Table of contents

This special issue of Plasma Physics and Controlled Fusion contains papers based on invited talks and poster contributions presented at the 10th IAEA Technical Meeting on H-mode Physics and Transport Barriers. This meeting was held at the Hotel Moscow in St Petersburg, Russia, 28–30 September 2005. The meeting was organized by the Ioffe Physical-Technical Institute, Russian Academy of Sciences. This was the tenth meeting of a series (San Diego 1987, Gut Ising 1989, Abingdon 1991, Naka 1993, Princeton 1995, Kloster Seeon 1997, Oxford 1999, Toki 2001, San Diego 2003).

The meeting programme was divided into six topics. The topics were:

• Internal transport barriers: critical issues

• Edge transport barriers: pedestal stability/dynamics and ELMs

• Transport barriers in non-axisymmetric devices

• Transport barrier theories

• Turbulence behaviour in the presence of transport barriers

• Improved confinement projections/issues for burning devices

For each topic there was an invited talk whose purpose was to present an overview of the topic, based on contributions to the meeting and on recently published external results. The other purpose of the talks was to initiate discussions around the topics. The discussion consisted of short presentations by contributing speakers and comments from the audience. For each topic there was an associated poster session for contributed papers, of which there were about 80 in total.

The topics were focused on the physics of internal and edge transport barriers with special consideration of critical and unresolved issues. Similarities and differences of barrier physics in axisymmetric and non-axisymmetric devices were extensively reviewed to get mutual benefits for communities involved in the corresponding studies. Developments in the theory of transport barrier formation since the previous meeting were featured. Open questions of a turbulence behaviour in the presence of barriers were pointed out. Since transport barriers are planned to be utilized in reactor devices and in ITER particularly, various aspects of barrier physics in burning plasmas were discussed.

The selection of topics and invited speakers and general organization of the scientific programme were carried out by the International Advisory Committee, consisting of:

• R Groebner (GA, USA)

• T S Hahm (PPPL, USA)

• A Hubbard (MIT, USA)

• K Ida (NIFS, Japan)

• S V Lebedev (Ioffe, Russia, Chair)

• G Saibene (EFDA, Germany)

• W Suttrop (IPP, Germany)

• T Takizuka (JAERI, Japan)

I am very grateful to the committee members for their enthusiastic work preparing the meeting scientific programme. I would also like to thank Leonid Askinazi, Vladimir Sergeev, Alexander Tukachinsky and Nickolay Zhubr, members of the Local Organizing Committee, for their great input in the organization of the meeting.

Plasmas regimes with improved core energy confinement properties, i.e. with internal transport barriers (ITB), provide a possible route towards simultaneous high fusion performance and continuous tokamak reactor operation in a non-inductive current drive state. High core confinement regimes should be made compatible with a dominant fraction of the plasma current self-generated (pressure-driven) by the bootstrap effect while operating at high normalized pressure and moderate current. Furthermore, ITB regimes with 'non-stiff' plasma core pressure break the link observed in standard inductive operation between fusion performances and plasma pressure at the edge, thus offering a new degree of freedom in the tokamak operational space. Prospects and critical issues for using plasmas with enhanced thermal core insulation as a basis for steady tokamak reactor operation are reviewed in the light of the encouraging experimental and modelling results obtained recently (typically in the last two years). An extensive set of data from experiments carried out worldwide has been gathered on ITB regimes covering a wide range of parameters (q-profile, T_i/T_e, gradient length, shaping, normalized toroidal Larmor radius, collisionality, Mach number, etc). In the light of the progress made recently, the following critical physics issues relevant to the extrapolation of ITB regimes to next-step experiments, such as ITER, are addressed:

(i) conditions for ITB formation and existence of a power threshold,

(ii) ITB sustainment at T_i ∼ T_e, with low toroidal torque injection, low central particle fuelling but at high density and low impurity concentration,

(iii) control of confinement for sustaining wide ITBs that encompass a large volume at high β_N,

(iv) real time profile control (q and pressure) with high bootstrap current and large fraction of alpha-heating and

(v) compatibility of core with edge transport barriers or with external core perturbations (such as frozen hydrogen isotope pellets injection).

It is shown that the present experimental results provide some valuable and promising answers to these critical issues.

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 T_e/T_i profiles accessible with 0.3 < (T_e/T_i)_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 T_e/T_i 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 T_e/T_i.

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.

