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Prospects for H-mode inhibition in negative triangularity tokamak reactor plasmas

Instability to high toroidal mode number ($\textit{n}$) ballooning modes has been proposed as the primary gradient-limiting mechanism for tokamak equilibria with negative triangularity (NT) (δ) shaping, preventing access to strong H-mode regimes when δ is sufficiently negative. To understand how this mechanism extrapolates to reactor conditions, we model the infinite-$\textit{n}$ ballooning stability as a function of internal profiles and equilibrium shape using a combination of the CHEASE and BALOO codes. While the critical δ required for avoiding 2nd stability to high-$\textit{n}$ modes is observed to depend in a complicated way on various shaping parameters, including the equilibrium inverse aspect ratio, elongation and squareness, equilibria with NT are robustly prohibited from accessing the 2nd stability region, offering the prediction that NT reactors should maintain L-mode-like operation. In order to access high-$\textit{n}$ 2nd stability, the local shear over the entire bad curvature region must be sufficiently negative to overcome curvature destabilization on the low field side. Finally, scalings of the ballooning-limited pedestal height are provided as a function of plasma parameters to aid future scenario design.

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Broadening of the Divertor Heat Flux Profile in High Confinement Tokamak Fusion Plasmas with Edge Pedestals Limited by Turbulence in DIII-D

Multimachine empirical scaling predicts an extremely narrow heat exhaust layer in future high magnetic field tokamaks, producing high power densities that require mitigation. Here, in the experiments presented, the width of this exhaust layer is nearly doubled using actuators to increase turbulent transport in the plasma edge. This is achieved in low collisionality, high confinement edge pedestals with their gradients limited by turbulent transport instead of large-scale, coherent instabilities. The exhaust heat flux profile width and divertor leg diffusive spreading both double as a high frequency band of turbulent fluctuations propagating in the electron diamagnetic direction doubles in amplitude. The results are quantitatively reproduced in electromagnetic XGC particle-in-cell simulations which show the heat flux carried by electrons emerges to broaden the heat flux profile, directly supported by Langmuir probe measurements.

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Electromagnetic turbulence simulation of tokamak edge plasma dynamics and divertor heat load during thermal quench

Abstract The edge plasma turbulence and transport dynamics, as well as the divertor power loads during the thermal-quench phase of tokamak disruptions, are numerically investigated with BOUT++’s flux-driven six-field electromagnetic turbulence model. Here, transient yet intense particle and energy sources are applied at the pedestal top to mimic the plasma power drive at the edge induced by a core thermal collapse, which flattens the core temperature profile. Interesting features, such as surging of divertor heat load (up to 50 times) and broadening of heat-flux width (up to four times) on the outer-divertor target plate, are observed in the simulation, in qualitative agreement with experimental observations. The dramatic changes in divertor heat load and width are due to the enhanced plasma turbulence activities inside the separatrix. Two cross-field transport mechanisms, namely, the E × B turbulent convection and the stochastic parallel advection/conduction, are identified to play important roles in this process. First, an elevated edge pressure gradient drives instabilities and subsequent turbulence in the entire pedestal region. The enhanced turbulence not only transports particles and energy radially across the separatrix via the E × B convection, which causes the initial divertor heat-load burst, but it also induces amplified magnetic fluctuation B ˜ . Once themagnetic fluctuation is large enough to break the magnetic flux surface, magnetic flutter effect provides an additional radial transport channel. In the late stage of our simulation, | B ˜ r / B 0 | reaches to 10 −4 level that completely breaks magnetic flux surfaces such that stochastic field lines are directly connecting pedestal top plasma to the divertor target plates or first wall, further contributing to the divertor heat-flux width broadening.

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Direct measurement of the electron turbulence-broadening edge transport barrier to facilitate core–edge integration in tokamak fusion plasmas

Abstract The integration of a high-performance core and a dissipative divertor, or the so-called ‘core–edge integration,’ has been widely identified as a critical gap in the design of future fusion reactors. In this letter, we report, for the first time, direct experimental evidence of electron turbulence at the DIII-D H-mode pedestal that correlates with the broadening of the pedestal and thus facilitates core–edge integration. In agreement with gyrokinetic simulations, this electron turbulence is enhanced by high η e ( η e = L n / L T e , where L n is the density scale length and L T e is the electron temperature scale length), which is due to a strong shift between the density and temperature pedestal profiles associated with a closed divertor. The modeled turbulence drives significant heat transport with a lower pressure gradient that may broaden the pedestal to a greater degree than the empirical and theoretically predicted pedestal width scalings. Such a wide pedestal, coupled with a closed divertor, enables us to achieve a good core–edge scenario that integrates a high-temperature low-collisionality pedestal (pedestal top temperature T e,ped > 0.8 keV and a pedestal top collisionality ν * ped < 1) under detached divertor conditions. This paves a new path toward solving the core–edge integration issue in future fusion reactors.

