Table of contents

The operational boundaries for the occurrence of various types of edge localized mode (ELM) instability in high-confinement-mode (H-mode) fusion plasmas are reviewed. The phenomenology of ELMs and the occurrence of different ELM types in parameter space are described. Favourable ELM regimes are observed in various experiments which combine small ELM losses with high edge pressure and thereby allow for good H-mode confinement even in situations where core confinement is strongly dependent on edge parameters. Recent progress of ELM models based on ideal or resistive MHD is described and their ability to describe the various ELM regimes discussed.

The transport barrier which exists at the plasma edge in the high-confinement (H-mode) regime is now recognized as important to global energy confinement. Recently, detailed measurements of the width and height of barriers in electron and ion density and/or temperature have been made on several divertor tokamaks. These results are reviewed, with an emphasis on scalings of the pedestal height and width. Many experiments observe situations in which the limiting pedestal pressure gradient is well described by ideal ballooning stability. In some cases the extreme edge is in the `second stable' regime. Differences between the widths Δ of pedestals in electron and ion temperature and densities are noted in several experiments. Some reported scalings are Δ_Ti = 3.3(ε)^1/2ρ_i,pol on JT-60U, and Δ_Pe/R∝β_pol,ped^0.4 on DIII-D. Δ_Te is independent of plasma current in many experiments. Theoretical modelling of the fully developed H-mode pedestal is reviewed. Several recent predictions of the pedestal parameters and their scalings are outlined and compared with experiments.

Recent results on the understanding and scaling of several of the operational boundaries found in ELMy H-mode plasmas are presented. Divertor geometry is found to be important in determining the H-mode transition power and temperature. Recent experiments from different tokamaks find apparently conflicting evidence for the role of the edge neutral density in controlling the H-mode transition and further intermachine comparisons are clearly warranted. Significant progress has been made both on the understanding and on the avoiding of the H-mode density limit. Models based on divertor detachment and on MARFE physics reproduce the empirical density limit scalings. The density limit in ELMy H-modes has been increased by changing the profile of the density in the divertor and in the main plasma. Highly radiating ELMy H-modes are currently being studied and display some of the favourable characteristics of the TEXTOR radiative improved confinement mode.

In configurations with transport barriers the improved edge and core confinement leads to a large pressure gradient and large edge bootstrap current density which often drive magnetohydrodynamic (MHD) instabilities terminating the discharge or reducing the discharge performance. The edge and the core transport barriers deteriorate or are completely lost. In this paper, recent experimental and theoretical developments concerning MHD instabilities occurring near/at the edge and the core transport barriers are summarized emphasizing the dominant instabilities and the comparison with theory.

Internal and edge transport barriers are widely observed in a number of devices, including tokamak and helical systems, with various heatings. The E×B flow shear suppression of turbulence seems to explain formation and subsequent propagation of transport barriers in many cases. However, the role of the safety factor profile has not been clearly understood. Moreover, electron transport still remains a major issue. Tokamak research is challenging the active control of transport barriers. Steady or quasisteady performance of H-modes with internal barriers has been gradually improving and stable sets of profiles close to the steady-state solution have been demonstrated at high β.

Radiative mantle experiments were performed on JET ELMy H-mode plasmas. The septum configuration was used where the X-point is embedded into the top of the septum. Argon radiated 50% of the input power from the bulk plasma while Z_eff rose from an intrinsic level of 1.5 to about 1.7 due to the injected argon. The total energy content and global energy confinement time decreased 15% when the impurities were introduced. In contrast, the effective thermal diffusivity in the core confinement region (r/a = 0.4-0.8) decreased by 30%. Usually, JET ELMy H-mode plasmas have confinement that is correlated to the edge pedestal pressure. The radiation lowered the edge pedestal and consequently lowered the global confinement. Thus the global confinement was changed by a competition between the edge pedestal reduction lowering the confinement and the weaker RI effect reducing the core transport coefficients. The ELM frequency increased from 10 Hz type-I ELMs, to 200 Hz type-III ELMs. The energy lost by each ELM reduced to 0.5% of the plasma energy content.

