The major increase in discharge duration and plasma energy in a next step DT fusion reactor will give rise to important plasma-material effects that will critically influence its operation, safety and performance. Erosion will increase to a scale of several centimetres from being barely measurable at a micron scale in today's tokamaks. Tritium co-deposited with carbon will strongly affect the operation of machines with carbon plasma facing components. Controlling plasma-wall interactions is critical to achieving high performance in present day tokamaks, and this is likely to continue to be the case in the approach to practical fusion reactors. Recognition of the important consequences of these phenomena stimulated an internationally co-ordinated effort in the field of plasma-surface interactions supporting the Engineering Design Activities of the International Thermonuclear Experimental Reactor project (ITER), and significant progress has been made in better understanding these issues. The paper reviews the underlying physical processes and the existing experimental database of plasma-material interactions both in tokamaks and laboratory simulation facilities for conditions of direct relevance to next step fusion reactors. Two main topical groups of interaction are considered: (i) erosion/redeposition from plasma sputtering and disruptions, including dust and flake generation and (ii) tritium retention and removal. The use of modelling tools to interpret the experimental results and make projections for conditions expected in future devices is explained. Outstanding technical issues and specific recommendations on potential R&D avenues for their resolution are presented.

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Plasma{material interactions in current tokamaks and their implications for next step fusion reactors

Progress in the area of MHD stability and disruptions, since the publication of the 1999 ITER Physics Basis document (1999 Nucl. Fusion 39 2137-2664), is reviewed. Recent theoretical and experimental research has made important advances in both understanding and control of MHD stability in tokamak plasmas. Sawteeth are anticipated in the ITER baseline ELMy H-mode scenario, but the tools exist to avoid or control them through localized current drive or fast ion generation. Active control of other MHD instabilities will most likely be also required in ITER. Extrapolation from existing experiments indicates that stabilization of neoclassical tearing modes by highly localized feedback-controlled current drive should be possible in ITER. Resistive wall modes are a key issue for advanced scenarios, but again, existing experiments indicate that these modes can be stabilized by a combination of plasma rotation and direct feedback control with non-axisymmetric coils. Reduction of error fields is a requirement for avoiding non-rotating magnetic island formation and for maintaining plasma rotation to help stabilize resistive wall modes. Recent experiments have shown the feasibility of reducing error fields to an acceptable level by means of non-axisymmetric coils, possibly controlled by feedback. The MHD stability limits associated with advanced scenarios are becoming well understood theoretically, and can be extended by tailoring of the pressure and current density profiles as well as by other techniques mentioned here. There have been significant advances also in the control of disruptions, most notably by injection of massive quantities of gas, leading to reduced halo current fractions and a larger fraction of the total thermal and magnetic energy dissipated by radiation. These advances in disruption control are supported by the development of means to predict impending disruption, most notably using neural networks. In addition to these advances in means to control or ameliorate the consequences of MHD instabilities, there has been significant progress in improving physics understanding and modelling. This progress has been in areas including the mechanisms governing NTM growth and seeding, in understanding the damping controlling RWM stability and in modelling RWM feedback schemes. For disruptions there has been continued progress on the instability mechanisms that underlie various classes of disruption, on the detailed modelling of halo currents and forces and in refining predictions of quench rates and disruption power loads. Overall the studies reviewed in this chapter demonstrate that MHD instabilities can be controlled, avoided or ameliorated to the extent that they should not compromise ITER operation, though they will necessarily impose a range of constraints.

