3.5, fBS ∼ 50%, fGw ∼ 1.0, and H98y2 ∼ 1.5) and pure RF power on EAST (βP ∼ 2.0, βN ∼ 1.6, fBS ∼ 50%, fGw ∼ 0.8, and H98y2 > 1.3). By tailoring the current density profile, a q-profile with local (off-axis) negative shear is achieved, which yields improved confinement and MHD stability. Transport analysis and simulation suggest that the combination of a high density gradient and high Shafranov shift allows turbulence stabilization and higher confinement. Using on-axis Electron Cyclotron Heating injection, tungsten accumulation is avoided on EAST, and this is reproduced in modeling. Reduced heat flux (by > 40%) and maintenance of high core confinement is achieved with active feedback control of the radiated divertor, an important result for long pulse operation in tokamaks. The improved physics understanding and validated modeling tools are used to design a 1 GW steady-state scenario for CFETR.

Excellent confinement has been routinely observed in DIII-D (J. L. Luxon, Nucl. Fusion 2002) high β p discharges, which are characterized by a strong large-radius internal transport barrier (ITB) in almost all kinetic channels. Typically, the ion thermal transport is neoclassical with conventional long-wavelength turbulence instabilities suppressed by α stabilization, while the mechanism for the anomalous electron thermal transport remains unclear [Garofalo et al., Nucl. Fusion 55(12), 123025 (2015)]. A new gyrokinetic analysis shows that while the large values of α in the ITB can stabilize all local electrostatic drift wave (ES-DW) instabilities as well as the kinetic ballooning mode, a new slab-like microtearing mode (MTM) with its eigenfunction mainly peaking on the high field slide is destabilized. This destabilization is shown to be more likely to happen in discharges with high safety factors. Nonlinear gyrokinetic simulations demonstrate that this MTM branch can reproduce the experimentally inferred electron thermal flux in the ITB region and, therefore, provide convincing evidence that the electron temperature profile in the ITB is regulated by the MTM. Extrapolations to the future scenarios, like ITER high β p plasmas, show that the dominant instability is likely to come back to ES-DW due to the lower density gradient and collisionality. However, even in this regime, some unusual features associated with MTMs predicted for DIII-D parameters, such as the high-field-side peaking and slab nature, may remain for the reactor ES-DW.

The findings of an investigation into the properties of the three dimensional (3D) saturated fluctuation intensity of the electric potential in gyrokinetic turbulence simulations is presented. Scans in flux surface elongation and Shafranov shift are used to isolate the tokamak geometric dependencies. The potential intensity required in order to compute exact fluxes by a quasilinear method is determined using linear eigenmodes computed with the gyrokinetic code. A model of this non-linear intensity is constructed using the linear eigenmode properties and the geometry shape functions obtained from the 3D intensity spectrum. The model computes the poloidal wavenumber spectrum of the electron and ion energy fluxes with unprecedented accuracy. New insights are gained into the way zonal flow mixing saturates ion-scale turbulence by controlling the radial wavenumber width of the turbulence spectrum.

On DIII-D, the high βp scenario has an internal transport barrier (ITB), βN~βp~3,q95~10, and very high normalized confinement H98,y2~1.6. Recently, plasmas starting with these conditions have been dynamically driven to q95~6 and βp~3, where we find the ITB and high performance persist for multiple energy confinement times. These conditions are projected to meet the ITER steady-state goal of Q= 5. The ITB is maintained at lower βp with a strong reverse shear, consistent with predictions that negative central shear can lower the βp threshold for the ITB. There are two observed confinement states in the highβp scenario: H-mode confinement state with a high edge pedestal, and an enhanced confinement state with a low pedestal and an ITB. It has been observed in a scan of external resonant magnetic perturbation amplitude that when there are no large type-I ELMs, there is no transition to enhanced confinement. This is consistent with the proposed mechanism for ITB formation being a type-I ELM. Quasilinear gyro-Landau fluid predictive modeling of ITER suggests that only a modest reverse shear is required to achieve the ITB formation necessary for Q=5 when electromagnetic physics including the kinetic ballooning mode (KBM) is incorporated.

