Table of contents

This special issue of Plasma Physics and Controlled Fusion contains invited and contributed papers presented at the 9th IAEA Technical Meeting on H-mode Physics and Transport Barriers. This meeting was held at the Catamaran Hotel in San Diego, California, on 24-26 September, 2003, and it was organized by General Atomics. As has been the tradition at the last four meetings of this series, the programme was sub-divided into six topics. For each topic there was an invited talk whose purpose was to give an overview of the topic, based on contributed papers presented at the meeting and on external results. These talks were followed by discussion periods, which were used for extended question and answer sessions for the invited speakers or for additional short presentations by contributing speakers. For each topic there was an associated poster session for contributed papers, of which there were about 70. The topics were:

Structure and dynamics of internal transport barriers

Structure and dynamics of the H-mode pedestal

Understanding transport barriers through modelling

Control of transport barriers

Transport within transport barriers: theorist's view of the future

Diagnostic and analysis issues for transport barriers

The topics were focused on the physics of edge and core transport barriers. Similar to the previous meeting, held in Toki, Japan, the universality of this physics in axisymmetric and non-axisymmetric machines was featured. In addition, the physics of transport barriers in relation to burning plasma experiments was emphasized. In particular, one of the hopes and goals of the participants is that the physics of transport barriers can be used to enhance the prospects for burning plasmas. Because this meeting occurred approximately 21 years after the discovery of the H-mode in 1982, a special session was held to commemorate more than 20 years of research on transport barriers. In this session, Dr R Stambaugh and Professor K Itoh presented personal views on the implications of the discovery and memories of the early days of H-mode research. In addition, Dr F Wagner, the leader of the team that published the seminal paper announcing the discovery of the H-mode, prepared remarks that were presented by Dr Stambaugh. The discovery of the H-mode provided great hope that a fusion reactor could be developed and opened the door to the field of transport barriers, a field that was beyond the dreams of most researchers in 1982. The selection of topics and invited speakers and general organization of the scientific programme were carried out by the International Programme Committee, consisting of:

S Lebedev (Ioffe, Russia)

K Ida (NIFS, Japan)

T Takizuka (JAERI, Japan)

G Saibene (EFDA, Germany)

W Suttrop (IPP, Germany)

M Greenwald (MIT, USA)

E Synakowski (PPPL, USA)

R Groebner (GA, USA)

I am very grateful to the committee members for their work and advice on the preparation of the meeting. In addition, I express deep thanks to Dr Punit Gohil, the Chair of the Local Organizing Committee, and to Lupe Cerda, the Conference Coordinator, who very ably took care of numerous details related to the organization of the meeting.

Models of radial electric field formation are discussed and compared with the results of numerical simulations from fluid transport codes and Monte Carlo codes. A comparison of the fluid and Monte Carlo codes is presented. A conclusion is arrived at that all the simulations do not predict any bifurcation of the electric field, i.e. no bifurcation of poloidal rotation from low to high Mach number values is obtained. In most of the simulations, the radial electric field is close to the neoclassical electric field. The deviation from neoclassical electric field at the separatrix due to the existence of a transitional viscous layer is discussed. Scalings for the shear of the poloidal rotation are checked versus simulation results. It is demonstrated that assuming the critical shear to be of the order of 10⁵ s⁻¹, it is possible to obtain a L–H transition power scaling close to that observed in the experiment. The dependence of the threshold on the magnetic field direction, pellet injection, aspect ratio and other factors are discussed on the basis of existing simulations. Transport codes where transport coefficients depend on the turbulence level and scenario simulations of L–H transition are analysed. However, the details of gyrofluid and gyrokinetic modelling should be discussed elsewhere. Simulations of internal transport barrier (ITB) formation are discussed as well as factors responsible for ITB formation.

Advanced tokamak regimes obtained in ASDEX Upgrade, DIII-D, FT-U, JET, JT-60U, TCV and Tore Supra experiments are assessed both in terms of their fusion performance and capability for ultimately reaching steady-state using data from the international internal transport barrier database. These advanced modes of tokamak operation are characterized by an improved core confinement and a modified current profile compared to the relaxed Ohmically driven one. The present results obtained in these experiments are studied in view of their prospect for achieving either long pulses ('hybrid' scenario with inductive and non-inductive current drive) or ultimately steady-state purely non-inductive current drive operation in next step devices such as ITER. A new operational diagram for advanced tokamak operation is proposed where the figure of merit characterizing the fusion performances and confinement, , is drawn versus the fraction of the plasma current driven by the bootstrap effect. In this diagram, present day advanced tokamak regimes have now reached an operational domain that is required in the non-inductive ITER current drive operation with typically 50% of the plasma current driven by the bootstrap effect (Green et al2003 Plasma Phys. Control. Fusion45 587). In addition, the existence domain of the advanced mode regimes is also mapped in terms of dimensionless plasmas physics quantities such as normalized Larmor radius, normalized collisionality, Mach number and ratio of ion to electron temperature. The gap between present day and future advanced tokamak experiments is quantitatively assessed in terms of these dimensionless parameters.