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Diagnostics: Chapter 8 of the special issue: on the path to tokamak burning plasma operation

This chapter presents the activity conducted by the ITPA topical group (TG) on Diagnostics over about the last 15 years. Following a general introduction of the ITER Diagnostics led by their measurement roles, the document is organized in several subchapters detailing the design support, research and development activity conducted by each of the specialist working groups (WGs) of the TG. Please note that the magnetic diagnostics were supported at the TG without a specific WG. Their status is included in the general introduction. In the following some highlights of the subchapter’s contents are provided. Recent advances in ITER first wall (FW) diagnostics for the measurements of plasma-metallic wall interaction in support of the ITER research plan are reported. An InfraRed imaging Video Bolometer for ITER has been developed and tested on several tokamaks to measure the radiated power loss. A laser-induced breakdown spectroscopy (LIBS) technique which utilizes a pulsed laser beam to ablate locally by forming a crater, will measure local tritium inventory in the FW material. Real-time Residual Gas Analyzers will measure the neutral gas composition in a divertor port and an equatorial port during plasma operation. Due to the full metallic FW environment, the plasma-wall interaction in ITER will face several challenges such as the compromised radiated power and divertor heat flux measurements by reflection. Ray tracing and analysis codes have been developed to eliminate and correct the effects of reflection in the measurements. The characteristics of the reflecting surfaces depending on the roughness and angle of the incidence have been measured by dedicated experiments, and the results were applied to the reflection elimination. For the measurement of the metallic impurity radiation induced by eroded metallic atoms, a vacuum ultraviolet spectrometer has been developed and tested. An extensive thermonuclear diagnostic suite will be required to support the operation of ITER and the planned experimental program for future burning plasma experiments. Due to the harsh environmental conditions, the implementation of diagnostic systems in ITER is a major challenge. These conditions include high levels of neutron and gamma fluxes, neutron heating, particle bombardment. Therefore, the selection and design of diagnostic systems must take into account a number of phenomena previously unseen in diagnostic design. For this reason, the measurement of neutrons and confined or lost fast ions, with particular emphasis on alpha particles, is critical to ITER. The diagnostics associated with these measurements will be important for future plasma-burning experiments at ITER. The high neutron emission and very large plasma size in ITER make neutron diagnostics the main diagnostic method used to measure plasma parameters such as fusion power, fusion power density, ion temperature, energy of fast ions and their spatial distributions in the plasma core. Active spectroscopy techniques are methods where a neutral particle beam is injected into the plasma and information on plasma parameters is extracted from the measurement of line emission resulting from the beam-plasma interaction, either by plasma ions or by beam atoms. Spatial localization is achieved by crossing the beamline and multiple observation lines. The ITER plasma will be a high temperature, moderately dense, fully ionized collisional plasma. The plasma facing surfaces are principally metallic being fashioned from beryllium or tungsten but many other elements, arising from either structural or from operational needs, may enter this plasma. The energy range of the emitted photons range from meV (infra-red) to multi keV (x-rays) and originate from all areas of the plasma volume. The primary role of passive emission diagnostics is to identify what is in the plasma from spectral signatures. Extracting quantitative information from these measurements such as impurity content, ion temperature, rotation, degree of detachment and radiated power depends on calibrated instruments, a physics model of the atomic and molecular processes and plasma transport and an analysis workflow that takes into account environmental effects such as reflections. The particular needs for ITER have prompted a multi-machine, many-year effort to address all these aspects and this chapter reviews the work on diagnostic design, experiments and new analysis techniques. An overview of the laser diagnostics to be implemented on ITER is also provided in this paper. This includes descriptions of the Thomson scattering in the core, edge and divertor regions, polarimetry and interferometry diagnostics used for measuring plasma density and also measurements of helium density in the divertor using Laser Induced Flourescence. Techniques which can allow improvements on current measurements are also addressed in particular expanding poloidal polarimetry measurements to measure field fluctuations and proposed use of dispersion interferometery which has a number of advantages over existing methods. This paper identifies particular areas where further research and testing on existing tokamaks is useful even at this advanced stage to inform the design of diagnostics for ITER. Outstanding areas of concern for the implementation of laser diagnostics, in particular with a view to reliable operation are identified. An overview of the latest developments of microwave diagnostic systems and techniques is given. The primary focus is the contributions for ITER—the next step burning plasma experiment—which is supplemented by describing recent progress of techniques applicable for fusion experiments beyond ITER. The contributions are intentionally kept concise, and are being supplemented by a rich list of references for further studies. Radiation induced effects are receiving continuous and well-deserved attention of the ITER diagnostic community and they are in many cases one of the primary design drivers of the ITER diagnostic systems. The paper summarizes recent progress in this area focusing