H-mode Edge Pedestal Research Articles

Projections of H-mode access and edge pedestal in the SPARC tokamak

In order to inform core performance projections and divertor design, the baseline SPARC tokamak plasma discharge is evaluated for its expected H-mode access, pedestal pressure and edge-localized mode (ELM) characteristics. A clear window for H-mode access is predicted for full field DT plasmas, with the available 25 MW of design auxiliary power. Additional alpha heating is likely needed for H-mode sustainment. Pressure pedestal predictions in the developed H-mode are surveyed using the EPED model. The projected SPARC pedestal would be limited dominantly by peeling modes and may achieve pressures in excess of 0.3 MPa at a density of approximately 3 × 1020m−3. High pedestal pressure is partially enabled by strong equilibrium shaping, which has been increased as part of recent design iterations. Edge-localized modes (ELMs) with >1 MJ of energy are projected, and approaches for reducing the ELM size, and thus the peak energy fluence to divertor surfaces, are under consideration. The high pedestal predicted for SPARC provides ample margin to satisfy its high fusion gain (Q) mission, so that even if ELM mitigation techniques result in a 2× reduction of the pedestal pressure,Q> 2 is still predicted.

Multi-scale interaction of pedestal instabilities in H-mode plasma on the EAST tokamak

A cross-scale interaction between a kink instability with toroidal mode number (n) of 1 and background microturbulence (mainly a coherent mode with n = 12–17) has been observed in the H-mode edge pedestal region in the EAST tokamak. The n = 1 kink mode with a frequency ~3.5 kHz is localized in the pedestal region. The amplitude of pedestal microturbulence is evidently modulated at the frequency of the n = 1 mode. This amplitude modulation is mainly for the fluctuation component with frequency less than 100 kHz, while no modulation by the n = 1 mode is observed for the component with frequency larger than 100 kHz. This implies that the observed amplitude modulation by the n = 1 mode is not due to the Doppler shift effect. A further analysis shows that the amplitude modulation of microturbulence could be attributed to modulation of the local temperature gradient by the n = 1 kink mode. In addition, bicoherence analysis indicates that there exists a possible direct nonlinear interaction between background microturbulence and the n = 1 kink instability. A preliminary analysis shows that this cross-scale interaction has no evident effect on the pedestal structure.

Global gyrokinetic simulations of the H-mode tokamak edge pedestal

Global gyrokinetic simulations of DIII-D H-mode edge pedestal show two types of instabilities may exist approaching the onset of edge localized modes: an intermediate-n, high frequency mode which we identify as the “kinetic peeling ballooning mode (KPBM),” and a high-n, low frequency mode. Our previous study [W. Wan et al., Phys. Rev. Lett. 109, 185004 (2012)] has shown that when the safety factor profile is flattened around the steep pressure gradient region, the high-n mode is clearly kinetic ballooning mode and becomes the dominant instability. Otherwise, the KPBM dominates. Here, the properties of the two instabilities are studied by varying the density and temperature profiles. It is found that the KPBM is destabilized by density and ion temperature gradient, and the high-n mode is mostly destabilized by electron temperature gradient. Nonlinear simulations with the KPBM saturate at high levels. The equilibrium radial electric field (Er) reduces the transport. The effect of the parallel equilibrium current is found to be weak.

Local and global Fokker–Planck neoclassical calculations showing flow and bootstrap current modification in a pedestal

In transport barriers, particularly H-mode edge pedestals, radial scale lengths can become comparable to the ion orbit width, causing neoclassical physics to become radially nonlocal. In this work, the resulting changes to neoclassical flow and current are examined both analytically and numerically. Steep density gradients are considered, with scale lengths comparable to the poloidal ion gyroradius, together with strong radial electric fields sufficient to electrostatically confine the ions. Attention is restricted to relatively weak ion temperature gradients (but permitting arbitrary electron temperature gradients), since in this limit a δf (small departures from a Maxwellian distribution) rather than full-f approach is justified. This assumption is in fact consistent with measured inter-ELM H-Mode edge pedestal density and ion temperature profiles in many present experiments, and is expected to be increasingly valid in future lower collisionality experiments. In the numerical analysis, the distribution function and Rosenbluth potentials are solved for simultaneously, allowing use of the exact field term in the linearized Fokker–Planck–Landau collision operator. In the pedestal, the parallel and poloidal flows are found to deviate strongly from the best available conventional neoclassical prediction, with large poloidal variation of a different form than in the local theory. These predicted effects may be observable experimentally. In the local limit, the Sauter bootstrap current formulae appear accurate at low collisionality, but they can overestimate the bootstrap current in the plateau regime. In the pedestal ordering, ion contributions to the bootstrap and Pfirsch–Schlüter currents are also modified.

