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Numerical simulations form an indispensable tool to understand the behavior of a hot plasma that is created inside a tokamak for providing nuclear fusion energy. Various aspects of tokamak plasmas have been successfully studied through the reduced magnetohydrodynamic (MHD) model. The need for more complete modeling through the full MHD equations is addressed here. Our computational method is presented along with measures against possible problems regarding pollution, stability, and regularity. The problem of ensuring continuity of solutions in the center of a polar grid is addressed in the context of a finite element discretization of the full MHD equations. A rigorous and generally applicable solution is proposed here. Useful analytical test cases are devised to verify the correct implementation of the momentum and induction equation, the hyperdiffusive terms, and the accuracy with which highly anisotropic diffusion can be simulated. A striking observation is that highly anisotropic diffusion can be treated with the same order of accuracy as isotropic diffusion, even on non-aligned grids, as long as these grids are generated with sufficient care. This property is shown to be associated with our use of a magnetic vector potential to describe the magnetic field.Several well-known instabilities are simulated to demonstrate the capabilities of the new method. The linear growth rate of an internal kink mode and a tearing mode are benchmarked against the results of a linear MHD code. The evolution of a tearing mode and the resulting magnetic islands are simulated well into the nonlinear regime. The results are compared with predictions from the reduced MHD model.Finally, a simulation of a ballooning mode illustrates the possibility to use our method as an ideal MHD method without the need to add any physical dissipation.

In order to reduce the risks for ITER Plasma Facing Components (PFCs), it is proposed to equip Tore Supra with a full tungsten divertor, benefitting from the unique long pulse capabilities, the high installed RF power and the long experience with actively cooled high heat flux components of the Tore Supra platform. The transformation from the current circular limiter geometry to the required X-point configuration will be achieved by installing a set of copper poloidal coils inside the vacuum vessel. The new configuration will allow for H-mode access, providing relevant plasma conditions for PFC technology validation. Furthermore, attractive steady-state regimes are expected to be achievable. The lower divertor target design will be closely based on that currently envisaged for ITER (W monoblocks), while the upper divertor region will be used to qualify the main first wall heat sink technology adopted for the ITER blanket modules (CuCrZr copper/stainless steel) with a tungsten coating (in place of the Be tiles which ITER will use). Extended plasma exposure will provide access to ITER critical issues such as PFC lifetime (melting, cracking, etc.), tokamak operation on damaged metallic surfaces, real time heat flux control through PFC monitoring, fuel retention and dust production.

In both JET and MAST, the Error Field Correction Coils (EFCCs) have been used recently in order to attempt to control Type I Edge Localised Modes (ELMs), which represent a major threat to the lifetime of plasma facing components in ITER. Using vacuum magnetic modelling it is suggested that the ELM mitigation observed at JET could be related to the stochastization of the magnetic field at the edge. Indeed, the onset of ELM mitigation is found to be correlated with a certain level of the Chirikov parameter profile. Initial MAST results are presented which show an effect of EFCCs on the ELMs, again compatible with edge stochastization according to the modelling. New coils dedicated to ELM control are ready for use on MAST this year and are presented here briefly.

A finite element method based on bicubic Bezier surfaces is applied to the simulation of MHD instabilities relevant to magnetically confined fusion. The major advantage of the new technique is that it allows a natural way to implement mesh refinement strategy, which is not supported by a pure Hermite formulation. Compared to a Lagrangian formulation the number of degrees of freedom is significantly reduced. The use of an isoparametric representation of the space coordinates allows an accurate alignment of the finite elements to the magnetic field line geometry in a tokamak plasma. The Bezier finite elements have been implemented in a MHD code using the non-linear reduced MHD model in toroidal geometry. As an illustration, results for Soloviev equilibrium and time-dependent current-hole computations are presented and discussed.

A wide range of studies on JET have contributed greatly to the development of the ELMy H-mode as a high-performance scenario for fusion devices and to the understanding of the physical processes that underlie it. Development has focused on the production of a high-performance, high-density, stationary scenario suited to deuterium-tritium operation and with small edge energy loads. Physics studies have made strong progress in the understanding of the L-H threshold, energy confinement, pedestal physics, and edge-localized mode behavior. A strong focus of this work has been providing a basis for extrapolation to future machines, such as ITER, for which, as the largest existing tokamak, JET has been of particular importance.

The Infrastructure and Software Integration Project must provide the hardware and software environment for the European integrated tokamak modelling taskforce to build and simulate a comprehensive fusion device. Several frameworks have been evaluated in 2006 and this paper reports on the current status of the gateway, the data communication system, the Web portal and the various ITM applications. The first version will be delivered in 2007, prefiguring the next decades' tools.

Reference CRPP-CONF-2009-047View record in Web of Science Record created on 2009-02-26, modified on 2017-05-12

