One of the scientific success stories of fusion research over the past decade is the development of the ExB shear stabilization model to explain the formation of transport barriers in magnetic confinement devices. This model was originally developed to explain the transport barrier formed at the plasma edge in tokamaks after the L (low) to H (high) transition. This concept has the universality needed to explain the edge transport barriers seen in limiter and divertor tokamaks, stellarators, and mirror machines. More recently, this model has been applied to explain the further confinement improvement from H (high)-mode to VH (very high)-mode seen in some tokamaks, where the edge transport barrier becomes wider. Most recently, this paradigm has been applied to the core transport barriers formed in plasmas with negative or low magnetic shear in the plasma core. These examples of confinement improvement are of considerable physical interest; it is not often that a system self-organizes to a higher energy state with reduced turbulence and transport when an additional source of free energy is applied to it. The transport decrease that is associated with ExB velocity shear effects also has significant practical consequences for fusion research. The fundamental physics involved in transport reduction is the effect of ExB shear on the growth, radial extent and phase correlation of turbulent eddies in the plasma. The same fundamental transport reduction process can be operational in various portions of the plasma because there are a number ways to change the radial electric field Er. An important theme in this area is the synergistic effect of ExB velocity shear and magnetic shear. Although the ExB velocity shear appears to have an effect on broader classes of microturbulence, magnetic shear can mitigate some potentially harmful effects of ExB velocity shear and facilitate turbulence stabilization.

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Effects of E×B velocity shear and magnetic shear on turbulence and transport in magnetic confinement devices

The understanding and predictive capability of transport physics and plasma confinement is reviewed from the perspective of achieving reactor-scale burning plasmas in the ITER tokamak, for both core and edge plasma regions. Very considerable progress has been made in understanding, controlling and predicting tokamak transport across a wide variety of plasma conditions and regimes since the publication of the ITER Physics Basis (IPB) document (1999 Nucl. Fusion 39 2137-2664). Major areas of progress considered here follow. (1) Substantial improvement in the physics content, capability and reliability of transport simulation and modelling codes, leading to much increased theory/experiment interaction as these codes are increasingly used to interpret and predict experiment. (2) Remarkable progress has been made in developing and understanding regimes of improved core confinement. Internal transport barriers and other forms of reduced core transport are now routinely obtained in all the leading tokamak devices worldwide. (3) The importance of controlling the H-mode edge pedestal is now generally recognized. Substantial progress has been made in extending high confinement H-mode operation to the Greenwald density, the demonstration of Type I ELM mitigation and control techniques and systematic explanation of Type I ELM stability. Theory-based predictive capability has also shown progress by integrating the plasma and neutral transport with MHD stability. (4) Transport projections to ITER are now made using three complementary approaches: empirical or global scaling, theory-based transport modelling and dimensionless parameter scaling (previously, empirical scaling was the dominant approach). For the ITER base case or the reference scenario of conventional ELMy H-mode operation, all three techniques predict that ITER will have sufficient confinement to meet its design target of Q = 10 operation, within similar uncertainties.

https://iopscience.iop.org/article/10.1088/0029-5515/47/6/S02/pdf

Chapter 2: Plasma confinement and transport

In addition to the operational limits imposed by MHD stability on plasma current and pressure, an independent limit on plasma density is observed in confined toroidal plasmas. This review attempts to summarize recent work on the phenomenology and physics of the density limit. Perhaps the most surprising result is that all of the toroidal confinement devices considered operate in similar ranges of (suitably normalized) densities. The empirical scalings derived independently for tokamaks and reversed-field pinches are essentially identical, while stellarators appear to operate at somewhat higher densities with a different scaling. Dedicated density limit experiments have not been carried out for spheromaks and field-reversed configurations, however, `optimized' discharges in these devices are also well characterized by the same empirical law. In tokamaks, where the most extensive studies have been conducted, there is strong evidence linking the limit to physics near the plasma boundary: thus, it is possible to extend the operational range for line-averaged density by operating with peaked density profiles. Additional particles in the plasma core apparently have no effect on density limit physics. While there is no widely accepted, first principles model for the density limit, research in this area has focussed on mechanisms which lead to strong edge cooling. Theoretical work has concentrated on the consequences of increased impurity radiation which may dominate power balance at high densities and low temperatures. These theories are not entirely satisfactory as they require assumptions about edge transport and make predictions for power and impurity scaling that may not be consistent with experimental results. A separate thread of research looks for the cause in collisionality enhanced turbulent transport. While there is experimental and theoretical support for this approach, understanding of the underlying mechanisms is only at a rudimentary stage and no predictive capability is yet available.