The formation of electron internal transport barriers (ITBs) was studied using electron cyclotron (EC) heating in JT-60U positive shear (PS) and reversed shear (RS) plasmas with scan of neutral beam (NB) power. With no or low values of NB power and with a small radial electric field (E_r) gradient, a strong, box-type electron ITB was formed in RS plasmas while a peaked profile with no strong electron ITBs was observed in PS plasmas within the available EC power. When the NB power and the E_r gradient were increased, the electron transport in strong electron ITBs with EC heating in RS plasmas was not affected, while electron thermal diffusivity was reduced in conjunction with the reduction of ion thermal diffusivity, and strong electron and ion ITBs were formed in PS plasmas.

Plasmas with an electron internal transport barrier (ITB), which is characterized by peaked electron temperature profiles, are obtained in the JT-60U tokamak and in the large helical device (LHD) when the electron cyclotron heating (ECH) is focused on the magnetic axis. The maximum values of , where R is the major radius and is the scale length of the electron temperature gradient, are similar for the LHD and JT-60U ITB plasmas. However, there is a clear jump of observed in LHD but not in JT-60U in the ECH power scan. This result is consistent with the fact that the trigger mechanism of the electron ITB is the fast transition of the radial electric field from a small negative E_r to a large positive E_r in LHD and a change of the magnetic shear from positive to negative is required for the formation of the electron ITB in JT-60U. There are also differences in the electron temperature profiles inside the ITB. The flattening of the electron temperature profile inside the strong ITB could be explained by the sharp increase of q values observed in JT-60U, while no flattening of the electron temperature profile is observed in LHD, where the central q values stay low.

A regime with electron heat confinement improvement was recently found in the initial phase of discharges in the TUMAN-3M tokamak. An internal transport barrier (ITB) formation in this regime was confirmed by Thomson scattering measurements and by transport modelling. Two possible reasons for the ITB formation are discussed in the paper: by reduction of turbulent transport in the presence of low magnetic shear or by plasma sheared rotation. It is demonstrated that low magnetic shear formation is possible in the current ramp-up phase of the Ohmic discharge. The low magnetic shear does not seem to be the only reason for the transport reduction. Results of Doppler reflectometry measurements of poloidal rotation of density fluctuations are presented. It is found that core confinement improvement correlates with the appearance of sheared rotation of the density fluctuations and with a burst of the MHD activity. The ITB formation in the regime seems to be a result of a combined action of reduced magnetic shear and plasma sheared rotation.

In the Alcator C-Mod tokamak, a high-resolution heterodyne ECE radiometer has been used to measure the electron temperature in plasma discharges with internal transport barriers (ITBs). ITBs are formed by the application of off-axis (r/a ∼ 0.5) ICRF power. Strong density peaking indicates the formation of the ITB. When the ITB is formed, the ECE radiometer detects a small amplitude mode localized near the magnetic axis. Surprisingly, as this mode amplitude grows a dip in the temperature profile is clearly observed at the same location. If sawteeth are present, the mode amplitude appears to be suppressed by the sawtooth crash and no dip in the temperate profiles is observed. TORAY, a ray-tracing code, has been used to investigate the possible refractive effects of the steep density gradients in the ITB and its effects on the ECE observations. The results show that refractive effects can explain the observed local changes in temperature. Ray-tracing also indicates that the observed modes are density fluctuations. Observations of broadband density fluctuations during 4.5 T ITBs are also described.

Transient transport experiments are performed in LHD plasma with electron internal transport barrier (e-ITB). Evidence for a reduction of electron heat diffusivity inside the ITB is observed from cold and heat pulse propagations. The observed enhancement of the cold pulse peak is explained by the temperature dependent electron heat diffusivity. The heat diffusivity inside the ITB decreases with an increase in the electron temperature in LHD.

L-mode to H-mode transitions (LH transitions) are obtained in a wide range of plasma parameters in TCV Ohmic discharges. LH transitions either occur directly, indicated by a single abrupt drop in D_α emission, or present an intermediate 'dithering' phase before the H-mode state is attained, in which D_α emission shows rapid excursions between L-mode and H-mode levels. The type of transition, with or without a dithering phase, depends on the plasma current and plasma triangularity. It is less sensitive to plasma density and divertor geometry. The relative direction of the ion ∇ B drift also plays a role in the characteristics of the LH transition.