Using a novel wavenumber-advection algorithm, we show that profile curvature (shear in the profile gradient) can be implemented with spectral accuracy in gyrokinetic turbulence simulations. This approach enables a global simulation capability with the relatively low cost and high accuracy of local simulations. Using this new algorithm, we show that for a well-studied tokamak core test case, the effect of temperature-gradient curvature is below the threshold of detectability for experimentally-relevant values of curvature.

Fusion performance in tokamaks depends on the core and edge regions as well as on their non-linear feedbacks. The achievable degree of edge confinement under the constraints of power handling in presence of a metallic wall is still an open question. Therefore, any improvement in the core temperature and density peaking is crucial for achieving target performance. This has motivated further progress in understanding core turbulent transport mechanisms, to help scenario development in present devices and improve predictive tools for ITER operations. In the last two decades, detailed experiments and their interpretation via the gyrokinetic theory of turbulent transport have led to a satisfactory level of understanding of the heat, particle, and momentum transport channels and of their mutual interactions. This paper presents some highlights of the progress, which stems from joint work of several devices and theory groups, in Europe and worldwide within the ITPA (International Tokamak Physics Activities) frame-work. On the other hand, the achievement of predictive capabilities of plasma profiles via integrated modeling, which also accounts for the nonlinear interactions inherent to the multi-channel nature of transport, is a priority in view of ITER. This requires using faster, reduced models, and the extent to which they capture the complex physics described by nonlinear gyrokinetics must be carefully evaluated. Present quasi-linear models match well experiments in baseline scenarios, and thus offer reliable predictions for the ITER reference scenario, but have issues in advanced scenarios. Some of these challenges are examined and discussed. In the longer term, advances in high performance computing will continue to drive physics discovery through increasingly complex gyrokinetic simulations, allowing also further development of reduced models. The development of neural network surrogate models is another recent advance that bridges the gap towards physics-based fast models for optimisation and control applications.

A long-standing enigma in plasma transport has been resolved by modeling of cold-pulse experiments conducted on the Alcator C-Mod tokamak. Controlled edge cooling of fusion plasmas triggers core electron heating on time scales faster than an energy confinement time, which has long been interpreted as strong evidence of nonlocal transport. This Letter shows that the steady-state profiles, the cold-pulse rise time, and disappearance at higher density as measured in these experiments are successfully captured by a recent local quasilinear turbulent transport model, demonstrating that the existence of nonlocal transport phenomena is not necessary for explaining the behavior and time scales of cold-pulse experiments in tokamak plasmas.

Experiments at the DIII-D tokamak have used dimensionless parameter scans to investigate the dependencies of intrinsic torque and momentum transport in order to inform a prediction of the rotation profile in ITER. Measurements of intrinsic torque profiles and momentum confinement time in dimensionless parameter scans of normalized gyroradius and collisionality are used to predict the amount of intrinsic rotation in the pedestal of ITER. Additional scans of Te/Ti and safety factor are used to determine the accuracy of momentum flux predictions of the quasi-linear gyrokinetic code TGLF. In these scans, applications of modulated torque are used to measure the incremental momentum diffusivity, and results are consistent with the E×B shear suppression of turbulent transport. These incremental transport measurements are also compared with the TGLF results. In order to form a prediction of the rotation profile for ITER, the pedestal prediction is used as a boundary condition to a simulation that uses TGLF to determine the transport in the core of the plasma. The predicted rotation is ≈20 krad/s in the core, lower than in many current tokamak operating scenarios. TGLF predictions show that this rotation is still significant enough to have a strong effect on confinement via E×B shear.

Intrinsic toroidal rotation of the deuterium main ions in the core of the DIII-D tokamak is observed to transition from flat to hollow, forming an off-axis peak, above a threshold level of direct electron heating. Nonlinear gyrokinetic simulations show that the residual stress associated with electrostatic ion temperature gradient turbulence possesses the correct radial location and stress structure to cause the observed hollow rotation profile. Residual stress momentum flux in the gyrokinetic simulations is balanced by turbulent momentum diffusion, with negligible contributions from turbulent pinch. The prediction of the velocity profile by integrating the momentum balance equation produces a rotation profile that qualitatively and quantitatively agrees with the measured main-ion profile, demonstrating that fluctuation-induced residual stress can drive the observed intrinsic velocity profile.

