Quiescent H-mode Research Articles

Advances in validating gyrokinetic turbulence models against L- and H-mode plasmas

Robust validation of predictive turbulent transport models requires quantitative comparisons to experimental measurements at multiple levels, over a range of physically relevant conditions. Toward this end, a series of carefully designed validation experiments has been performed on the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] to obtain comprehensive multifield, multipoint, multiwavenumber fluctuation measurements and their scalings with key dimensionless parameters. The results of two representative validation studies are presented: an elongation scaling study performed in beam heated L-mode discharges and an electron heating power scan performed in quiescent H-mode (QH-mode) discharges. A 50% increase in the elongation κ is observed to lead to a ∼50% increase in energy confinement time τe and accompanying decrease in fluctuation levels, qualitatively consistent with a priori theoretical predictions and nonlinear GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] simulations. However, these simulations exhibit clear quantitative differences from experiment in the predicted magnitudes and trends with radius of turbulent fluxes and fluctuation levels which cannot be fully accounted for by uncertainties due to transport stiffness. In the QH-mode study, local nonlinear GYRO simulations that neglect fast ion effects show a similar proportional response to the applied electron cyclotron heating as the experiment, but overpredict the magnitudes of transport and fluctuation levels by a factor of 10 or more. Possible sources of this overprediction, namely nonlocal effects and self-consistent fast beam ions, are identified and discussed.

Observation of reduced core electron temperature fluctuations and intermediate wavenumber density fluctuations in H-mode plasmas

In this paper, we report observations of reduced core electron temperature and intermediate-scale density fluctuations in H-mode. Electron temperature fluctuation levels are observed to decrease from L-mode levels ( for kθρs < 0.5 as measured by correlation electron cyclotron emission radiometry) by at least a factor of four in H- and quiescent H-mode regimes in the DIII-D tokamak (r/a = 0.7). Linear stability calculations (using the trapped gyro-Landau fluid (TGLF) code) indicate that the observed temperature fluctuations are associated with L-mode ITG turbulence which is shear-stabilized at the L- to H-mode transition. Recent results from DIII-D provide the first experimental evidence that, in addition, intermediate-scale turbulence (0.5 < kθρs ⩽ 3) is reduced at the L–H transition. A 30–40% prompt reduction (r/a ⩾ 0.7) has been found at the L–H transition in co-injected medium density plasmas, with a larger decrease (⩾75%) observed near the pedestal top. Experimental results and TGLF calculations indicate that intermediate/small scale turbulence persists in H-mode at a reduced amplitude (0.6 ⩽ r/a ⩽ 1) and may substantially contribute to the residual anomalous H-mode electron heat transport.

Edge pedestal control in quiescent H-mode discharges in DIII-D using co-plus counter-neutral beam injection

We have made two significant discoveries in our recent studies of quiescent H-mode (QH-mode) plasmas in DIII-D. First, we have found that we can control the edge pedestal density and pressure by altering the edge particle transport through changes in the edge toroidal rotation. This allows us to adjust the edge operating point to be close to, but below the ELM stability boundary, maintaining the ELM-free state while allowing up to a factor of two increase in edge pressure. The ELM boundary is significantly higher in more strongly shaped plasmas, which broadens the operating space available for QH-mode and leads to improved core performance. Second, for the first time on any tokamak, we have created QH-mode plasmas with strong edge co-rotation; previous QH-modes in all tokamaks had edge counter-rotation. This result demonstrates that counter-NBI and edge-counter rotation are not essential conditions for QH-mode. Both these investigations benefited from the edge stability predictions based on peeling–ballooning mode theory. The broadening of the ELM-stable region with plasma shaping is predicted by that theory. The theory has also been extended to provide a model for the edge harmonic oscillation that enhances edge transport in the QH-mode. Many of the features of that theory agree with the experimental results reported either previously or in this paper. One notable example is the prediction that co-rotating QH-mode is possible provided sufficient shear in the edge rotation can be created.