Evolution of the H-mode edge pedestal between ELMs

The evolution of edge pedestal parameters between edge-localized modes (ELMs) is analyzed for an H-mode DIII-D (Luxon 2002 Nucl. Fusion 42 612) discharge. Experimental data are averaged over the same sub-intervals between successive ELMs to develop data that characterize the evolution of density, temperature, rotation velocities, etc over the interval between ELMs. These data are interpreted within the context of the constraints imposed by particle, momentum and energy balance, in particular in terms of the pinch–diffusion relation for radial particle flux that is required by momentum balance. It is found that in the edge pedestal there is an increase in both inward (pinch) electromagnetic and outward (diffusive) pressure gradient forces over the inter-ELM interval.

Analysis of pedestal plasma transport

An H-mode edge pedestal plasma transport benchmarking exercise was undertaken for a single DIII-D pedestal. Transport modelling codes used include 1.5D interpretive (ONETWO, GTEDGE), 1.5D predictive (ASTRA) and 2D ones (SOLPS, UEDGE). The particular DIII-D discharge considered is 98889, which has a typical low density pedestal. Profiles for the edge plasma are obtained from Thomson and charge-exchange recombination data averaged over the last 20% of the average 33.53 ms repetition time between type I edge localized modes. The modelled density of recycled neutrals is largest in the divertor X-point region and causes the edge plasma source rate to vary by a factor ∼102 on the separatrix. Modelled poloidal variations in the densities and temperatures on flux surfaces are small on all flux surfaces up to within about 2.6 mm (ρN > 0.99) of the mid-plane separatrix. For the assumed Fick's-diffusion-type laws, the radial heat and density fluxes vary poloidally by factors of 2–3 in the pedestal region; they are largest on the outboard mid-plane where flux surfaces are compressed and local radial gradients are largest. Convective heat flows are found to be small fractions of the electron (≲10%) and ion (≲25%) heat flows in this pedestal. Appropriately averaging the transport fluxes yields interpretive 1.5D effective diffusivities that are smallest near the mid-point of the pedestal. Their ‘transport barrier’ minima are about 0.3 (electron heat), 0.15 (ion heat) and 0.035 (density) m2 s−1. Electron heat transport is found to be best characterized by electron-temperature-gradient-induced transport at the pedestal top and paleoclassical transport throughout the pedestal. The effective ion heat diffusivity in the pedestal has a different profile from the neoclassical prediction and may be smaller than it. The very small effective density diffusivity may be the result of an inward pinch flow nearly balancing a diffusive outward radial density flux. The inward ion pinch velocity and density diffusion coefficient are determined by a new interpretive analysis technique that uses information from the force balance (momentum conservation) equations; the paleoclassical transport model provides a plausible explanation of these new results. Finally, the measurements and additional modelling needed to facilitate better pedestal plasma transport modelling are discussed.

Simulation of electron thermal transport in H-mode discharges

Electron thermal transport in DIII-D H-mode tokamak plasmas [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] is investigated by comparing predictive simulation results for the evolution of electron temperature profiles with experimental data. The comparison includes the entire profile from the magnetic axis to the bottom of the pedestal. In the simulations, carried out using the automated system for transport analysis (ASTRA) integrated modeling code, different combinations of electron thermal transport models are considered. The combinations include models for electron temperature gradient (ETG) anomalous transport and trapped electron mode (TEM) anomalous transport, as well as a model for paleoclassical transport [J. D. Callen, Nucl. Fusion 45, 1120 (2005)]. It is found that the electromagnetic limit of the Horton ETG model [W. Horton et al., Phys. Fluids 31, 2971 (1988)] provides an important contribution near the magnetic axis, which is a region where the ETG mode in the GLF23 model [R. E. Waltz et al., Phys. Plasmas 4, 2482 (1997)] is below threshold. In simulations of DIII-D discharges, the observed shape of the H-mode edge pedestal is produced when transport associated with the TEM component of the GLF23 model is suppressed and transport given by the paleoclassical model is included. In a study involving 15 DIII-D H-mode discharges, it is found that with a particular combination of electron thermal transport models, the average rms deviation of the predicted electron temperature profile from the experimental profile is reduced to 9% and the offset to −4%.