The physics of strong internal transport barriers (ITBs) in JT-60U reversed-magnetic-shear (RS) plasmas has been studied through the modelling on the 1.5 dimensional transport simulation. The key physics to produce two scalings on the basis of the JT-60U box-type ITB database are identified. As for the scaling for the narrow ITB width proportional to the ion poloidal gyroradius, the following three physics are important: (1) the sharp reduction of the anomalous transport below the neoclassical level in the RS region, (2) the autonomous formation of pressure and current profiles through the neoclassical transport and the bootstrap current and (3) the large difference between the neoclassical transport and the anomalous transport in the normal-shear region. As for the scaling for the energy confinement inside ITB (_fβ_p,core ≈ 0.25, where _f is the inverse aspect ratio at the ITB foot and β_p,core is the core poloidal beta value), the value of 0.25 is found to be a saturation value due to the MHD equilibrium. The value of _fβ_p,core reaches the saturation value, when the box-type ITB is formed in the strong RS plasma with a large asymmetry of the poloidal magnetic field, regardless of the details of the transport and the non-inductively driven current.

The spontaneous toroidal rotation velocity under the no/low direct toroidal momentum input, particularly from the electron cyclotron (EC) wave injection has been investigated in JT-60U plasmas. It is found that the response of toroidal rotation velocity to the central EC injection is towards the co-current direction in L-mode plasma. The region of the change in the toroidal rotation velocity is wider than the EC deposition profile and similar to that in electron temperature. The observed co-rotation velocity in the combined heating of EC and lower hybrid wave increases with the increase in the stored energy and a large positive radial electric field is formed in the strong co-rotating plasma. Furthermore the short pulse off-axis EC injection experiment shows that the perturbation of the toroidal rotation velocity towards the co-direction propagates to the centre with increase in its amplitude, suggesting an inward pinch in momentum transport.

The progress that has been made in understanding the processes responsible for edge localized modes is reviewed. Attention is restricted to the role of ideal magneto-hydrodynamics and extensions of this model. As well as reviewing the current understanding, future research needs are discussed and speculative ideas for further development are proposed.

Radial electric field is known to be an important factor affecting transport and confinement in toroidal fusion plasmas. Langmuire probe measurements of peripheral radial electric field evolution in the presence of a rotating MHD island were performed on the TUMAN-3M tokamak in order to clear up the possible connection between the radial electric field and the island rotation, both in L and H-modes. The measurements showed that E_r became positive, if the island was large enough, in spite of the constant direction of the island's rotation. Comparing similar ohmic H-mode discharges with or without a rotating MHD island, it was found that in the presence of the large island E_r was always more positive. Possible explanations of this observation are discussed.

Improved models are developed for integrated simulations of pedestal formation and edge localized mode (ELM) cycles at the edge of H-mode tokamak plasmas. The H-mode pedestal is formed in the simulations when flow shear and magnetic shear reduce the transport driven by drift modes at the edge of the plasma (Pankin A Y et al2005 Plasma Phys. Control. Fusion47 483). A large part of the flow shear is produced by the diamagnetic drift and the poloidal velocity, which is computed using a neoclassical model. Ion thermal transport is reduced to near the neoclassical level while electron thermal transport is reduced to the electron temperature gradient mode transport. A relatively large current density is driven in the pedestal by the bootstrap current. If the heating power is large enough, the pedestal growth is limited by ELM crashes, which are triggered by ideal MHD instabilities. Integrated simulations using these improved models are validated by comparing the simulation results with data for plasma profiles during the pedestal formation and with data for the ELM crash frequency. Simulations using the validated model are carried out for 31 Inernational Profile Database DIII-D and JET discharges.

The experiments described in the paper are aimed at investigating the possible influence of the low frequency magnetohydrodynamic (MHD) activity burst on the Ohmic H-mode in the TUMAN-3M tokamak. During the MHD burst a transient deterioration of improved confinement was observed. The study has been focused on the measurements of plasma fluctuation poloidal velocity performed by microwave Doppler reflectometry. The plasma fluctuation rotation observed before the MHD burst in the vicinity of the edge transport barrier was in the direction of plasma drift in the negative radial electric field. During the MHD activity the measured poloidal velocity was drastically decreased and even changed its sign. Radial profiles of the poloidal velocity measured in a set of reproducible tokamak shots exhibited the plasma fluctuation rotation in the ion diamagnetic drift direction at the location of the peripheral transport barrier. The possible reasons for this phenomenon are discussed.

A survey of global performance parameters and their correlation with pedestal parameters is performed for standard H-mode, QH-mode and the enhanced confinement regimes of VH-mode, hybrid and advanced tokamak in the DIII-D tokamak. This study shows that there is a trend for global confinement quality or global beta to increase as the pedestal electron pressure or beta increases. However, there are also improvements in core confinement and beta, observed at fixed pedestal pressure or beta, which indicate that factors other than pedestal parameters also contribute to the best core performance. Several other pedestal structure parameters are found to be similar among these regimes. The scale lengths for electron pressure in the pedestal are in the range 0.8–1.6 cm at the outer midplane, most η_e values are in the range 1–3 in the middle of the T_e pedestal and the T_e and n_e pedestals tend to penetrate the same distance into the plasma.