Long period sawteeth have been observed to result in low-beta triggering of neo-classical tearing modes, which can significantly degrade plasma confinement. Consequently, a detailed physical understanding of sawtooth behaviour is critical, especially for ITER where fusion-born a particles are likely to lead to very long sawtooth periods. Many techniques have been developed to control, and in particular to destabilize the sawteeth. The application of counter-current neutral beam injection (NBI) in JET has resulted in shorter sawtooth periods than in Ohmic plasmas. This result has been explained because, firstly, the counter-passing fast ions give a destabilizing contribution to the n=1 internal kink mode-which is accepted to be related to sawtooth oscillations-and secondly, the flow shear strongly influences the stabilizing trapped particles. A similar experimental result has been observed in counter-NBI heated plasmas in MAST. However, the strong toroidal flows in spherical tokamaks mean that the sawtooth behaviour is determined by the gyroscopic flow stabilization of the kink mode rather than kinetic effects. In NBI heated plasmas in smaller conventional aspect-ratio tokamaks, such as TEXTOR, the flow and kinetic effects compete to give different sawtooth behaviour. Other techniques applied to destabilize sawteeth are the application of electron cyclotron current drive (ECCD) or ion cyclotron resonance heating (ICRH). In JET, it has been observed that localized ICRH is able to destabilize sawteeth which were otherwise stabilized by a co-existing population of energetic trapped ions in the core. This is explained through the dual role of the ICRH in reducing the critical magnetic shear required to trigger a sawtooth crash, and the increase in the local magnetic shear which results from driving current near the q=1 rational surface. Sawtooth control in ITER could be provided by a combination of ECCD and co-passing off-axis negative-NBI fast ions.

This paper summarizes results of dimensionless identity experiments in JT-60U and JET, aimed at the comparison of the H-mode pedestal and ELM behaviour in the two devices. Given their similar size, dimensionless matched plasmas are also similar in their dimensional parameters (in particular, the plasma minor radius a is the same in JET and JT-60U). Power and density scans were carried out at two values of Ip, providing a q scan (q95 = 3.1 and 5.1) with fixed (and matched) toroidal field. Contrary to initial expectations, a dimensionless match between the two devices was quite difficult to achieve. In general, pped in JT-60U is lower than in JET and, at low q, the pedestal pressure of JT-60U with a Type I ELMy edge is matched in JET only in the Type III ELM regime. At q95 = 5.1, a dimensionless match in ?*, ?* and ?p,ped is obtained with Type I ELMs, but only with low power JET H-modes. These results motivated a closer investigation of experimental conditions in the two devices, to identify possible 'hidden' physics that prevents obtaining a good match of pedestal values over a large range of plasmas parameters. Ripple-induced ion losses of the medium bore plasma used in JT-60U for the similarity experiments are identified as the main difference with JET. The magnitude of the JT-60U ripple losses is sufficient to induce counter-toroidal rotation in co-injected plasma. The influence of ripple losses was demonstrated at q95 = 5.1: reducing ripple losses by ?2 (from 4.3 to 1.9?MW) by replacing positive with negative neutral beam injection at approximately constant Pin resulted in an increased pped in JT-60U, providing a good match to full power JET H-modes. At the same time, the counter-toroidal rotation decreased. Physics mechanisms relating ripple losses to pedestal performance are not yet identified, and the possible role of velocity shear in the pedestal stability, as well as the possible influence of ripple on thermal ion transport are briefly discussed. Toroidal rotation of the ITER reference inductive Q = 10 H-mode is predicted to be rather low, of the order of ~1/10 of the frequency of typical JET H-modes. Nonetheless, fast ion ripple losses in that scenario are also predicted to be negligible (1%), and therefore plasma toroidal rotation slow-down or ripple-induced counter-rotation should not affect pedestal parameters and stability in ITER. Finally, the possible effect of ripple on thermal transport may deserve more attention in future experiments and modelling, since the ripple magnitude of ITER is intermediate between that of JET and JT-60U.

A number of designs for external or in-vessel coils generating Resonant Magnetic Perturbations (RMPs) for type I ELMs control in ITER are analyzed. The RMPs generated by the I-coils in the successful DIII-D ELMs control experiments are taken as a reference. The three ITER characteristic scenarios (H-mode, hybrid and steady-state) are studied. In a second part of the paper, the first results of a self-consistent non-linear MHD modelling of the plasma response to the RMPs with the JOREK code, for a DIII-D case, are presented.

The early phase of a tokamak plasma discharge can have a dramatic impact on the main heating phase. This has been a persistent problem for the development of the steady state, fully non-inductive scenario using lower hybrid current drive (LHCD) on Tore Supra. The present paper reports on recent experimental and numerical investigations showing that a tearing mode coupled to the internal kink grows on q = 2 in the ohmic phase when the total current is too low, due to the weakening of field line curvature stabilization. Then, the application of LHCD drives the island to a larger size and undermines the development of the non-inductive phase. Decreasing the edge safety factor or increasing the Lundquist number S is found to be beneficial in both the linear and non-linear MHD analyses. The experimental database, which allows covering the edge safety factor dependence, supports this interpretation.

Measurements of electron temperature fluctuations by means of correlation electron cyclotron emission (ECE) diagnostics aid in understanding the nature of the turbulent transport infusion plasmas. On Tore Supra tokamak, a 32-channel heterodyne ECE radiometer has been upgraded to include two channels for temperature fluctuation measurements. The central frequency of the yttrium iron garnet filter on each channel is remotely monitored by a driver, allowing one to shift the observation volume in the plasma radially. To resolve the fluctuation amplitude of 0.1%, integration times of similar to 3 s at 1 MHz sampling rate are required for the statistical error level of 0.05%. Together with the 32-channel profile radiometer, correlation ECE is a powerful and unique tool for simultaneous observation of the magnetohydrodynamic phenomena and studies of the plasma transport properties in various heating regimes during long-shot multimegawatt operation. First measurements of temperature fluctuations, of various origins, on Tore Supra (including the observation of the toroidicity-induced Alfven eigenmodes), as well as a description of the analysis methods used in the data evaluation, are reported in this paper.