primarily on the ITER diagnostics but in some cases provides also outlook for the possible solutions for even more demanding radiation environment of fusion reactors beyond ITER. Despite advancements in the area of modeling and simulation of various radiation induced effects, experimental testing in a nuclear environment as close as possible to the target one is still seen as unavoidable for proper qualification of particular diagnostic functional elements. Recent advancement within three diagnostic areas: optical diagnostics, magnetics and bolometers is covered. Encouraging results on qualification of silica glass vacuum window assemblies are presented. In the area of magnetic sensors, progress of irradiation tests performed on ITER in-vessel LTCC inductive sensors is presented with outlook for novel technological approaches to inductive sensors utilizing thick printing and photolithography technologies being highlighted. Summary of advancements in the area of steady state magnetic field sensors based on Hall effect is given. New results of neutron irradiation test of the ITER borosilicate glass inserts for vacuum electrical feedthroughs are summarized finding negligible swelling at target level of neutron fluence. Off-line irradiation tests of fiber optic current sensors for plasma current measurement demonstrated that both for gamma doses up to 5 MGy and a total neutron fluence up to 10 15 cm −2 , radiation induced changes are still compatible with required measurement accuracy on ITER. The ITER bolometers are given as an example how considering radiation effects may influence the diagnostic design. Finally, outlook for future main R&D directions is outlined. All optical and laser-based diagnostics in ITER will be using mirrors to guide plasma radiation toward detectors, cameras and sensors. In the hostile plasma, radiation and particle environment the optical characteristics of diagnostic mirrors will degrade directly affecting the entire performance of involved diagnostic systems. An assessment of factors affecting mirror performance is provided. Among the prime adverse factors are deposition of plasma impurities, sputtering of mirror surface and steam ingress in the vicinity of mirrors. Within the International Tokamak Physics Activity with active support by ITER central team and domestic agencies, the structured research and development (R&D) program on mitigation of risks for diagnostic mirrors is underway. Within this program the mirror material development, the passive mitigation of mirror degradation by using diagnostic ducts and shutters along with an active mirror recovery program comprising the in-situ mirror cleaning and calibration is underway. Recent developments in diagnostic mirror R&D are described in this Chapter along with an example of their implementation of R&D solutions in ITER Infrared Thermography diagnostic. An assessment of still open engineering and physics questions, considerations on mirror risks during an early phase of ITER operation are given along with an overview of diagnostic mirror evolution in the late ITER operation stage toward the demonstration fusion power plant. Several crucial areas of diagnostic R&D outlined in ITER Research Plan are addressed. The basic control groups in a fusion reactor can be broken-down in five categories: (1) plasma position, magnetic configuration, and plasma current control, (2) profile control and confinement optimization, (3) MHD control and suppression, (4) edge dissipation control, radiation and plasma exhaust control and (5) break-down optimization. These categories are coupled via the physics (a control action in one domain will affect the other domains) and via shared actuators (e.g. ECRH for impurity accumulation avoidance, current density distribution control and MHD suppression). Consequently, a supervisory control system should determine the priority of the various control tasks, their couplings, and the interfaces with the safety and interlock system. For the systematic development of the various controllers taking the complexity of the plasma and the control system into account, a model-based approach is required. A short historical overview is given of the developments in systems and control theory and control engineering with special emphasis on those developments that are most relevant for Nuclear Fusion research and operation. An overview is given of the state of the field of fusion plasma control for the control categories. It will be shown how synthetic diagnostics are being developed in ITER and how they are used in diagnostic design and design validation and how they can be in model-based controller synthesis using relatively simple models. In modern control methods, multiple diagnostics are used to constrain relatively simple models. The constrained models provide an estimate for the state. This opens the route to state controllers, such as model predictive control. A major challenge in nuclear fusion research is the coherent combination of data from heterogeneous diagnostics and modeling codes for machine control and safety as well as physics studies. Measured data from different diagnostics often provide information about the same subset of physical parameters. Additionally, information provided by some diagnostics might be needed for the analysis of other diagnostics. A joint analysis of complementary and redundant data allows, e.g. to improve the reliability of parameter estimation, to increase the spatial and temporal resolution of profiles, to obtain synergistic effects, to consider diagnostics interdependencies and to find and resolve data inconsistencies. Physics-based modeling and parameter relationships provide additional information improving the treatment of ill-posed inversion problems. A coherent combination of all kind of available information within a probabilistic framework allows for improved data analysis results. The concept of integrated data analysis (IDA) in the framework of Bayesian probability theory is outlined and contrasted with conventional data analysis. Components of the probabilistic approach are summarized and specific ingredients beneficial for data analysis at fusion devices are discussed.

