Progress, since the ITER Physics Basis publication (ITER Physics Basis Editors et al 1999 Nucl. Fusion 39 2137–2664), in understanding the processes that will determine the properties of the plasma edge and its interaction with material elements in ITER is described. Experimental areas where significant progress has taken place are energy transport in the scrape-off layer (SOL) in particular of the anomalous transport scaling, particle transport in the SOL that plays a major role in the interaction of diverted plasmas with the main-chamber material elements, edge localized mode (ELM) energy deposition on material elements and the transport mechanism for the ELM energy from the main plasma to the plasma facing components, the physics of plasma detachment and neutral dynamics including the edge density profile structure and the control of plasma particle content and He removal, the erosion of low- and high-Z materials in fusion devices, their transport to the core plasma and their migration at the plasma edge including the formation of mixed materials, the processes determining the size and location of the retention of tritium in fusion devices and methods to remove it and the processes determining the efficiency of the various fuelling methods as well as their development towards the ITER requirements. This experimental progress has been accompanied by the development of modelling tools for the physical processes at the edge plasma and plasma–materials interaction and the further validation of these models by comparing their predictions with the new experimental results. Progress in the modelling development and validation has been mostly concentrated in the following areas: refinement in the predictions for ITER with plasma edge modelling codes by inclusion of detailed geometrical features of the divertor and the introduction of physical effects, which can play a major role in determining the divertor parameters at the divertor for ITER conditions such as hydrogen radiation transport and neutral–neutral collisions, modelling of the ion orbits at the plasma edge, which can play a role in determining power deposition at the divertor target, models for plasma–materials and plasma dynamics interaction during ELMs and disruptions, models for the transport of impurities at the plasma edge to describe the core contamination by impurities and the migration of eroded materials at the edge plasma and its associated tritium retention and models for the turbulent processes that determine the anomalous transport of energy and particles across the SOL. The implications for the expected performance of the reference regimes in ITER, the operation of the ITER device and the lifetime of the plasma facing materials are discussed.

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Chapter 4: Power and particle control

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

The pressure at the top of the edge transport barrier (or “pedestal height”) strongly impacts tokamak fusion performance. Predicting the pedestal height in future devices such as ITER [ITER Physics Basis Editors, Nucl. Fusion 39, 2137 (1999)] remains an important challenge. While uncertainties remain, magnetohydrodynamic stability calculations at intermediate wavelength (the “peeling-ballooning” model), accounting for diamagnetic stabilization, have been largely successful in determining the observed maximum pedestal height, when the edge barrier width is taken as an input. Here, we develop a second relation between the pedestal width in normalized poloidal flux (Δ) and pedestal height (Δ=0.076βθ,ped1/2), using an argument based upon kinetic ballooning mode turbulence and observation. Combining this relation with direct calculations of peeling-ballooning stability yields two constraints, which together determine both the height and width of the pedestal. The resulting model, EPED1, allows quantitative prediction of the pedestal height and width in both existing and future experiments. EPED1 is successfully tested both against a dedicated experiment on the DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] tokamak, in which predictions were made before the experiment, and against a broader DIII-D data set, including ITER demonstration discharges. EPED1 is found to quantitatively capture the observed complex dependencies of the pedestal height and width. An initial set of pedestal predictions for the ITER device is presented.

https://web.gat.com/pubs-ext/APS08/Snyder.pdf

Development and validation of a predictive model for the pedestal height

The pressure at the top of the edge transport barrier (or 'pedestal height') strongly impacts fusion performance, while large edge localized modes (ELMs), driven by the free energy in the pedestal region, can constrain material lifetimes. Accurately predicting the pedestal height and ELM behavior in ITER is an essential element of prediction and optimization of fusion performance. Investigation of intermediate wavelength MHD modes (or 'peeling–ballooning' modes) has led to an improved understanding of important constraints on the pedestal height and the mechanism for ELMs. The combination of high-resolution pedestal diagnostics, including substantial recent improvements, and a suite of highly efficient stability codes, has made edge stability analysis routine on several major tokamaks, contributing both to understanding, and to experimental planning and performance optimization. Here we present extensive comparisons of observations to predicted edge stability boundaries on several tokamaks, both for the standard (Type I) ELM regime, and for small ELM and ELM-free regimes. We further discuss a new predictive model for the pedestal height and width (EPED1), developed by self-consistently combining a simple width model with peeling–ballooning stability calculations. This model is tested against experimental measurements, and used in initial predictions of the pedestal height for ITER.

https://iopscience.iop.org/article/10.1088/0029-5515/49/8/085035/pdf

Pedestal stability comparison and ITER pedestal prediction

Edge conditions in DIII-D are being quantified in order to provide insight into the physics of the H?mode regime. Several studies show that electron temperature is not the key parameter that controls the L-H transition. Gradients of edge temperature and pressure are much more promising candidates for elements of such parameters. They systematically increase during the L phases of discharges which make a transition to H?mode, and these increases are typically larger than the increases in the underlying quantities. The quality of H?mode confinement is strongly correlated with the height of the H?mode pedestal for the pressure. The gradient of the pressure is limited by MHD modes, in particular by ideal kink ballooning modes with finite mode number n. For a wide variety of discharges, the width of the barrier for electron pressure is well described by a relationship that is proportional to (?pedp)1/2. A new regime of confinement, called the quiescent H?mode, which provides steady state operation with no ELMs, low radiated power and normal H?mode confinement, has been discovered. A coherent edge MHD mode provides adequate particle transport to control the plasma density while permitting the pressure pedestal to remain almost identical to that observed in ELMing discharges.

/pdf/progress-in-quantifying-the-edge-physics-of-the-h-mode-4re9nzruxr.pdf

Progress in quantifying the edge physics of the H mode regime in DIII-D

The structure and scaling of the H-mode pedestal are examined for discharges in the DIII-D tokamak. For typical conditions, the pedestal values of the ion and electron temperatures T{sub i} and T{sub e} are comparable. Measurements of main ion and C{sup 6+} profiles indicate that the ion pressure gradient in the barrier is 50%--100% of the electron pressure gradient for deuterium plasmas. The magnitude of the pressure gradient in the barrier often exceeds the predictions of infinite-n ballooning mode theory by a factor of two. Moreover, via the bootstrap current, the finite pressure gradient acts to entirely remove ballooning stability limits for typical discharges. For a large dataset, the width of the pressure barrier {delta} is best described by the dimensionless scaling {delta}/R {proportional_to} ({beta}{sub pol}{sup ped}){sup 0.4} where ({beta}{sub pol}{sup ped}) is the pedestal value of poloidal beta and R is the major radius. Scalings based on the poloidal ion gyroradius or the edge density gradient do not adequately describe overall trends in the data set and the propagation of the pressure barrier observed between edge-localized modes. The width of the T{sub i} barrier is quite variable and is not a good measure of the width of the pressure barrier.

https://digital.library.unt.edu/ark:/67531/metadc704569/m2/1/high_res_d/672006.pdf

R. J. Groebner

Papers

Scaling studies of the high mode pedestal