Comparisons of H-mode regimes were carried out on the Alcator C-Mod and JFT-2M tokamaks. Shapes were matched apart from aspect ratio, which is lower on C-Mod. The high recycling steady H-mode on JFT-2M and enhanced D-alpha (EDA) regime on C-Mod, both of which feature very small or no ELMs, are found to have similar access conditions in q₉₅ − ν* space, occurring for pedestal collisionality ν^* ≳ 1. Differences in edge fluctuations were found, with lower frequencies but higher mode numbers on C-Mod. In both tokamaks an attractive regime with small ELMs on top of an enhanced D_α baseline was obtained at moderate ν^* and higher pressure. The JFT-2M shape favoured the appearance of ELMs on C-Mod and also resulted in the appearance of a lower frequency component of the quasicoherent mode during EDA.

Effects of plasma rotation and losses of fast ions on Type-I ELM characteristics have been systematically studied in the JT-60U tokamak, scanning combinations of NBI (tangential co-, balanced- and counter-NBI plus perpendicular NBI) in the three types of plasma configurations (corresponding toroidal field ripple at the plasma edge, δ_r ∼ 0.4, 1.0 and 2.0%). New findings on the Type-I ELM characteristics are as follows: smaller ELM energy loss normalized by pedestal stored energy, ΔW_ELM/W_ped, and faster ELM frequency, f_ELM, are confirmed in the counter-NBI in comparison with the co-NBI discharges. Nevertheless, the power loss due to ELM, P_ELM (= ΔW_ELM × f_ELM), normalized by heating power crossing the separatrix, P_SEP, is constant regardless of the direction of the momentum injection at each plasma configuration. In contrast, the P_ELM/P_SEP decreases with increasing δ_r. The relationship between ELMs, rotation and the losses of fast ions are discussed.

An experimental study is performed to investigate the underlying physics of ELM triggering by imposing local perturbations at the plasma edge. Deuterium is injected during type-I ELMy H-mode phases by small solid pellets or as a supersonic gas jet. In both cases the repetition rate is small compared with the intrinsic ELM frequency, aiming for a small perturbation of the intrinsic ELM cycle. Active triggering of ELMs requires a density perturbation in the gradient region about 1 cm inside the separatrix (measured at horizontal mid-plane), a condition that is achieved by pellets of any size and speed but not by even the strongest available gas jets. The pellet-induced triggering of ELMs always occurs when pellets reach the H-mode barrier region. A density perturbation produced by a gas jet remains localized at the separatrix, and even if larger by a factor of at least 100, is not sufficient to trigger an ELM. No significant dependence of the ELM size on the ELM onset time was found, measured from the onset of the previous ELM.

This report summarizes Type I edge localized mode (ELM) dynamics measurements from a number of tokamaks, including ASDEX-Upgrade, DIII-D, JET, JT-60U and MAST, with the goal of providing guidance and insight for the development of ELM simulation and modelling. Several transport mechanisms are conjectured to be responsible for ELM transport, including convective transport due to filamentary structures ejected from the pedestal, parallel transport due to edge ergodization or magnetic reconnection and turbulent transport driven by the high edge gradients when the radial electric field shear is suppressed. The experimental observations are assessed for their validation, or conflict, with these ELM transport conjectures.

Ohmic H-mode discharges in the Tokamak à Configuration Variable (TCV) have recently been heated for the first time by electron cyclotron (EC) waves at the 3rd harmonic (X3) at full power. New edge localized mode (ELM) behaviour has been found, with larger amplitudes at lower frequency than are typical in ohmic H-modes. This new regime required the full available X3-EC Heating (X3-ECH) power to avoid the ELM-free phase, which occurred when less heating power was applied. The energy loss per ELM can be up to 15% of the total stored energy, with values in the range 4–5% being typical of the smaller ELMs usually found in the ohmic H-mode regime. Despite these high-energy losses, the plasma temperature raises significantly in the X3 heated H-modes, doubling the stored energy from its ohmic value. The confinement time decreases when the ECH is applied, but can recover its ohmic H-mode value later in the discharge depending on the EC wave coupling. It is still not possible to provide an unambiguous classification of these ELMs as Type I.

Several small/no ELM regimes such as EDA, grassy ELM, HRS, QH-mode, type II and V ELMs with good confinement properties have been obtained in Alcator C-Mod, ASDEX-Upgrade, DIII-D, JET, JFT-2M, JT-60U and NSTX. All these regimes show considerable reduction of instantaneous ELM heat load onto divertor target plates in contrast to conventional type I ELM, and ELM energy losses are evaluated as less than 5% of the pedestal stored energy. These small/no ELM regimes are summarized and widely categorized by their pedestal conditions in terms of the operational space in non-dimensional pedestal parameters and requirement of plasma shape/configuration. The characteristics of edge fluctuations and activities of ideal MHD stability leading to small/no ELMs are also summarized.