Quiescent H-Mode Plasmas with Strong Edge Rotation in the Cocurrent Direction

For the first time in any tokamak, quiescent H-mode (QH-mode) plasmas have been created with strong edge rotation in the direction of the plasma current. This confirms the theoretical prediction that the QH mode should exist with either sign of the edge rotation provided the magnitude of the shear in the edge rotation is sufficiently large and demonstrates that counterinjection and counteredge rotation are not essential for the QH mode. Accordingly, the present work demonstrates a substantial broadening of the QH-mode operating space and represents a significant confirmation of the theory.

Dependence of SOL widths on plasma current and density in NSTX H-mode plasmas

The dependence of various SOL widths on the line-averaged density ( n ¯ e ) and plasma current ( I p) for the quiescent H-mode plasmas with Type-V ELMs in the National Spherical Torus Experiment (NSTX) was investigated. It is found that the heat flux SOL width ( λ q), measured by the IR camera, is virtually insensitive to n ¯ e and has a strong negative dependence on I p. This insensitivity of λ q to n ¯ e is consistent with the scaling law from JET H-mode plasmas that shows a very weak dependence on the upstream density. The electron temperature, ion saturation current density, electron density, and electron pressure decay lengths ( λ Te, λ jsat, λ ne, and λ pe, respectively) measured by the probe showed that λ Te and λ jsat have strong negative dependence on I p, whereas λ ne and λ pe revealed only a little or no dependence. The dependence of λ Te on I p is consistent with the scaling law in the literature, while λ ne and λ pe dependence shows a different trend.

Weak hysteresis in a simplified model of the L-H transition

A simple one-field L-H transition model is studied in detail, analytically and numerically. The dynamical system consists of three equations coupling the drift wave turbulence level, zonal flow speed, and the pressure gradient. The fourth component, i.e., the mean shear velocity, is slaved to the pressure gradient. Bursting behavior, characteristic for predator-prey models of the drift wave - zonal flow interaction, is recovered near the transition to the quiescent H-mode (QH) and occurs as strongly nonlinear relaxation oscillations. The latter, in turn, arise as a result of Hopf bifurcation (limit cycle) of an intermediate fixed point (between the L- and H-modes). The system is shown to remain at the QH-mode fixed point even after the heating rate is decreased below the bifurcation point (i.e., hysteresis, subcritical bifurcation), but the basin of attraction of the QH-mode shrinks rapidly with decreasing power. This suggests that the hysteresis in the H-L transition may be less than that expected from S-curve models. Nevertheless, it is demonstrated that by shaping the heating rate temporal profile, one can reduce the average power required for the transition to the QH-mode.

Investigation of pellet-triggered MHD events in the ASDEX upgrade

In order to gain deeper insight into the process of MHD activity triggered by pellets we extended our previous analysis (standard type-I edge localized modes (ELMs)) to type-I ELMs in radiative edge scenarios, type-III ELMs, the quiescent H-mode regime, and core mode activity such as neoclassical tearing modes or snakes. Pellet triggering of mode activity has turned out to be a quite general feature, but only in case of the ELMs can it be unambiguously attributed to prompt local impact by the pellet. For edge plasma conditions characterized by higher resistivity, the growth time of spontaneous ELMs increases while the plasma changes from the type-I into the type-III regime. However, pellet-triggered ELMs retain fast rise times. In the quiescent Hmode, pellets still trigger ELM-like mode activity, but no longer accompanied by a significant release of energy from the plasma.

Edge stability of stationary ELM-suppressed regimes on DIII-D

We discuss the MHD stability of the H-mode pedestal region in two edge localized mode (ELM)-suppressed H-mode regimes on DIII-D, the quiescent (Q)H-mode and resonant magnetic perturbation (RMP) H-mode. The QH-mode is obtained at low density with most of the neutral beam power injected counter to the plasma current, and is characterized by a continuous, low toroidal mode number (n), edge harmonic oscillation (EHO). QH-mode is observed to transition back to ELMing H-mode as the rotational shear is decreased by increasing the co-current neutral beam power fraction or by increasing the plasma to conducting wall distance, consistent with a model for the EHO as a peeling instability with added drive from rotational shear, which saturates through self transport of momentum or damping of rotation through drag of the mode on the conducting wall. In RMP H-mode, an n = 3 coil provides the non-axisymmetric perturbation. Two regimes of RMP ELM suppression are observed. At low collisionality with large resonant field perturbation, the pedestal pressure gradient and current density are reduced below the peeling-ballooning mode stability limit; while at higher collisionality with large non-resonant perturbation there is little change in the pedestal parameters and type II ELMs are enhanced.

