Table of contents

This special issue of Plasma Physics and Controlled Fusion contains invited and contributed papers presented to the 8th IAEA Technical Committee Meeting on H-mode and Transport Barrier Physics. The meeting took place in Toki from 5--7 September 2001, and was organized by the National Institute for Fusion Science, Japan. This was the eighth meeting of a series (San Diego 1987, Gut Ising 1989, Abingdon 1991, Naka 1993, Princeton 1995, Kloster Seeon 1997, Oxford 1999). In the eighth meeting in Toki, the topics were expanded to the general physics in the transport of toroidal plasmas including tokamak and helical plasmas. The programme of the meeting covered H-mode and transport barrier physics in axisymmetric (tokamak) and non-axisymmetric (helical) magnetic field configurations. The aim of this meeting was to extract the general physics elements on H-mode and transport barriers from various experimental observations and theoretical results by comparing the characteristics of transport in different configurations of magnetic field. The topics selected for the workshop were:

Summary of critical issue and current state of transport barrier research

Comparison of transport barriers in axisymmetric and non-axisymmetric devices

Spatial structure of transport barriers (internal and edge)

Dynamics of transport barrier formation and destruction (internal and edge)

Energy and particle transport in plasmas with transport barriers

Theory and simulation of transport barriers

Six invited papers were presented in sessions devoted to the topics above and 77 contributed papers on the topics were presented in poster sessions. The choice of topics and the abstract selection were carried out by the Scientific Programme Committee. The members of the Scientific Programme Committee were:

K Ida (Chair NIFS, Japan)

M Greenwald (MIT, USA)

R Groebner (GA, USA)

Y Hamada (NIFS, Japan)

S Lebedev (Ioffe, Russia)

G Saibene (EFDA, Germany)

E Synakowski (PPPL, USA)

T Takizuka (JAERI, Japan)

R Wolf (IPP, Germany)

I would like to thank U Schneider (IAEA Scientific Secretary) for her competent and timely guidance in the organization of the workshop.

Katsumi Ida

Guest Editor

Transport barriers in the present stellarators are reviewed in comparison with those in tokamaks. Peculiarities of stellarator plasma structures are introduced in order to obtain a unified view of the barrier formation mechanism. Particular attention is paid to neoclassical (-driven) internal transport barriers that are commonly observed in stellarators. Discussion is made about important aspects of structural formation; e.g. the formation or bifurcation mechanism of radial electric field and its causal link with the transport barrier, and effects of magnetic field configuration on the barrier formation.

Recent studies on spatial structures of internal and edge transport barriers (ITB and ETB) in tokamaks are presented. For the ETB, steady H-mode regimes with small or no edge localized modes, which are important for future reactors, are mainly treated. For the ITBs, the radial profile has larger variety and the situation is more complicated than that in ETB; its criterion, ITBs under reactor-relevant conditions, the foot location, the box-type shape and the ITB at a high bootstrap current fraction are discussed. For the combined ITB and ETB, sustainment of combined ITB and ETB and the linkage between them are discussed.

The formation of transport barriers in fusion plasmas is studied through examination of mechanisms which can stabilize plasma turbulence and, thereby, reduce turbulence-driven transport. These include the effects of E×B velocity shear, negative central magnetic shear and the Shafranov shift. Transport barriers formed at the plasma edge and in the plasma core are considered, as well as the formation of multiple barriers. The access conditions for barrier formation are examined, particularly by considering local conditions compared to global parameters. Processes that can destroy transport barriers, such as magnetohydrodynamic instabilities, are described. Plasmas with high confinement and good plasma stability then require effective control of plasma profiles and transport. Efforts towards real-time control of transport barriers are described.

Up to five regions with different transport properties can be identified in tokamak plasma with edge and internal transport barriers. This includes edge and core barriers, the region near the separatrix, which is dominated by atomic physics, the core plasma (within 0.4⩽ρ⩽0.8, where ρ is a normalized minor radius) and the central part of plasma volume, which is often dominated by large-scale MHD phenomena. An overview of the present understanding of heat and particle transport in these five regions will be given, which includes progress in experimental observations, theory of plasma microturbulence and predictive modelling.

The common physics elements behind various transport barrier theories and simulations, and the related experimental observations mainly from tokamaks, are discussed. These include: a hierarchy of the E×B shear effects on turbulence, the role of q profiles, the electron thermal transport mechanism, basic transport barrier dynamics, and the causality of transitions and the possible role of turbulence generated zonal flows.