High frequency (> 100 kHz) modes have been observed for the first time in combined LHCD and ICR-heated minority H (D) plasmas on Tore Supra by means of a correlation ECE diagnostic and by fluctuation reflectometers. These modes have been identified as the toroidicity-induced Alfven eigenmodes (TAEs) that are destabilized by fast minority hydrogen ions with energies above 250 keV. In reversed central shear plasmas with non-linear oscillations of the central temperature, evolution of the TAE frequency is linked to the development of the local safety factor. This confirms that the central temperature and the q-profile evolve as a non-linearly coupled system in the so-called O-regime in Tore Supra.

The development of scenarios characterized by H-mode confinement and internal transport barriers (ITBs) in high triangularity, δ ~ 0.4–0.5, discharges is of particular interest for ITER advanced tokamak operation. Previous JET experiments have shown that high triangularity favours H-modes which are ELM-free or develop type I edge localized mode (ELM) activity, which inhibits long lasting ITBs. The recent experiments reported here concentrate on integrated optimization of edge and core conditions. The stability of the edge pedestal was controlled using gas injection, deuterium or light impurities, and plasma current ramps. Both methods yield more ITB-friendly edge pedestal conditions, varying from small type I to type III ELMs and, in extreme cases, resulting in L-mode. In parallel, the conditions for triggering and sustaining ITBs encompassing a large proportion of the plasma volume (outer ITBs) were optimized, as opposed to less performing ITBs located closer to the plasma centre (inner ITB). These plasmas have deeply reversed target current profiles with qmin ~ 3 and a narrow inner ITB, located typically at a small normalized radius ρ < 0.5 and close to the reversed shear region, is routinely observed. Large radius outer ITBs are only triggered at an input power in excess of 20 MW, but they do not usually survive the transition into H-mode. The best results, in terms of sustained high confinement, have been obtained with neon injection; an outer ITB is triggered during the phase with L-mode edge and survives into H-mode for about 2 s, corresponding to ~10 times the global energy confinement time τE, at q95 = 7.5, H89βN ~ 3.5–4 and ~60% of the Greenwald density limit. In summary, a high triangularity scenario has been developed, which combines the desirable characteristics of controlled edge, long lasting wide ITBs and high performance at density higher than the low triangularity JET scenarios.

The ideal MHD model of peeling–ballooning modes for the onset of the edge localized mode (ELM) is reviewed with some of the previous results that lead to the present understanding of the MHD stability of the edge transport barrier. Extensions to the ideal MHD theory are discussed followed by recent developments in the observations, theory and simulations of the non-linear phase of the ELM and the peeling and ballooning modes.

The influence of the separatrix on the stability of edge current driven external kink (peeling) modes has been studied. Two approaches have been compared: taking the limit towards the separatrix using linear ideal and resistive MHD stability codes and including the complete x-point geometry using a new resistive MHD code. A strong stabilizing effect has been observed for the ideal and the resistive peeling mode for instabilities driven by the edge current gradient. Both approaches are in good agreement. A new resistive instability remains unstable and is not significantly affected by the separatrix. This mode is a combination of a kink and a tearing type mode and could be called a peeling–tearing mode.

This paper describes a new approach for modelling the pedestal energy transport in the presence of a small radial magnetic perturbation. The cases of a ballooning instability leading to Type I edge localized modes (ELMs) and a magnetic perturbation generated by external coils are treated. The model for Type I ELMs is based on the linear ideal MHD code MISHKA coupled with the non-linear energy transport code TELM in a realistic tokamak geometry. The main mechanism of the increased transport through the external transport barrier in this model of ELMs is due to the appearance of a radial velocity and a radial magnetic field perturbation due to the MHD mode. Both lead to additional transport perpendicular to the magnetic surface and hence to a relaxation of the pressure profile in the unstable zone. The typical Type I ELM time-cycle was reproduced numerically including the destabilization of the ballooning modes leading to the fast (250 μ s) collapse of the pedestal pressure followed by the edge pressure profile re-building on a diffusive time scale. A possible mechanism for the control of Type I ELMs using a stochastic plasma boundary created by external coils is modelled in this paper using data on ELM suppression by I-coils from the DIII-D experiment. In the stochastic layer the transverse transport is effectively increased by diffusion of the magnetic field lines. The modelling results demonstrate the possibility of decreasing the edge pressure gradient to a value that is just below the ideal ballooning limit, leading to a high confinement regime without Type I ELMs.

To shed some light on the development of the fast m/n = 1/1 precursor to the sawtooth crash and its influence on plasma transport properties in the vicinity of the q = 1 surface, series of dedicated experiments have been conducted on the Tore Supra and TEXTOR tokamaks. It has been concluded that, before a crash, the hot core gets displaced with respect to the magnetic axis, drifts outwards by as much as 8–10 cm and may change its shape. Observation of the magnetic reconnection process has been made by means of electron cyclotron emission diagnostics. The heat pulse is seen far outside the inversion radius. The colder plasma develops a magnetic island on the former magnetic axis, after the hot core expulsion. Different kinds of behaviour of the m = 1 precursor before the crash, with respect to the displacement of the hot core and the duration of the oscillating phase, have been observed. An ideal kink model alone cannot be used for explanation; therefore, resistive effects play an important role in the mode development. Possible mechanisms that lead an m = 1 mode to such behaviour, and their links to the change in the central q-profile, are discussed. Results have been discussed in the light of various theoretical models of the sawtooth.

The paper reviews recent theoretical and experimental results focussing on the identification of the key factors controlling ELM energy and particle losses both in natural ELMs and in the presence of external controlling mechanisms. Present experiment and theory pointed out the benefit of the high plasma shaping, high q(95) and high pedestal density in reducing the ELM affected area and conductive energy losses in Type I ELMs. Small benign ELMs regimes in present machines (EDA, HRS, Type II, Grassy, QH, Type III in impurity seeded discharges at high delta) and their relevance for ITER are reviewed. Recent studies of active control of ELMs using stochastic boundaries, small pellets and edge current generation are presented. (c) 2004 Elsevier B.V. All rights reserved.

