[en] There is compelling empirical [1] and theoretical [2] evidence that the global confinement of H-mode discharges increases as the pedestal pressure or temperature increases. Therefore, confidence in the performance of future machines requires an ability to predict the pedestal conditions in those machines. At this time, both the theoretical and empirical understanding of transport in the pedestal are incomplete and are inadequate to predict pedestal conditions in present or future machines. Recent empirical results might be evidence of a fundamental relation between the electron temperature T_e and electron density n_e profiles in the pedestal. A data set from the ASDEX-Upgrade tokamak has shown that η_e, the ratio between the scale lengths of the n_e and T_e profiles, exhibits a value of about 2 throughout the pedestal, despite a large range of the actual density and temperature values [3]. Data from the DIII-D tokamak show that over a wide range of pedestal density, the width of the steep gradient region for the T_e profile is about 1-2 times the corresponding width for the n_e profile, where both widths are measured from the plasma edge [4]. Thus, the barrier in the density might form a lower limit for the barrier in the electron temperature

[en] The scaling of pedestal pressure with global beta, shaping, and toroidal rotation is examined. The pedestal pressure is observed to increase with higher global beta and increased shaping, but is not significantly affected by changes to toroidal rotation. Stability analysis of the pedestal is utilized to extract the respective contributions of pedestal gradient and pedestal width to the scaling of the pedestal pressure. An increase in pedestal width accounts for approximately half of the observed increase in pedestal pressure with improved edge stability. The pedestal width is observed to scale with the normalized pedestal pressure as Δ∝β_ped^1/2. No ion gyroradius dependence of the pedestal width is observed

[en] We assess the accuracy and limitations of two analytic models of the tokamak bootstrap current: (1) the well-known Sauter model (1999 Phys. Plasmas 6 2834, 2002 Phys. Plasmas 9 5140) and (2) a recent modification of the Sauter model by Koh et al (2012 Phys. Plasmas 19 072505). For this study, we use simulations from the first-principles kinetic code NEO as the baseline to which the models are compared. Tests are performed using both theoretical parameter scans as well as core-to-edge scans of real DIII-D and NSTX plasma profiles. The effects of extreme aspect ratio, large impurity fraction, energetic particles, and high collisionality are studied. In particular, the error in neglecting cross-species collisional coupling—an approximation inherent to both analytic models—is quantified. Furthermore, the implications of the corrections from kinetic NEO simulations on MHD equilibrium reconstructions is studied via integrated modeling with kinetic EFIT. (paper)

[en] Understanding the stability physics of the H-mode pedestal in tokamak devices requires an accurate measurement of plasma current in the pedestal region with good spatial resolution. Theoretically, the high pressure gradients achieved in the edge of H-mode plasmas should lead to generation of a significant edge current density peak through bootstrap and Pfirsh-Schl(umlt u)ter effects. This edge current is important for the achievement of second stability in the context of coupled magneto hydrodynamic (MHD) modes which are both pressure (ballooning) and current (peeling) driven. Many aspects of edge localized mode (ELM) behavior can be accounted for in terms of an edge current density peak, with the identification of Type 1 ELMs as intermediate-n toroidal mode number MHD modes being a natural feature of this model. The development of a edge localized instabilities in tokamak experiments code (ELITE) based on this model allows one to efficiently calculate the stability and growth of the relevant modes for a broad range of plasma parameters and thus provides a framework for understanding the limits on pedestal height. This however requires an accurate assessment of the edge current. While estimates of j_edge can be made based on specific bootstrap models, their validity may be limited in the edge (gradient scalelengths comparable to orbit size, large changes in collisionality, etc.). Therefore it is highly desirable to have an actual measurement. Such measurements have been made on the DIII-D tokamak using combined polarimetry and spectroscopy of an injected lithium beam. By analyzing one of the Zeeman-split 2S-2P lithium resonance line components, one can obtain direct information on the local magnetic field components. These values allow one to infer details of the edge current density. Because of the negligible Stark mixing of the relevant atomic levels in lithium, this method of determining j(r) is insensitive to the large local electric fields typically found in enhanced confinement (H-mode) edges, and thus avoids an ambiguity common to MSE measurements of B_pol

[en] In recent DIII-D experiments, we concentrated on extending the operating range and improving the overall performance of quiescent H-mode (QH) plasmas. The QH-mode offers an attractive, high-performance operating mode for burning plasmas due to the absence of pulsed edge-localized-mode-driven losses to the divertor (ELMs). Using counter neutral-beam injection (NBI), we achieve steady plasma conditions with the presence of an edge harmonic oscillation (EHO) replacing the ELMs and providing control of the edge pedestal density. These conditions have been maintained for greater than 4s (∼30 energy confinement times, τ_E, and 2 current relaxation times, τ_R [1]), and often limited only by the duration of auxiliary heating. We discuss results of these recent experiments where we use triangularity ramping to increase the density, neutral beam power ramps to increase the stored energy, injection of rf power at the electron cyclotron (EC) frequency to control density profile peaking in the core, and control of startup conditions to completely eliminate the transient ELMing phase

