R. J. Groebner

Equilibrium analysis of current profiles in tokamaks

An efficient method is given for self-consistent reconstruction of the tokamak current profiles and their associated magnetic topology using the magnetohydrodynamic (MHD) equilibrium constraint from external magnetic measurements, kinetic profile measurements, internal poloidal magnetic field measurements, and topological information from soft X-ray (SXR) measurements. Illustrative examples for beam heated H-mode divertor discharges in the DIII-D tokamak are presented, using the experimentally measured kinetic profile information and external magnetic data from the existing diagnostics. Comparative reconstructions of the current profile using various combinations of diagnostics are given. Also presented is an alternative magnetic analysis method in which the MHD equilibrium is reconstructed using external magnetic data and a constraint on the edge pressure gradient. The results of a sensitivity study are given which show that the axial safety factor q(0) can be more accurately determined when additional information from internal poloidal magnetic measurements is used in conjunction with the external magnetic, kinetic and SXR topological data.

An emerging understanding of H‐mode discharges in tokamaks*

A remarkable degree of consistency of experimental results from tokamaks throughout the world has developed with regard to the phenomenology of the transition from L‐mode to H‐mode confinement in tokamaks. The transition is initiated in a narrow layer at the plasma periphery where density fluctuations are suppressed and steep gradients of temperature and density form in a region with large first and second radial derivatives in the vE=(E×B)/B2 flow velocity. These results are qualitatively consistent with theories which predict suppression of fluctuations by shear or curvature in vE. The required vE flow is generated very rapidly when the magnitude of the heating power or of an externally imposed radial current exceed threshold values and several theoretical models have been developed to explain the observed changes in the vE flow. After the transition occurs, the altered boundary conditions enable the development of improved confinement in the plasma interior on a confinement time scale. The resulting H‐...

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.

Divertor heat flux reduction by D2 injection in DIII-D

D{sub 2} gas injected into ELMing H-mode discharges in DIII-D reduced total integrated heat flux to the divertor by {approximately}2{times} and peak heat flux by {approximately}5{times}, with only modest degradation to plasma stored energy. Steady gas injection without particle pumping results in eventual degradation in stored energy. The initial reduction in peak heat flux at the divertor tiles may be primarily due to the increase in radiated power from the X-point/divertor region. The eventual formation of a high density region near the X-point appears to play a role in momentum (and energy) transfer from the flux surfaces near the outboard strike point to flux surfaces farther out into the scrapeoff. This may also contribute to further reduction in peak heat flux.

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...

The EPED pedestal model and edge localized mode-suppressed regimes: Studies of quiescent H-mode and development of a model for edge localized mode suppression via resonant magnetic perturbations

The EPED model predicts 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. We present detailed tests of the EPED model in discharges with edge localized modes (ELMs), employing new high resolution measurements, and finding good quantitative agreement across a range of parameters. The EPED model is then applied for the first time to quiescent H-mode (QH), finding a similar level of agreement between predicted and observed pedestal height and width, and suggesting that the model can be used to predict the critical density for QH-mode operation. Finally, the model is applied toward understanding the suppression of ELMs with 3D resonant magnetic perturbations (RMP). Combining EPED with plasma response physics, a new working model for RMP ELM suppression is developed. We propose that ELMs are suppressed when a “wall”...