The crash of monster sawteeth in Tore Supra ion cyclotron resonance heated plasmas is observed to trigger long-lived magneto hydrodynamic (MHD) activity, dominated by a (m = 3, n = 2) magnetic perturbation at the edge. This phenomenon is reminiscent of the triggering of neoclassical tearing modes, although in Tore Supra the MHD activity decays and eventually vanishes. It can be explained by the linear destabilization of the (3, 2) mode as the current sheet developed in the non-linear stage of the internal kink relaxation gets closer to q = 3/2. However, the lifetime of the (3, 2) island is longer than the period of linear instability. We find that the neoclassical drive is essential for explaining the observed lifetime and width of the island, although the overall dynamics is controlled by the relaxation of the current profile on a resistive time scale.

Simulations of four Joint European Torus (JET) [Rebut et al., Nucl. Fusion 25, 1011 (1985)] type I ELMy high confinement mode discharges in a triangularity scan are carried out using the JETTO integrated modeling code [Erba et al., Plasma Phys. Contolled Fusion 39, 261 (1997)] with a predictive core transport model and a pedestal model that includes the effects of edge localized modes (ELMs). The pedestal pressure gradient is limited by the magnetohydrodynamic (MHD) ballooning mode instability, which triggers ELM crashes in these simulations. The validation of the pressure gradient limit used in the simulations is confirmed by a stability analysis carried out using the HELENA and MISHKA codes [Mikhailovskii et al., Plasma Phys. Rep 23, 713 (1997)]. The MHD stability analysis includes infinite-n ideal ballooning, finite-n ballooning, and low-n kink/peeling modes. It is shown that higher triangularity plasmas have easier access to the second stability region, which allows the edge pressure gradients in the ...

The effects of nonresonating hot ions on the spectrum of magnetohydrodynamic (MHD) waves and instabilities in tokamaks are studied in the limit when the width of the hot ion drift orbits is much larger than the radial scale length of the MHD perturbations. Due to the large magnetic drift velocities the hot ions cannot contribute to the MHD perturbations directly, but two main effects of the hot ions, the hot-ion density-dependent effect and the hot-ion pressure-dependent effect, influence the MHD perturbations indirectly. The physics of both effects is elucidated and it is shown that both these effects can be described in MHD approach. A new code, MISHKA-H (MISHKA including the hot-ion indirect effects), is developed as an extension of the ideal MHD code MISHKA-D [Huysmans et al., Phys. Plasmas 8, 4292 (2002)]. Analytical benchmarks for this code are given. Results of the MISHKA-H code on Alfven spectrum in a shear-reversed discharges with ion-cyclotron resonance frequency (ICRF) heating are presented. Mo...

Simulations of three Joint European Torus [P. H. Rebut et al., Nucl. Fusion 25, 1011 (1985)] type I ELMy high-confinement discharges in a power scan are carried out using the JETTO integrated modeling code [M. Erba et al., Plasma Phys. Controlled Fusion 39, 261 (1997)] with predictive core and pedestal models, which include the effect of edge localized modes (ELMs). It is found that current-driven peeling modes trigger the ELM crashes in these discharges and, as a result, yield an explanation of the experimentally observed increase in pedestal height with heating power. After each ELM crash, the pressure gradient and the related bootstrap current density at the edge of plasma rapidly increase with increasing heating power, while the total current density rises only slowly because the total current density is impeded by a back electromotive force. Hence, as the heating power is increased, the pedestal pressure can rise to higher values during an ELM cycle before the current density reaches the level requir...

Toroidicity-induced Alfv?n eigenmodes (TAEs) are destabilized in ASDEX Upgrade using ion cyclotron resonant heating (ICRH). Unstable TAEs are observed in the magnetic probes, reflectometer and soft x-ray cameras when the ICRH power exceeds PICRH > 2.5?MW in both conventional and advanced scenarios. The most unstable TAEs have toroidal mode numbers n = 3, 4, 5, 6, and experiments with reversed currents and magnetic fields have shown that the TAEs propagate in the co-current direction, i.e. in the ion diamagnetic drift direction, confirming that these modes are destabilized by the ICRH-produced energetic ions. The characterization of the TAE instability in ASDEX Upgrade is reported, focusing on the identification of the toroidal, poloidal and radial mode structures. The data are compared with the ideal magnetohydrodynamic model.

Mixed type I-II ELMy H-mode, a mode operation with small, frequent type II edge localized modes (ELMs) interrupted by occasional large type I ELMs, has been observed in various experimental situations. This paper combines two simple models for type I and type II ELMs, respectively (used e.g. in Lonnroth et al 2003 Plasma Phys. Control. Fusion 45 1689) into an improved scheme for modelling of mixed type I-II ELMy H-mode, which has been implemented in the 1.5D core transport code JETTO together with simple schemes for modelling of pure type I and type II ELMy H-modes based on the same ideas. In the ELM modelling, transport during the ELMs is enhanced by edge-localized radially Gaussian-shaped perturbations to the transport coefficients. Type I and type II ELMs are represented by perturbations with different widths and amplitudes and controlled by different stability limits derived from magnetohydrodynamic (MHD) stability analysis. Some justification from theory and numerical analysis is given for the representation of each ELM type. Predictive transport simulations with JETTO demonstrate that the experimental dynamics of mixed type I-II ELMy H-mode can be qualitatively reproduced using the present model. For completeness, the modelling of mixed type I-II ELMy H-mode is compared with reference simulations of pure type I and pure type II ELMy H-mode and the differences, e.g. in confinement are explained. In addition, this paper presents the results of MHD stability analysis of a number of situations experimentally found to be favourable for the occurrence of type II ELMs, namely situations with strong external neutral gas puffing, a quasi-double-null magnetic configuration, high poloidal β (ratio of the total pressure to the kinetic pressure) and combinations of high edge safety factor q95 and high triangularity δ. The results of the analysis of the given scenarios are such that the model used in this paper can explain why these situations can be favourable for mixed type I-II or pure type II ELMy H-mode.

