T.H. Osborne

Edge localized modes and the pedestal: A model based on coupled peeling–ballooning modes

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.

Chapter 2: Plasma confinement and transport

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 first-principles predictive model of the pedestal height and width: development, testing and ITER optimization with the EPED model

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.

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 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 pre...

Role of the radial electric field in the transition from L (low) mode to H (high) mode to VH (very high) mode in the DIII-D tokamak

The hypothesis of stabilization of turbulence by shear in the E×B drift speed successfully predicts the observed turbulence reduction and confinement improvement seen at the L (low)–H (high) transition; in addition, the observed levels of E×B shear significantly exceed the value theoretically required to stabilize turbulence. Furthermore, this same hypothesis is the best explanation to date for the further confinement improvement seen in the plasma core when the plasma goes from the H mode to the VH (very high) mode. Consequently, the most fundamental question for H‐mode studies now is: How is the electric field Er formed? The radial force balance equation relates Er to the main ion pressure gradient ∇Pi, poloidal rotation vθi, and toroidal rotation vφi. In the plasma edge, observations show ∇Pi and vθi are the important terms at the L–H transition, with ∇Pi being the dominant, negative term throughout most of the H mode. In the plasma core, Er is primarily related to vφi. There is a clear temporal and sp...

Physics of the L-mode to H-mode transition in tokamaks

Combined theoretical and experimental work has resulted in the creation of a paradigm which has allowed semi-quantitative understanding of the edge confinement improvement that occurs in the H-mode. Shear in the E*B flow of the fluctuations in the plasma edge can lead to decorrelation of the fluctuations, decreased radial correlation lengths and reduced turbulent transport. Changes in the radial electric field, the density fluctuations and the edge transport consistent with shear stabilization of turbulence have been seen in several tokamaks. The purpose of this paper is to discuss the most recent data in the light of the basic paradigm of electric field shear stabilization and to critically compare the experimental results with various theories.

Suppression of large edge localized modes with edge resonant magnetic fields in high confinement DIII-D plasmas

Large sub-millisecond heat pulses due to Type-I edge localized modes (ELMs) have been eliminated reproducibly in DIII-D for periods approaching nine energy confinement times (τE) with small dc currents driven in a simple magnetic perturbation coil. The current required to eliminate all but a few isolated Type-I ELM impulses during a coil pulse is less than 0.4% of plasma current. Based on magnetic field line modelling, the perturbation fields resonate with plasma flux surfaces across most of the pedestal region (0.9 ≤ ψN ≤ 1.0) when q95 = 3.7 ± 0.2, creating small remnant magnetic islands surrounded by weakly stochastic field lines. The stored energy, βN, H-mode quality factor and global energy confinement time are unaltered by the magnetic perturbation. Although some isolated ELMs occur during the coil pulse, long periods free of large Type-I ELMs (Δt > 4–6 τE) have been reproduced numerous times, on multiple experimental run days in high and intermediate triangularity plasmas, including cases matching the baseline ITER scenario 2 flux surface shape. In low triangularity, lower single null plasmas, with collisionalities near that expected in ITER, Type-I ELMs are replaced by small amplitude, high frequency Type-II-like ELMs and are often accompanied by one or more ELM-free periods approaching 1–2 τE. Large Type-I ELM impulses represent a severe constraint on the survivability of the divertor target plates in future burning plasma devices. Results presented in this paper demonstrate that non-axisymmetric edge magnetic perturbations provide a very attractive development path for active ELM control in future tokamaks such as ITER.

STABILITY AND DYNAMICS OF THE EDGE PEDESTAL IN THE LOW COLLISIONALITY REGIME: PHYSICS MECHANISMS FOR STEADY-STATE ELM-FREE OPERATION

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 with observation and predictions for future devices. We briefly review recent progress in the peeling–ballooning model, including experimental validation of ELM onset and pedestal height predictions, and nonlinear 3D simulations of ELM dynamics, which together lead to an emerging understanding of the physics of the onset and dynamics of ELMs in the standard intermediate to high collisionality regime. We also discuss new studies of the apparent power dependence of the pedestal, and studies of the impact of sheared toroidal flow. 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 from the DIII-D tokamak 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.

Physics of the L to H transition in the DIII‐D tokamak

The L to H transition in the DIII‐D tokamak [Plasma Physics and Controlled Nuclear Fusion Research 1986 (IAEA, Vienna, 1987), Vol. I, p. 159] is associated with a decrease in the edge density and magnetic fluctuations. In addition, in single‐null divertor plasmas, a reduction in the heat flux asymmetry between the inner and outer divertor hit spots occurs. These observations indicate that the L to H transition is associated with the reduction in anomalous, fluctuation‐connected transport across the outer midplane of the plasma. Magnetic fluctuations are measured with a poloidally distributed set of Mirnov loops while density fluctuations are detected with multiple fixed‐frequency microwave reflectometers. Spectroscopic observations of edge poloidal and toroidal rotation have allowed the inference that the radial electric field just inside the separatrix is negative in the L mode and becomes more negative at the L to H transition. These changes in fluctuations and in the edge electric field occur in plasma...

ELMs and constraints on the H-mode pedestal: peeling-ballooning stability calculation and comparison with experiment

We review and test the peeling–ballooning model for edge localized modes (ELMs) and pedestal constraints, a model based upon theoretical analysis of magnetohydrodynamic (MHD) instabilities that can limit the pedestal height and drive ELMs. A highly efficient MHD stability code, ELITE, is used to calculate quantitative stability constraints on the pedestal, including constraints on the pedestal height. Because of the impact of collisionality on the bootstrap current, these pedestal constraints are dependent on the density and temperature separately, rather than simply on the pressure. ELITE stability calculations are directly compared with experimental data for a series of plasmas in which the density is varied and ELM characteristics change. In addition, a technique is developed whereby peeling–ballooning pedestal constraints are calculated as a function of key equilibrium parameters via ELITE calculations using series of model equilibria. This technique is used to successfully compare the expected pedestal height as a function of density, triangularity and plasma current with experimental data. Furthermore, the technique can be applied for parameter ranges beyond the purview of present experiments, and we present a brief projection of peeling–ballooning pedestal constraints for burning plasma tokamak designs.