Fusion whole device modeling simulations require comprehensive models that are simultaneously physically accurate, fast, robust, and predictive. In this paper we describe the development of two neural-network (NN) based models as a means to perform a snon-linear multivariate regression of theory-based models for the core turbulent transport fluxes, and the pedestal structure. Specifically, we find that a NN-based approach can be used to consistently reproduce the results of the TGLF and EPED1 theory-based models over a broad range of plasma regimes, and with a computational speedup of several orders of magnitudes. These models are then integrated into a predictive workflow that allows prediction with self-consistent core-pedestal coupling of the kinetic profiles within the last closed flux surface of the plasma. The NN paradigm is capable of breaking the speed-accuracy trade-off that is expected of traditional numerical physics models, and can provide the missing link towards self-consistent coupled core-pedestal whole device modeling simulations that are physically accurate and yet take only seconds to run.

Cold pulses are introduced in Ohmic DIII-D tokamak plasmas via injection of impurities with a laser blow-off system, revealing for the first time in this machine a quick increase in core electron temperature shortly after the edge cold-pulse injection at low collisionality. The experimental results are consistent with predict-first simulations of heat transport enabled by the Trapped Gyro-Landau-Fluid transport model. Measurements of electron density evolution during the cold-pulse propagation are enabled by a high time resolution density profile reflectometer. The density evolution reveals the quick propagation of a pulse from edge to core, which is a mechanism to transiently increase core temperature in low-collisionality plasmas. Local transport simulations with measured density evolution demonstrate that the core temperature response can indeed be explained by the stabilization of Trapped Electron Mode turbulence at low collisionality, thus providing confidence that local transport modeling is enough to explain cold-pulse propagation and associated phenomenology.Cold pulses are introduced in Ohmic DIII-D tokamak plasmas via injection of impurities with a laser blow-off system, revealing for the first time in this machine a quick increase in core electron temperature shortly after the edge cold-pulse injection at low collisionality. The experimental results are consistent with predict-first simulations of heat transport enabled by the Trapped Gyro-Landau-Fluid transport model. Measurements of electron density evolution during the cold-pulse propagation are enabled by a high time resolution density profile reflectometer. The density evolution reveals the quick propagation of a pulse from edge to core, which is a mechanism to transiently increase core temperature in low-collisionality plasmas. Local transport simulations with measured density evolution demonstrate that the core temperature response can indeed be explained by the stabilization of Trapped Electron Mode turbulence at low collisionality, thus providing confidence that local transport modeling is enough ...

Recent experiments on C-mod seeding nitrogen into ohmic plasmas with [subscript q]95 = 3.4 found that the seeding greatly reduced long-wavelength (ITG-scale) turbulence. The long-wavelength turbulence that was reduced by the nitrogen seeding was localized to the region of r/a≈0.85, where the turbulence is well above marginal stability (as evidenced by Q[subscript i]/Q[subscript GB]≫1). The nonlinear gyrokinetic code GYRO was used to simulate the expected turbulence in these plasmas, and the simulated turbulent density fluctuations and turbulent energy fluxes quantitatively agreed with the experimental measurements both before and after the nitrogen seeding. Unexpectedly, the intrinsic rotation of the plasma was also found to be affected by the nitrogen seeding, in a manner apparently unrelated to a change in the electron-ion collisionality that was proposed by other experiments., United States. Dept. of Energy. Office of Fusion Energy Sciences (Award E-FG02-94-ER54235)

The article “DIII-D Research to Prepare for Steady State Advanced Tokamak Power Plants”, written by R. J. Buttery, B. Covele, J. Ferron, A. Garofalo, C. T. Holcomb, T. Leonard, J. M. Park, T. Petrie, C. Petty, G. Staebler, E. J. Strait, M. Van Zeeland, was originally published electronically on the publisher’s Internet portal ( https://doi.org/10.1007/s10894-018-0185-y ) on 3 September 2018 without open access.