Recent experimental results and plasma edge stability studies of ELMs are presented for both H-mode and optimized shear (OS) plasmas in JET. High triangularity (δ~0.5) ELMy \mbox{H-mode} experiments in JET achieved simultaneously high confinement (H_IPB(y,2) = 1) and high density (~0.9 n_GR). At high pedestal density (~1.1n_GR), an anomalous decrease of type I ELMs frequency and energy losses per ELM was observed. A specific for high triangularity and high density (δ~0.5 and n_e~1.1n_GR) MHD activity with broad-band frequency spectrum (<30 kHz) between type I ELMs was associated with type II-like ELMs which were observed in JET at rather low q₉₅~3, compared to other machines. The coupled JETTO-MISHKA codes transport and MHD stability analysis for these scenarios confirmed a possible access to the second stability zone for the ballooning modes and stability for peeling modes at the same time. The second part of the paper is devoted to the experimental comparative study of the transition from type I to type III ELMs , carried out in the same plasma configurations for standard ELMy \mbox{H-modes} and OS plasmas. The type III to type I ELM transition in OS discharges is found to deviate strongly from the known power scaling for this transition, derived for standard H-mode plasmas. In fact, type III ELMs are still observed at much higher power in OS scenarios, and this experimental observation suggests that larger current fraction at the plasma edge in OS discharges, compared to standard H-mode could prevent the type III to I ELMs transition.

Operating scenarios in the Mega-Ampère Spherical Tokamak (MAST) have been recently developed to access routinely H-mode plasmas over a wide range of plasma conditions. Gas refuelling at the inboard mid-plane has proved invaluable in facilitating L- to H-mode transitions. Already, a comprehensive range of H-mode behaviour has been observed providing similar and contrasting comparisons with conventional tokamaks. For example, similarities are found in H-mode edge and global evolutions, increases in confinement and ELM behaviour. In contrast, H-mode threshold powers are about an order of magnitude higher in MAST than those predicted by conventional aspect ratio tokamak scalings. At the highest β_θ values obtained so far, transient confinement times of ~100 ms are achieved and calculations indicate that bootstrap currents may approach 50% of the plasma current.

The quiescent double barrier (QDB) regime is a high performance regime recently identified in DIII-D and characterized by a double transport barrier structure (core and edge) that can be maintained for several seconds, often limited only by the pulse length capabilities of the DIII-D hardware. The QDB regime has been sustained for up to 25 τ_E with fusion performance of up to β_NH₈₉≈7. The edge barrier is ELM-free, but modulated by low frequency MHD activity that allows density control via an external cryopump. The core barrier is similar to those seen in previous internal transport barrier experiments, but is maintained without complete stabilization of turbulence. Instead, the turbulence correlation lengths become very short so as to minimize the transport length scales. The two barriers are separated by a region of high transport that is a consequence of a zero-crossing in the E×B shearing rate. These discharges typically possess highly peaked density profiles. This has several implications: narrow bootstrap current profile, reduced beta limit and increased impurity retention. We will report on studies of each of these issues.

Toward the study of steady-state operation of fusion plasma, it is important to assess the confinement characteristics under a condition in which fractional power of electron heating is dominant to the total heating power. In a fusion plasma electron heating by α particles is dominant. Especially, the influence on the internal transport barrier (ITB) is an important issue, since formation of ITB is a key issue in advanced steady-state operation from a viewpoint of both attaining highly improved confinement and larger bootstrap current fraction to the total current. In JT-60U, the influence on ITBs when fractional power of electron heating to the total power is increased has been investigated by using negative-ion based neutral beam injection and electron cyclotron range of frequency (ECRF). It is found that in a reversed magnetic shear plasma of high confinement improvement, still higher over all confinement can be achieved at electron heating powers of 50-60% to the total absorbed power. Reduction of the ion temperature at ECRF injection is observed in an ITB plasma of positive shear. And with intense electron central heating on lower hybrid current drive plasma, high central electron temperature with ITB has been formed.

L-mode to H-mode (LH) transitions are observed in a large variety of plasma conditions in TCV Ohmic plasmas. The power flowing through the separatrix at the LH transition differs by up to a factor of two from the predicted H-mode threshold power. Variations in this deviation are due to the large operational domain covered by the transitions as well as from the different scenarios identified to access the H-mode regime. LH transitions obtained during the plasma current ramp at low plasma current, elongation and triangularity have a threshold power below the standard expression while transitions at high current and triangularity or during the stationary phase of the discharge have a threshold power above the standard expression.

Recent experiments at ASDEX Upgrade have concentrated on advanced scenarios, specifically ELMy H-mode discharges without an internal transport barrier which obtain a high β_N = 3.5 in steady state. A highly shaped plasma configuration is used at 800 kA, with a triangularity δ = 0.42 and edge safety factor, q₉₅, in the range 3.6-4.1. The product β_NH89-P reaches up to 8.0 in plasmas approaching a stationary conditions, and β_NH89-P{} = 11.5 is achieved transiently. These discharges are at high density, 80-90% of the Greenwald density limit. Discharges at the highest density show a strong reduction of the ELM activity, similar to type II activity, eliminating transient high heat loads on the divertor target. Finally, the non-inductively driven current approaches 70% of the total current making this regime a serious candidate for an advanced scenario in a reactor, and a benchmark for other advanced scenarios.