The time delay between an LH transition and the preceding sawtooth crash has been measured in every TCV H-mode discharge. Most LH transitions are found to occur in the first 30% of the sawtooth cycle, i.e. in the first 2 ms after a sawtooth crash. Moreover, LH transitions often occur soon after a large crash of a 'double sawtooth'. The distribution function of these time delays clearly indicates a synchronization of these two processes. However, the heat pulse released during a sawtooth crash has a transit time from the q = 1 surface to the plasma edge, which is much shorter than the time delay between the sawtooth crash and the LH transition.

Results from recent experiments to study the effects of divertor geometry and increased plasma shaping on the L–H transition threshold on JET are reported. Equivalent septum configurations run with the new septum replacement plate (SRP) in the MkII Gas Box divertor have shown that the presence of the septum lowers the L–H transition power threshold, P_th, by 20%. For X-point to virtual septum top distances of less than 6 cm, the SRP plasmas also demonstrate a significant decrease of the L–H P_th and pedestal electron temperature, T_e with reduced X-point height. Although, the SRP plasma's P_th remains above that with the septum, there is no difference in the pedestal T_e at the L–H transition. The influence of plasma shaping on the L–H transition has also been investigated for the first time on JET in a series of density scans at I_p/B_t of 2.5 MA/2.7 T. While keeping the lower triangularity, δ_lower, and divertor geometry constant, the upper triangularity, δ_upper, has been increased from 0.23 to 0.34 with no effect on P_th or the pedestal T_e or T_i. In a separate edge n_e scan, two configurations with different δ_upper/δ_lower values of 0.23/0.23 and 0.43/0.33 have been compared. A large difference in the transition threshold is observed at values of edge n_e above 1.8 × 10¹⁹ m⁻³, with the higher δ plasmas characterized by P_th of up to 25% lower at the highest densities scanned. This is thought to be the result of lowered X-point and outer strike point heights with increased δ.

Edge profiles during the L–H transition and pedestal evolution in the Alcator C-Mod tokamak have been measured with high spatial and time resolution. For input power near the threshold, periodic 'dithering' cycles are seen, and the sustained transition occurs in a series of steps that appear related to this oscillatory behaviour. Even at a higher power, there is evidence of non-smooth T_e evolution, and the pedestal T_e shows a double break-in-slope at the transition. Calculations with a fluctuation-shear flow model, for parameters typical of this experiment, reproduce much of the observed behaviour. Profiles just before the L–H transition, averaged over steady or dithering periods, are compared with an analytic criterion based on shear suppression by zonal flows (Guzdar P N et al 2002 Phys. Rev. Lett.89 265004). The experimental values of are about 50% below the theoretical threshold, for a range of B_T.

We study the radial structure of high confinement modes in a simplified, one-dimensional model of the self-consistent interaction of fluctuations, shear flow, and pressure gradient. The model describes the plasma edge with an energy flux coming from the core, which is used as a boundary condition for the pressure transport equation. As the energy flux increases, there is an L–H transition bifurcation which is described near marginal instability using a reduced Ginzburg–Landau model for the shear flow coupled to a transport equation for the pressure. For higher values of the energy flux, a second transition takes place in which the H-mode exhibits a finite-k instability. Numerical results show that this instability leads in the nonlinear regime to the spontaneous formation of a pedestal in the pressure profile, where the effective diffusivity exhibits a sharp drop. A further increase in the energy flux leads to multiple pedestals across the simulation domain.

The edge transport barrier (ETB) for particle transport is formed in the neutral beam (NB) heated hydrogen discharges in compact helical system (CHS). The transition to the ETB formation and the back transition are controlled by the heating power. The existence of the heating power threshold is confirmed and it is roughly proportional to the density. The Hα emission signal shows a clear drop at the transition (the timescale of signal decrease is ∼1 ms for the high heating power case). The ETB formation continues for the full duration of NB injection (100 ms) with a moderate level of radiation power loss. Local density profile measurement shows increase of the edge density and the movement of the density gradient region towards the edge.

