Culham Centre for Fusion Energy

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.

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.

Solitary electrostatic structures involving density depletions have been observed in the upper ionosphere by the Freja satellite [ Dovner et al. , 1994]. If these are interpreted as ion sound solitons, the difficulty arises that the standard Korteweg‐de Vries description predicts structures with enhanced rather than depleted density. Here we show that the presence of non‐thermal electrons may change the nature of ion sound solitary structures and allow the existence of structures very like those observed.

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.

A procedure which reconciles long parallel wavelength, characteristic of plasma instabilities, with periodicity in a sheared toroidal magnetic field is described. Applied to the problem of high-$n$ ballooning modes in tokamaks it makes possible a full minimization of the potential energy functional $\ensuremath{\delta}W$ and shows that previous calculations overestimated stability.

A model based on magnetohydrodynamic (MHD) stability of the tokamak plasma edge region is presented, which describes characteristics of edge localized modes (ELMs) and the pedestal. The model emphasizes the dual role played by large bootstrap currents driven by the sharp pressure gradients in the pedestal region. Pedestal currents reduce the edge magnetic shear, stabilizing high toroidal mode number (n) ballooning modes, while at the same time providing drive for intermediate to low n peeling modes. The result is that coupled peeling–ballooning modes at intermediate n (3<n<20) are often the limiting instability which constrains the pedestal and triggers ELMs. These modes are characterized in shaped tokamak equilibria using an efficient new numerical code, and simplified models are developed for pedestal limits and the ELM cycle. Results are compared to several experiments, and nonideal MHD effects are briefly discussed.

Scientific understanding of any kind of radiation effects starts from the primary damage, i.e. the defects that are produced right after an initial atomic displacement event initiated by a high-energy particle. In this Review, we consider the extensive experimental and computer simulation studies that have been performed over the past several decades on what the nature of the primary damage is. We review both the production of crystallographic or topological defects in materials as well as radiation mixing, i.e. the process where atoms in perfect crystallographic positions exchange positions with other ones in non-defective positions. All classes of materials except biological materials are considered. We also consider the recent effort to provide alternatives to the current international standard for quantifying this energetic particle damage, the Norgett-Robinson-Torrens displacements per atom (NRT-dpa) model for metals. We present in detail new complementary displacement production estimators (“athermal recombination corrected dpa”, arc-dpa) and atomic mixing (“replacements per atom”, rpa) functions that extend the NRT-dpa, and discuss their advantages and limitations.

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.

This chapter reviews the progress accomplished since the redaction of the first ITER Physics Basis (1999 Nucl. Fusion 39 2137-664) in the field of energetic ion physics and its possible impact on burning plasma regimes. New schemes to create energetic ions simulating the fusion-produced alphas are introduced, accessing experimental conditions of direct relevance for burning plasmas, in terms of the Alfvenic Mach number and of the normalised pressure gradient of the energetic ions, though orbit characteristics and size cannot always match those of ITER. Based on the experimental and theoretical knowledge of the effects of the toroidal magnetic field ripple on direct fast ion losses, ferritic inserts in ITER are expected to provide a significant reduction of ripple alpha losses in reversed shear configurations. The nonlinear fast ion interaction with kink and tearing modes is qualitatively understood, but quantitative predictions are missing, particularly for the stabilisation of sawteeth by fast particles that can trigger neoclassical tearing modes. A large database on the linear stability properties of the modes interacting with energetic ions, such as the Alfven eigenmode has been constructed. Comparisons between theoretical predictions and experimental measurements of mode structures and drive/damping rates approach a satisfactory degree of consistency, though systematic measurements and theory comparisons of damping and drive of intermediate and high mode numbers, the most relevant for ITER, still need to be performed. The nonlinear behaviour of Alfven eigenmodes close to marginal stability is well characterized theoretically and experimentally, which gives the opportunity to extract some information on the particle phase space distribution from the measured instability spectral features. Much less data exists for strongly unstable scenarios, characterised by nonlinear dynamical processes leading to energetic ion redistribution and losses, and identified in nonlinear numerical simulations of Alfven eigenmodes and energetic particle modes. Comparisons with theoretical and numerical analyses are needed to assess the potential implications of these regimes on burning plasma scenarios, including in the presence of a large number of modes simultaneously driven unstable by the fast ions.

Type-I edge-localized modes (ELMs) have been mitigated at the JET tokamak using a static external n=1 perturbation field generated by four error field correction coils located far from the plasma. During the application of the n=1 field the ELM frequency increased by a factor of 4 and the amplitude of the D(alpha) signal decreased. The energy loss per ELM normalized to the total stored energy, DeltaW/W, dropped to values below 2%. Transport analyses shows no or only a moderate (up to 20%) degradation of energy confinement time during the ELM mitigation phase.