The variation of the density profile shape of H-modes in ASDEX Upgrade is governed by time constants much larger than τ_E. A method to determine these time constants is presented. Especially high density discharges with moderate heating and constant gas puff show very long phases of increasingly peaking density profiles which may not reach a steady state, although the H-mode pedestal remains constant during the peaking process. If heated more centrally with ICRH the peaking is strongly reduced and a steady state is reached. The behaviour can be well modelled using D≈0.1χ and the neoclassical Ware-pinch. Strongly peaked density profiles lead to an earlier onset of neoclassical tearing modes (NTMs) in agreement with theoretical predictions of the strong influence of ∇n/n on the bootstrap current. Also for impurities an effect of the heat flux profile is observed: central heating with ECRH leads to a reduction of heavy ions in the plasma core.

Rapidly developing diagnostic, operational, and analysis capability is enabling the first detailed local physics studies to begin in high β plasmas of the National Spherical Torus Experiment (NSTX). These studies are motivated in part by the observation of energy confinement times in neutral-beam-heated discharges that are favourable with respect to predictions from the ITER-89P scaling expression. For plasmas heated with neutral beam injection (NBI), analysis based on profile measurements suggests that electron heat conduction is the dominant thermal loss channel. Cases where early analysis indicates that ion thermal conduction may be exceptionally low is motivating studies of possible sources of ion heating not presently accounted for by classical collisional processes. Gyrokinetic microstability studies indicate that long wavelength turbulence with k_θρ_i~0.1-1 may be stable or suppressed by E×B shear in these plasmas, while modes with k_θρ_i~50 may be robust. High harmonic fast wave (HHFW) heating efficiently heats electrons on NSTX, and studies have begun using it to assess transport in the electron channel. Regarding edge transport, H-mode transitions occur with either NBI or HHFW heating. The power required for L- to H-mode transitions far exceeds that expected from empirical ELM-free H-mode scaling laws derived from moderate aspect ratio devices. Finally, initial fluctuation measurements made with two techniques are permitting the first characterizations of edge turbulence.

It is shown that fuelling from the inboard midplane extends the operation window for H-mode in comparison with fuelling from the outboard midplane. In Ohmically heated plasmas, the minimum line-averaged density required for transition to ELM-free H-mode is approximately ~30% lower in comparison with the fuelling from the outboard midplane. The power at the transition to H-mode is similarly reduced.

Temporal and spatial resolutions of thermal helium beam, Doppler diagnostics and Thomson scattering were improved to study the edge parameter evolutions during the L-H transitions and ELMs. At L-H and H-L transitions, the diagnostics demonstrate a coincident temporal and spatial evolution of gradients in the radial electric field and electron pressure. During regular ELM behaviour similar evolutions are observed.

Positive radial electric field, E_r, was observed at the edge region in the low-density NBI plasmas of the Large Helical Device (LHD). Ion thermal diffusivities, χ_i, are evaluated by the local transport analysis for two different density plasmas and for two cases of the magnetic axis position. In the standard configuration case, χ_i was reduced by large positive E_r, while no reduction in χ_i was found in the inward shifted case. A certain level of suppression of the neoclassical ripple transport by E_r seems to be confirmed since the neoclassical transport is considered to be more dominant in the standard magnetic configuration plasmas.

The bootstrap current analyses have been carried out for two different kinds of discharges of compact helical system (CHS) heliotron/torsatron. One is the electron cyclotron resonance heating (ECRH) discharge with moderate density and without internal transport barrier (ITB) (n_e(0)>0.5×10¹⁹ m^-3, T_e(0)<1.2 keV). Another is the neoclassical ITB (NC ITB) discharge, which has been achieved in the rather low electron density condition (n_e<0.4×10¹⁹ m^-3) with ECRH and co-NBI. The NC ITB mode is characterized by steeply peaked electron temperature profile (T_e(0)>2.0 keV) in the core domain and large positive radial electric field (E_r~ + 10 kV m^-1). The dependence of toroidal net current on magnetic axis position R_ax was investigated for ECRH discharges without ITB. There is good agreement in the tendency of R_ax dependence of the net toroidal current between experiment and neoclassical calculation. In the NC ITB discharges, the experimental net current including both bootstrap and beam-driven current is largely reduced compared with that in the L-mode and it drops to almost zero. It seems as if the reversal of bootstrap current takes place in the NC ITB phase but such a view is inconsistent with neoclassical prediction. The observed reduction of the plasma current in the ITB phase is not explained by the neoclassical theory.

The plasma with neoclassical internal transport barrier (N-ITB) has been observed for electron cyclotron heated (ECH) plasma in the Compact Helical System Heliotron/Torsatron. The N-ITB is characterized by the peaked electron temperature, with a large temperature gradient (0.43 keV cm^-1) and a large electric field shear at the barrier location. The transport analysis shows that the electron thermal conductivity in plasma with N-ITB is lower than that without N-ITB at the transport barrier. The neoclassical transport is calculated from the analytical model for the neoclassical particle flux. In the ECH plasma with N-ITB, the electron thermal conductivity χ_e is at the level of the neoclassical χ_e at the barrier transport which demonstrates that the anomalous transport is reduced to a level well below the neoclassical transport.