Some models for the suppression of turbulence in the L to H transition, suggest that the width of the H-mode edge barrier is either proportional or is of the order of the thermal or the fast-ion poloidal Larmor radius. This would require that the width of the edge barrier should depend on the plasma current. This dependence has been clearly verified at JET in experiments designed to control the edge MHD stability of ELM-free hot-ion H-mode plasmas. The effects of isotopic mass and the applicability of several edge barrier models to the hot-ion H-mode plasmas were analysed in (Guo H Y et al 2000 Edge transport barrier in JET hot-ion H-modes Nucl. Fusion40 69) using a large database containing both deuterium-only and deuterium-tritium plasmas. This database has now been enlarged to include discharges from a plasma shape scan, allowing one to study the dependence of the pedestal height on the edge shear. In addition, the range of plasma currents was extended up to 6 MA. It is shown that the edge data are best described by a model where the edge barrier width is determined by the fast ions weighted towards the components with largest poloidal Larmor radii. However, it is not possible to conclusively eliminate the thermal ion model.

The effect of plasma shape variation (in particular, variation of the upper and lower triangularity δ) on edge localized modes (ELMs) and H-mode pedestal properties in ASDEX Upgrade is reported here. Strongly shaped plasmas (high δ) show an increased edge pressure gradient and, without external gas puff, type-I ELMs generally have larger losses and lower frequency than in plasmas with low δ. With external gas puff, ELM losses at high δ are reduced and in the same range as found for low δ. The average ELM power loss is a constant fraction of the total loss power, independent of triangularity. The width of the steep electron temperature and pressure gradient zone remains essentially constant at low δ while at high δ it shows a variation inconsistent with a poloidal gyroradius scaling. The edge pressure gradient and the pedestal pressure scales strongly with plasma current and triangularity. In type-I ELM H-modes, the pedestal pressure is directly related to the global stored plasma energy, independent of plasma shape.

In the compact helical system, several bifurcation patterns have been observed in potential profiles of electron-cyclotron-heated plasmas. In a bifurcation pattern with a strong shear of radial electric field, an internal transport barrier is confirmed to be established for electron thermal energy. Probabilistic treatment with realization of the pattern or internal transport barrier is discussed.

The effects of radial electric field and plasma rotation on the characteristics of internal transport barriers (ITBs) and core confinement properties are studied in JT-60U reversed shear plasmas. The combination of on-axis and off-axis tangential NBI in the co- and counter-directions allows various profiles of the toroidal rotation. With the same core absorbed power, the case of a small momentum source at the ITB layer is more favourable for sustainment of the ITB layer and the retention of the core energy confinement than the cases of the excess co- or counter-momentum source.

A stationary advanced tokamak scenario with an internal transport barrier (ITB) for ions and electrons, particles and momentum in combination with an H-mode barrier and flat shear (q₀≈1) was maintained for 40 confinement times and several internal skin times with H_ITERL-89P β_N≈5. Raising the density by edge gas fuelling close to 50% of the Greenwald density to integrate proper exhaust conditions causes an increase of the threshold power to sustain an ITB and a decrease of Z_eff below 2. In contrast, a density increase caused by improved core particle confinement at more triangular plasma shapes does not change the ITB onset conditions. No temporal impurity accumulation even with high-Z Ar puffing was observed despite of peaked impurity density profiles.

MHD modes contribute to the stationarity of the shear profile. In the ITB/H-mode scenario (1,1) fishbones with a large reconnection area `clamp' the q-value in the vicinity of one and avoid sawteeth during the whole high-performance phase. In ITB scenarios with reversed shear (q_min ⩾2) fishbones can clamp the current profile development near the q = 2 surface without deteriorating energy confinement, whereas double-tearing modes, acting in a similar form, lead to substantial confinement losses.

Applying central ECRF heating and current drive to beam heated reversed-shear ITB discharges shows an substantial effect on MHD stability, affecting the passage of the q-profile through q_min = 2, and degrading or prolonging the reversed-shear phase depending on the CD direction. Moreover, reactor relevant T_e⩾T_i operation with temperatures in excess of 10 keV was achieved with internal transport barriers for both electrons and ions simultaneously.