The many sources of uncertainty in validation studies of plasma turbulence in magnetically confined fusion devices are well-known. In this paper, we investigate how to efficiently transform uncertainties in experimentally derived transport model inputs into model prediction uncertainties, using the quasilinear trapped-gyro-Landau-fluid (TGLF) turbulent transport model [Staebler et al., Phys. Plasmas 14, 055909 (2007)]. We use the rapidly converging and computationally inexpensive non-intrusive probabilistic collocation method (PCM) to propagate input parameter uncertainty probability distribution functions (PDFs) through TGLF, yielding PDFs of predicted transport fluxes. We observe in many cases that the flux PDFs exhibit significant non-normal features such as strong skewness, even when the input distributions were normal. To illustrate the utility of the PCM approach, we apply this methodology to transport predictions for a DIII-D ITER baseline plasma [Grierson et al., Phys. Plasmas 25, 022509 (2018)] in which the mix of neutral beam injection (NBI) and electron cyclotron heating (ECH) was varied. The model predictions show clear changes in the parametric dependencies and sensitivities of the turbulence between the two heating mixes. Specifically, when only NBI heating was used, the transport fluxes responded significantly only to the ion temperature gradient scale length. However, when both NBI and ECH were applied, the electron transport channels demonstrate a strong sensitivity to the electron temperature and density gradients not observed in the NBI-only case. Additional context for the PCM approach is provided by comparing its predictions with those obtained via a local flux-matching approach. A new set of validation metrics based on the Wasserstein distance is proposed for PDF-based comparisons.

A review of the recent progress in understanding the transport in fully non-inductive, high bootstrap fraction H-mode discharges, developed on the DIII-D tokamak, is given in this paper. Experiments have demonstrated improved energy confinement due to the formation of an internal transport barrier in high bootstrap fraction H-mode discharges. Gyrokinetic analysis, and quasi-linear predictive modeling, demonstrates that the observed transport barrier is due to the suppression of turbulence, primarily due to the large Shafranov shift. E × B velocity shear does not play a significant role in the transport barrier due to the high safety factor. The ion energy transport is reduced to neoclassical for DIII-D discharges and electron energy and particle transport is reduced, but still turbulent, within the barrier. Deeper into the plasma, high levels of electron transport are observed. The electron energy transport in DIII-D is found to be due to electromagnetically enhanced electron scale modes. A contribution from fast ion driven instabilities is also possible. The kinetic ballooning mode plays a strong role in the region between the internal and H-mode edge transport barriers with two types of self-organized pedestal states observed.

Experiments have demonstrated improved energy confinement due to the spontaneous formation of an internal transport barrier in high bootstrap fraction discharges. Gyrokinetic analysis, and quasilinear predictive modeling, demonstrates that the observed transport barrier is caused by the suppression of turbulence primarily from the large Shafranov shift. It is shown that the Shafranov shift can produce a bifurcation to improved confinement in regions of positive magnetic shear or a continuous reduction in transport for weak or negative magnetic shear. Operation at high safety factor lowers the pressure gradient threshold for the Shafranov shift-driven barrier formation. Two self-organized states of the internal and edge transport barrier are observed. It is shown that these two states are controlled by the interaction of the bootstrap current with magnetic shear, and the kinetic ballooning mode instability boundary. Election scale energy transport is predicted to be dominant in the inner 60% of the profile. Evidence is presented that energetic particle-driven instabilities could be playing a role in the thermal energy transport in this region.

For the first time, we report increased edge electron temperature and density turbulence levels ( Te and ne) in Edge Localized Mode free Quiescent H-mode (ELM-free QH-mode) plasmas as compared to the ELMing time period. ELMs can severely damage plasma facing components in fusion plasma devices due to their large transient energy transport, making ELM-free operation a highly sought after goal. The QH-mode is a candidate for this goal as it is ELM-free for times limited only by hardware constraints. It is found that the driving gradients decrease during the QH-mode compared to the ELMing phase, however, a significant decrease in the ExB shearing rate is also observed that taken together is consistent with the increased turbulence. These results are significant as the prediction and control of ELM-free H-mode regimes are crucial for the operation of future fusion devices such as ITER. The changes in the linear growth rates calculated by CGYRO [Candy et al., J. Comput. Phys. 324, 73 (2016)] and the measured...