[en] The specific size and structure of the edge current profile has important effects on the magnetohydrodynamic stability and ultimate performance of many advanced tokamak (AT) operating modes. This is true for both bootstrap and externally driven currents that may be used to tailor the edge shear. Absent a direct local measurement of j(r), the best alternative is a determination of the poloidal field. Measurements of the precision (0.1^o--0.01^o in magnetic pitch angle and 1--10 ms) necessary to address issues of stability and control and provide constraints for EFIT are difficult to do in the region of interest (ρ=0.9--1.1). Using Zeeman polarization spectroscopy of the 2S--2P lithium resonance line emission from the DIII-D LIBEAM [D. M. Thomas, Rev. Sci. Instrum. 66, 806 (1995); D. M. Thomas, A. W. Hyatt, and M. P. Thomas, Rev. Sci. Instrum. 61, 340 (1990)] measurements of the various field components may be made to the necessary precision in exactly the region of interest to these studies. Because of the negligible Stark mixing of the relevant atomic levels, this method of determining j(r) is insensitive to the large local electric fields typically found in enhanced confinement (H mode) edges, and thus avoids an ambiguity common to motional Stark effect measurements of B. Key issues for utilizing this technique include good beam quality, an optimum viewing geometry, and a suitable optical prefilter to isolate the polarized emission line. A prospective diagnostic system for the DIII-D AT program will be described

[en] The evolution and performance limits for the pedestal in H-mode are dependent on the two main drive terms for instability: namely the edge pressure gradient and the edge current density. These terms are naturally coupled though neoclassical (Pfirsch-Schluter and bootstrap) effects. On DIII-D, local measurements of the edge current density are made using an injected lithium beam in conjunction with Zeeman polarimetry and compared with pressure profile measurements made with other diagnostics. These measurements have confirmed the close spatial and temporal correlation that exists between the measured current density and the edge pressure in H- and QH-mode pedestals, where substantial pressure gradients exist. In the present work we examine the changes in the measured edge current for DIII-D pedestals which have a range of values for the ion and electron collisionalities {υ_i*,υ_e*} due to fuelling effects. Such changes in the collisionality in the edge are expected to significantly alter the level of the bootstrap current from the value predicted from the collisionless limit and therefore should correspondingly alter the pedestal stability limits. We find a clear decrease in measured current as ν increases, even for discharges having similar edge pressure gradients

[en] Quiescent double barrier (QDB) conditions often form when an internal transport barrier is created with high-power neutral-beam injection into a quiescent H-mode (QH) plasma. These QH-modes offer an attractive, high-performance operating scenario for burning plasma experiments due to their quasi-stationarity and lack of edge localized modes (ELMs). Our initial experiments and modeling using ECH/ECCD in QDB shots were designed to control the current profile and, indeed, we have observed a strong dependence on the q-profile when EC-power is used inside the core transport barrier region. While strong electron heating is observed with EC power injection, we also observe a drop in the other core parameters; ion temperature and rotation, electron density and impurity concentration. These dynamically changing conditions provide a rapid evolution of T_e T_i profiles accessible with 0.3 < (T_e T_i)_axis < 0.8 observed in QDB discharges. We are exploring the correlation and effects of observed density profile changes with respect to these time-dependent variations in the temperature ratio. Thermal and particle diffusivity calculations over this temperature ratio range indicate a consistency between the rise in temperature ratio and an increase in transport corresponding to the observed change in density

[en] 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=0.076β_θ,ped^1/2), 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.

[en] The quiescent H (QH) mode, an edge localized mode (ELM)-free, high-confinement mode, combines well with an internal transport barrier to form quiescent double barrier (QDB) stationary state, high performance plasmas. The QH-mode edge pedestal pressure is similar to that seen in ELMing phases of the same discharge, with similar global energy confinement. The pedestal density in early ELMing phases of strongly pumped counter injection discharges drops and a transition to QH-mode occurs, leading to lower calculated edge bootstrap current. Plasmas current ramp experiment and ELITE code modeling of edge stability suggest that QH-modes lie near an edge current stability boundary. At high triangularity, QH-mode discharges operate at higher pedestal density and pressure, and have achieved ITER level values of β_PED and ν*. The QDB achieves performance of α_NH₈₉ ∼ 7 in quasi-stationary conditions for a duration of 10 tE, limited by hardware. Recently we demonstrated stationary state QDB discharges with little change in kinetic and q profiles (q₀ > 1) for 2 s, comparable to ELMing ''hybrid scenarios'', yet without the debilitating effects of ELMs. Plasma profile control tools, including electron cyclotron heating and current drive and neutral beam heating, have been demonstrated to control simultaneously the q profile development, the density peaking, impurity accumulation and plasma beta