Effect of radial electric field and ripple on edge neutral beam ion distribution in ASDEX Upgrade

The neutral beam injected fast ion distribution at the ASDEX Upgrade edge region is studied focusing on the difference between co- and counter-injected neutral beams. The slowing-down distribution of beam ions is simulated using the orbit-following Monte Carlo code ASCOT. The edge fast ion density and its gradient are higher for counter-injection than for co-injection. Also the distribution in the velocity space is different: for co-injection, there exists a population of untrapped particles which for counter-injection is found only when the effect of a non-constant, experimentally obtained quiescent H-mode radial electric field is included in the simulation. Toroidal ripple removes ions having small particle pitch, thereby reducing the density and density gradient, whereas the radial electric field has the opposite effect. Including simultaneously the effects of both ripple and the radial electric field restores the distribution close to the ideal case where both of them are neglected. The radial electric field is found to squeeze the orbit of a counter-injected neutral beam ion but to widen the orbit of a co-injected ion, and to cause transitions in the orbit topologies which are reflected in the fast ion distribution.

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.

Surface loads and edge fast ion distribution for co- and counter-injection in ASDEX Upgrade

The fast particle flux onto the material surfaces and the fast ion edge distribution are compared between ASDEX Upgrade H-mode and quiescent H-mode (QH-mode) in the presence of toroidal ripple and radial electric field Er by using the orbit-following Monte Carlo code ASCOT. So far, the QH-mode has been obtained only with counter-injection of the neutral beams. The wall load caused by co-injected beams in H-mode is small and without ripple it is negligible. With counter-injection (QH-mode case), the wall load is substantial even without the ripple. The ripple always increases the wall load, but the divertor load is either decreased or is unchanged. The effect of Er alone is small, but it boosts the ripple-trapping of beam particles near the location of its maximum absolute value on the horizontal midplane. The fast ion density and its gradient in the pedestal region are higher for counter-injected than for co-injected particles. The ripple decreases the density gradient in both the cases. To make a connection with the experiment, the flux of high-energy tritons from beam–plasma interactions onto the surfaces is evaluated. The simulated flux of tritons impinging on the material surfaces is in qualitative agreement with the measured tritium distribution on the wall and divertor.

Density and temperature profile modifications with electron cyclotron power injection in quiescent double barrier discharges on DIII-D

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. Our initial experiments and modelling 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, namely ion temperature and rotation, electron density and impurity concentration. At onset and termination of the EC pulse, dynamically changing conditions are induced that provide a rapid evolution of Te/Ti profiles accessible with 0.3 < (Te/Ti)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. Increases in the measured ion thermal and particle diffusivities inside the barrier region during an ECH pulse correlate with electron heating and a rise in the core Te/Ti ratio as the ion temperature and density profiles flatten with this change in transport. The change in transport is consistent with a destabilization of ITG turbulence as inferred from the reduction of the stability threshold due to the change in Te/Ti.

Control of plasma profiles in DIII-D discharges

Active control of plasma profiles is an essential requirement for operating within plasma stability limits, for steady-state operation and for optimization of the plasma performance. In DIII-D, plasma profiles have been actively controlled using various actuators in the following manner: (a) real time closed loop control of the q profile evolution using electron cyclotron heating and neutral beam injection as actuators; (b) active control of the density and pressure profiles in quiescent H-mode and quiescent double barrier plasmas using electron cyclotron current drive (ECCD) and pellet injection; (c) active control of the edge profiles to suppress edge localized modes using resonant magnetic perturbation with toroidal mode number n = 3, (d) real time control of the current density profile to suppress neoclassical tearing modes using localized deposition of co-ECCD.