https://iopscience.iop.org/article/10.1088/0029-5515/47/6/S03/pdf

Chapter 3: MHD stability, operational limits and disruptions

The ITER Physics Basis presents and evaluates the physics rules and methodologies for plasma performance projections, which provide the basis for the design of a tokamak burning plasma device whose goal is to demonstrate the scientific and technological feasibility of fusion energy for peaceful purposes. This Chapter summarizes the physics basis for burning plasma projections, which is developed in detail by the ITER Physics Expert Groups in subsequent chapters. To set context, the design guidelines and requirements established in the report of ITER Special Working Group 1 are presented, as are the specifics of the tokamak design developed in the Final Design Report of the ITER Engineering Design Activities, which exemplifies burning tokamak plasma experiments. The behaviour of a tokamak plasma is determined by the interaction of many diverse physics processes, all of which bear on projections for both a burning plasma experiment and an eventual tokamak reactor. Key processes summarized here are energy and particle confinement and the H-mode power threshold; MHD stability, including pressure and density limits, neoclassical islands, error fields, disruptions, sawteeth, and ELMs; power and particle exhaust, involving divertor power dispersal, helium exhaust, fuelling and density control, H-mode edge transition region, erosion of plasma facing components, tritium retention; energetic particle physics; auxiliary power physics; and the physics of plasma diagnostics. Summaries of projection methodologies, together with estimates of their attendant uncertainties, are presented in each of these areas. Since each physics element has its own scaling properties, an integrated experimental demonstration of the balance between the combined processes which obtains in a reactor plasma is inaccessible to contemporary experimental facilities: it requires a reactor scale device. It is argued, moreover, that a burning plasma experiment can be sufficiently flexible to permit operation in a steady state mode, with non-inductive plasma current drive, as well as in a pulsed mode where current is inductively driven. Overall, the ITER Physics Basis can support a range of candidate designs for a tokamak burning plasma facility. For each design, there will remain a significant uncertainty in the projected performance, but the projection methodologies outlined here do suffice to specify the major parameters of such a facility and form the basis for assuring that its phased operation will return sufficient information to design a prototype commercial fusion power reactor, thus fulfilling the goal of the ITER project.

https://iopscience.iop.org/article/10.1088/0029-5515/39/12/301/pdf

Chapter 1: Overview and summary

Nonlinear gyrokinetic equations play a fundamental role in our understanding of the long-time behavior of strongly magnetized plasmas. The foundations of modern nonlinear gyrokinetic the- ory are based on three important pillars: (1) a gyrokinetic Vlasov equation written in terms of a gyrocenter Hamiltonian with quadratic low-frequency ponderomotive-like terms; (2) a set of gyrokinetic Maxwell (Poisson-Ampere) equations written in terms of the gyrocenter Vlasov dis- tribution that contain low-frequency polarization (Poisson) and magnetization (Ampere) terms derived from the quadratic nonlinearities in the gyrocenter Hamiltonian; and (3) an exact energy conservationlaw for the gyrokineticVlasov-Maxwell equations that includes all the relevant linear and nonlinear coupling terms. The foundations of nonlinear gyrokinetic theory are reviewed with an emphasis on the rigorous applications of Lagrangian and Hamiltonian Lie-transform perturba- tion methods used in the variationalderivationof nonlineargyrokineticVlasov-Maxwell equations. The physical motivations and applications of the nonlinear gyrokinetic equations, which describe the turbulent evolution of low-frequency electromagnetic fluctuations in a nonuniform magnetized plasmas with arbitrary magnetic geometry, are also discussed.

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Foundations of nonlinear gyrokinetic theory

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

Radial impurity density profiles in the H-mode edge pedestal region of Alcator C-Mod have been quantitatively derived from very high-resolution ( mm) measurements of , , and x-ray emissivity of fluorine at two poloidal locations (outboard midplane and top). At the midplane, the observed inward shift of the fluorine density ( ) pedestal with respect to the pedestal is found to be consistent with the neoclassical pinch velocity, both in magnitude and spatial structure. The empirically observed dependencies of the soft x-ray emissivity pedestal width on plasma parameters and H-mode type are shown to be indicative of changes in the impurity diffusion coefficient, , at the plasma edge. The soft x-ray pedestal profile at the top of the plasma varies considerably from that at the midplane, implying that impurity density is not constant on flux surfaces. Specifically, the top pedestal is close to the separatrix, unlike the midplane pedestal. An accumulation of impurities at the top of the plasma could, in principle, explain this difference, and is qualitatively consistent with the neoclassically predicted Pfirsch-Schl¨ uter return flow in the pedestal region in response to the ion drift.

Robert Granetz

Papers

Radial and Poloidal Impurity Transport in the H-mode Edge Pedestal of Alcator C-Mod