Recent progress in experimental and theoretical studies of edge localized mode (ELM) physics is reviewed for the reactor relevant plasma regimes, namely the high confinement regimes, that is, H-modes and advanced scenarios.Theoretical approaches to ELM physics, from a linear ideal magnetohydrodynamic (MHD) stability analysis to non-linear transport models with ELMs are discussed with respect to experimental observations, in particular the fast collapse of pedestal pressure profiles, magnetic measurements and scrape-off layer transport during ELMs.High confinement regimes with different types of ELMs are addressed in this paper in the context of development of operational scenarios for ITER. The key parameters that have been identified at present to reduce the energy losses in Type I ELMs are operation at high density, high edge magnetic shear and high triangularity. However, according to the present experimental scaling for the energy losses in Type I ELMs, the extrapolation of such regimes for ITER leads to unacceptably large heat loads on the divertor target plates exceeding the material limits. High confinement H-mode scenarios at high triangularity and high density with small ELMs (Type II), mixed regimes (Type II and Type I) and combined advanced regimes at high βp are discussed for present-day tokamaks. The optimum combination of high confinement and small MHD activity at the edge in Type II ELM scenarios is of interest to ITER. However, to date, these regimes have been achieved in a rather narrow operational window and far from ITER parameters in terms of collisionality, edge safety factor and βp.The compatibility of the alternative internal transport barrier (ITB) scenario with edge pedestal formation and ELMs is also addressed. Edge physics issues related to the possible combination of small benign ELMs (Type III, Type II ELMs, quiescent double barrier) and high performance ITBs are discussed for present-day experiments (JET, JT-60U, DIII-D) in terms of their relevance for ITER. Successful plasma edge control, at high triangularity (~0.5) and high density (~0.7nGR), in ITB scenarios in JET is reported.Active control of ELMs by edge current, pellet injection, impurities and external magnetic perturbations creating an ergodic zone localized at the separatrix are discussed for present-day experiments and from the perspective of future reactors.

Scenarios of steady-state, fully non-inductive current in Tore Supra are predicted using a package of simulation codes (CRONOS). The plasma equilibrium and transport are consistently calculated with the deposition of power. The achievement of high injected energy discharges up to 1 GJ is shown. Two main scenarios are considered: a low density regime with 90% non-inductive current driven by lower hybrid waves-lower hybrid current drive (LHCD)-and a high density regime combining LHCD and ion cyclotron resonance heating with a bootstrap current fraction up to 25%. The predictive simulations of existing discharges are also reported.

Edge plasma parameters influence plasma performance in many different ways (profile stiffness is probably one of the best known examples). In the ELMy H-mode plasma, a thin region with improved transport characteristics (the edge transport barrier) links the core and the scrape-off layer. There is a strong coupling between these three areas, so that even a modest variation of plasma parameters in one region can lead to a dramatic change in the overall plasma performance. A systematic MHD stability analysis and self-consistent integrated predictive modeling of a series of JET ELMy H-mode plasmas, including scans in gas fueling and triangularity, are presented. The main conclusion is that plasma performance indeed sensitively depends on the edge plasma parameters, which should be modeled in a self-consistent way.

While present plasma scenarios rely on self generated plasma conditions, active control with ergodic divertor coils provide the means to operate in H-mode with divertor and SOL plasma conditions that are compatible with the technical constraints. The stochastisation of field lines in the vicinity of the separatrix, will produce a localized enhancement of electron heat transport. This will provide a control on the edge temperature (and thus pressure) barriers. Consequently, the local current profile, which is essentially bootstrap, will be modified. H-mode edge barriers can be controlled and type I Elms avoided in this way. Such controls are required for advanced regimes. The paper will discuss this in light of the theoretical and experimental advances of the last years: Tore Supra experiments gave evidence of the fine tuning capability of the perturbation on a well defined magnetic configuration while JFT-2M experiments showed that the edge stochastisation of the X point configuration has widened the operating windows of the type III ELM regime. The possible implementations of such control in a medium size tokamak (DIII-D) and eventually on ITER will also be described.

Numerical analysis of the images in visible light from the JET tangential camera show that the edge localised mode (ELM) events are characterised by impacts on the low-field side components. The increase of emission is not restricted to the components closest to the plasma. One finds also that the deposition on the low-field side components does not exhibit any poloidal or toroidal symmetry and varies from ELM to ELM. Conversely the increase of emission on the divertor baffles, or the top protection tiles, is close to axisymmetric.

Recent operation of JET with centrally strongly reversed magnetic shear, produced with the help of lower hybrid current drive, has extended the domain in which internal transport barriers (ITBs) can be formed in JET. Performance is frequently limited by magnetohydrodynamic (MHD) instabilities in these reversed shear regimes. The most severe limit is a pressure driven kink mode which leads to a disruption. This disruptive limit is essentially the same in ITB plasmas with low or strongly reversed shear. Unique to the reversed shear regime is a dominantly n = 1 mode, which has multiple harmonics. This mode is a seemingly common limit to performance, in the highest performance plasmas. Also unique to the reversed shear regime are q > 1 sawteeth events, which can in turn trigger n = 1 post-cursor oscillations. In general, these post-cursor oscillations are benign but do provide valuable information on the q-profile. Other instabilities, including 'snakes' at the outer q = 3 surface, are also observed to limit the performance of reversed magnetic shear ITB regimes.