Edge density profile modifications associated with edge localized modes (ELMs) and edge harmonic oscillations (EHOs) have been measured using fast profile reflectometry in DIII-D H-mode plasmas. Specifically, high time (down to 10 µs) and spatial (∼4 mm) resolution density profile measurements from 0 × 10¹⁹ to 3.1 × 10¹⁹ m⁻³ provide us with new tools to study the dynamics of pedestal perturbations. During ELMs, it has been observed that the SOL density profile expands outwards to the vessel wall while the pedestal density reduces. These measurements provide direct evidence for enhanced particle radial transport to the vessel wall at the onset of ELMs. A large SOL density profile radial expansion velocity is observed during ELMs. A comparison of the velocities for different pedestal densities is made. The density scale length, density at the wall, and density fluctuations during ELMs are determined as a function of pedestal density, as well as particle transport during ELMs. Measurements in quiescent H-mode plasmas indicate that the pedestal density profile is modulated at the fundamental frequency of the EHO. A comparison between reflectometer and beam emission spectroscopy measurements regarding the EHO density fluctuation profile is presented.

The peeling–ballooning model for edge localized modes (ELMs) and pedestal constraints, based on ideal MHD instabilities driven by pressure gradients and current in the edge barrier region, has been broadly applied toward understanding ELM and pedestal behaviour in a number of tokamak experiments. Due in part to multiple driving terms, multiple wavelengths and second stability access physics, the peeling–ballooning stability limits which are proposed to constrain the pedestal and trigger ELMs depend sensitively on many details of the tokamak equilibrium. Here we present a technique for characterizing these stability constraints as a function of important parameters, using carefully constructed model equilibria. We discuss comparisons of calculated stability constraints to observed pedestal behaviour, in which an encouraging level of agreement is found. We then present results of an extensive series of calculations which characterize the peeling–ballooning stability constraints as a function of pedestal width, magnetic field, plasma current, density, and triangularity.

High frequency coherent magnetic fluctuations related to the type I edge localized mode (ELM) cycle have been found in ASDEX Upgrade. Typical frequencies are in the range 300–500 kHz, and the poloidal mode number, m, measured at the outboard midplane, is estimated to be 10–15. These MHD modes are present in many low density (low collisionality) discharges, while they have not been found in high density ones yet. New findings on already known low frequency type I ELM precursors confirm that in ASDEX Upgrade type I ELM mode precursors are normally phase locked to the wall in discharges with NBI heating parallel to and in the direction of the plasma current (co-injection) and can be seen with a non-zero rotation frequency only in shots with anti-parallel NBI (counter-injection). Additional information is given by ECE data. The existence of low and high frequency MHD events suggests an interpretation in the framework of the peeling–ballooning model. The high frequency magnetic activity seems to be related strictly to the increase in (and eventual saturation of) edge electron temperature, while low frequency modes are related directly to the ELM crash itself.

In a recent campaign with counter-current neutral beam injection (NBI), the quiescent high confinement mode (QH-mode) is studied in ASDEX Upgrade. The QH-mode regime is obtained with all accessible NBI angles, with and without additional ion cyclotron heating, at various values of edge safety factor q₉₅ and at values of Z_eff down to 2.5 after fresh boronization. In contrast to the ELMy H-mode, the pedestal pressure depends significantly on radial heat flux in the QH-mode, giving rise to a reduced heating power degradation of H-mode confinement. The 'edge harmonic oscillation', a characteristic MHD feature of the QH-mode that replaces ELMs, occurs at rational surfaces in the H-mode barrier region, and has so far been found only with a toroidal mode number n = 1. These conditions seem to define windows in q₉₅ for favourable QH-mode access.

A new operating regime, 'high recycling steady' (HRS) H-mode regime, has been discovered in the JFT-2M tokamak. It is easily reproduced with neutral beam heating of any co-, balanced-, or counter-injection under wall fuelling from the boronized first wall. The HRS is characterized by good energy confinement (H_89P ∼ 1.6) at a high density (n_e/n_GW ∼ 0.7; n_GW is the Greenwald density), low radiation loss power fraction ( , typically), and the complete disappearance of large ELMs. Accompanying the HRS H-mode transition, the coherent magnetic fluctuations in the frequency range of the order of 10–100 kHz with significant variation are seen on magnetic probes at the vessel wall. In addition, the HRS H-mode edge condition is compatible with an improved core confinement. We have demonstrated that an internal transport barrier can be produced under a HRS H-mode edge condition, achieving β_NH_89P ∼ 6 at n_e/n_GW ∼ 0.7–1.0, transiently.

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

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

The H-mode pedestal characteristics on the mega ampère spherical tokamak (MAST) are measured in a variety of disconnected double null discharges and the effect of edge localized modes (ELMs) on the pedestal is presented. The edge density pedestal width in spatial co-ordinates is similar on both the inboard and outboard sides. Neutral penetration may be able to explain the density pedestal width but it alone cannot explain the characteristics of the temperature pedestal. The data from MAST can be used to improve temperature pedestal width scalings by extending the ranges in pedestal collisionality, magnetic field, elongation and aspect ratio studied by other machines. Convective transport is found to dominate energy losses during ELMs and the fractional loss of pedestal energy during an ELM on MAST correlates better with SOL ion transit time than with pedestal collisionality.