Dimensionless parameter dependence of H-mode pedestal width using hydrogen and deuterium plasmas in JT-60U

The characteristics of the spatial width of the H-mode pedestal were investigated in hydrogen and deuterium plasmas in JT-60U. Both the database analysis and the dedicated experiments on the mass scan indicated that the pedestal width depends very weakly on the plasma particle species or . Identical profiles of the edge ion temperature Ti were obtained in the experiments with hydrogen and deuterium plasmas while the profile for the H-mode edge pedestal is not fixed but differs by a factor of ∼1.4 (which is the square root of the mass ratio). In addition, an experiment on edge βpol scan was also performed. Higher βpol plasma had higher pedestal Ti value accompanied by greater pedestal width in spite of almost identical at the pedestal. Based on these dimensionless parameter scans, the scaling of the pedestal width was evaluated as .

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.

Initial results of H-mode edge pedestal turbulence evolution with quadrature reflectometer measurements on DIII-D

High-resolution quadrature reflectometer measurements of density fluctuation levels have been obtained on DIII-D for H-mode edge pedestal studies. Initial results are presented from the L–H transition to the first ELM for two cases: (i) a low pedestal beta discharge, in which density turbulence in the pedestal has little change during the ELM-free phase, and (ii) a high pedestal beta discharge in which both density and magnetic turbulence are observed to increase before the first ELM. These high beta data are consistent with the existence of electromagnetic turbulence suggested by some transport models. During Type-I ELM cycles, when little magnetic turbulence can be observed, pedestal turbulence increases just after an ELM crash and then decreases before next ELM strikes, in contrast to a drop after ELM crash and then it re-grows when strong magnetic turbulence shows similar behavior. Clear ELM precursors are observed on ⩽20% of Type-I ELMs observed to date.

Quantitative density fluctuation measurements utilizing quadrature reflectometers on DIII-D

Fixed-frequency reflectometers utilizing quadrature phase detection are employed on DIII-D to study both coherent and turbulent density fluctuations. For coherent fluctuations, the reconstructed phase information successfully identifies MHD/coherent mode activity, e.g. tearing modes, compressional Alfvén eigenmodes, etc. For an m = 3/n = 2 tearing mode, a basic 1D phase screen model is applied to infer fluctuation levels, and the result is consistent with the beam emission spectroscopy (BES) measurement. For turbulent fluctuation studies, a 2D full-wave code (Valeo E.J., Kramer G.J. and Nazikian R. 2002 Plasma Phys. Control. Fusion 44 L1) is applied to interpret reflectometry data obtained in the H-mode edge pedestal region to deduce density fluctuation levels. The measurement is simulated using realistic geometry, plasma conditions and antenna patterns. Comparison of the fluctuation level deduced from the 2D code with BES measurement shows reasonable agreement.

Far SOL ELM ion energies in JET

There is an increasing body of evidence that the energy lost from diverted tokamak plasmas due to edge localized mode (ELM) activity may not be confined solely to deposition on divertor components. Plasma-facing surfaces in the main confinement chamber also appear to intercept significant fluxes. Whilst this is of no practical consequence for the operation of present day facilities, concerns are being raised over the possible impact on future devices, in which ELMs carrying higher energies are expected. A key parameter required in this assessment is the energy transported by ions in the ELM as it moves through the scrape-off layer (SOL). This contribution presents the first known direct experimental demonstration that ELM events can convect ions with considerable energies to regions in the far SOL. These measurements, obtained on the JET tokamak with an ion energy analyser probe, are combined with a recently developed SOL transient model to show that the ions can, indeed, reach first limiting surfaces with energies that are a considerable fraction (∼50%) of those found in the H-mode edge pedestal region. This experiment–theory comparison supports a picture of the ELM in which filaments of hot plasma originating in the pedestal region dissipate energy primarily through parallel losses to the divertor targets during their radial propagation across the SOL.