Quasi-steady operation has been achieved at JET in the high-confinement regime with internal transport barriers (ITBs). The ITB has been maintained up to 11 s. This duration, much larger than the energy confinement time, is already approaching a current resistive time. The high-performance phase is limited only by plant constraints. The radial profiles of the thermal electron and ion pressures have steep gradients typically at mid-plasma radius. A large fraction of non-inductive current (above 80%) is sustained throughout the high-performance phase with a poloidal beta exceeding unity. The safety factor profile plays an important role in sustaining the ITB characteristics. In this regime where the self-generated bootstrap current (up to 1.0 MA) represents 50% of the total current, the resistive evolution of the non-monotonic q-profile is slowed down by using off-axis lower-hybrid current drive.

A new computational tool, edge localized instabilities in tokamaks equilibria (ELITE), has been developed to help our understanding of short wavelength instabilities close to the edge of tokamak plasmas. Such instabilities may be responsible for the edge localized modes observed in high confinement H-mode regimes, which are a serious concern for next step tokamaks because of the high transient power loads which they can impose on divertor target plates. ELITE uses physical insight gained from analytic studies of peeling and ballooning modes to provide an efficient way of calculating the edge ideal magnetohydrodynamic stability properties of tokamaks. This paper describes the theoretical formalism which forms the basis for the code.

Internal transport barriers (ITBs) can be produced in JET by the application of strong additional heating during the current rise of plasma discharges. These `so-called' optimized shear experiments with low positive magnetic shear have revealed a strong dependence between the formation of the barrier and the integer q magnetic surfaces (q = 2 or q = 3). Further analysis also shows a correlation between the emergence of the ITB and the edge external MHD activity which is triggered when an integer q surface occurs at the edge of a strongly heated plasma (q = 4, q = 5 or q = 6). Mode coupling is the prime candidate to explain the link between the internal integer flux surfaces, where the ITB is triggered, and the plasma edge. Modelling of the MHD behaviour confirms the possibility of such a mechanism. Once coupled, this destabilized mode is thought to enhance locally the E×B shearing rate, either by magnetic braking or by the radial transport losses resulting from the modification of the field line topology. This could then trigger an ITB inside the internal integer surface at q = 2 or q = 3.

Lower hybrid enhanced performance (LHEP) discharges have been successfully operated on Tore Supra, with a significant improvement in electron core-confinement and remarkable steady-state features. However, recent attempts to operate such discharges with better confinement performance were hindered by the systematic onset of large MHD activity, preventing any good performance recovery. The associated MHD limit is found to result from reaching the tearing mode limit as the current profile is driven from centrally peaked towards off-axis peaked by the lower hybrid (LH) wave. The specific feature of the considered discharges is that they achieve a weak magnetic shear over a broader core region than past LHEP discharges, then leading to systematic fast MHD onset (m/n = 2/1 tearing mode) when qmin approaches 2. The present paper reports on experimental observations and modelling which support this finding and analyses the perspectives of improving the LHEP scenario by combining the current profile control through the LH wave with a significant increase in pressure through ion cyclotron wave coupling.

A new code, MISHKA-D (Drift MHD), has been developed as an extension of the ideal magnetohydrodynamics (MHD) code MISHKA-1 in order to investigate the finite gyroradius stabilizing effect of ion diamagnetic drift frequency, ω*i, on linear ideal MHD eigenmodes in tokamaks in general toroidal geometry. The MISHKA-D code gives a self-consistent computation of both stable and unstable eigenmodes with eigenvalues |γ|≅ω*i in plasmas with strong radial variation in the ion diamagnetic frequency. Test results of the MISHKA-D code show good agreement with the analytically obtained ω*i spectrum and stability limits of the internal kink mode, n/m=1/1, used as a benchmark case. Finite-n ballooning and low-n kink (peeling) modes in the edge transport barrier just inside the separatrix are studied for high confinement mode (H-mode) plasmas with the ω*i effect included. The ion diamagnetic stabilization of the ballooning modes is found to be most effective for narrow edge pedestals. For low enough plasma density the ω*i stabilization can lead to a second zone of ballooning stability, in which all the ballooning modes are stable for any value of the pressure gradient. For internal transport barriers typical of the Joint European Torus [JET, P. H. Rebut et al., Proceedings of the 10th International Conference, Plasma Physics and Controlled Nuclear Fusion, London (International Atomic Energy Agency, Vienna, 1985), Vol. I, p. 11] optimized shear discharges, the stabilizing influence of ion diamagnetic frequency on the n=1 global pressure driven disruptive mode is studied. A strong radial variation of ω*i is found to significantly decrease the stabilizing ω*i effect on the n=1 mode, in comparison with the case of constant ω*i estimated at the foot of the internal transport barrier.

The formation of a core region with improved electron confinement is reported in the recent full current drive operation of Tore Supra, where the plasma current is sustained with the lower hybrid (LH) wave. Current profile evolution and thermal electron transport coefficients are assessed directly by using the data of the new fast electron bremsstrahlung tomography that provides the most accurate determination of the LH current and power deposition profiles. The spontaneous rise of the core electron temperature observed a few seconds after the application of the LH power is ascribed to a bifurcation towards a state of reduced electron transport. The role of the magnetic shear is invoked to partly stabilize the anomalous electron turbulence. The electron temperature transition occurs when the q-profile evolves towards a non-inductive state with a non-monotonic shape, i.e. when the magnetic shear in the plasma core is reduced to close to zero. The improved core confinement phase is often terminated by a sudden MHD activity when the minimum q approaches 2.