Analysis of Type I ELMs from ongoing experiments shows that ELM energy losses are correlated with the density and temperature of the pedestal plasma before the ELM crash. The Type I ELM plasma energy loss normalized to the pedestal energy is found to correlate across experiments with the collisionality of the pedestal plasma (ν<sub>*ped</sub>), decreasing with increasing ν<sub>*ped</sub>. Other parameters affect the ELM size, such as the edge magnetic shear, etc, which influence the plasma volume affected by the ELMs. ELM particle losses are influenced by this ELM affected volume and are weakly dependent on other pedestal plasma parameters. In JET and DIII-D, under some conditions, ELMs can be observed (`minimum' Type I ELMs with energy losses acceptable for ITER), that do not affect the plasma temperature. The duration of the divertor ELM power pulse is correlated with the typical ion transport time from the pedestal to the divertor target (τ<sub>║</sub><sup>Front</sup> = 2πRq<sub>95</sub>/c<sub>s,ped</sub>) and not with the duration of the ELM-associated MHD activity. Similarly, the timescale of ELM particle fluxes is also determined by τ<sub>║</sub><sup>Front</sup>. The extrapolation of the present experimental results to ITER is summarized.

Abstract In the investigation of stability of a plasma confined by magnetic fields some of the most important modes of oscillation are those with long wavelength parallel to the magnetic field and short wavelength perpendicular to it. However, these characteristics conflict with the requirement of periodicity in a toroidal magnetic field with shear. This conflict can be resolved by transforming the calculation to one in an infinite domain without periodicity constraints. This transformation is the starting point for a full investigation of the magnetohydrodynamic stability of an axisymmetric plasma at large toroidal wave number n. (Small values of n can be studied by direct numerical computation but this fails when n is large.) For n > 1 there are two distinct length scales in the problem and a systematic approximation is developed around an eikonal representation, formally as an expansion in 1/n. In lowest order the oscillations of each magnetic surface are decoupled and a local eigenvalue is obtained. However, the mode structure is not fully determined in this lowest order. In higher orders a second eigenvalue equation is obtained which completes the determination of the structure of the mode and relates the local eigenvalue of the lower order theory to the true eigenvalue for the problem. This higher order theory shows that unstable modes are localized in the vicinity of the surface with the smallest local eigenvalue, that the true eigenvalue is close to the lowest local eigenvalue and that the most unstable high n modes occur for n-> oo. Hence the local theory, which involves no more than the solution of an ordinary differential equation, is normally adequate for the determination of stability of any axisymmetric plasma to high mode number oscillations.

We investigate the structure and mobility of single self-interstitial atom and vacancy defects in body-centered-cubic transition metals forming groups 5B (vanadium, niobium, and tantalum) and 6B (chromium, molybdenum, and tungsten) of the Periodic Table. Density-functional calculations show that in all these metals the axially symmetric ⟨111⟩ self-interstitial atom configuration has the lowest formation energy. In chromium, the difference between the energies of the ⟨111⟩ and the ⟨110⟩ self-interstitial configurations is very small, making the two structures almost degenerate. Local densities of states for the atoms forming the core of crowdion configurations exhibit systematic widening of the ``local'' $d$ band and an upward shift of the antibonding peak. Using the information provided by electronic structure calculations, we derive a family of Finnis-Sinclair-type interatomic potentials for vanadium, niobium, tantalum, molybdenum, and tungsten. Using these potentials, we investigate the thermally activated migration of self-interstitial atom defects in tungsten. We rationalize the results of simulations using analytical solutions of the multistring Frenkel-Kontorova model describing nonlinear elastic interactions between a defect and phonon excitations. We find that the discreteness of the crystal lattice plays a dominant part in the picture of mobility of defects. We are also able to explain the origin of the non-Arrhenius diffusion of crowdions and to show that at elevated temperatures the diffusion coefficient varies linearly as a function of absolute temperature.

A summary is given of the present status of research on plasma-surface interactions in tokamaks. Three groups of important interactions are considered: recycling of the principal ion species, usually hydrogen or deuterium; the release and effect of low-Z contaminants; and the release and effect of high-Z contaminants. In each case the basic physical processes are reviewed and the relevant data from particlebeam measurements are summarized. Emphasis is given to discussing the effect of the various surface interactions in present-day tokamak discharges and in future fusion reactors. Surface studies in tokamaks are reviewed and methods of controlling the surface interactions and their effects are considered.

The ITER neutral beam (NB) injectors are the first injectors that will have to operate under conditions and constraints similar to those that will be encountered in a fusion reactor. These injectors will have to operate in a hostile radiation environment and they will become highly radioactive due to the neutron flux from ITER. The injectors will use a single large ion source and accelerator that will produce 40 A 1 MeV D − beams for pulse lengths of up to 3600 s. Significant design changes have been made to the ITER heating NB (HNB) injector over the past 4 years. The main changes are: Modifications to allow installation and maintenance of the beamline components with an overhead crane. The beam source vessel shape has been changed and the beam source moved to allow more space for the connections between the 1 MV bushing and the beam source. The RF driven negative ion source has replaced the filamented ion source as the reference design. The ion source and extractor power supplies will be located in an air insulated high voltage (−1 MV) deck located outside the tokamak building instead of inside an SF 6 insulated HV deck located above the injector. Introduction of an all metal absolute valve to prevent any tritium in the machine to escape into the NB cell during maintenance. This paper describes the status of the design as of December 2008 including the above mentioned changes. The very important power supply system of the neutral beam injectors is not described in any detail as that merits a paper beyond the competence of the present authors. The R&D required to realize the injectors described in this paper must be carried out on a dedicated neutral beam test facility, which is not described here.