The improvement in the particle confinement of pellet shots on the Large Helical Device (LHD) was found after methane (CH₄) mixed hydrogen gas-puff discharges. Only four discharges introducing ~20 Pa m³ of CH₄ caused the reduction in the radiation loss and the level of metal impurities, together with the enhanced recycling, which is expected as the real time carbonization effect. The decay rate of the electron density was mitigated in the pellet shot after CH₄ discharges. Transport analysis shows 60% reduction in the particle transport coefficient at half the averaged minor radius.

A mild pedestal has been observed in the large helical device (LHD) discharges. Broad profile pedestal leads to enhancement of the energy confinement. The shapes of the electron temperature profile in the gas puff divertor discharges are very close to parabolic profile, nearly being independent of density, input power and magnetic field. The plasma tends to preserve the temperature scale length (or local shape), ∇T/T even with a large island or during radiative collapse.

Effects of MHD activities on the pressure profile in NBI plasmas in the range of ⟨β⟩⩽3% have been investigated in Large Helical Device (LHD). The ⟨β⟩ dependence of the n/m = 1/2 mode in the core region and the ι = 1 resonant modes in the peripheral region are focused. The n/m = 1/2 mode has been observed in the ⟨β_dia⟩ range of less than 2.3% and disappears when the plasma reaches the Mercier stable region. The pressure profile becomes broader with increasing ⟨β⟩, and a large pressure gradient forms in the peripheral region. The amplitudes of the ι = 1 resonant modes in the peripheral region increase monotonically with ⟨β⟩.

Viscous damping and effective helical ripple have been quantitatively estimated for a proposed quasi-axisymmetric stellarator CHS-qa configuration. It is predicted that viscous damping against plasma flow in CHS-qa is low enough to sustain large E×B shear as observed in the H-modes and internal transport barriers in many tokamaks. Effective helical ripple in CHS-qa is adjusted to be on the order of 10^-2 or lower, which is suitable to trigger transport barriers due to non-ambipolar neoclassical fluxes peculiar to conventional helical devices. For experimental flexibility, viscous damping and effective helical ripple in CHS-qa can be extensively controlled over a range of about one order by modifying modular coil currents.

The flattening of the electron density profiles due to the static magnetic island is observed when the n/m = 1/1 perturbation field is applied by the external coil. The iso-density widths are estimated from the model fitting analysis. The temporal history of the iso-density width and its dependence on normalized collision frequency and plasma β are estimated from a single shot. The iso-density width increases as the external perturbation field increases. Although determination errors are not small compared with the dynamic range of the estimated iso-density width, the following tendencies are observed. The iso-density width shows positive dependence on logarithm of normalized collision frequency and negative dependence on β.

Reversal of turbulent particle flux near the plasma edge of CHS heliotron/ torsatron was observed on various discharge conditions, i.e. during tangential neutral beam injection, electron cyclotron heating at the far edge, and the sawtooth crash. For all cases, the reversal is realized at a narrow particular layer near the plasma edge, when plasma parameters go into low collisionality. The reversal is caused by the change in the cross phase between density (n_e) and poloidal electric field (E_θ) fluctuations. The turbulent flux is always inward when the radial electric field shear (E_r') exceeds a certain threshold of ~1×10⁶ V m^-2. In the sawtoothing plasmas, the arrival of a heat pulse due to the sawtooth crash enhances both n_e and E_θ fluctuations but changes the cross phase to π in low-frequency range. As a result, a large inward flux is generated by the sawtooth crash. The particle flux reversal in these cases did not lead to obvious confinement improvement.

The energy confinement time of net current-free plasmas in the Large Helical Device (LHD) is comparable to ELMy H-mode with q = 4.5 on the scale of IPB98(y,2). Broad temperature with high edge pressure, which is of robust nature in LHD, recalls the pedestal structure in tokamak H-mode. Basic parameter dependence is, however, weak gyro-Bohm in both edge and core regions. This suggests that one physical model could explain the observed profile. The edge temperature is proportional to the square root of heating power and inversely proportional to the square root of edge density. This means that edge pressure and its gradient are not limited and can be increased by heating power.

H-mode operation is the choice for next-step tokamak devices based either on 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. Recent experimental results from DIII-D have demonstrated a new operating regime, the quiescent H-mode regime, which solves these problems. We have achieved quiescent H-mode operation which is ELM-free and yet has good density control. In addition, we have demonstrated that an internal transport barrier can be produced and maintained inside the H-mode edge barrier for long periods of time (>3.5 s or >25 energy confinement times τ_E). By forming the core barrier and then stepping up the input power, we have achieved β_NH₈₉ = 7 for up to 10 times the τ_E of 160 ms. The β_NH₈₉ values of 7 substantially exceed the value of 4 routinely achieved in standard ELMing \mbox{H-mode.} The key factors in creating the quiescent H-mode operation are neutral beam injection in the direction opposite to the plasma current (counter injection) plus cryopumping to reduce the density. Density control in the quiescent H-mode is possible because of the presence of an edge MHD oscillation, the edge harmonic oscillation, which enhances the edge particle transport while leaving the energy transport unaffected.