ELMy H-mode pulses have been obtained with different hydrogenic isotopes (H and D) but having the same profiles of the dimensionless parameters ρ^*,β,ν^* and q, to test whether the confinement scale invariance principle is valid in a tokamak. The fact that the confinement times, the ELM and sawtooth frequencies in the two pulses all scale as expected suggests that the invariance principle is satisfied through the plasma radial extent, in spite of the differing physical processes taking place in the plasma centre, core and edge regions. An application of this `isotope windtunnel technique' to predicting the D-T performance of the next step devices is discussed.

A type of large eddy simulation model is proposed which consists of three hierarchies, i.e. transport, magnetohydrodynamics (MHD) and turbulence. These classes are categorized by the poloidal and toroidal mode number (m, n). A (0, 0) mode represents transport, low (m, n) modes represent MHD and high (m, n) modes represent turbulence. Mutual interactions between three classes are possible via nonlinearities such as Reynolds stress, renormalized eddy viscosity and so on. As a starting point, a two-hierarchical model of MHD and turbulence is derived and applied for the analysis of magnetic island dynamics in the presence of a strong pressure gradient. It is found that the growth of the magnetic island is accelerated by the anomalous resistivity, whereas it causes the rotation of the magnetic island to decelerate.

An ELMy ASDEX Upgrade plasma equilibrium is reconstructed taking into account the bootstrap current. The peeling mode stability of the equilibrium is numerically analysed using the GATO [1] code, and it is found that the bootstrap current can drive the plasma peeling mode unstable. A high-n ballooning mode stability analysis of the equilibria revealed that, while destabilizing the peeling modes, the bootstrap current has a stabilizing effect on the ballooning modes. A combination of these two instabilities is a possible explanation for the type I ELM phenomenon. A triangularity scan showed that increasing triangularity stabilizes the peeling modes and can produce ELM-free periods observed in the experiments.

Turbulence suppression by shear in the E×B flow is a widely accepted mechanism. Edge polarization experiments on TEXTOR-94 have been used to study the dependence on the toroidal magnetic field, plasma current and plasma composition of the critical E×B shear, defined as the highest rate of change in the diffusion coefficient with shear. Our experiments show that an increase of the isotopic mass and/or a decrease of the toroidal magnetic field leads to higher critical E×B flow shear, whereas a change of the plasma current seems to have no effect.

A view of the latest experimental results and progress in the understanding of the role of poloidal flows driven by fluctuations via Reynolds stress is given. Reynolds stress shows a radial gradient close to the velocity shear layer location in tokamaks and stellarators, indicating that this mechanism may drive significant poloidal flows in the plasma boundary. Observation of the generation of E×B sheared flows via Reynolds stress at the ion Bernstein resonance layer has been noticed in toroidal magnetized plasmas. The experimental evidence of shearedE×B flows linked to the location of rational surfaces in stellarator plasmas might be interpreted in terms of Reynolds stress sheared driven flows. These results show that E×Bsheared flows driven by fluctuations can play an important role in the generation of transport barriers.

Oblique pellet injection experiments have been performed in RTP ohmic and electron cyclotron (EC) heated plasmas. Peripheral cooling induces a transient rise of the electron temperature (T_e) in the plasma core, with the formation of a region of a high T_e gradient (transient transport barrier). The position of the barrier appears to be linked with the location of low-order rational magnetic surfaces. For Ohmic and EC heated plasmas with resonance moderately off-axis, the T_e rise is peaked in the plasma centre and the footpoint of the barrier is located close to the q = 2 surface. For EC plasmas with far off-axis resonance, i.e. in plasmas exhibiting hollow T_e profiles, the T_e rise starts off-axis, near the innermost low order rational surface (typically q = 3). It then propagates to the centre in a seemingly diffusive way.

The possibility of controlling the transport processes in the tokamak plasma in the lower hybrid heating (LHH) experiment has been demonstrated. We illustrate experimentally the observed transport barrier formation initialized by the LHH for different plasma experiment scenarios. First, it was found during LHH. The next method to trigger improved confinement is a combination of fast current ramp-up with LHH. The mechanisms of internal barrier formation have been put forward to explain the observed regime of improved core confinement. The increased shear of the radial electric field stimulates the internal barrier formation.