The evolution and performance limits for the pedestal in H-mode are dependent on the two main drive terms for instability: namely the edge pressure gradient and the edge current density. These terms are naturally coupled though neoclassical (Pfirsch–Schluter and bootstrap) effects. On DIII-D, local measurements of the edge current density are made using an injected lithium beam in conjunction with Zeeman polarimetry and compared with pressure profile measurements made with other diagnostics. These measurements have confirmed the close spatial and temporal correlation that exists between the measured current density and the edge pressure in H- and QH-mode pedestals, where substantial pressure gradients exist. In the present work we examine the changes in the measured edge current for DIII-D pedestals which have a range of values for the ion and electron collisionalities { } due to fuelling effects. Such changes in the collisionality in the edge are expected to significantly alter the level of the bootstrap current from the value predicted from the collisionless limit and therefore should correspondingly alter the pedestal stability limits. We find a clear decrease in measured current as ν increases, even for discharges having similar edge pressure gradients.

By conducting power scan experiments in three cases of toroidal field ripple configurations (δ_r ≃ 0.4, 1.0 and 2.0%) with variation of the toroidal momentum source (co, balanced, counter) relative to the direction of the plasma current, the roles of the loss of fast ions and toroidal rotation on the H-mode pedestal structure were investigated. It was found that the pedestal pressure was increased with a decrease in fast ion loss power. On the other hand, the variation in toroidal rotation did not affect strongly the pedestal pressure, although the loss of fast ions due to existing large toroidal field ripple forced the toroidal rotation basically to the counter direction in JT-60U. Due to the enhanced counter toroidal rotation induced by the loss of fast ions, similar V_tor profiles were obtained for discharges with different toroidal momentum source and loss of fast ions. When the loss of fast ions became smaller, pedestal density was raised remarkably while there was no significant difference in the temperature profiles.

In the Large Helical Device (LHD), edge coherent MHD modes such as m/n = 2/3 or 1/2 (m, n: poloidal and toroidal mode numbers), of which the rational surface is located in the plasma edge region of the magnetic hill, are strongly enhanced after an L–H transition. In this case, an edge MHD mode localized in a region further in than the location of the enhanced MHD modes is often stabilized because of the decrease in the pressure gradient there. Enhancement of the edge MHD mode amplitude stops a substantial rise in the edge pressure gradient after the transition. In an L–H transition plasma, soft x-ray (SX) fluctuations, δI_sx, related to edge MHD modes are clearly detected. The radial profiles of the amplitude and the phase differences among the SX-detector channels are sensitively dependent on the m-number. The relative amplitudes of the SX fluctuations, δI_sx/I_sx, which may reflect the eigenfunction of the MHD mode, rapidly increase towards the plasma edge in which the relevant rational surface exists.

We investigated the relative change in ion temperature (ΔT_i/T_i), electron temperature (ΔT_e/T_e), pedestal stored energy (ΔW_ELM/W_ped), and toroidal rotation velocity (V_t) due to type-I ELMs using diagnostics with fast temporal resolution in JT-60U. The increase in V_t was found in the direction of the plasma current right after the ELM. The recovery of V_t was found to be faster than that of W_dia, T_e and T_i. It is also found that ΔT_i/T_i can be larger than ΔT_e/T_e.

This paper presents the physics of two bifurcations in confinement of helical devices—(1) to the H-mode and (2) to internal transport barrier (ITB)-like electron temperature profiles as they develop under neoclassical electron root conditions in 3-dimensional systems. With their characteristics—low or negative magnetic shear, strong toroidal flow damping, experimental variability of poloidal flow damping, radial electric field enforced by ambipolarity, diagnostic access to sophisticated spatial and temporal structures of turbulence thanks to low-power operation with external confinement—helical devices provide unique contributions to the physics of transport barriers. The bifurcation to confinement with external transport barrier seems to be soft and the leading role of the electric field gradient is confirmed; the one to ITB-like core profiles is a hard transition and it is the electric field which governs it. The paper summarizes the status of H-mode research in helical systems and discusses the impact of the electron root on core confinement.

Spontaneous changes in confined plasma parameters have been observed recently in the l = 3/m = 9 Uragan-3M torsatron with an RF produced and heated plasma, these being interpreted as transition to an improved confinement mode due to ITB formation near the ι = 1/4 rational magnetic surface. In the work presented joint studies are carried out of changes in some edge and diverted plasma characteristics that accompany ITB formation. It is shown that ITB formation induces a hard E_r bifurcation at the boundary presumably driven by the ion orbit loss. As a result, E_r becomes more negative, and an E_r shear layer occurs, where the low-frequency microturbulence and the turbulence-induced anomalous transport are suppressed, i.e. an ETB is formed. At the pre-bifurcation phase of transition a reduction of fast ion loss takes place. The bifurcation results in an improvement of electron confinement, while the ion loss increases.