This paper reports the first results of collaborative experiments in JT-60U and JET to compare ELMy H-mode characteristics in the two machines. The JT-60U/JET identity experiments were aimed explicitly at matching edge pedestal parameters in plasmas of the same geometry. The similar size of the two devices allows plasma configurations and conditions to be established for which the match of the dimensionless parameters (ρ^*, ν^*, β and q₉₅) and of the equilibrium geometry is carried out in plasmas that are also almost identical in dimensional terms.

The results of the power and density scans at fixed (and matched) I_p − B_T show that, in a common range of ρ^*, the pedestal electron collisionality, , and normalized pressure, β_p,ped do not match in the two machines, against expectations. In particular, the range of β_p,ped of JT-60U ELMy H-modes with Type I ELMs is accessible to JET plasmas only with a Type III ELM edge, and in JT-60U is consistently higher by ≈2 than in JET, for the same ρ^*. A comparison of n_e and T_e pedestal profiles indicates that ∇T_e is comparable in the two devices, while JET n_e profiles are steeper than JT-60U. The global energy confinement enhancement factor (H98y − 2) is higher in JET than in JT-60U, and part of this difference is attributed to the reduced pedestal pressure in JT-60U compared with JET.

The two experiments are analysed in detail to try to identify 'hidden' physics that may be the cause of the failure to achieve the pedestal identity as predicted. Although a full explanation for the different behaviour of the edge pedestal in the two devices has not yet been found, the possible influence of aspect ratio effects on MHD stability, differences in the plasma current profile and ripple loss (and rotation) effects are discussed.

While most of the dimensionless parameters that govern energy transport are readily apparent, there is some controversy as to whether the collisionality should be represented by the collision frequency normalized to the bounce frequency (ν_*) or the density normalized to the Greenwald density limit (n/n_limit). To help resolve this question, experiments on the DIII-D and JET tokamaks have compared the normalized energy transport in ELMing H-mode plasmas with matched dimensionless parameters. When ν_* was kept fixed, the normalized energy transport on JET and DIII-D was in good agreement, but when n/n_limit was kept fixed, the normalized energy confinement time on DIII-D was 20% lower than on JET (for all cases, n/n_limit < 1). Therefore, ν_* appears to be the correct form of the normalized density, and scaling transport properties from present day tokamaks to ITER at fixed n/n_limit can result in incorrect predictions.

The disagreement between the weak dependence of the energy confinement time on normalized pressure, β, observed in dedicated scans and the strongly negative dependence in the confinement scaling laws used for the design of next step tokamaks and future reactors, remains an outstanding problem. As such, scans of β have been undertaken in single null, low triangularity (δ ≈ 0.2) ELMy H-mode plasmas in JET with the MarkIIGB-SRP divertor. The scans varied β by a factor of 2.8 (normalized β from 0.72 to 2.04) and covered a range of magnetic fields (1.5–2.3 T), plasma currents (1.5–2.75 MA) and safety factors (q₉₅ = 2.8 and 3.3). A weak β dependence was observed both globally (B₀τ_E varied less than 9% across any one scan) and locally. A scan within Type I ELMy H-modes suggests that this weaker dependence is not due to ELM regimes. A statistical analysis indicates that these results are consistent with log–linear regressions performed on a wide JET database of ELMy H-modes, if correlations in this database are considered.

An analysis of the international tokamak physics activity (ITPA) H-mode power threshold database is advanced to study the roles of the aspect ratio, A, the absolute magnetic field and the effective charge number, Z_eff. A new scaling expression for the power threshold, P_thr, is presented. The absolute B at the outer surface is used instead of B_t in the scaling, and the I_p dependence of P_thr in low-A tokamaks is described without the explicit use of the I_p variable. A clear and strong dependence on Z_eff is found; . Both the scattering nature in the data fitting and the 'low-density anomaly' can be reduced. A nonlinear A dependence is also suggested. The P_thr in ITER is predicted on the basis of the present scaling.

Electrode biasing is one of the methods for controlling the radial electric field externally and can induce a transition to an improved confinement state. We have shown theoretically that a solitary E_r structure with a single peak is formed selectively by electrode biasing in our previous works. That a multiple-peaked E_r structure, which has a wider E × B flow shear region, can exist stably was also derived. In this paper, accessibility to a double-peaked E_r structure is demonstrated theoretically by double electrode biasing with an applied voltage ramp-up.