Neoclassical tearing modes are one of the most serious concerns for operation on a next-step tokamak device. The modes occur on present tokamaks at normalized pressure (beta (N)) values comparable to those envisaged For baseline scenarios in future devices, such as ITER-FEAT. Further, empirical scalings based on data from many of the present machines point to much lower thresholds on a larger device. However, physics-based models indicate an important role for the seed island mechanisms, which may in fact give rise to increased stability on larger devices-i.e. if the seed island width (required to trigger the NTM) falls below the critical levels required. Fits based on these models suggest this is the case, bur are too badly constrained at present to make reliable predictions, and the physics is complex, making quantitative theoretical calculation difficult. Further experiments are required to examine the scaling of the seed, as well as to identify the role and relative sizes of the stabilizing terms that set the critical size for mode growth. In the event that the modes are unavoidable, promising feedback stabilization techniques are being developed with the use of localized RF current drive to change the stability properties of the plasma. Further work is needed to demonstrate sustained access to higher beta (N) and provide data to refine models. This paper reviews the underlying physics and key issues, commenting on the present status of understanding and further work required.

The islands from tearing modes driven unstable and sustained by the helically perturbed neoclassical bootstrap current often provide the practical limit to long-pulse, high confinement tokamak operation. The destabilization of such “metastable” plasmas depends on a “seed” island exceeding a threshold. A database from similar regimes [high confinement H-mode with periodic edge localized modes (ELMs) and periodic central sawteeth] was compiled from the tokamaks ASDEX Upgrade (AUG) [Plasma Phys. Controlled Fusion 41, 767 (1999)], DIII-D [Nucl. Fusion 38, 987 (1998)], and JET (Joint European Torus) [Plasma Phys. Controlled Fusion 41, B1 (1999)]. A comparison is made of the measured critical beta for onset of the m/n=3/2 mode (m and n being the poloidal and toroidal Fourier harmonics, respectively) to a model in terms of dimensionless parameters for the seed and threshold islands. This modeling is then used for extrapolation to a reactor-grade tokamak design such as ITER/FDR (International Thermonuclear Experi...

Results achieved on JET during the 1997-1999 experimental campaigns in the physics of energetic ions and runaway electrons are reviewed. Heating of deuterium-tritium (DT) plasmas by fusion born alpha particles is found to be similar to that achieved by comparable ICRF heating of deuterium plasmas. The stability of alpha particle driven Alfv?n eigenmodes (AEs) in the highest fusion power ELM-free H mode discharges is shown to be consistent with the existing theoretical analysis for AEs. Direct measurements of the trapped alpha particle and knock-on deuteron distribution functions by a neutral particle analyser (NPA) are described. New ICRF heating scenarios tested in JET DT plasmas are presented in view of the possible use of the ICRF heating of ITER-like DT plasmas on route to ignition. The energetic ion pinch in the presence of toroidally asymmetric ICRF waves is studied experimentally on JET. Recent experimentally observed effects of ICRF accelerated ions on sawteeth in JET are reviewed. Detailed time and space resolved X ray images of the electron runaway beam in flight spontaneously generated by disruptions on JET are described.

High performance discharges are routinely obtained on JET with low or reversed magnetic shear (s = (r/q)dq/dr), and the potential for steady state operation of such discharges is under investigation. With the use of the proper heating and fuelling, these `optimized shear' (OS) discharges exhibit an internal transport barrier (ITB), resulting in a strong peaking of the pressure profile, and thus in high fusion performance. These regimes have been extensively studied during the last (DD and DT) JET campaigns in order to promote this type of scenario as the basis for `advanced tokamak' operation. A review is given of the highest performance achieved on JET OS discharges during the last experimental campaigns, in both DD (up to 5.6 × 1016neutrons/s) and DT operation (fusion power up to 8.2 MW, ni0Ti0τE up to 1021 m-3 keV s). The role of the plasma edge is pointed out, as the power required to trigger an ITB is often higher than the H mode power threshold, leading to double barrier regimes. The presence of an H mode pedestal both modifies the ITB and induces edge bootstrap and ELM activity, which should be controlled to prolong such discharges. The operational procedure of optimization is then discussed, addressing the problems of ITB formation (power threshold, timing of the main heating phase, i.e. optimization of the target q profile, influence of the heating scheme, electron versus ion ITBs), ITB evolution (expansion of the ITB footpoint, H mode formation) and ITB termination (disruptive and/or `soft' MHD limits). Finally, the crucial problem of the route to steady state for such OS discharges is addressed, both in terms of ITB sustainment and control within the stability domain and in terms of edge pedestal control by means of impurity injection. The impurity behaviour is found, and examples of high performance discharges sustained for several energy confinement times are given (βN = 1.95, H89 = 2.3, Pfusioneq~10 MW, QDTeq~0.4 sustained for ~3 s). Extrapolation towards fully non-inductive current drive is discussed.