An analytic model for the width of the electron density transport barrier shows qualitative and quantitative agreement with systematic data obtained in the DIII-D tokamak. The width of the barrier in H-mode decreases as the pedestal density increases. Moreover, for L-mode and H-mode density profiles with the same pedestal density, the gradients of the barriers are of similar magnitude even though the temperature and pressure gradients are much larger in H-mode. These results are consistent with the hypothesis that neutral penetration provides important physics which helps to set the width of the H-mode barrier for the electron density.

The dependence of the edge pedestal electron pressure on magnetic geometry is studied using the international pedestal database. For type I ELM discharges, the pressure normalized to B² is found to scale roughly inversely with major radius and inverse aspect ratio. In addition, a strong increase in pressure with increasing shape is found when the pressure is normalized to a ballooning type scaling. Ballooning stability calculations suggest that there is significant variation in the normalized edge pressure gradient in the database. The observed shape dependence reflects this variation, although the applicability of the log-linear type dependences used here must be in question if phase changes such as from first to second stability are spanned by the data. This question can only be resolved by upgrading the database to include edge pressure profiles, or fits to profiles, rather than only pedestal-top values.

With the high-field-side multiple pellet injection into high-triangularity high-β_p type I ELMy H-mode discharges, JT-60U has extended the density range with a favourable integrated performance. The pellet injected discharge has a high pedestal pressure compared with the gas fuelled discharges, and the pedestal temperature does not decrease even at high pedestal density. At high triangularity, the pedestal β_p and the edge α-parameter increase with increasing total β_p. Possible linkage among pedestal and core parameters has been proposed based on a variety of JT-60U experiments. Grassy ELMy discharges have been achieved at the low safety factor regime q₉₅<4 for the first time in JT-60U with high triangularity (~0.6). The full non-inductive operation has been demonstrated with grassy ELMs.

An improved confinement state can be attained by imposing a radial electric field at the plasma edge. This is characterized by a change of the E_r structure. A charge conservation equation with a diffusion term has been solved to explain this mechanism. Various types of E_r structures with multiple peaks are allowed for the same boundary condition. The relationship between the voltage and the current is obtained by numerical calculation. Both stable and unstable regions exist in the stationary solutions and their boundary points are critical points for transition from one state to another. Multiple transitions and hysteresis are predicted. The magnitude of the collision frequency affects the existence of solutions with multiple peaks.

The nonlinear saturation mechanism of resistive drift-Alfvén instability in a current-carrying magnetized cylindrical plasma is investigated. Sheared flow generated by the nonlinear resistive drift-Alfvén instability is an essential ingredient for the saturation, which almost suppresses the dominant linear instability. Sometimes, although the generated sheared flow reduces the linear growth rates of the most unstable mode, it destabilizes the other harmonics.

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.

The minimum energy state under the constraint of the total toroidal angular momentum is examined. The result is applied to actual tokamak plasmas with an internal transport barrier (ITB). The study shows that tokamak plasmas with ITB are in the minimum energy state under the constraint of the total toroidal angular momentum and that they are likely to be self-organized.

The transport process of ELM heat and particle fluxes responsible for the rapid plasma deposition on the divertor target was investigated. The scrap-off layer (SOL) plasma flow driven along the field lines was measured in the ELMy \mbox{H-mode} plasma, for the first time, at three important locations (i.e. outer midplane, x-point and high-field-side SOL) using electrostatic probes (Mach probe) on the JT-60U tokamak. The radial profiles of the plasma flow were determined. Just below the x-point of the low-field-side SOL, a rapid increase in the flow velocity up to the ion sonic level was observed during 200-300 µs after ELM events, and the radial width was 1.0-1.5 cm (mapping to the midplane SOL). The duration and width of the rapid plasma flow were comparable to the deposition duration and width of the heat load to the outer divertor target measured with an infrared TV camera (250 µs time resolution). A simple model analysis showed that convective transport gives a large contribution to the ELM heat deposition process. On the other hand, at the high-field-side SOL, SOL flow towards the inner divertor was not observed after ELM events. The ELM heat and particle fluxes in the high-field-side SOL were not explained by the simple convective transport model.

The dynamic evolution of the first National Spherical Torus Experiment (NSTX) H-modes will be discussed. The H-modes were obtained in lower-single null divertor discharges with various forms of plasma heating. The exact timing of divertor formation and also the NBI power level affects both whether or not the discharge exhibits ELMs and the duration of the ELM-free phase. ELM-free discharges had energy confinement as high as 120 ms, whereas the few discharges with ELMs had confinement times ~50-70 ms. Buildup of a steep edge density gradient and formation of `ears' on the density profile were observed within a few ms of the L-H transition, yielding broader density and pressure profiles. The L-H transition was marked by a decrease in edge visible light and simultaneous increase in electron Bernstein wave emission, reflecting a steepening of the edge density gradient. Gas puff imaging of He-I light during the H-mode phase showed rapid formation of a narrow emission layer ~2 cm wide in the H-mode phase, which returned within 20 microseconds at termination of the H-mode phase to a broader turbulent emission layer. All of the H-modes were terminated by an MHD reconnection event. The first power threshold (P_th) study showed the neutral beam injection power (P_b) component of P_th to be ⩽0.84 MW, higher than that predicted by the ITER database scaling.