The characteristics of the H-mode are studied in discharges with varying triangularity and squareness. The pressure at the top of the H-mode pedestal increases strongly with triangularity, primarily due to an increase in the margin by which the edge pressure gradient exceeds the ideal ballooning mode first stability limit. Two models are considered for how the edge may exceed the ballooning mode limit. In one model, access to the ballooning mode second stable regime allows the edge pressure gradient and associated bootstrap current to continue to increase until an edge localized, low toroidal mode number, ideal kink mode is destabilized. In the second model, the finite width of the H-mode transport barrier and diamagnetic effects raise the pressure gradient limit above the ballooning mode limit. We observe a weak inverse dependence of the width of the H-mode transport barrier, Δ, on triangularity relative to the previously obtained scaling Δ∝(β^PE_P)^1/2. The energy loss for Type I ELMs increases with triangularity in proportion to the pedestal energy increase. At low density, the energy confinement of high-triangularity discharges is larger than discharges with low triangularity, as a result of an increase in the energy in the H-mode pedestal. At high density, both the change in pedestal pressure and the response of the density profile are found to play a role in setting the energy confinement. The highest energy confinement at high density was obtained in low-triangularity discharges.

Monte Carlo ion simulation of the tokamak edge, based on the neoclassical radial current balance, shows that a considerable E×B shear, relevant for turbulence suppression, can be generated by orbit losses. In contrast to earlier orbit loss models, no spontaneous bifurcation of the radial electric field E_r is found. However, a bifurcation and a solitary E_r generation are found in simulations with electrode polarization.

Significant improvements have been made to edge diagnostics on COMPASS-D enabling detailed studies of the H-mode dynamics. New experiments have been carried out with current ramps in high-power ECR discharges to test the influence of the peeling mode on the low-density H-mode transition. Observations and analysis suggest that the peeling mode is not the controlling mechanism. Density-ramp experiments indicate that the edge electron pressure gradient is correlated with transition behaviour and links are made with global observations.

The transition to H-mode is conditional to the achievement of certain critical conditions, generally dependent on both local quantities and global plasma parameters. A physical understanding of the L-H transition process cannot improve without the development of theoretical models and their testing against such experimental evidence. The aim of the present paper, therefore, is to compare some of the physics-based theoretical models with the experimental conditions for the L-H transition in JET plasmas. The results show that although the models considered can offer a partial understanding of the processes involved in the formation of the edge transport, none of them can uniquely explain all the results.

We study the characteristics of self-generated zonal flows as observed in nonlinear global gyrokinetic simulations of toroidal ion temperature gradient (ITG) turbulence for typical parameters of DIII-D core plasmas. In addition, we discuss various possibilities for experimental measurements and the development of new diagnostics.

At ASDEX Upgrade the influence of triangularity on the H-mode performance has been studied intensively. It has been found that confinement increases with δ for a fixed line-averaged density. Though confinement decreases with increasing density for all analysed values of δ, H-factors (ITERH-98P) at the Greenwald density could be raised to 1 for the highest δ values achieved so far. The H-mode density limit could be increased by ≈20%. There is a scatter of about 30% on the confinement data, which is anti-correlated to the average density in the scrape-off layer or the neutral fluxes outside the plasma. For nearly all discharges analysed so far, the temperature profiles are self-similar. This indication of profile stiffness could be verified by changing the heat-flux profile by changing the beam-voltage of the neutral-beam injection (NBI) at high density. At low density, first results indicate a deviation from this stiff behaviour.

This paper presents the evidence for the role of turbulence-driven poloidal flow generation in the L-H transition induced by a turbulent heating pulse on the HT-6M tokamak. It is found that the poloidal flow υ_θ plays a key role in developing the electric field E_r and triggering the transition. The acceleration of υ_θ across the transition is clearly correlated with the enhancement of the Reynolds stress gradient.

The plasma performance in two design options of the reduced-technical objectives/reduced cost (RTO/RC) ITER, i.e. IAM (intermediate aspect ratio machine) and LAM (low aspect ratio machine) is analysed. It is shown that Q = P_fus/P_aux~10 can be obtained in both options at inductively driven ELMy H-mode operation. The operation domain in LAM is found to be marginally larger than that in IAM. The non-inductive operation with Q≈5 will be possible in both machines, provided a large amount of power with a high current drive efficiency is applied, or substantial improvement of the energy confinement time relative to the ELMy H-mode (H_H = 1.2-1.4) is obtained. The required values of H_H and β_N are marginally smaller in IAM. The IAM-like machine, ITER-FEAT (fusion energy advanced tokamak), proposed for a detailed engineering design is discussed in brief.