Cold pulse inversion in a helical plasma is observed in the Large Helical Device (LHD) and thus the strong non-local effects are evident in the helical device as well as in tokamaks. A hydrogen pellet or tracer encapsulated solid pellet is injected into the edge of the LHD plasmas. A significant rise of the electron temperature is observed in the central region in response to the edge cooling. Transient analysis indicates a heat flux jump despite the absence of a change in the local temperature gradient. The non-local temperature rise takes place in the low density and high temperature regime just as predicted by the TFTR scaling.

A series of hot cathode biasing experiments with marginal conditions for improved mode transition were carried out in the Tohoku University Heliac (TU-Heliac). Spontaneous transitions were observed accompanied by a delay of a few milliseconds. Transition conditions were explored over a wide operation range. The transition points can be identified clearly and easily in the operation range, because the plasma parameters changed slowly until the spontaneous transition. Although operation conditions were spread over a wide range, poloidal Mach numbers for transitions were concentrated in the range of −M_p = 1–2 and normalized driving forces for poloidal rotation agreed well with the local maximum value of ion viscosity predicted by neoclassical theory. The local maximum of ion viscosity against the poloidal Mach number was found to play a key role in the L–H transition. Marginal hot cathode biasing is suitable to determine the threshold conditions for the L–H transition.

Magnetic configurations of LHD are characterized by the presence of chaotic magnetic field, the so-called ergodic layer, surrounding the core plasma. H-mode-like discharges have been obtained at an outwardly shifted configuration of R_ax = 4.00 m with a thick ergodic layer, where the ι/2π = 1 position is located in the middle of the ergodic layer. A clear density rise and a reduction of magnetic fluctuation were observed. ELM-like Hα bursts also appeared with a radial propagation of density bursts. These H-mode-like discharges can be triggered by changing P_NBI(<12 MW) from three beams to two beams in a density range (4–8) × 10¹³ cm⁻³. The ELM-like bursts vanished with a small change of the edge rotational transform. A precise profile measurement of the edge density bursts confirmed that ELM-like bursts occur at the ι/2π = 1 position.

The edge transport barrier (ETB) produced by the L–H transition was measured by a triple Langmuir probe (LP) at two toroidal sections of the compact helical system (CHS), of which diagnostic method has good time and spatial resolutions. The radial profiles of electron density (n_e), electron temperature (T_e) and space potential (V_s) in the ETB region have different shapes at two different toroidal sections. These profiles are deformed inside the ETB region at one location and are formed with rather smooth variations at the other. These deformations gradually disappear in the deep H-phase (after ∼15 ms from the transition) and the profiles inside the ETB become similar at both sections. The deformation seems linked to the presence of a non-rotating magnetic island at the rational surface of the rotational transform ι/2π = 1.

The density and potential fluctuations were measured in hot-cathode biasing plasma at the Tohoku University Heliac. In the improved mode, high-frequency fluctuations (>100 kHz) appeared in the density signal. On the other hand, low-frequency fluctuations (<100 kHz) in the density and potential signals were suppressed. The characteristics of high-frequency fluctuation were compared with three kinds of instability, and they were consistent with those of the flute instability driven by the supersonic poloidal rotation. The suppression of low-frequency fluctuations in improved mode is considered the effect of E × B poloidal rotation or its shear. The profile of the anomalous particle flux was estimated by analysing the low-frequency fluctuation signals. The flux decreased in the improved mode in most of the region, although the decrease in flux was small near the rational surface (n/m = 5/3).

On the Large Helical Device (LHD), low to high confinement (L–H) transition and edge transport barrier (ETB) formation were observed in the low beta regime (⟨β_dia⟩ < 1%, ⟨β_dia⟩: volume-averaged beta derived from diamagnetic measurement) as well as in relatively high beta regime (>1.5%). In most of ETB plasmas electron density preferentially increases in the edge region without a substantial rise of the edge electron temperature. The ETB zone develops inside the ergodic field layer calculated in the vacuum field. The ETB formation strongly destabilizes edge coherent modes such as m/n = 2/3 or 1/2 (m, n: poloidal and toroidal mode numbers), because the plasma edge region is in the magnetic hill. The ETB is partially destroyed by the combination of these edge MHD modes and ELM-like activities. For a particular experimental condition, the forced generation of a sizable m/n = 1/1 magnetic island near the edge by application of external field perturbations facilitates the L–H transition at a lower electron density and suppresses edge MHD modes and ELM-like activities to lower levels.

Boronization of the vacuum chamber of the L-2M stellarator has resulted in modification of the electron temperature profile. In particular, a well-defined jump in the electron temperature to T_e ∼ 100 eV in a narrow region Δr/r ∼ 0.05 is observed in the temperature profile at the plasma edge. In the present paper, the value and shape of the jump in T_e are studied at different values of plasma parameters and ECR heating power. A jump in T_e is absent at a power of P ∼ 100 kW, whereas at P ∼ 200 kW the electron temperature drops from 150 eV to zero within Δr ∼ 0.5 cm. The value of threshold power for the formation of a jump in T_e at n_e ∼ 1.7 × 10¹⁹ m⁻³ lies within the range P ∼ 100–160 kW. In terms of power per particle this power threshold is P/V/N_e ∼ 0.2–0.3 Mw/m³/10¹⁹m⁻³, the value of which coincides with threshold power for ETB formation found recently in the CHS stellarator. When the helical-field strength is 25% or 50% below its standard value, a jump in T_e at the plasma edge in L-2M is absent.