Self-consistent modelling of energy and particle transport of the plasma background and impurities has been performed with the code RITM for argon seeded high density H-mode plasmas in JET. The code can reproduce both the profiles in the plasma core and the structure of the edge pedestal. The impact of argon on core transport is found to be small; in particular, no significant change in confinement is observed in both experimental and modelling results. The same transport model, which has been used to reproduce density peaking in the radiative improved mode in TEXTOR, reveals a flat density profile in Ar seeded JET H-mode plasmas in agreement with the experimental observations. This behaviour is attributed to the rather flat profile of the safety factor in the bulk of H-mode discharges.

A new model for the type I ELMy H-mode based on linear ballooning stability theory is presented. The model can be written as a linear differential equation for the amplitude of an unstable ballooning mode and is coupled to a system of transport equations. The differential equation for the ballooning mode amplitude has two terms—one representing the growth rate of the perturbation and one controlling the decay rate of the mode and driving the mode amplitude towards the level of background fluctuations. A critical pressure gradient limit is used to control whether the growth rate differs from zero. When coupled to a JETTO transport simulation, the model qualitatively reproduces the experimental dynamics of a type I ELMy H-mode, including an edge localized mode (ELM) frequency that increases with the external heating power. This paper also discusses why the linear ballooning model, in the first place, produces discrete oscillations when coupled to a transport simulation rather than a stationary state with a slightly enhanced ballooning mode amplitude.

Integrated core–pedestal–SOL modelling is performed for ITER using the MMM95 model for energy transport, modified with additional magnetic shear stabilization to produce a pedestal. The additional stabilization term is calibrated against experiment. The operating space of ITER predicted by the model with neoclassical accumulation of intrinsic carbon impurity is determined. The relationship to an SOL-based density limit is investigated. A reasonable window for operation, with Q larger than 10 is found.

A new gyro-Landau fluid model for the Landau damping of circulating particles is presented. Since trapped particles can bounce average low frequency waves, they are not affected by Landau damping. The loss of bounce averaging when the mode frequency exceeds the trapped particle bounce frequency is included in the model by changing the phase space integration boundary. An excellent fit to the kinetic response for the circulating particle density and the parallel and perpendicular pressure is obtained with six-moment equations.

Current profile tailoring has been performed by application of electron cyclotron heating (ECH) and electron cyclotron current drive, leading to improved energy confinement in the plasma core of the TCV tokamak. The improved confinement is characterized by a substantial enhancement (H-factor) of the global electron energy confinement time relative to the prediction of the RLW scaling law (Rebut P H et al 1989 Proc. 12th Int. Conf. of Plasma Physics and Controlled Fusion Research (Nice, 1988) vol 2 (Vienna: IAEA) p 191), which predicts well Ohmic and standard ECH discharges on TCV. The improved confinement is attributed to a hollow current density profile producing a reversed shear profile creating an electron internal transport barrier. We relate the strength of the barrier to the depth of the hollow current density profile and the volume enclosed by the radial location of the peak current density. The (Tresset G et al 2002 Nucl. Fusion42 520) criterion is used to evaluate the performance of the barrier relative to changes in the ECH parameters or the addition of Ohmic current, which aid in identifying the control parameters available for improving either the strength or volume of the barrier for enhanced performance. A figure of merit for the global scaling factor is used that scales the confinement enhancement as the product of the barrier volume and strength.

Optimization has been carried out on the operational regime where neoclassical internal transport barriers (N-ITBs) are formed. The condition of the forming N-ITB is sensitive to the location of the electron cyclotron heating resonance zone. A high electron temperature is obtained for the central heating (−2 cm < R_resonance < 2 cm). The variation of the magnetic axis location affects the formation of the N-ITB. The electron and ion temperatures at the magnetic axis location (R_ax) of 94.9 cm are higher than those at 92.1 and 97.4 cm. This result indicates that the neoclassical flux and the created radial electric field are influenced by the magnetic field structure.

In the Mega Ampère Spherical Tokamak (MAST) plasmas have been generated with internal (ITB) or edge (ETB) transport barriers. ITBs were achieved in both the electron and the ion energy channel. In the presence of an ITB in the ion energy channel, transport analysis shows that the ion thermal diffusivity, χ_i, is reduced to almost neoclassical values while the ITB persists. The widely tested criteria for ITB formation (ρ_s: Larmor radius at sound speed) obtained from dimensional analysis of JET discharges is easily exceeded on MAST. Even without the evidence of an ITB often applies, showing that this criterion in its current form is not generally applicable. ETBs are most easily formed in MAST if in a double null divertor configuration the discharge is vertically balanced, so that both X-points are almost on the same flux surface (CDND), and if the plasma is refuelled from the high field side mid-plane. The H-mode threshold power, P_thr = 0.5 MW, in connected double null diverted (CDND) is only about half of that in a similar disconnected discharge with the ion ∇ B drift towards the X-point on the last closed flux surface (LDND). P_thr scales between lower double null diverted (LDND) and the single null diverted configuration with the plasma surface area on MAST.

