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.

A stochastic magnetic boundary, produced by an applied edge resonant magnetic perturbation, is used to suppress most large edge-localized modes (ELMs) in high confinement (H-mode) plasmas. The resulting H mode displays rapid, small oscillations with a bursty character modulated by a coherent 130 Hz envelope. The H mode transport barrier and core confinement are unaffected by the stochastic boundary, despite a threefold drop in the toroidal rotation. These results demonstrate that stochastic boundaries are compatible with H modes and may be attractive for ELM control in next-step fusion tokamaks.

A critical issue for fusion plasma research is the erosion of the first wall of the experimental device due to impulsive heating from repetitive edge magneto-hydrodynamic (MHD) instabilities known as "edge-localized modes" (ELMs). Here, we show that the addition of small resonant magnetic field perturbations completely eliminates ELMs while maintaining a steady-state highconfinement (H-mode) plasma. These perturbations induce a chaotic behaviour in the magnetic field lines, which reduces the edge pressure gradient below the ELM instability threshold. The pressure gradient reduction results from a reduction in particle content of the plasma, rather than an increase in the electron thermal transport. This is inconsistent with the predictions of stochastic electron heat transport theory. These results provide a first experimental test of stochastic transport theory in a highly rotating, hot, collisionless plasma and demonstrate a promising solution to the critical issue of controlling edge instabilities in fusion plasma devices. Nature Physics. 3Maximizing the fusion power production in toroidally symmetric magnetic confinement devices (tokamaks 1,2 ) requires high-confinement (H-mode) plasma conditions that have high edge plasma pressures. A ubiquitous feature of these high edge pressure, steady state, H-mode tokamak plasmas is repetitive instabilities known as "edge-localized modes" (ELMs) which release a significant fraction of the thermal energy of the plasma to the first wall of the device.These instabilities are a class of ideal magneto-hydrodynamic (MHD) modes produced in a high pressure gradient region at the plasma edge (called the "pedestal") where pressure gradient driven "ballooning" modes can couple to current density driven "peeling" modes 3 . While ELMs provide a natural transport process that controls the core plasma density and edge impurity ion penetration, they also represent a significant concern for burning plasma devices such as the ! n e ped ) to achieve significant fusion power gain factors, Q ≥ 10, they must operate below ! " e * = 0.1. In this case each ELM is expected to expel up to 20% of the pedestal energy over a time interval of a few hundred µs. If allowed to reach plasma-facing wall components, energy impulses of this magnitude will cause increased erosion of plasma facing components and significantly reduce their lifetime 5,6 . Thus, controlling ELMs by replacing the energy impulses with an equivalent but more continuous transport process is a high priority issue for tokamak fusion research.A particularly appealing ELM control approach in low the RMP field causes a larger change in the edge particle balance (i.e., changes in the balance between outward particle transport and edge particle sources and sinks) rather than in the thermal transport across the pedestal is both surprising and theoretically challenging.As in previous high is satisfied, these small ELMs disappear, leaving the plasma in a very quiet state (Fig. 3a), and the pedestal density ! n e ped begins to fall w...

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.

The ‘Progress in the ITER Physics Basis’ (PIPB) document is an update of the ‘ITER Physics Basis’ (IPB), which was published in 1999 [1]. The IPB provided methodologies for projecting the performance of burning plasmas, developed largely through coordinated experimental, modelling and theoretical activities carried out on today's large tokamaks (ITER Physics R&D). In the IPB, projections for ITER (1998 Design) were also presented. The IPB also pointed out some outstanding issues. These issues have been addressed by the Participant Teams of ITER (the European Union, Japan, Russia and the USA), for which International Tokamak Physics Activities (ITPA) provided a forum of scientists, focusing on open issues pointed out in the IPB. The new methodologies of projection and control are applied to ITER, which was redesigned under revised technical objectives. These analyses suggest that the achievement of Q > 10 in the inductive operation is feasible. Further, improved confinement and beta observed with low shear (= high βp = ‘hybrid’) operation scenarios, if achieved in ITER, could provide attractive scenarios with high Q (> 10), long pulse (>1000 s) operation with beta