Recent measurements from the DIII-D tokamak indicate that shear in the group velocity of the edge density fluctuations is at least partly responsible for the factor 2 change in the H-mode power threshold that is observed when the direction of the ion ∇B drift relative to the X-point location is reversed. Spatially resolved edge density fluctuation measurements show a change in the poloidal group velocity of the fluctuations when the ∇B drift direction was changed, even though the edge profiles of density and temperature remained nearly the same. High (low) shear in the poloidal velocity is associated with a low (high) power threshold.

Although both the transport barriers in the plasma interior and edge, namely internal transport barrier (ITB) and H-mode, are simultaneously required to sustain high-β and improved confinement in steady state, experimental observations suggest that theL-H transition and ITB formation are independent phenomena with different formation conditions, and they often exhibit apparent contradictions to each other. Accordingly, the compatibility conditions of edge and internal barrier formation have been investigated in JT-60U. The L-H threshold power is substantially increased in strong ITB plasmas, and high-performance discharges often persist in L-mode. On the other hand, the ITB formation power increases in H-mode plasmas. It was found, however, that the L-H transition criteria expressed in terms of the edge quantities are similar in plasmas with and without the ITB, and the edge density is extremely low in strong ITB plasmas. It has also been demonstrated in JT-60U that the controlled degradation of the ITB quality, in terms of the changes of toroidal torque input, results in an increase of edge density and induces theL-H transition. Therefore, the quality of ITB modifies the L-H transition threshold power, indicating that the additional `hidden' parameter is present in ITB plasmas. Other approaches of dynamically controlling the L-H transition in ITB plasmas, such as the triangularity ramp developed in JT-60U, are also discussed in this paper.

A fundamental reality throughout the space and laboratory plasmas is the existence of magnetic field-aligned flows. It is usually believed that the spatial transverse shear in the parallel flow destabilizes many low-frequency instabilities and this may be the origin of low-frequency oscillations in the ionosphere. Here we show that this notion of the destabilizing influence of the shear in the parallel flow can be changed altogether if one takes the effect of the flow curvature (second spatial derivative) into account. The transverse curvature in the parallel flow can overcome the destabilizing influence of the shear and can render the low-frequency ion temperature gradient-type instabilities stable.

Local edge electron parameters are measured in the Alcator C-Mod tokamak, during discharges in which input power is continuously ramped up and down, leading to transitions from the low-confinement mode (L-mode) to high-confinement mode (H-mode) mode and back to L-mode. This allows measurement of the accessible portions of the non-monotonic flux-gradient relationship proposed by models of the H-mode as a critical transition. Results are consistent with a dependence of conductivity χ on the temperature gradient, where a very sharp decrease in χ occurs above a critical ∇T. Other possible flux-gradient relations are also examined, and the data are compared with theoretical formulations. The initial transient of pedestal energy in the first few ms after the L-H transition is also analysed and found to be consistent with a sudden decrease in χ across the pedestal region.

Transient transport in high-temperature and turbulent plasmas is investigated. Microscopic fluctuations in toroidal plasmas are localized in the outside of the torus, so that the radial correlation length of fluctuations is meso-scale (hybrid between micro-scale and system size). The long radial correlation induces the interference of gradient and flux in different radii, and causes a fast propagation of transient response. The upper bound of thermal diffusivity, deduced from transients, is derived. The role of geometry in transport far from thermodynamical equilibrium is highlighted.

ELM time series from TCV Ohmic H-mode plasmas are analysed in order to extract information on the ELM process. Firstly, signatures of a chaotic behaviour called unstable periodic orbits become visible when particular plasma conditions are reached. Secondly, the ELMs are sometimes synchronized with the sawteeth activity. The dependence of the phase of the synchronization and the ratio of the ELM frequency to the sawteeth frequency on the plasma parameters is described.

Abrupt in time (correlated within a few ms with L-H and H-L transitions) and wide in space (from the edge up to ~0.3 of minor radius in the extreme case) variations of electron heat diffusivity δχ_e were found in reversed shear (RS) JT-60U tokamak plasmas with internal transport barrier (ITB) at various profiles of safety factor q. The δχ_e profile follows the position of q minimum (q_min ) and penetrates into the RS region deeper for the weak ITB than for the strong one, suggesting the presence of `global' edge-core connection throughout q_min in a ms timescale at L-H and H-L confinement bifurcations. The δχ_e value at the position of q_min is small for the strong ITB (~0.05 m² s^-1) and increases by an order of magnitude for the weak ITB. The ITB event is another non-local transport bifurcation (improvement or degradation) inside and around ITB. The case of strong ITB formation in H-mode via a series of ITB events in ELM-induced L-mode is described. ITB event degradation in the positive shear zone causes L-H transition.

For the first time, data from eight different tokamaks have been combined in an international database for internal transport barriers (ITBs). An analysis of the data for the formation of an ITB with dominant ion heating shows a clear dependence of the threshold power on the minor radius and line-averaged electron density for the formation of ion ITBs. The dependence of ITB formation on the toroidal magnetic field is weak. For the formation of ITBs with dominant electron heating, the database is smaller, but for the threshold power a strong increase with plasma size and a weak toroidal field dependence could also be identified. Based on these results, an expression for the power required to form an ITB is given using global variables only. These results give a basis for the analysis of the database using local values (like magnetic shear) and a detailed comparison with theory-based models.