Pedestal Studies in DIII-D

Studies of the H-mode pedestal in the DIII-D tokamak are presented. The global energy confinement increases as the plasma pressure on top of the pedestal increases. The best empirical description for a pedestal width parameter is Δpe ∝ (βpolPED)0.4, where Δpe is the width of the electron pressure pedestal and βpolPED is the poloidal beta at the top of the pedestal. The edge profiles of electron density ne, electron temperature Te, and ion temperature Ti can all have different shapes. Thus, a simple width scaling for the edge might not exist, and studies of the physics of individual profiles have been initiated. A model for the ne profile, based on self-consistent treatment of edge particle sources and edge particle transport, agrees with several experimental observations. The steep gradient region for the Te profile often extends farther into the plasma than the ne pedestal step. Magnetohydrodynamic stability provides the ultimate limits to the evolution of the pedestal and usually leads to edge instabilities called edge-localized modes (ELMs). However, the absence of ELMs in a regime called the Quiescent H-mode shows that large pedestals can be produced without ELMs.

Studies of the ‘Quiescent H-mode’ regime in ASDEX Upgrade and JET

The stationary edge localized mode (ELM)-free ‘Quiescent H-mode’ (QH-mode) regime, obtained with counter neutral beam injection, is studied in ASDEX Upgrade and Joint European Torus. QH-mode plasmas have high pedestal and core ion temperatures together with good High-confinement mode (H-mode). ELMs are replaced by continuous MHD oscillations, the ‘edge harmonic oscillation’ (EHO) and the ‘high frequency oscillation’. Stationarity of particle and impurity densities is linked to the occurrence of these MHD modes. The EHO location in the steep-gradient region and its appearance with increasing edge pressure points towards the edge pressure or pressure gradient as possible drivers for the EHO. Injection of small cryogenic pellets can raise the plasma density to about 40% of the Greenwald density limit without triggering ELMs. Orbit following calculations of the slowing-down distribution show the presence of an enhanced fast particle density in the H-mode barrier region despite the large loss currents with counter-injection. The radial electrical field in the edge barrier region, about twice as large in QH-mode as in ELMy H-mode, is large enough to reverse the precession drift direction of injected beam ions, leading to a resonance of the EHO with the drift precession frequency.

Advances in understanding quiescent H-mode plasmas in DIII-D

Recent QH-mode research on DIII-D [J. L. Luxon et al., Plasma Physics and Controlled Nuclear Fusion Research 1996 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159] has used the peeling-ballooning modes model of edge magnetohydrodynamic stability as a working hypothesis to organize the data; several predictions of this theory are consistent with the experimental results. Current ramping results indicate that QH modes operate near the edge current limit set by peeling modes. This operating point explains why QH mode is easier to get at lower plasma currents. Power scans have shown a saturation of edge pressure with increasing power input. This allows QH-mode plasmas to remain stable to edge localized modes (ELMs) to the highest powers used in DIII-D. At present, the mechanism for this saturation is unknown; if the edge harmonic oscillation (EHO) is playing a role here, the physics is not a simple amplitude dependence. The increase in edge stability with plasma triangularity predicted by the peeling-ballooning theory is consistent with the substantial improvement in pedestal pressure achieved by changing the plasma shape from a single null divertor to a high triangularity double null. Detailed ELITE calculations for the high triangularity plasmas have demonstrated that the plasma operating point is marginally stable to peeling-ballooning modes. Comparison of ELMing, coinjected and quiescent, counterinjected discharges with the same shape, current, toroidal field, electron density, and electron temperature indicates that the edge radial electric field or the edge toroidal rotation are also playing a role in edge stability. The EHO produces electron, main ion, and impurity particle transport at the plasma edge which is more rapid than that produced by ELMs under similar conditions. The EHO also decreases the edge rotation while producing little change in the edge electron and ion temperatures. Other edge electromagnetic modes also produce particle transport; this includes the incoherent, broadband activity seen at high triangularity. Pedestal values of ν* and βT bracketing, those required for International Experimental Thermonuclear Reactor [Nucl. Fusion 39, 2137 (1999)] have been achieved in DIII-D, demonstrating the QH-mode edge densities are sufficient for future devices.