Structure, stability and ELM dynamics of the H-mode pedestal in DIII-D

Experiments are described that have increased our understanding of the transport and stability physics that set the H-mode edge pedestal width and height, determine the onset of Type-I edge localized modes (ELMs) and produce the nonlinear dynamics of the ELM perturbation in the pedestal and scrape-off layer (SOL). Models now exist for the ne pedestal profile and the pe height at the onset of Type-I ELMs, and progress has been made towards models of the Te pedestal width and nonlinear ELM evolution. Similarity experiments between DIII-D and JET suggested that neutral penetration physics plays an important role in the relationship between the width and height of the ne pedestal. Plasma physics appears to dominate in setting the Te pedestal width. Measured pedestal conditions including edge current at ELM onset agree with intermediate-n peeling–ballooning (P–B) stability predictions. Midplane ELM dynamics data show the predicted (P–B) structure at the ELM onset, large rapid variations of the SOL parameters and fast radial propagation in later phases, similar to features in nonlinear ELM simulations.

An Understanding of H-Mode Pedestal Instabilities in the DIII-D Tokamak

The experimental and modeling results on H-mode edge-localized mode (ELM) instabilities from the DIII-D tokamak project are reviewed. This work has led to the conclusion that the most common type of ELM, called Type I, is triggered by a coupled peeling-ballooning instability driven by the pressure gradient and current density in the H-mode edge pedestal region. Good agreement is found between theoretically predicted stability boundaries and toroidal mode numbers for this instability and experimental observations of edge pedestal parameters and ELM amplitude and frequency as a function of discharge shape and edge-region collisionality. The range of toroidal mode numbers for which there is access to a second stability regime is shown to play an important role. This model of H-mode edge stability has been used to predict the pedestal parameters for ITER and FIRE.

Pedestal profiles during QH-mode operation on DIII-D

The quiescent high confinement mode (QH-mode) on DIII-D exhibits an H-mode like edge pedestal, with values of pedestal pressure and global energy confinement similar to those of the ELMing H-mode, but without ELMs. In many cases this mode is observed to reach a nearly stationary operating point, limited in duration only by hardware constraints. This mode is usually obtained in a plasma configuration that is strongly pumped with electron densities at the top of the pedestal below 0.3 of the Greenwald density. Electron temperatures at the top of the pedestal range from 1.2 to 2.2 keV. Ion temperatures at the pedestal are much higher, ranging up to 5 keV. In this paper, we will present edge profiles observed in the QH-mode. A selection of these profiles are used as input to the Corsica code to calculate the edge current profile, which is dominated by the bootstrap current. We discuss the implications of these edge profiles on the stability of the QH edge against ballooning/peeling modes. We also discuss results of experiments in which we attempt to expand the range of edge parameters, especially the edge density, achievable in the QH-mode.

Examinations on various scalings for the H-mode edge pedestal width

In this paper, we compare various scalings for the H-mode edge pedestal width proposed so far empirically or based on theoretical or semi-empirical models, and examine possible inter-relations between them. Many of the scalings include poloidal or toroidal Larmor radius, beta-poloidal, normalized Greenwald density and machine size. Some of the scalings include explicitly the local magnetic shear, which is expected to play an essential role in determining the width of the transport barrier through MHD stability and turbulence suppression. Emphasis is placed on the comparison between those scalings without magnetic shear and those with shear. By considering the safety factor dependence of the magnetic shear and its spatial profile, some of the scalings without shear are shown to have a close relation with the scaling including shear.

Quasisteady high-confinement reversed shear plasma with large bootstrap current fraction under full noninductive current drive condition in JT-60U.

A quasisteady reversed shear plasma with a large bootstrap current fraction ( approximately 80%) has been obtained for the first time in the JT-60U tokamak. The shrinkage of reversed shear region was suppressed by the bootstrap current peaked at the internal transport barrier (ITB) layer and the ITBs at a large radius were sustained, which, by combination with an H-mode edge pedestal, resulted in a high confinement or 2.2 times the H-mode scaling for 6 times energy confinement time or 2.7 s. Furthermore, a full noninductive current drive was obtained by the bootstrap current and the beam driven current.