The difference in the H-mode power threshold in divertor and limiter configurations is numerically investigated by analysing the effect of boundary conditions imposed on the last closed magnetic surface (LCMS) and given by prescribed density and temperature e-folding lengths, δ_n and δ_T, respectively. It is demonstrated that the variation of δ_n and δ_T significantly affects the H-mode power threshold. This is explained by the change in the balance between conductive and convective heat losses at the edge. For the ratio δ_n/δ_T large enough, when the convective loss does not exceed 45% of the total power, the threshold agrees well with the experimental multi-machine scaling for divertor tokamaks. With reduction in δ_n/δ_T and increase in convective loss above this critical level, the power threshold significantly exceeds the scaling, in agreement with observations on different limiter tokamaks. By considering the power and particle balances in the scrape-off layer it is shown that the ratio δ_n/δ_T is controlled by the distance which recycling neutrals pass before entering the confined plasma and which is normally much larger in divertor machines than in the limiter ones. The calculations for the limiter tokamak TEXTOR have predicted the experimentally found conditions for the L–H transition in advance.

In the edge transport barrier of H-mode plasmas, a large poloidal flow exists and the electrostatic potential and density can have steep gradients both in the radial and poloidal directions. The accessibility to a two-dimensionally steep structure is demonstrated by solving the model equation including the poloidal structure, combined with the equation giving the time evolution of the radial electric field. The analysis is carried out with the parameter set of the electrode biasing experiment and shows the existence of the convective particle flux arising from poloidal inhomogeneity. This study provides an essential explanation for improving the transport analyses in H-modes by taking account of the two-dimensional effect in toroidal plasmas.

A direct implicit ion polarization gyrokinetic full f particle-in-cell approach is implemented with kinetic electrons in global tokamak transport simulations. The method is applicable for calculations of rapid transients and steep gradients in the plasma, which is made feasible by recording the charge density change by the ion polarization drift together with the particle advancing. The code has been successfully validated against the linear and nonlinear predictions of the unstable mode growth rates and frequencies and their turbulent saturation level. A first global validation of the neoclassical radial electric field in the presence of turbulence for a heated collisional tokamak plasma is obtained. The neoclassical radial electric field together with the related geodesic acoustic mode oscillations is found to regulate the turbulence and heat and particle diffusion levels in a large aspect ratio tokamak at low plasma current.

Oscillatory zonal flows called geodesic acoustic modes (GAMs) appearing in a high safety factor region of tokamak plasmas show nonlocal behaviour in their frequency. The frequency of the GAMs is unchanged over a certain radial region and the radial variation of the frequency is step-like. The effects of ρ_* = ρ_i/a on the nonlocal behaviour of the GAMs are investigated by global ion temperature gradient driven turbulence simulations, where ρ_i is an ion Larmor radius and a is a minor radius of a torus. It is found that the radial width in which the GAMs have the same frequency is almost proportional to , while the radial wavelength of the GAMs is proportional to ρ_i. As for turbulent transport, the boundary between a high transport region where the GAMs are dominant and a low transport region becomes clearer for smaller ρ_*.

Box-type electron temperature profiles observed in negative central shear plasmas with electron internal transport barriers are explained with the help of a novel instability mechanism that is predicted when keeping account of the radial component of the trapped electron gradB and curvature drifts in the theory of the trapped electron mode. These radial velocity components lead to a new term in the quasi-slab radial eigenvalue equation which modifies the asymptotic behaviour in such a way that growing–decaying pairs of bounded solutions are obtained (instead of the usual magnetic shear damped solutions) if . There are no bounded solutions if . As L_Te = T_e/∂_rT_e is usually negative, instability requires negative magnetic shear . The driving mechanism is largest for quasi-slab modes in view of the poloidal angle dependence of the radial drift components. The ratio , where Q_e is the anomalous electron energy flux and Γ_e the particle flux, is quite large owing to the non-adiabatic trapped electron response and the condition that must be satisfied to avoid ion Landau damping on the side-bands ( is the electron diamagnetic frequency, l the toroidal mode number, 1/qR the parallel wave vector of the side-bands and the sound speed).