The mitigation of the large pulsed heat loads induced by edge-localized modes (ELMs) on the divertor plates is one of the most important issues for a tokamak fusion reactor. However, ELMs have been completely suppressed in the quiescent H-mode (QH-mode) plasmas produced in the DIII-D tokamak (see Burrell K H et al2002 Plasma Phys. Control. Fusion44 A253). One of the key conditions for producing QH-mode plasmas is that the direction of neutral beam injection (NBI) should be opposite to that of the plasma current (i.e. ctr-NBI), which then leads to the toroidal rotation velocity being in the counter direction to the plasma current. By using various combinations of NBI lines in JT-60U, it has been possible to investigate the impact of the toroidal rotation velocity on ELM behaviour by changing the toroidal momentum input in a detailed manner for similar absorbed NB heating power. It has been determined that the ELM frequency decreases with increased counter toroidal rotation velocity at the plasma edge even to the point of the ELMs disappearing. In addition, the magnitude of the pulsed D_α signal at the divertor decreases with decreasing ELM frequency. These results indicate that it is possible to control the ELM behaviour through the toroidal momentum input.

The dependence of H-mode access on the poloidal location of the gas injection source has been investigated in NSTX. We find that gas fuelling from the centre stack midplane area produces the most reproducible H-mode access, with generally the lowest L–H threshold power in the lower single-null configuration. The edge toroidal rotation velocity of C2+ is largest (in the direction of the plasma current) just before the L–H transition with centre stack midplane fuelling and then reverses direction after the L–H transition. Simulation of these results with a guiding centre Monte Carlo neoclassical transport code (XGC) is qualitatively consistent with the trends in the measured velocities. Double-null discharges exhibit H-mode access with gas fuelling from either the centre stack midplane or centre stack top locations, indicating a reduced sensitivity of H-mode access to fuelling location in that shape.

For identical edge pedestal conditions in plasmas with gas puff and with pellet injection, edge localized mode (ELM) mitigation during fully pellet-controlled ELMy H-modes has been demonstrated. When the ELM frequency is set to the pellet frequency, the ELM energy losses are significantly reduced at fixed pedestal collisionality, while pellets only weakly enhance the ELM loss power. The ELM affected region of the density profile is reduced by pellet injection, while the temperature perturbation profile does not change significantly. For constant source particle flux into the plasma edge at the same pedestal parameters, the reduction in convective losses per ELM during pellet-induced ELMs is balanced by increased ELM frequency and pellet fuelling of the pedestal region.

We study the simplest problem of turbulence spreading corresponding to the spatio-temporal propagation of a patch of turbulence from a region where it is locally excited to a region of weaker excitation or even local damping. A single model equation for the local turbulence intensity, I(x, t), includes the effects of local linear growth and damping, spatially local nonlinear coupling to dissipation and spatial scattering of turbulence energy induced by nonlinear coupling. In the absence of dissipation, front propagation into the linearly stable zone occurs with the property of rapid progression at small t, followed by slower sub-diffusive progression at late times. The turbulence radial spreading into the linearly stable zone reduces the turbulent intensity in the linearly unstable zone and introduces an additional dependence on the ρ^* ≡ ρ_i/a to the turbulent intensity and the transport scaling. These are in broad, semi-quantitative agreement with a number of global gyrokinetic simulation results with zonal flows and without zonal flows. Front propagation stops when the radial flux of fluctuation energy from the linearly unstable region is balanced by local dissipation in the linearly stable region.

The collisional effects on nonlinear coherent structures of zonal flows in a toroidal plasma are investigated. They weaken the flows and enhance turbulent transport. Expressions for the zonal flow velocity, scale length and the turbulent transport coefficients are obtained. In the limit of small collisional flow damping, the turbulent transport coefficient remains finite. A phase diagram is obtained, which shows the parameter domain where the zonal flow has finite amplitude.

The occurrence of stochastic transitions is investigated in the presence of triggers by turbulence noise and external events. The probability of observing the transition is calculated assuming that the global controlling parameters change in time. This is another important prediction of statistical theory in addition to the long time average. This explains the feature of transient response of the system with stochastic transitions. The interpretation of the experimental threshold database is discussed.