Multi-scale fluctuations measured by turbulence diagnostics spanning long and short wavelength spatial scales impact energy confinement and the scale-lengths of plasma kinetic profiles in the DIII-D ITER baseline scenario with direct electron heating. Contrasting discharge phases with ECH + neutral beam injection (NBI) and NBI only at similar rotation reveal higher energy confinement and lower fluctuations when only NBI heating is used. Modeling of the core transport with TGYRO using the TGLF turbulent transport model and NEO neoclassical transport reproduces the experimental profile changes upon application of direct electron heating and indicates that multi-scale transport mechanisms are responsible for changes in the temperature and density profiles. Intermediate and high-k fluctuations appear responsible for the enhanced electron thermal flux, and intermediate-k electron modes produce an inward particle pinch that increases the inverse density scale length. Projection to ITER is performed with TGLF an...

The objective of the Fusion Development Facility (FDF) under consideration is to carry forward advanced tokamak physics for optimization of fusion reactors and enable development of fusion’s energy...

The response of plasma parameters and broad wavenumber turbulence (1–39 cm−1, kρs = 0.1–10, relevant to ion temperature gradient, trapped electron mode and electron temperature gradient mode turbulence, here ρs = ion gyroradius) to auxiliary electron cyclotron heating (ECH) is reported on. One fluid thermal fluxes and diffusivities increase appreciably with ECH. Significant changes to the density fluctuations over the full range of measured wavenumbers are observed, with an increase for lower wavenumbers and a more spatially complicated response at high k. Spatially resolved high k measurements (k = 39 cm−1, kρs = 4–10) show a varying response to ECH, with decreasing at r/a = 0.35 and increasing at r/a = 0.6 and 1. These variations were found to have a positive correlation with ∇Te evaluated at nearby locations, consistent with a ∇Te drive. Comparison of the changes in high k fluctuation levels with linear gyrokinetic growth rates show qualitative agreement at the innermost location, r/a = 0.35 and disagreement at r/a = 0.6.

Density fluctuation measurements covering a wavenumber range relevant to ITG, TEM and ETG type instabilities (k⊥ ρi ≈ 0.2→ 10) are compared during Ohmic and neutral beam injection (NBI). These short time duration NBI perturbations modified the background temperature as well as the density fluctuation behaviour but had little effect on the background density. It is found that both the measured and calculated responses to these perturbations varied with wavenumber supporting the need for broad wavenumber comparisons. The experimentally measured fluctuation changes and calculated growth rates (from the linear gyrokinetic code GKS) show qualitative similarities to each other at low and intermediate k while the comparison at high k is inconclusive.

© 2015 IAEA, Vienna. In this paper we show that changing from an ion temperature gradient (ITG) to a trapped electron mode (TEM) dominant turbulence regime (based on linear gyrokinetic simulations) results experimentally in a strong density pump-out (defined as a reduction in line-averaged density) in low collisionality, low power H-mode plasmas. We vary the turbulence drive by changing the heating from predominantly ion heated using neutral beam injection to electron heated using electron cyclotron heating, which changes the ratio and the temperature gradients. Perturbed gas puff experiments show an increase in transport outside , through a strong increase in the perturbed diffusion coefficient and a decrease in the inward pinch. Linear gyrokinetic simulations with TGLF show an increase in the particle flux outside the mid-radius. In conjunction an increase in intermediate-scale length density fluctuations is observed, which indicates an increase in turbulence intensity at typical TEM wavelengths. However, although the experimental changes in particle transport agree with a change from ITG to TEM turbulence regimes, we do not observe a reduction in the core rotation at mid-radius, nor a rotation reversal.