There is general agreement that the creation of transport barriers in magnetized plasmas is associated with the reduction in turbulence-driven transport. The fundamental physics involved in barrier formation is the effect of equilibrium E × B shear and zonal flows on turbulence and transport. This paper focuses on three major issues in turbulence and transport barriers that were discussed at the Tenth IAEA Technical Committee Meeting on H-Mode Physics and Transport Barriers: (1) zonal flows and their effects on turbulence, (2) spatial spreading of turbulence from regions of instability to regions of stability and (3) the effects of short wavelength turbulence. This work gives a short summary of experimental work bearing on each of the themes and raises fundamental questions to motivate future research in each of these areas.

Spectral changes in electric field fluctuation are measured using twin heavy ion beam probes in compact helical system (CHS) before and after an internal transport barrier is broken down. Wavelet analysis reveals intermittent behaviour of the fluctuations and a significant correlation between fluctuation powers of the low (2.5 < f < 10 kHz) and high (30 < f < 250 kHz) ranges. The high frequency (turbulence) fluctuation increases with a decrease in the low frequency fluctuation after the back-transition. The change in the power distribution between these two frequency ranges may contribute to the improved transport on the barrier.

The new diagnostic technique for investigation of ETG mode-scale tokamak turbulence–correlative enhanced scattering is developed at the FT-2 tokamak. Fine scale drift wave modes possessing unusually high frequency are observed using this technique in the ohmic discharge under conditions when the ETG mode should be unstable.

Two types of small-poloidal wavelength low frequency floating potential fluctuations (∼1 kHz, and 10–15 kHz) are observed in the edge region of ohmically heated plasmas in the JFT-2M tokamak. The higher frequency fluctuations are inferred as geodesic acoustic modes (GAMs). Significant bicoherences between both modes and the broad-band fluctuations are observed simultaneously; however, frequency ranges are different. A significant bicoherence range is from 70 to 125 kHz at the lower frequency modes (LFM) and is from 20 to 125 kHz at the GAM. Phase angles at the significant bicoherences are coherent around π. These results indicate that both modes are nonlinearly coupled to the broad-band fluctuations. Two spectral peaks are observed around the GAM frequency and the difference in peak frequencies is around the LFM frequency, suggesting nonlinear couplings between the LFM and the GAM. However, the modulation of the GAM by the LFM is not conclusive. In this paper, the results of the letter (Nagashima et al 2005 Phys. Rev. Lett.95 095002) are presented in detail.

The delta-f gyrokinetic model originally formulated for core turbulence is extended to treat medium-amplitude electromagnetic turbulence expected in the transcollisional edge regions of modern tokamaks. Both electrons and ions, and the field polarization equations, are followed. The effect on the turbulence of an externally applied E × B velocity shear and alternatively an initial E × B vorticity profile to which the turbulence can back-react are studied. Imposed shear reduces the short wavelength component but increases the long wavelengths. The localized vorticity layer has a more general suppressive effect.

A comparative analysis is done of data on turbulent fluxes measured in the edge plasma in the L-2M stellarator and the FT-2 tokamak. This analysis is performed using the estimation-maximization algorithm to determine finite mixtures of normal distributions that give the best fit to the probability distributions (PDFs) of the increments of turbulent fluxes. The resulting PDFs indicate non-Brownian motion of particles, and the weight of rare transport events (heavy tails of PDFs of fluxes) can be calculated. The number of the normal processes in model mixtures, as well as their weights in the PDFs of the increments of the turbulent flux, change during L–H transition in FT-2. Characteristically, the number of normal processes for the H-regime of FT-2 is the same as for the L-2M stellarator, and the parameters of Gaussians are also similar. This fact may be interpreted as an indirect indication that the L-2M stellarator operates in the mode of improved plasma confinement (which is consistent with the neoclassical theory for stellarators).

Further transport reduction is induced by a pellet or electron cyclotron (EC) wave injection after the formation of an internal transport barrier in JT-60U reversed shear plasmas. After pellet injection, the O-mode reflectometer signal drastically decreases, indicating reduction in the electron density fluctuation level. The ion thermal diffusivity decreases by one order of magnitude and reaches the neoclassical level. The effective particle diffusivity also decreases by one order of magnitude, but the electron thermal diffusivity remains constant. After EC wave injection, when no reduction of the O-mode reflectometer signal is observed, the electron thermal diffusivity decreases by a factor of ∼2–3, while decreases in the ion thermal diffusivity and the effective particle diffusivity are small. These results indicate that the ion heat transport and particle transport were coupled with the measured density fluctuation, but electron heat transport was decoupled. Ion heat and particle transport and electron heat transport were dominated by different types of fluctuation.

Turbulence spreading in reversed shear plasmas is investigated using a simple, multi-fluid model of ITG turbulence in toroidal geometry. The temperature profile modification is accompanied by avalanche processes. In addition, it is found that the turbulence spreads inwards and outwards, owing to the nonlinear interactions of turbulence. Analysis of the simulation results indicates that the spatio-temporal propagation of the turbulence front is quantitatively consistent with the scaling of speed predicted by the Fisher front theory.

