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 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 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.

A new modular code called BOUT++ is presented, which simulates 3D fluid equations in curvilinear coordinates. Although aimed at simulating Edge Localised Modes (ELMs) in tokamak x-point geometry, the code is able to simulate a wide range of fluid models (magnetised and unmagnetised) involving an arbitrary number of scalar and vector fields, in a wide range of geometries. Time evolution is fully implicit, and 3 rd -order WENO schemes are implemented. Benchmarks are presented for linear and non-linear problems (the Orszag-Tang vortex) showing good agreement. Performance of the code is tested by scaling with problem size and processor number, showing efficient scaling to thousands of processors.Linear initial-value simulations of ELMs using reduced ideal MHD are presented, and the results compared to the ELITE linear MHD eigenvalue code. The resulting mode-structures and growth-rate are found to be in good agreement (γBOUT ++ = 0.245ωA, γELIT E = 0.239ωA, with Alfvénic timescale 1/ωA = R/VA). To our knowledge, this is the first time dissipationless, initial-value simulations of ELMs have been successfully demonstrated.

A new computational tool, edge localized instabilities in tokamaks equilibria ͑ELITE͒, has been developed to help our understanding of short wavelength instabilities close to the edge of tokamak plasmas. Such instabilities may be responsible for the edge localized modes observed in high confinement H-mode regimes, which are a serious concern for next step tokamaks because of the high transient power loads which they can impose on divertor target plates. ELITE uses physical insight gained from analytic studies of peeling and ballooning modes to provide an efficient way of calculating the edge ideal magnetohydrodynamic stability properties of tokamaks. This paper describes the theoretical formalism which forms the basis for the code.

Understanding the physics of the edge pedestal and edge localized modes (ELMs) is of great importance for ITER and the optimization of the tokamak concept. The peeling-ballooning model has quantitatively explained many observations, including ELM onset and pedestal constraints, in the standard H-mode regime. The ELITE code has been developed to efficiently evaluate peeling-ballooning stability for comparison to observation and predictions for future devices. We briefly present recent progress in the peelingballooning model, including studies of the apparent power dependence of the pedestal, and studies of the impact of sheared toroidal flow. Nonlinear 3D simulations of ELM dynamics using the BOUT code are also described, leading to an emerging understanding of the physics of the onset and dynamics of ELMs in the standard intermediate to high collisionality regime. Recently, highly promising low collisionality regimes without ELMs have been discovered, including the quiescent H-mode (QH) and resonant magnetic perturbation (RMP) regimes. We present recent observations of the density, shape and rotation dependence of QH discharges, and studies of the peeling-ballooning stability in this regime. We propose a model of the QH-mode in which the observed edge harmonic oscillation (EHO) is a saturated kink/peeling mode which is destabilized by current and rotation, and drives significant transport, allowing a near steady-state edge plasma. The model quantitatively predicts the observed density dependence, and qualitatively predicts observed mode structure, rotation dependence, and outer gap dependence. Low density RMP discharges are found to operate in a similar regime, but with the EHO replaced by an applied magnetic perturbation.

A closed set of fluid moment equations including models of kinetic Landau damping is developed which describes the evolution of collisionless plasmas in the magnetohydrodynamic parameter regime. The model is fully electromagnetic and describes the dynamics of both compressional and shear Alfvén waves, as well as ion acoustic waves. The model allows for separate parallel and perpendicular pressures p∥ and p⊥, and, unlike previous models such as the Chew–Goldberger–Low theory, correctly predicts the instability threshold for the mirror instability. Both a simple 3+1 moment model and a more accurate 4+2 moment model are developed, and both could be useful for numerical simulations of astrophysical and fusion plasmas.