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Core inductive electric field during sawtooth crashes on DIII-D

Sawtooth crashes on tokamak plasmas exhibit relaxation much faster than resistive time scales via a mechanism not fully understood. Using core magnetic measurements from the Radial Interferometer-Polarimeter (RIP) diagnostic on the DIII-D tokamak, Grad–Shafranov equilibria constrained by internal magnetic measurements that have high time resolution (<1μs) can be computed, allowing analysis of how equilibrium parameters such as safety factor q, current density J, and parallel electric field E ∥ , particularly on-axis, evolve. At the sawtooth crash, on-axis safety factor q 0 is observed to rise by 5% but remain below 1 throughout the cycle, and on-axis current density J 0 is observed to drop by 5%. On-axis parallel electric field E ∥ (0) is found to be balanced by ηJ 0 (resistivity times on-axis current density) except during the 200 µs crash period, where E ∥ (0) reaches 22 V m –1 , exceeding ηJ 0 by a factor of more than 2000. These first measurements in tokamak plasmas verify that generalized Ohm's law is not balanced during the crash by resistive effects alone; this is a finding expected due to the relaxation being much faster than resistive timescales. As a result, measurement of the electric field during the tokamak sawtooth serves to illuminate the physical mechanisms at work.

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Shadow masks predictions in SPARC tokamak plasma-facing components using HEAT code and machine learning methods

Here, this work uses machine learning (ML) to complement HEAT (Heat flux Engineering Analysis Toolkit) by developing 3-D footprint surrogate models for fast and accurate heat load calculations in the divertor of the SPARC tokamak. The focus is on shadowed regions, or magnetic shadows, caused by the 3-D geometry of plasma-facing components (PFCs). ML classifiers are employed to create a surrogate model for HEAT generated shadow masks, predicting these shadow masks and divertor heat flux profiles based on a diverse range of equilibria and only the plasma current, safety factor(q95) at the edge, and magnetic flux angles as input parameters. The ultimate goal is to integrate the model for real-time control and future operational decisions.

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Integration of full divertor detachment with improved core confinement for tokamak fusion plasmas

Divertor detachment offers a promising solution to the challenge of plasma-wall interactions for steady-state operation of fusion reactors. Here, we demonstrate the excellent compatibility of actively controlled full divertor detachment with a high-performance (β N ~ 3, H 98 ~ 1.5) core plasma, using high-β p (poloidal beta, β p > 2) scenario characterized by a sustained core internal transport barrier (ITB) and a modest edge transport barrier (ETB) in DIII-D tokamak. The high-β p high-confinement scenario facilitates divertor detachment which, in turn, promotes the development of an even stronger ITB at large radius with a weaker ETB. This self-organized synergy between ITB and ETB, leads to a net gain in energy confinement, in contrast to the net confinement loss caused by divertor detachment in standard H-modes. These results show the potential of integrating excellent core plasma performance with an efficient divertor solution, an essential step towards steady-state operation of reactor-grade plasmas.

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MHD, disruptions and control physics: Chapter 4 of the special issue: on the path to tokamak burning plasma operation