The advanced tokamak is considered as the basis for a fusion power plant. The ARIES-AT design has an aspect ratio of A ≡ R / a = 4.0 , an elongation and triangularity of κ = 2.20 , δ = 0.90 (evaluated at the separatrix surface), a toroidal beta of β = 9.1 % (normalized to the vacuum toroidal field at the plasma center), which corresponds to a normalized beta of β N ≡ 100 × β / ( I P ( M A ) / a ( m ) B ( T ) ) = 5.4 . These beta values are chosen to be 10% below the ideal MHD stability limit. The bootstrap-current fraction is f BS ≡ I BS / I P = 0.91 . This leads to a design with total plasma current I P = 12.8 MA, and toroidal field of 11.1 T (at the coil edge) and 5.8 T (at the plasma center). The major and minor radii are 5.2 and 1.3 m. The effects of H-mode edge gradients and the stability of this configuration to non-ideal modes is analyzed. The current drive system consists of ICRF/FW for on-axis current drive and a Lower Hybrid system for off-axis. Transport projections are presented using the drift-wave based GLF23 model. The approach to power and particle exhaust using both plasma core and scrape-off-layer radiation is presented.

The advanced tokamak programme on DIII-D is to develop the scientific basis for steady state, high performance operation in future devices. We report on experiments attempting to demonstrate sustainment of 100% noninductive current for several seconds at high beta, using up to 2.5 MW of off-axis electron cyclotron current drive and up to 15 MW of neutral beam injection with q95 ≈ 5. A 100% noninductive condition was achieved with βT = 3.6%, βN = 3.5, H89 = 2.4 and improved current drive alignment. However, the duration of this phase was limited by the pressure profile evolution leading to magnetohydrodynamic instabilities after about 0.7 s. In a separate discharge, a nearly (~90%) noninductive, stationary condition was maintained for one current relaxation time (1.8 s) only limited by the duration of the hardware system. These experiments have achieved normalized fusion performance with bootstrap current fraction fBS ≈ 60%, consistent with requirements for the ITER Q = 5 steady-state scenarios. The modelling tools that were successfully employed to devise experiments in DIII-D are applied to ITER, indicating that full noninductive operation is plausible for an ITER steady-state scenario with Q ≈ 5.

Two experiments on DIII-D have been performed with the purpose of searching for evidence of a critical electron temperature gradient or gradient scale length. Both experiments employed off-axis electron cyclotron heating to vary the local value of inverse temperature scale length 1/L-Te, = -del T-e/T-e while holding the total heating power and thus edge temperatures constant. The incremental or heat pulse thermal diffusivity was monitored as a means of identifying the existence of a threshold or critical value of 1/L-Te, k(crit), where a large increase in heat pulse diffusivity may occur while going from below to above kcrit. No evidence of a critical value was found, but the existence of one cannot be ruled out by the experimental results. The results can be used to place an upper bound on k(crit). If k(crit) exists, the experimental results indicate kcrit < 3.8 m(-1) at rho = 0.45 and k(crit) < 2.5 m(-1) at rho = 0. 29 corresponding to temperature scale lengths relative to the plasma minor radius of LTe/a > 0.43 and 0.65, respectively. Over most of the plasma radius (rho >= 0.3) the temperature profile in the L-mode discharges studied exceeds these upper bounds on k(crit). A transport model based on a critical gradient is consistent with experimental observations but is not unique. Models other than one based on the existence of a critical gradient are also consistent with experimental observations.

Advanced tokamak (AT) research in DIII-D seeks to provide a scientific basis for steady-state high performance operation in future devices. These regimes require high toroidal beta to maximize fusion output and high poloidal beta to maximize the self-driven bootstrap current. Achieving these conditions requires integrated, simultaneous control of the current and pressure profiles and active magnetohydrodynamic stability control. The building blocks for AT operation are in hand. Resistive wall mode stabilization by plasma rotation and active feedback with non-axisymmetric coils allows routine operation above the no-wall beta limit. Neoclassical tearing modes are stabilized by active feedback control of localized electron cyclotron current drive (ECCD). Plasma shaping and profile control provide further improvements. Under these conditions, bootstrap supplies most of the current. Steady-state operation requires replacing the remaining inductively driven current, mostly located near the half radius, with non-inductive external sources. In DIII-D this current is provided by ECCD, and nearly stationary AT discharges have been sustained with little remaining inductive current. Fast wave current drive is being developed to control the central magnetic shear. Density control, with divertor cryopumps, of AT discharges with ELMing H-mode edges facilitates high current drive efficiency at reactor relevant collisionalities. An advanced plasma control system allows integrated control of these elements. Close coupling between modelling and experiment is key to understanding the separate elements, their complex nonlinear interactions, and their integration into self-consistent high performance scenarios. This approach has resulted in fully non-inductively driven plasmas with ?N ? 3.5 and ?T ? 3.6% sustained for up to 1?s, which is approximately equal to one current relaxation time. Progress in this area, and its implications for next-step devices, will be illustrated by results of these and other recent experiment and simulation efforts.