High-density discharges in JT-60U have been analysed with the aim of establishing a mechanism for the H-mode density limit (DL). The data support the view that the density behaviour in the H-mode is mainly affected by confinement, with the hard limit on the H-mode density being imposed by the H-L transition. Analysis of highly radiating NBI-heated plasmas with MARFE and detachment has enabled one to discriminate between detachment and the H-L transition as mechanisms for the H-mode DL. Although strong detachment is observed near the H-L transition in JT-60U, by itself it was found to impose no limit on the density rise.

The H-mode standard shot of ASDEX Upgrade provides an overview of the long term evolution of machine conditions and scatter of H-mode power threshold and confinement. This type-I ELMy H-mode is run every day of plasma operation since 1999. After a long opening for in-vessel work, the power threshold drops rapidly by about 50% over 100 discharges and then much slower by about 20% over the remaining 1000 plasma discharges made in a campaign. At the natural density without gas puffing, confinement increases by about 30% over about 500 discharges. Afterwards the peak-to-peak scatter is about 20%, smaller at high density. Conditioning causes changes of edge density and temperature, similar to the confinement degradation observed with gas puffing.

The International Global H-mode Threshold Database has been revised and cleaned from inadequate data for some tokamaks. This significantly reduces the scatter for the corresponding datasets. The resulting new analyses including all ten tokamaks yields results comparable to previous work. In this case, the uncertainties are essentially determined by the inability of the linear models to take the different dependencies into account with sufficient accuracy. However, restricting the database to a more homogeneous subset of medium and large size tokamaks with single-null elongated plasma shapes yields expressions with much lower scatter. In this case the contribution from the experimental scatter in the individual machines plays a role. These regressions are stable against excluding one tokamak in turn.

An energy confinement scaling for reversed-shear plasmas with box-type internal transport barrier (ITB) and L-mode edge is developed based on the JT-60U data. The stored energy is divided into two parts: L-mode base part and core part surrounded by the ITB. The core stored energy W_core does not simply increase with the net heating power P_net. A scaling of core stored energy is given as W_scale = Cε_f^-1B_p,f²V_core, where ε_fis the inverse aspect ratio at the ITB foot, B_p,f is the poloidal magnetic field at the outer midplane ITB foot, and V_core is the core volume inside the ITB foot. This scaling is equivalent to the condition for the core poloidal beta ε_fβ_p,core = C₁ with C₁≈¼. Though W_core is little dependent on P_net, the estimated heat diffusivity in the ITB region moderately correlates with a neoclassical diffusivity, and the neoclassical transport is not inconsistent with the data. The physics background of the present scaling is discussed.

The overlap of pulses in the pedestal database and the global H-mode confinement database has been increased. This has resulted in a new improved combined dataset with core and pedestal energy data. Regression analysis of this dataset indicates that in ELMy H-mode the pedestal energy scales differently from the core energy and degrades strongly with plasma pressure β. Using these regression results to estimate the pedestal energy in the full ELMy dataset of the global H-mode confinement database, a new two-term scaling for ELMy H-mode confinement has been found that indicates that the core confinement scales as a pure gyro-Bohm scaling with no β degradation. At present, these findings are not conclusive as the dataset is limited in the range of data and has strong correlations between the plasma parameters.

The effects of the conductive heat flow on the energy transport concerning the temperature profile similarity have been analysed for (\ref{eq1}) high triangularity and (2) Ar seeded ELMy H-mode plasmas on JT-60U. The temperature profiles of the plasma core on the logarithmic plot are shape preserving and independent of the varying pedestal height. As the conductive heat flux increases, the effective heat conductivity, χ_eff, adjusts itself to sustain a constant ∇(ln T_i) in the plasma core. In high triangularity discharges, highly improved energy confinement quality accompanied by high core temperature is obtained when the boundary temperature rises with an increase in β_pol. On the other hand, the peaked density profiles in Ar seeded discharges allow the temperature at the pedestal shoulder to be higher relative to the cases without Ar gas injection, and the core temperature is also raised. As the conductive heat flux is reduced by increasing the radiation loss flux in Ar seeded H-mode plasmas, χ_eff decreases with a similar ∇(ln T_i) of the plasma core in the case without Ar gas injection. Improved particle confinement due to Ar gas puff raises the achievable density and contributes to the reduction in χ_eff.

We carry out transport simulations of the L-H transition by the Shaing L-H transition model based on ion orbit losses, and find that the time scale of the L-H transition and the time scale for development of the H-mode pedestal are consistent with experimental observations. We also compare the power threshold derived from the Shaing L-H transition model with L-H transition threshold power scaling laws. We find that the magnetic field, B_t, plasma density, n_e, and plasma current, I_p, scaling can be reproduced.