In this chapter, we review the progress in MHD stability, disruptions and control in magnetic fusion research that has occurred over the past (more than) one and a half decades since the publication by Hender et al in 2007 on the same topic as part of the update of ITER Physics Basis. During this period, remarkable progress has been achieved in the understanding of the basic physics and overall control of MHD instabilities through a wide spectrum of dedicated experiments, theory and modeling. The sawtooth activities are probably today one of the best understood of MHD events and very robust control schemes have been developed for reliable operation of tokamaks through core heating. Similarly, significant improvements have been achieved in understanding and control of neoclassical tearing modes, resistive wall modes or locked modes and their control through ECCD or error field control. The field of disruption prediction through application of artificial intelligence, machine learning or deep learning methods, which had already started at the time of the 2007 review, has progressed significantly due to general progress in these fields and application of newer, more sophisticated algorithms. However, although remarkable progress has been achieved in the field of Disruptions, their understanding, prediction, possible avoidance and mitigation still remain probably the most active fields of R&D globally in this field. This is especially because reactor grade machines like ITER and DEMO will be much less tolerant in respect of disruptions and runaway currents, and their occurrences must be either avoided altogether or minimized to an acceptable value without causing any significant hindrance to robust machine operations. This review is intended to present a broad spectrum of the R&D that has occurred in this field in support of ITER, which will also be of immense significance for all future machines, especially reactors like DEMO.

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Modeling q 95 windows for the suppression of edge localized modes by resonant magnetic perturbations in the DIII-D tokamak

A toroidal asymptotic matching model of the response of a tokamak plasma to a static resonant magnetic perturbation (RMP) is used to simulate the n = 3 RMP-induced edge-localized-mode-suppression windows in q 95 that are evident when the plasma current is slowly ramped in DIII-D discharge #145380. All quantities employed in the simulation are derived from experimental measurements, apart from the neutral particle data. Three cases are considered. In the first case, the natural frequencies of tearing modes resonant in the plasma are determined by the ion flows at the corresponding resonant surfaces, which is the prediction of nonlinear tearing mode theory. In the second case, the natural frequencies are determined by the local E x B velocities at the resonant surfaces. In the third case, the natural frequencies are determined by the electron flows at the resonant surfaces, which is the prediction of linear tearing mode theory. The second case gives the best agreement between the simulations and the experimental observations. The first and third cases only lead to partial agreement between the simulations and the observations. In the first case, the lack of complete agreement may be a consequence of using an inaccurate assumption for the neutral particle distribution in the pedestal. In the third case, the lack of complete agreement is probably due to the fact that the response of a tokamak plasma to an RMP is not accurately described by linear tearing mode theory.

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Projections of H-mode access and edge pedestal in the SPARC tokamak

In order to inform core performance projections and divertor design, the baseline SPARC tokamak plasma discharge is evaluated for its expected H-mode access, pedestal pressure and edge-localized mode (ELM) characteristics. A clear window for H-mode access is predicted for full field DT plasmas, with the available 25 MW of design auxiliary power. Additional alpha heating is likely needed for H-mode sustainment. Pressure pedestal predictions in the developed H-mode are surveyed using the EPED model. The projected SPARC pedestal would be limited dominantly by peeling modes and may achieve pressures in excess of 0.3 MPa at a density of approximately 3 × 10 20 m -3 . High pedestal pressure is partially enabled by strong equilibrium shaping, which has been increased as part of recent design iterations. Edge-localized modes (ELMs) with >1 MJ of energy are projected, and approaches for reducing the ELM size, and thus the peak energy fluence to divertor surfaces, are under consideration. The high pedestal predicted for SPARC provides ample margin to satisfy its high fusion gain (Q) mission, so that even if ELM mitigation techniques result in a 2x reduction of the pedestal pressure, Q > 2 is still predicted.

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Compression of tokamak boundary plasma simulation data using a maximum volume algorithm for matrix skeleton decomposition

This report demonstrates satisfactory data compression of SOLPS-ITER simulation output ranging from 2D fields, 1D profiles, and 0D scalar variables with a novel matrix decomposition approach. The singular value decomposition (SVD) scales poorly for large matrix sizes and is unsuited to the application on high dimensional data common to fusion plasma physics simulation. In this work, we employ the columns-submatrix-rows (CUR) matrix factorization technique in order to compute a low-rank approximation up to two orders of magnitude faster than the SVD, but within a nominal L2-norm relative error of ε = 10 –2 . In addition, the CUR approach maintains the original format of the data, in its extracted columns and rows, allowing for interpretable data storage at the original resolution of the simulation. We utilize an iterative algorithm to compute the CUR decomposition of simulation output by maximizing the volume, or linearly independent information content, of a low-rank submatrix contained within the data. Experiments over $\textit{n} × \textit{n}$ randomized test matrices with embedded rank-deficient features show that this maximum volume implementation of CUR matrix approximation has reduced asymptotic computational complexity on the order of n compared to the SVD, which scales approximately as $n^3$. These results show that the CUR technique can be used to effectively select time step snapshots (columns) of over 140 SOLPS-ITER output variables and the associated discretized coordinate timeseries (rows) allowing for reconstruction of the complete simulation dynamics.