The optimization of a tokamak towards steady state and high performance has been the focus of advanced tokamak (AT) research for the past decade. A central theme of AT research line is plasma control: control of the plasma shape; of the profiles of current, pressure, and rotation; of transport; and of MHD stability. To optimize the performance, measurements of crucial parameters such as the current density and the plasma pressure are required with appropriate spatial coverage and resolution. In addition, measurements of other parameters will be necessary to develop a fundamental understanding of the complex nonlinear interactions amongst the current density profile, the pressure profile and transport (e.g. turbulence) in high β AT plasmas. Present day experiments are providing physics insight into what a burning plasma experiment (BPX) will require as measurements. Recent research has focused on MHD stability aspects such as the neoclassical tearing mode and resistive wall mode stabilization and control of the current profile. However, in burning plasmas, new factors such as alpha particles, with their heating contribution and their relationship to transport barriers, will be increasingly important. The close relationship between measurements and active control, and the resultant impact on the requirements, will be discussed.

A new analytical method using a combination of the O-mode reflectometer and a time-dependent two-dimensional full-wave simulation code has been developed for the quantitative evaluation of density fluctuations in JT-60U. Two statistical parameters of the reflectometer signals, fluctuation index (F) and elongation factor (χ), are introduced as measures of the fluctuation amplitude (γ) and the width of the poloidal wave number spectrum (k_θ0). This method is applied to the edge transport barrier (ETB) and internal transport barrier (ITB). At the transition to the ELM free H-mode phase, analysis suggests that the density fluctuation level reduced from 1.9–3.2% to 0.29–0.44%, while the value of k_θ0 changed from 1.6–2.0 to 0.77–0.81 cm⁻¹ in the ETB region. On the other hand, the amplitude of the density fluctuation was evaluated as 1.0–2.0% at the ITB region, even after the formation of the box type ITB. Instead, when a pellet was injected into the plasma with a box type ITB as an external perturbation, a remarkable change in the frequency spectrum was observed. Analysis suggests a reduction in the density fluctuation level to 0.4–0.6% after the pellet injection.

Understanding the L–H transition in tokamaks has been an important area of research for more than two decades. High time resolution diagnostics on DIII-D allow detailed characterization of the L–H transition and, therefore, testing and benchmarking of theoretical models. An experiment was performed in DIII-D utilizing a novel, high temporal and spatial resolution reflectometer density profile system to measure densities from the SOL to the inside separatrix. Initial data analysis indicates different density profile evolution during L–H transitions in upper single-null and lower single-null divertor configuration plasmas. A detailed comparison of the density gradient and fluctuation changes is presented for these two cases.

A radially sheared azimuthal flow is observed in a cylindrical helicon plasma device. The shear flow is roughly azimuthally symmetric and contains both time-stationary and slowly varying components. The turbulent radial particle flux is found to peak near the density gradient maximum and vanishes at the shear layer location. The shape of the radial plasma potential profile associated with the azimuthal E × B flow is predicted accurately by theory. The existence of the mean shear flow in a plasma with finite flow damping from ion–neutral collisions and no external momentum input implies the existence of radial angular momentum transport from the turbulent Reynolds-stress.

Results of coherent edge fluctuation measurements using three diagnostics (a reciprocating Langmuir probe, a two channel O-mode reflectometer, and fast magnetic probes) in H-mode discharges on JFT-2M are presented. In discharges in which a high recycling steady (HRS) H-mode phase is obtained through a transient phase with slightly enhanced D_α intensity, two types of coherent fluctuations are observed. The higher frequency mode (around 300 kHz) is the high frequency mode (HFM) observed in the HRS H-mode (Kamiya K et al 2003 9th IAEA Tech. Meeting H-mode Workshop Topic B-14). The lower frequency mode has a frequency of around 80 kHz. The HFM is detected by a Langmuir probe over a wide region in the SOL, as well as by the reflectometer and magnetic probes. However, the HFM is not detected by the higher frequency (38 GHz) channel of the reflectometer after the HRS transition, suggesting that the HFM is not located deeply inside the plasma. The 80 kHz mode is detected by both channels of the reflectometer and by a Langmuir probe, but not by magnetic probes, suggesting that it is an electrostatic mode. In contrast to the HFM, the 80 kHz mode is detected by the Langmuir probe only near the separatrix during the transient phase, which leads to either the HRS phase or the ELMy phase, and is similar to the fluctuations reported in Shinohara K et al (1998 J. Plasma Fusion Res. 74 607).