Theoretical and experimental research in the reversed-field pinch (RFP) is reviewed. In this system, Bθ ∼ Bϕ, q < 1 and Bϕ reverses in the outer regions of the plasma; stability at relatively high values of β is possible because there is high shear and, experimentally, confinement with β > 10% has been observed. Following a historical review of pinch research, the basic theoretical properties of the RFP are established including the equilibrium, toroidal displacement, diffusion and confinement; studies of ideal and dissipative MHD stability theory are then described. Experimental and theoretical work on relaxation and self-reversal, the process whereby an RFP distribution can be set up spontaneously and subsequently sustained, is presented and discussed. There follows a general account of RFP experiments. These are divided into 'fast experiments', which utilize small-bore insulating tori in which the distribution is usually set up by fast programming on microsecond timescales, and 'slow experiments', carried out in large metal-walled tori in which the field configuration is set up slowly by self-reversal on millisecond timescales. A brief account of RFP reactor studies and of new and future experiments is then given, followed finally by a general discussion in which the main conclusions are presented.

We present an investigation of systematic trends for the self-interstitial atom (SIA) defect behavior in body-centered cubic (bcc) transition metals using density-functional calculations. In all the nonmagnetic bcc metals the most stable SIA defect configuration has the $⟨111⟩$ symmetry. Metals in group 5B of the periodic table (V, Nb, Ta) have significantly different energies of formation of the $⟨111⟩$ and $⟨110⟩$ SIA configurations, while for the group 6B metals (Cr, Mo, W) the two configurations are linked by a soft bending mode. The relative energies of SIA defects in the nonmagnetic bcc metals are fundamentally different from those in ferromagnetic bcc $\ensuremath{\alpha}$-Fe. The systematic trend exhibited by the SIA defect structures in groups 5B and 6B transition metals correlates with the observed thermally activated mobility of SIA defects.

The maximum normalized beta achieved in long-pulse tokamak discharges at low collisionality falls significantly below both that observed in short pulse discharges and that predicted by the ideal MHD theory. Recent long-pulse experiments, in particular those simulating the International Thermonuclear Experimental Reactor (ITER) [M. Rosenbluth et al., Plasma Physics and Controlled Nuclear Fusion (International Atomic Energy Agency, Vienna, 1995), Vol. 2, p. 517] scenarios with low collisionality νe*, are often limited by low-m/n nonideal magnetohydrodynamic (MHD) modes. The effect of saturated MHD modes is a reduction of the confinement time by 10%–20%, depending on the island size and location, and can lead to a disruption. Recent theories on neoclassical destabilization of tearing modes, including the effects of a perturbed helical bootstrap current, are successful in explaining the qualitative behavior of the resistive modes and recent results are consistent with the size of the saturated islands. Also, a strong correlation is observed between the onset of these low-m/n modes with sawteeth, edge localized modes (ELM), or fishbone events, consistent with the seed island required by the theory. We will focus on a quantitative comparison between both the conventional resistive and neoclassical theories, and the experimental results of several machines, which have all observed these low-m/n nonideal modes. This enables us to single out the key issues in projecting the long-pulse beta limits of ITER-size tokamaks and also to discuss possible plasma control methods that can increase the soft β limit, decrease the seed perturbations, and/or diminish the effects on confinement.

We develop and test a model, EPED1.6, for the H-mode pedestal height and width based upon two fundamental and calculable constraints: (1) onset of non-local peeling–ballooning modes at low to intermediate mode number, (2) onset of nearly local kinetic ballooning modes at high mode number. Calculation of these two constraints allows a unique, predictive determination of both pedestal height and width. The present version of the model is first principles, in that no parameters are fit to observations, and includes important non-ideal effects. Extensive successful comparisons with existing experiments on multiple tokamaks, including experiments where predictions were made prior to the experiment, are presented, and predictions for ITER are discussed.

In JET, both high density and low-q operation are limited by disruptions. The density limit disruptions are caused initially by impurity radiation. This causes a contraction of the plasma temperature profile and leads to an MHD unstable configuration. There is evidence of magnetic island formation resulting in minor disruptions. After several minor disruptions, a major disruption with a rapid energy quench occurs. This event takes place in two stages. In the first stage there is a loss of energy from the central region. In the second stage there is a more rapid drop to a very low temperature, apparently due to a dramatic increase in impurity radiation. The final current decay takes place in the resulting cold plasma. During the growth of the MHD instability the initially rotating mode is brought to rest. This mode locking is believed to be due to an electromagnetic interaction with the vacuum vessel and external magnetic field asymmetries. The low-q disruptions are remarkable for the precision with which they occur at qψ = 2. These disruptions do not have extended precursors or minor disruptions. The instability grows and locks rapidly. The energy quench and current decay are generally similar to those of the density limit.