H-mode operation in the low-shear stellarator W7-AS is achieved for specific plasma edge topologies characterized by three `operational windows' of the edge rotational transform. An explanation for this strong influence of the magnetic configuration could be the increase of viscous damping if rational surfaces and thus island structures occur within the relevant plasma edge layer, thereby impeding the development of an edge transport barrier. Prior to the final transition to a quiescent state, the plasma edge passes a rich phenomenology of dynamic behaviour such as dithering and ELMs. Plasma edge parameters indicate that a quiescent H-mode occurs if a certain edge pressure is achieved.

Very steep internal transport barriers (ITBs) have been observed in all four transport channels on DIII-D. These ITBs are among the most highly localized (width⩽5 cm), simultaneous core transport barriers observed on any machine to date, and have only been observed in discharges with a negative central magnetic shear (NCS discharges), at power levels above ~8 MW. Profile gradients and scale lengths at the location of the core (ρ~0.3-0.4) transport barriers are similar to those observed at the plasma edge during H-mode, while profiles inside the transport barriers are flat. The spatial location of the transport barriers coincides in all four transport channels, although the temporal evolution of the profiles is different; very steep gradients in the electron density and temperature profiles form after such gradients are first observed in the ion temperature and angular momentum profiles. Turbulence measurements during the evolution of the core particle transport barrier show no decrease in low-wavenumber (0-6 cm^-1) turbulence levels in the plasma centre, including within the steep gradient ITB region. Several possible interpretations for this observation are presented.

In JT-60U H-mode plasmas, giant (type I) ELMs disappear and minute grassy ELMs appear when triangularity δ, edge safety factor q₉₅ and β_p are high enough. Complete suppression of giant ELMs was observed at δ≳0.45, q₉₅≳6 and β_p≳1.6. At higher δ (0.54), giant ELMs can disappear at a lower q₉₅ (~4.0). In the grassy ELMy H-mode, edge temperature and pressure can be higher than those in giant ELMy H-mode and a favourable confinement can be sustained without an increase of the impurity concentration. An edge stability analysis suggests that the edge plasma is accessing the second stability regime of the high n ballooning mode in the grassy ELMy discharges.

In this paper we summarize the results of recent measurements of the high confinement mode (H-mode) edge transport barrier in Alcator C-Mod. A number of new, high-resolution edge diagnostics provide measurements of plasma parameters (electron density and temperature, and impurity density) in the pedestal region. Pedestal parameters are measured both at the top edge of the plasma and at the midplane. Very narrow (2-5 mm) electron density and temperature and impurity density pedestals are observed. The impurity pedestal is located inside the density and temperature pedestals in the midplane measurements, but coincides with the n_e pedestal at the top edge. Correlation of both width and height of the pedestals at the midplane with global plasma parameters and core confinement characteristics is observed. At the same time there are no clear indications of scaling for the electron density and impurity pedestal widths measured at the top of the plasma.

Studies of the enhanced D_α H-mode (EDA) have been extended to include ohmic plasmas. No clear difference in the EDA/ELMfree boundary or in other phenomenology are seen between ohmic and ICRF-heated plasmas, suggesting that neither the effect of ion tails nor direct RF/edge plasma interaction plays a role in EDA. Edge safety factor (q₉₅) is the principal variable which determines which regime a discharge will be in. When q₉₅ is greater than 4.0 for standard-shaped plasmas, the discharge is almost always EDA, while when it is less than 3.5, the plasma is almost always ELMfree. New edge diagnostics have allowed measurement of pedestal profiles with resolution of the order of 1 mm. Sudden changes in profile widths are not seen when the plasma makes a transition from EDA to ELMfree; however, the widths do vary with the same parameters that determine the EDA/ELMfree boundary. Strong edge-density fluctuations are observed to accompany EDA and may be responsible for the change in particle transport which is observed. The fluctuations have a quasi-coherent component whose frequency varies inversely with the pedestal width as measured by a visible continuum diagnostic.