A new gyro-Landau fluid model for the Landau damping of circulating particles is presented. Since trapped particles can bounce average low frequency waves, they are not affected by Landau damping. The loss of bounce averaging when the mode frequency exceeds the trapped particle bounce frequency is included in the model by changing the phase space integration boundary. An excellent fit to the kinetic response for the circulating particle density and the parallel and perpendicular pressure is obtained with six-moment equations.

The GLF23 and multi-mode core transport models are used along with models for the H-mode pedestal to predict the fusion performance for the International Thermonuclear Experimental Reactor, Fusion Ignition Research Experiment, and IGNITOR tokamak designs. Simulations using combinations of core and pedestal models have also been compared with experimental data for H-mode profiles in DIII-D, JET, and Alcator C-Mod. Power-independent (ballooning mode limit) and power-dependent pedestal scalings lead to very different predictions when used with the core models. Although the two drift-wave transport models reproduce the core profiles in a wide variety of tokamak discharges, they differ in their projections to burning plasma experiments for the same pedestal parameters. Differences in the core transport models in their response to the ion temperature gradient (i.e. their stiffness) and impact of the power dependence of the H-mode pedestal on fusion performance predictions are discussed.

Fusion power predictions are presented using the GLF23 drift-wave transport model for several next-step tokamak designs including ITER, FIRE, and IGNITOR. The GLF23 model has been renormalized using recent gyrokinetic simulations and a database of nearly 50 H-mode discharges from three different tokamaks. The renormalization reduces the ion temperature gradient/trapped electron mode (ITG/TEM)-driven transport by a factor of 3.7 while electron temperature gradient (ETG) mode transport is increased by a factor of 4.8 with respect to the original model. Using the renormed model, the fusion power performance is uniformly assessed, and the pedestal requirements are summarized for each device. The renormed model is still quite stiff and yields somewhat more optimistic predictions for next-step burning plasma experiments. The consequences of stiff transport in the plasma core are discussed. A fusion fit formula is derived whereby the GLF23 results follow a universal stiff model curve for the normalized fusion power versus pedestal temperature.

The gyrokinetic equations predict that various drift type waves or modes can be unstable in a tokamak. For some of these modes, such as the ion temperature gradient mode and the electron temperature gradient mode, there exists a critical gradient, above which the mode is unstable. There are also drift type modes, such as the trapped electron mode, which do not have a critical ion temperature gradient, but have a threshold which depends upon a variety of parameters. Since the existence of unstable modes can cause increased transport, plasmas which are centrally heated tend to increase in temperature gradient until the modes become unstable. Here the measured ion temperature gradients are compared to the “critical” gradients as calculated by a gyrokinetic linear stability (GKS) code [M. Kotschenreuther et al., Phys. Plasmas 2, 2381 (1995)]. Also, the maximum linear growth rate as calculated by this code is compared to experimentally derived transport coefficients. The results show that for low confinement m...

Key DIII-D advanced tokamak (AT) experimental and modelling results are applied to examine the physics and control issues for ITER to operate in a negative central shear (NCS) AT scenario. The effects of a finite edge pressure pedestal and current density are included based on the DIII-D experimental profiles. Ideal and resistive stability analyses demonstrate that feedback control of resistive wall modes by rotational drive or flux conserving intelligent coils is crucial for these AT configurations to operate at attractive βN values in the range 3.0–3.5. Vertical stability and halo current analyses show that reliable disruption mitigation is essential and mitigation control using an impurity gas can significantly reduce the local mechanical stress to an acceptable level. Core transport and turbulence analyses indicate that control of the rotational shear profile is essential to reduce the pedestal temperature required for high β. Consideration of edge stability and core transport suggests that a sufficiently wide pedestal is necessary for the projected fusion performance. Heat flux analyses indicate that, with core-only radiation enhancement, the outboard peak divertor heat load is near the design limit of 10 MW m−2. Detached operation may be necessary to reduce the heat flux to a more manageable level. Evaluation of the ITER pulse length using a local step response approach indicates that the 3000 s ITER long-pulse scenario is probably both necessary and sufficient for demonstration of local current profile control.