https://iopscience.iop.org/article/10.1088/0741-3335/44/8/201/pdf

Density limits in toroidal plasmas

This is a review of what is known about fluctuations and anomalous transport processes in tokamaks. It mostly considers experimental results obtained after, and not included in, the reviews of Liewer [Nucl. Fusion 25, 543 (1985)], Robinson [in Turbulence and Anomalous Transport in Magnetized Plasmas (Ecole Polytechnique, Palaiseau, France, 1986), p. 21], and Surko [in Turbulence and Anomalous Transport in Magnetized Plasmas (Ecole Polytechnique, Palaiseau, France, 1986), p. 93]. Therefore much of the pioneering work in the field is not covered. Emphasis is placed on results where comparisons between fluctuations and transport properties have been attempted, particularly from the tokamak TEXT [Nucl. Technol./Fusion 1, 479 (1981)]. A brief comparison of experimentally measured total fluxes with the predictions of neoclassical theory demonstrates that transport is often anomalous; fluctuations are thought to be the cause.The measurements necessary to determine any such fluctuation‐driven fluxes are described. The diagnostics used to measure these quantities, together with some of the statistical techniques employed to analyze the data, are outlined. In the plasma edge detailed measurements of the quantities required to directly determine the fluctuation‐driven fluxes are available. The total and fluctuation‐driven fluxes are compared: the result emphasizes the importance of edge turbulence. No model adequately describes all the measured properties. In the confinement region experimental observations are presently restricted to measurements of density and potential fluctuations and their correlations. Various distinct turbulence features that have been observed are described, and their characteristics compared with the predictions of various models. Correlations observed between these fluctuations and plasma transport properties are summarized. A separate section on magnetic fluctuations shows there is very little information available inside the plasma, generally prohibiting quantified comparisons between fluctuation levels and transport. Both coherent and turbulent magnetic fluctuations are addressed, and the differences between low and high plasma pressure (low and high beta) are noted. The contributions of alternate confinement devices, such as stellarators and reversed field pinches, to understanding tokamak anomalous transport are discussed. Finally, future directions are proposed.

Fluctuations and anomalous transport in tokamaks

The mechanism for generation of mean poloidal flow by turbulence is identified and elucidated. Two methods of calculating poloidal flow acceleration are given and shown to yield predictions which agree. These methods link flow generation to the quasilinear radial current or the Reynolds stress 〈VrVθ〉. It is shown that poloidal acceleration will occur if the turbulence supports radially propagating waves and if radial gradients in the turbulent Reynolds stress and wave energy density flux are present. In practice, these conditions are met in the tokamak edge region when waves propagate through the outermost closed flux surface or when convection cells with large radial correlation length are situated in steep gradient regions. The possible impact of these results on the theory of the L→H transition is discussed.

Theory of mean poloidal flow generation by turbulence

The electrostatic fluctuations are decorrelated in the region of a naturally occurring ${\mathbf{E}}_{\mathit{r}}$\ifmmode\times\else\texttimes\fi{}B velocity shear close to the outermost closed flux surface of regular Ohmic TEXT discharges. The concomitant local steepening of the density profile and suppression of the fluctuations are consistent with theoretical predictions. The high-confinement mode found in other tokamaks shows, in exaggerated form, similar characteristics, and could thus be related to the same mechanism leading to a locally improved confinement.

Evidence for confinement improvement by velocity-shear suppression of edge turbulence.

A quantitative comparison of the fluctuation-induced energy flux with the total energy flux has been made in the edge region of the TEXT tokamak using fluctuation measurements from Langmuir, heavy-ion-beam, and magnetic probes. At all but the lowest densities the convected energy flux due to electrostatic fluctuations dominates the energy losses caused by plasma transport. Energy loss through magnetic fluctuations is insignificant in the edge.

Fluctuation-induced energy flux in the tokamak edge.

A new scheme to extend the triple Langmuir probe technique for the measurement of electron temperature fluctuations and the fluctuation‐driven transport has been developed. The extension is aimed at reducing the phase delay error introduced by finite probe tip separations in standard triple‐probe method. The modified triple‐probe scheme provides a more reliable measurement of the temperature fluctuations for a proper interpretation of the density and potential fluctuations and the transport measurement from Langmuir probe data. New results on fluctuations have been obtained from Phaedrus‐T and TEXT‐U tokamaks.

A new scheme for Langmuir probe measurement of transport and electron temperature fluctuations

A heavy ion beam probe has been used to measure the plasma space potential profiles in the tokamak TEXT [Nucl. Fusion Technol. 1, 479 (1981)]. The Ohmic discharges studied were perturbed by externally produced resonant magnetic fields (an ergodic magnetic limiter or EML). Without these perturbations the plasma central potential is generally consistent with the value calculated from radial ion momentum balance, using experimental values of density and ion temperature and assuming a neoclassical poloidal rotation velocity. Exceptions to the agreement are found when operating with reduced plasma parameters. Possible reasons for this discrepancy are explored, in particular, the effects of intrinsic magnetic field fluctuations, and modifications to the self‐consistent radial electric sheath. With the application of the EML fields the edge electric field and potential increase during periods of magnetic island overlap. A test particle calculation of electron transport shows increases in diffusivity also occur during periods of magnetic island overlap. These calculated changes in diffusivity are interpreted in terms of a stochastic layer width, which is itself used to predict a potential change for comparison with the experimental results.

The space potential in the tokamak text

Using the technique first described by Robinson and Rusbridge [Plasma Phys. 11, 73 (1969)] electron temperature fluctuations have been measured in the scrape‐off layer of the TEXT tokamak [Nucl. Technol. Fusion 1, 479 (1981)] to be Te/Te ≂0.4ne/ne. Particle and energy transport were estimated from 〈ne Eθ〉 and 〈Te Eθ〉 correlations. The fluctuation‐driven particle transport was consistent with earlier measurements and with measurements of global particle confinement. A high correlation of temperature and electric field fluctuations and a low but positive correlation between density and temperature fluctuations were observed.

H. Lin

Papers

Evidence for confinement improvement by velocity-shear suppression of edge turbulence.

Fluctuation-induced energy flux in the tokamak edge.

A new scheme for Langmuir probe measurement of transport and electron temperature fluctuations

The space potential in the tokamak text

Temperature fluctuations and transport in a tokamak edge plasma