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 phenomenology of edge localized modes (ELMs), an MHD instability occurring in the edge of H-mode plasmas in toroidal magnetic fusion experiments, is described. ELMs are important to obtain experimental control of the particle inventory of fusion plasmas. From an analysis of the ELM behaviour of different magnetic fusion experiments, three distinct types are identified, namely dithering cycles, type III and type I ELMs. A physical picture of these phenomena is established on the grounds of theoretical models put forward to describe the different ELM phenomena.

https://iopscience.iop.org/article/10.1088/0741-3335/38/2/001/pdf

Edge localized modes (ELMs)

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

Effects of the plasma boundary can have a substantial influence on the behaviour of the entire plasma in tokamaks. Progress in the field, particularly that over the last decade, is reviewed, with emphasis on experimental observation. Simple modelling for interpretation is also included.

Plasma boundary phenomena in tokamaks

The input power requirements for accessing H-mode at low density and maintaining it during the density ramp in ITER is addressed by statistical means applied to the international H-mode threshold power database. Following the recent addition of new data, the improvement of existing data and the improvement of selection criteria, a revised scaling law that describes the threshold power required to obtain an L-mode to H-mode transition is presented. Predictions for ITER give a threshold power of ~52MW in a deuterium plasma at a line average density ne = 0.5×10 20 m -3 . At the nominal ITER H-mode density, ne = 1.0×10 20 m -3 , the threshold power required is ~86MW. Detailed analysis of data from individual devices suggests that the density dependence of the threshold power might increase with the plasma size and the magnetic field. On the other hand, the density at which the threshold power is minimal is found to decrease with the plasma size and increase with magnetic field. The influence of these effects on the accessibility of the H-mode regime in ITER plasmas is discussed. Analyses of the confinement database show that, in present day devices, H-modes are generally maintained with powers exceeding the threshold power by a factor larger than 1.5, and that, on the other hand, good confinement can be obtained close to the threshold power although rarely demonstrated.

https://iopscience.iop.org/article/10.1088/1742-6596/123/1/012033/pdf

Power requirement for accessing the H-mode in ITER

The authors' data indicate that the L-mode to H-mode transition in the DIII-D tokamak is associated with the sudden reduction in anomalous, fluctuation-connected transport across the outer midplane of the plasma. In addition to the reduction in edge density and magnetic fluctuations observed at the transition, the edge radial electric field becomes more negative after the transition. They have determined the scaling of the H-mode power threshold with various plasma parameters; the roughly linear increase with plasma density and toroidal field are particularly significant. Control of the ELM frequency and duration by adjusting neutral beam input power has allowed us to produce H-mode plasmas with constant impurity levels and durations up to 5 s. Energy confinement time in ohmic H-mode plasmas and in deuterium H-mode plasmas with deuterium beam injection can exceed saturated ohmic confinement times by at least a factor of two. Energy confinement times above 0.3 s have been achieved in these beam-heated plasmas with plasma currents in the range of 2.0 to 2.5 MA. Local transport studies have shown that electron and ion thermal diffusivities and angular momentum diffusivity are comparable in magnitude and all decrease with increasing plasma current.

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S L Allen

Papers

Confinement physics of H-mode discharges in DIII-D