Observations of fast ion loss to the plasma facing wall during quiescent H-modes on DIII-D

The Quiescent H-mode exhibits H-mode levels of confinement and edge pedestal pressures, but does not exhibit ELMs. To date this mode has only been observed in tokamaks during beam heating with some or all of the beams injected counter to the direction of plasma current. During QH-mode, fast ion loss to the low field side plasma facing surfaces has been observed. Some of the fast ion loss is calculated to be the result of outwardly directed banana orbits of the energetic beam ions created in the edge region. Other fast ion loss has been observed to be associated with bursts or oscillations in broadband, high-frequency, magnetic fluctuations. The relationship of the fast ion loss to the ELM stabilization or edge particle transport during QH-mode is not yet understood.

Extraction of poloidal velocity from charge exchange recombination spectroscopy measurements

An approach has been implemented on the DIII-D tokamak to allow the correct determination of the plasma poloidal velocity from charge exchange spectroscopy measurements. Unlike usual techniques, the need for detailed atomic physics calculations to properly interpret the results is alleviated. Instead, the needed atomic physics corrections are self-consistently determined directly from the measurements, by making use of specially chosen viewing chords. Modeling results are presented that were used to determine a set of views capable of measuring the correction terms. We present the analysis of a quiescent H-mode discharge, illustrating that significant modifications to the velocity profiles are required in these high ion temperature conditions. We also present preliminary measurements providing a direct comparison of the standard cross-section correction to the atomic physics calculations.

Impact of toroidal rotation on ELM behaviour in the H-mode on JT-60U

The mitigation of the large pulsed heat loads induced by edge-localized modes (ELMs) on the divertor plates is one of the most important issues for a tokamak fusion reactor. However, ELMs have been completely suppressed in the quiescent H-mode (QH-mode) plasmas produced in the DIII-D tokamak (see Burrell K H et al 2002 Plasma Phys. Control. Fusion 44 A253). One of the key conditions for producing QH-mode plasmas is that the direction of neutral beam injection (NBI) should be opposite to that of the plasma current (i.e. ctr-NBI), which then leads to the toroidal rotation velocity being in the counter direction to the plasma current. By using various combinations of NBI lines in JT-60U, it has been possible to investigate the impact of the toroidal rotation velocity on ELM behaviour by changing the toroidal momentum input in a detailed manner for similar absorbed NB heating power. It has been determined that the ELM frequency decreases with increased counter toroidal rotation velocity at the plasma edge even to the point of the ELMs disappearing. In addition, the magnitude of the pulsed Dα signal at the divertor decreases with decreasing ELM frequency. These results indicate that it is possible to control the ELM behaviour through the toroidal momentum input.

Edge radial electric field structure in quiescent H-mode plasmas in the DIII-D tokamak

H-mode operation is the choice for next step tokamak devices based on either conventional or advanced tokamak physics. This choice, however, comes at a significant cost for both the conventional and advanced tokamaks because of the effects of edge localized modes (ELMs). ELMs can produce significant erosion in the divertor and can affect the β limit and reduced core transport regions needed for advanced tokamak operation. Experimental results from DIII-D over the past four years have demonstrated a new operating regime, the quiescent H-mode (QH-mode) regime, that solves these problems. QH-mode plasmas have now been run for over 4 s (>30 energy confinement times). Utilizing the steady-state nature of the QH-mode edge allows us to obtain unprecedented spatial resolution of the edge ion profiles and the edge radial electric field, Er, by sweeping the edge plasma slowly past the view points of the charge exchange spectroscopy system. We have investigated the effects of direct edge ion orbit loss on the creation and sustainment of the QH-mode. Direct loss of ions injected into the velocity-space loss cone at the plasma edge is not necessary for creation or sustainment of the QH-mode. The direct ion orbit loss has little effect on the edge Er well. The Er at the bottom of the well in these cases is about −100 kV m−1 compared with −20 to −30 kV m−1 in the standard H-mode. The well is about 1 cm wide, which is close to the diameter of the deuteron gyro-orbit. We also have investigated the effect of changing edge triangularity by changing the plasma shape from upwardly biased single null to magnetically balanced double null. We have now achieved the QH-mode in these double-null plasmas. The increased triangularity allows us to increase pedestal density in QH-mode plasmas by a factor of about 2.5 and overall pedestal pressure by a factor of 2. Pedestal β and ν* values matching the values desired for ITER have been achieved. In these higher density plasmas, the Er well is significantly shallower and broader.