Characteristics of the edge pedestal has been studied for the high β_p ELMy H mode and the reversed shear ELMy H mode in JT-60U. The contribution of the pedestal is around 20% for the confinement improvement factor, the normalized beta, and the bootstrap fraction. The upper boundary of the fusion performance measure increases with the pedestal poloidal beta, β_p-ped. At high triangularity, δ, β_p-ped increases with the total β_p (β_p − tot) almost linearly for positive shear type I ELMy discharges. This dependence is not due to the profile stiffness, since the dependence is the same for the discharges both with and without an internal transport barrier (ITB). In the reversed shear ELMy H mode, β_p-ped increases with β_p-tot on the same line as the positive shear cases except at high q₉₅ = 8–9.3. In the high plasma current regime, the final structure with both an ITB and edge transport barrier seems to be determined by the balance between the expanding ITB-foot radius and deepening ELM penetration: the ELM penetration radius deepens with increasing pedestal stored energy and then reaches the ITB-foot radius. The ITB-foot seems to behave as a barrier against the ELM crash penetration, and shrinks after a few ELM attacks, and the ELM penetration follows the shrinking ITB-foot.

The addition of high power, low aspect ratio data from the NSTX and MAST experiments has motivated a new investigation of the effect of aspect ratio on confinement scaling. Various statistical methods, including those that incorporate estimates of measurement error, have been applied to datasets constrained by the standard set of criteria in addition to the range of κ and M_eff appropriate to ITER operation. Development of scalings using engineering parameters as predictor variables results in ε-scaling coefficients that range from 0.38 to 1.29; the transformation of these scalings to physics variables results in an unfavourable dependence of Bτ on β, but a favourable dependence on ε. Because the low aspect ratio devices operate at low B_T and therefore high β_T, a strong correlation exists between ε and β, and this makes scalings based on physics variables imprecise.

The predicted H-mode power threshold, P_L−H, for ITER is generally estimated from the international global H-mode threshold database (IGDBTH) by ordinary least squares log–linear (OLS) regressions. Such fits assume that errors are uncorrelated and (i) errors in P_L−H are much greater than those in the other parameters, (ii) errors are normally distributed and (iii) relative errors are equal for all experiments. In this paper, the validity of this statistical model for the IGDBTH is examined, by use of the more generalized maximum-likelihood method. Results indicate that all three assumptions bias the resulting scaling and so need to be relaxed. A fit relaxing all three constraints lies outside the error bars of the OLS, indicating that the choice of the statistical model makes a significant contribution to the resulting scaling. A chi-squared analysis shows that none of the studied models are entirely consistent with the data, indicating that further refinement of the physical and statistical model is required. For ITER-like parameters, a maximum-likelihood analysis shows a predicted threshold of 38.4 MW, compared with 31.1 MW for the OLS, indicating that OLS tends to under predict and that quoted confidence intervals tend to be too small. However, further studies of the sources of errors in the IGDBTH would be required before estimates based on more detailed statistical models can be given with confidence.

The ITER plasma performance is assessed on the basis of the newly-proposed confinement scalings, using 1.5D simulations with the ASTRA code. In the simulations, the transport coefficients are adjusted to satisfy HH ≡ τ_E/τ_E(scaling) = 1 for each scaling. It is shown that for plasma current I = 15 MA and plasma minor radius a = 2 m for each scaling there exists an operational window within the range of moderate densities n/n_G = 0.65–0.85 where n_G is the Greenwald density n_G (10²⁰ m⁻³) = I/π a². The fusion power P_fus = 250–600 MW can be obtained with neutral beam injection of 33 MW and ion cyclotron central heating of 0–20 MW. The operational windows predicted by the three scalings are close to each other. The fusion multiplication factor Q can achieve values in the range of 10–20 even with a more conservative assumption on helium pumping that corresponds to the ratio of the effective helium confinement time to the energy confinement time . The impact of enhanced particle confinement and increased threshold power for L to H mode transition on the ITER operational space is studied.

Results from an extensive profile database analysis of JET density profiles in H-mode show that the density peaking factor n_e0/ < n_e > in JET H-modes increases as the effective collisionality drops from ∼1 at mid-radius to below 0.1 as expected for ITER. Density peaking is also strongly correlated with the Greenwald number N_G, the particle outward flux Γ from the neutral beam source and T_i/T_e. The correlations with l_i, q₉₅, β_N, ρ*, L_Te, L_Ti, the toroidal Mach number and its shear are weak or insignificant. H- modes heated only by ICRH are, on average, only slightly less peaked than H-modes dominated by NBI, demonstrating that neutral beam fuelling can only explain a modest part (∼20%) of the peaking. Scaling expressions involving ν_eff, N_G, RΓ/(n_eχ) and T_i/T_e suggest that n_e0/<n_e > may exceed 1.5 in ITER, providing a boost of fusion power of more than 30% for fixed β and average density with respect to the usual assumption of a flat density profile.