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2D analysis of tokamak divertor-plasma detachment-bifurcation with operational parameters and geometries

UEDGE simulations with density scans for various input power, transport coefficients and outer poloidal leg length are performed to study the conditions for the existence of a bifurcation-like drop of T e at the outer strike point, commonly referred to as a detachment cliff, when transitioning to a detached plasma from an attached plasma in the outer divertor as the upstream density increases (McLean et al., 2015). The simulation results show that a detachment cliff tends to occur with a higher power input regardless of diffusivities and leg length. Further analysis of change of plasma profiles at a cliff indicate that, in addition to the sharp reduction of the E x B drift fluxes in the outer divertor studied in Jaervinen et al., (2018), the substantial change of the Mach number in the outer divertor and the decrease of the outer mid-plane T e due to the radiation front moving across the separatrix into the confinement region above the X-point consistently occur for all UEDGE density scans that have a detachment cliff. UEDGE time-dependent simulation of the evolution of a detachment cliff shows that the rapid increase of radiation above the X-point occurs in a time scale of ~0.3–0.5, which could possibly be the trigger for the formation of a detachment cliff, quicker than the Mach number change in a time scale of ~1 ms and the drop of T e in a time scale of ~2–3 ms in the outer divertor.

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How fast ions mitigate turbulence and enhance confinement in tokamak fusion plasmas

Along with high temperature and density, magnetic fusion requires good confinement and a degree of transport control for thermal plasmas. Meanwhile, fast ions are generated by the external heating used to raise plasma temperature and by the fusion reactions. As a result, the fusion plasmas are effectively rendered into systems with two coexisting populations of main interest — namely, the fast ions and the thermal plasma. Interestingly, several recent experiments indicate that the fast-ion population can improve the confinement of the thermal plasmas by mitigating turbulence. Here, in this Review, we describe the physical mechanisms that underpin the improved confinement and discuss recent experimental results in terms of these mechanisms.

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Turbulence-driven flow dynamics in general axisymmetric toroidal geometry

The present work gives the equations governing the generation of toroidally axisymmetric flows by turbulent Reynolds and Maxwell stresses in finite aspect ratio, general cross section tokamak plasmas. Inclusion of the divergence-free flow constraint in lowest order changes the time scale for evolution of the poloidal flows driven by turbulence by substantial factors. In the pedestal region for present day machines, comparing to earlier cylindrical models, the time scale evaluated using a large aspect ratio circular cross section model can be two orders of magnitude longer while the present, general geometry result can be about one order of magnitude longer. Inclusion of gyroviscosity in the calculation shows that the only lowest order radial velocity fluctuations that enter the problem are those due to fluctuating E×B flows. Toroidal and poloidal flow effects on the toroidally axisymmetric flows are inextricably coupled due to the neoclassical poloidal viscosity. Accordingly, the physics is inherently three dimensional and measurements of all three velocity components are required to obtain the information needed to quantitatively test the theory. The parallel and angular momentum equations for the lowest order, toroidally axisymmetric flows look like radial transport equations when the turbulence is included. The turbulence terms provide the radial transport fluxes. In standard neoclassical theory, the parallel flow equation is local on each flux surface; there is no radial derivative term. However, adding turbulence gives a way, in principle, for radial transport to lead to poloidal flows that deviate from the neoclassical prediction. As a result, the inclusion of the Maxwell stress provides a mechanism for MHD fluctuations to alter the toroidally axisymmetric flows.

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Stochastic fluctuation and transport of tokamak edge plasmas with the resonant magnetic perturbation field

Here we present that a statistical method known as the complexity–entropy analysis is useful to characterize a state of plasma turbulence and flux in the resonant magnetic perturbation (RMP) edge localized mode (ELM) control experiment. The stochastic pedestal top temperature fluctuation in the RMP ELM suppression phase is distinguished from the chaotic fluctuation in the natural ELM-free phase. It is discussed that the stochastic temperature fluctuation can be originated from the narrow layer of the field penetration on the pedestal top. The forced magnetic island can emit the resonant drift wave of comparable sizes (relatively low-k) in the RMP ELM suppression phase, and it can result in the generation of stochastic higher wavenumber fluctuations coupled to tangled fields around the island. The analysis of the ion saturation current measurement around the major outer striking point on the divertor shows that it also becomes more stochastic as the stronger plasma response to the RMP field is expected.

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