Spontaneous shear flow generation in magnetized fusion plasmas is thought to occur by an interaction of the turbulent Reynolds stress with the shear flow. This interaction can be viewed as a transfer of turbulent energy to the shear flow scales via a three-wave coupling process, which suggests that investigations of bispectral quantities may be of interest. In this paper, we discuss the theory of mean flow generation when described via the bispectrum. Simple theoretical analysis is used to demonstrate the connection between the bispectrum and the nonlinear amplification mechanism for zonal shear flows. We also discuss results from analysis of edge fluctuations from DIII-D during an L-H transition. These results indicate a transient rise and fall of three-wave coupling during the transition, which is spatially localized to inside the separatrix. Future efforts to determine the direction and rate of turbulent energy transfer during shear-flow formation will also be discussed.

In the last few years, significant progress has been made in the understanding of H-mode plasmas (e.g. ion temperature profile stiffness, pedestal physics, etc). Based on this improved understanding, a set of rules (models) comprising a physics picture of the H-mode has been implemented in the ASTRA code in order to improve the understanding of experimental observations and ultimately to provide a predictive capability for ITER complementary to the scaling relations. The model has been verified for consistency with experimental observations in ASDEX-UG and JET plasmas. Numerical coefficients for the transport, required because of simplifications or missing quantitative information, are determined for one plasma (e.g. from JET) and then held constant for all others (JET, ASDEX-UP, ITER).

After benchmarking the model to experimental results, it was also applied to ITER. It predicts that Q = 10 can be achieved in ITER but only with at least a 50% deep fuelling contribution (inside the H-mode pedestal). However, in existing machines as well as in our model runs for existing machines, gas puffing is sufficient to achieve the observed density pedestal and line average densities. A second important result from the predictive runs for ITER is that electron energy transport in the plasma core, the neoclassical transport in the pedestal and the CX losses at the plasma edge are important constraints for a better performance. Thus future theoretical and experimental work should concentrate on these areas in order to improve our predictions.

Transition phenomena between thermal noise state and turbulent state observed in a submarginal turbulent plasma are analysed with statistical theory. Time-development of turbulent fluctuation is obtained by numerical simulations of Langevin equation which contains hysteresis characteristics. Transition rates between two states are analysed. Transition from turbulent state to thermal noise state occurs in the entire region between subcritical bifurcation point and linear stability boundary.

A self-sustained turbulence model for collisionless trapped electron mode is presented to examine the role of dynamics of trapped electrons in forming electron internal transport barrier (ITB) in tokamak plasmas with negative magnetic shear. Results show that strong negative magnetic shear as well as large Shafranov shift can lead to the precession drift reversal of trapped electrons and large reduction of anomalous electron heat conductivity; it may further trigger the formation of electron ITB. The complete precession drift reversal seems to be in good agreement with the onset condition of electron ITB observed in JT-60U discharges.

Transport barrier formation due to the ion-temperature-gradient (ITG)-driven mode is studied with a low-dimensional dynamical model composed of 18 mode coupling equations. This is an extention of the Hu-Horton model composed of 11 mode coupling equations. The 18 degrees of freedom model describes an intermittent behaviour of cross-field thermal transport, which is related to formation of sheared poloidal flow to suppress convection due to the ITG mode. Thus an edge localized mode (ELM-)-like behaviour is observed for the Nusselt number characterizing the cross-field thermal transport.

The theory-based Weiland transport model has been applied to JET discharges with internal transport barriers (ITBs) for the first time. The agreement of the modelling results with the experiments has been found to be comparable with the agreement of the modelling results produced by the semi-empirical Bohm/gyro-Bohm transport model. Weiland model overestimates the width of the ITB and the electron temperature. There is evidence that the density gradient in the Weiland model plays a more important role in governing the ITB formation dynamics for JET discharges than the suppression of turbulence by the ω_E×B flow shearing rate.

A set of transport equations is analysed, including the bifurcation of the electric field. The structure of the electric field is studied by use of the theoretical model for the anomalous transport diffusivities. Multiple solutions of E_r for the ambipolar condition are examined in the structure of the radial electric field. Parameter region in which the multiple solutions of electric field exist is studied by using the device parameter of compact helical system. A spatial structure of the radial electric field is also examined in the case using the device parameter of large helical device.

When resistive interchange modes (RIMs) are unstable in a Stellarator/Heliotron device, they may change the pressure profile even for β values lower than the ideal β limit. The nonlinear RIM with n/m = 2/3 modifies the density profile in the vicinity of the resonant surface with ι = 2/3 easily under the assumption of constant temperature. Here m(n) is a poloidal (toroidal) mode number and ι is a rotational transform. Also poloidal shear flow is generated there, which limits the region of density profile modification substantially. The sign of the density gradient becomes positive at the resonant surface. A quasi-stationary profile is obtained for low-collisional plasmas. When the collision frequency is high, local humps are produced in the background density profile, and they have a tendency to move to the resonant surface. It is also shown that the density profile including humps is correlated with the poloidal velocity shear profile. Here the typical shearing rate of the poloidal flow at the saturated state exceeds the linear growth rate of the (m,n) = (3,2) mode.