Results are presented for fluid-equation simulations of transport and turbulence in the edge region of a tokamak using the transport code UEDGE and the turbulence code BOUT. UEDGE calculates two-dimensional plasma and neutral gas profiles using empirical radial transport coefficients, while BOUT simulates three-dimensional plasma turbulence and resulting transport using experimental or UEDGE plasma profiles. Using UEDGE, the radial electric field structure near the magnetic separatrix is studied for variations of core power, anomalous perpendicular ion viscosity, ν_a⊥, and prompt ion loss. A BOUT simulation measures the effective ν_a⊥from the calculated turbulence-induced radial ion current, giving a value similar to the ion heat diffusivity.

With a careful choice of the viewing parameters, neutral-particle analysers could be used to detect small changes in the radial electric field E_r immediately next to the separatrix with a submillisecond (50-100 µs) resolution. In particular, the poloidal viewing angle has to be optimized according to the ripple- and plasma geometry. In addition, the use of a small diagnostic beam is proposed to improve the signal level and quality.

Edge pedestal parameters (pedestal temperature and density, pedestal width) for JT-60U and DIII-D are studied and compared. For the discharges used in the study, the JT-60U H-mode operation space is in the high edge ion temperature and low edge electron density region, whereas DIII-D discharges have higher edge electron density and lower electron temperature. The pedestal width scaling has been studied separately in each machine. We tested these pedestal scalings against each other using JT-60U ion temperature pedestal width data and DIII-D electron temperature pedestal width data. Three previous scalings for pedestal width (Δ∝ε0.5ρpi, Δ/R∝(ρpi/R)0.66, Δ/R∝(βpPED)0.4) are tested using temperature pedestal widths from both machines. The relations between pedestal width and dimensionless parameters are examined. We propose a new pedestal width scaling for Te and Ti based on this study of the two machines. The new scaling includes normalized poloidal gyroradius and Greenwald density: Δ∝aρ*0.4nG*0.3κ-1.5. The result of the comparison of these scalings is that the new scaling and Δ/R∝(βpPED)0.4 are well fitted and the fitting errors are almost the same as experimental error. However, further study is necessary for scaling parameters.

A remarkable reduction of the L-H threshold power was observed in JT-60U under the W-shaped pumped divertor geometry, in comparison with the results for the previous open divertor. The density range was extended to 0.6n_GWL ( = I_p/πa²), where a stronger than linear density dependence was found. A reduction of the radiation power and edge temperature as well as a nonlinear increase in edge density were also observed. The poloidal distribution of the neutral particle density was first examined in this work, and it was found that compression of neutral particles near the X-point or loss of homogeneity on a flux surface produced by the modification of the divertor geometry may be an influential determinant of the L-H threshold power.

This is an analysis of the H-mode threshold physics by the International H-mode Threshold Database Working Group. The data from 10 different tokamaks world-wide are combined in an attempt to determine the physics of the H-mode transition as well as the scaling of the plasma parameters relevant to the H-mode transition to future magnetic fusion devices. The input power required to achieve H-mode is fitted with log-linear regressions of global plasma parameters such as density, toroidal magnetic field and plasma size. An attempt to cross-validate this analysis method is made by removing each tokamak in turn and recalculating the fit. Based on these global scalings, the hysteresis in the threshold power can be defined in terms of how far away from the threshold scaling plasma parameters can be obtained and remain in H-mode. Local edge temperatures and densities are also analysed at the H-mode threshold in an attempt to find a scaling with plasma parameters. Changes in divertor geometry also have strong effects on the H-mode threshold, so scalings are compared for open and closed divertors.

Potential and density/temperature fluctuations at the L-H transition are measured by a heavy ion beam probe (HIBP) on JFT-2M. It has been observed that the time scale of potential change is as fast as 10-100 µs when the input power (P_in) is larger than the L-H threshold power (P_th). When P_in = P_th, the confinement is improved step by step, with sawteeth crashes accompanied by a decrease of potential. After a few sawteeth crashes, the potential drops rapidly to the level of the ELM-free H-mode. At that time, the density/temperature fluctuations are suppressed simultaneously. The observations of the temporal behaviour of the potential and fluctuations in such an L-H transition are reported.