Using off-axis electron cyclotron current drive (ECCD), self-consistent integrated advanced tokamak operation has been demonstrated on DIII-D [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159], combining high β (>3%) at high q (qmin>2.0) with good energy confinement (H89∼2.5) and high noninductive current fraction (fBS∼55%,fNI∼90%). Modification of the current profile by ECCD led to internal transport barrier formation even in the presence of type I edge localized modes. Improvements were observed in all transport channels, and increased peaking of profiles led to higher bootstrap current in the core. Separate experiments have shown the ability to maintain a nearly steady-state current profile for up to 1 s with qmin>1.5. Modeling indicates that this favorable current profile can be maintained indefinitely at a higher βN using tools available to the near-term DIII-D program. Modeling and simulation have become essential tools fo...

Results from recent experiments on the DIII-D tokamak have revealed many important details on transport barriers at the plasma edge and in the plasma core. These experiments include: (a) the formation of the H-mode edge barrier directly by pellet injection; (b) the formation of a quiescent H-mode edge barrier (QH-mode) which is free from edge localized modes, but which still exhibits good density and radiative power control; (c) the formation of multiple transport barriers, such as the quiescent double barrier (QDB) which combines an internal transport barrier with the quiescent H-mode edge barrier. Results from the pellet-induced H-mode experiments indicate that: (a) the edge temperature (electron or ion) does not need to attain a critical value for the formation of the H-mode barrier, (b) pellet injection leads to an increased gradient in the radial electric field, Er, at the plasma edge; (c) the experimentally determined edge parameters at barrier transition are well below the predictions of several theories on the formation of the H-mode barrier, (d) pellet injection can lower the threshold power required to form the H-mode barrier. The quiescent H-mode barrier exhibits good density control as the result of continuous magnetohydrodynamic activity at the plasma edge called the edge harmonic oscillation (EHO). The EHO enhances the edge particle transport whilst maintaining a good energy transport barrier. The ability to produce multiple barriers in the QDB regime has led to long duration, high-performance plasmas with βNH89 values of 7 for up to 10 times the confinement time. Density profile control in the plasma core of QDB plasmas has been demonstrated using on-axis electron cyclotron heating.

Quiescent double barrier discharges (QDB) on DIII-D [Luxon et al., Fusion Technol. 8, Part 2A, 441 (1985)] exhibit near steady high performance (βNH∼7) with a quiescent H-mode edge, i.e., free of edge localized modes (ELMs), but with effective particle control and strongly peaked density profiles. These QDB discharges exhibit an internal transport barrier with low ion thermal transport despite incomplete turbulence suppression. Very short correlation lengths, which reduce the transport step size, however, characterize the residual turbulence. This observation is consistent with simulations using the GLF23 [Waltz et al., Phys. Plasmas 4, 2482 (1997)] model, which reproduce the core ion temperature profile even in the presence of finite turbulence. Increased retention of high-Z impurities is observed and core nickel concentrations (an intrinsic impurity in DIII-D) are as high as 0.3%. To quantify impurity transport, trace impurity injection has been performed in steady QDB discharges showing a fast influx f...

Results are presented for simulations of tokamak discharges exhibiting internal transport barriers (ITBs) with significant reductions in the core thermal transport using a comprehensive theory-based model for drift-wave transport. The predicted temperature and toroidal velocity profiles from the GLF23 model are compared against the experimental data for twenty-two L- and high-confinement mode (H-mode) ITB discharges from three large tokamaks including DIII-D [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)], Tokamak Fusion Test Reactor [D. J. Grove and D. M. Meade, Nucl. Fusion 25, 1167 (1985)], and Joint European Torus [P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987)]. The combined effects of E×B shear and Shafranov shift stabilization of the turbulent transport are essential in reproducing the barriers in the plasma core. Shafranov shift or α-stabilization is found to be an essential ingredient in suppressing the thermal transport due to ion and electron temperature gradient and tra...