Some models for the suppression of turbulence in the L to H transition, suggest that the width of the H-mode edge barrier is either proportional or is of the order of the thermal or the fast-ion poloidal Larmor radius. This would require that the width of the edge barrier should depend on the plasma current. This dependence has been clearly verified at JET in experiments designed to control the edge MHD stability of ELM-free hot-ion H-mode plasmas. The effects of isotopic mass and the applicability of several edge barrier models to the hot-ion H-mode plasmas were analysed in (Guo H Y et al 2000 Edge transport barrier in JET hot-ion H-modes Nucl. Fusion 40 69) using a large database containing both deuterium-only and deuterium-tritium plasmas. This database has now been enlarged to include discharges from a plasma shape scan, allowing one to study the dependence of the pedestal height on the edge shear. In addition, the range of plasma currents was extended up to 6 MA. It is shown that the edge data are best described by a model where the edge barrier width is determined by the fast ions weighted towards the components with largest poloidal Larmor radii. However, it is not possible to conclusively eliminate the thermal ion model.

The effects of changing beam and plasma species on the edge transport barrier are investigated for ELM-free hot ion H mode discharges from the recent DT experiments on JET. The measured pressure at the top of the pedestal is higher for mixed deuterium and tritium and pure tritium plasmas over and above the level measured in pure deuterium plasmas at the same heating power. The pedestal pressure increases with beam tritium concentration for mixed deuterium-tritium beam injection into deuterium plasmas where the measured edge tritium concentration remains low. Alpha heating plays a significant role in the core of such plasmas, and the possible impact on the edge is discussed together with possible direct isotopic effects. Heuristic models for the transport barrier width are proposed, and used to explore a wider range of edge measurements including full power DD and DT pulses. This analysis supports the plasma current and mass dependence for a barrier width set by the orbit loss of either thermal or fast ions, though it does not unambiguously distinguish between them. The fast ion hypothesis could well account for some of the JET observations, though more theoretical work and direct experimental measurement would be required to confirm this. An ad hoc model for the power loss through the separatrix, Ploss ∝ nedge2 Zeff,edgeIp-1, is proposed based on neoclassical theory, a ballooning limit to the edge gradient and a barrier width set by the poloidal ion gyroradius. Such a model is compared with experimental data from JET. In particular, the model ascribes the systematic difference in loss power between the Mark I and Mark II divertors to the change in the measured Zeff. This change in Zeff is consistent with the observed change in impurity production, which is described in some detail, together with a possible explanation provided by the temperature dependence of chemical sputtering.

Ideal MHD limits to beta and bootstrap fraction are computed for pressure profiles similar to those of JET discharges with both internal and H mode transport barriers. Several non-monotonic current profiles are tested, and the pressure profile is constrained so that no negative current drive is required in steady state. Calculations are made both with and without an ideally conducting wall. The main result is that, for such peaked pressure profiles, the limits to beta and bootstrap fraction improve at low internal inductance, in particular when wall stabilization is taken into account. The highest limits to beta, and often also to normalized beta, occur for the maximum plasma current. There is also a weak dependence on qmin, for which three favourable regions have been identified. A highly advantageous region is found at qmin 1.6, where the limits to β* are 7.0% with, and 4.8% without, wall stabilization. The corresponding limits are 68 and 50%, respectively, for the bootstrap fraction and 4.0 and 2.9 for the normalized beta. These equilibria have low internal inductance, li = 0.62. For higher inductance, an optimum occurs when qmin 1.2, where the limit to β* is 5.3% with a wall and 4.7% without. The corresponding bootstrap fractions are about 46 and 38%, respectively. A third type of equilibrium that is interesting for steady state operation has qmin 2.1 and low inductance. Here the β* limits are lower, 4.9 and 3.4%, but the bootstrap fractions are higher, 77 and 60%.

High power combined NBI + ICRF heating experiments have been carried out in the JET Mark IIa divertor configuration in the hot ion ELM-free H mode regime, both in deuterium (DD) and in deuterium-tritium (DT) plasmas. Results are presented from a wide range of additional heating power levels, ICRF up to 9.5 MW tuned to the fundamental hydrogen minority, NBI up to 22 MW, and for plasma currents up to 4.2 MA and toroidal fields up to 3.6 T. Discharges with combined NBI + ICRF heating show a clear improvement in electron temperature, DD neutron yield and stored energy with respect to NBI only discharges. High energy neutral particle analyser data show that acceleration of the NBI deuterons takes place due to absorption of ICRF power at the second harmonic deuterium resonance. This is confirmed by numerical simulations with the PION code, indicating that up to 40% of the ICRF power is absorbed by bulk and NBI ions. ICRF heating has been an essential ingredient in the DT experiments in the ELM-free hot ion regime, contributing to the achievement of a record fusion power of 16.1 MW and a record stored energy of 17 MJ.

An assessment is presented of the impact of recent magnetohydrodynamic research results on performance projections for reactor scale tokamaks as exemplified by the ITER Final Design Report (ITER/FDR) facility. For nominal ELMy H mode operation, the presence and amplitude of neoclassical tearing modes governs the achievable β value. Recent work finds that the scaling of β at which such modes onset agrees well with a polarization drift model, with the consequence that, with reasonable assumptions regarding seed island width, the mode onset β will be lower in reactor scale tokamaks than in contemporary devices. Confinement degradation by such modes, on the other hand, depends on relative saturated island size which is governed principally by β and secondarily by ν* effects on bootstrap current density. Relative saturated island size should be comparable in present and reactor devices. DT ITER demonstration discharges in JET exhibited no confinement degradation at the planned ITER operating value of βN = 2.2. Theory indicates that electron cyclotron current drive can either stabilize these modes or appreciably reduce saturated island size. Turning to operation in candidate steady state, reverse shear, high bootstrap fraction configurations, wall stabilization of external kink modes is effective while the plasma is rotating but (so far) rotation has not been maintained. Recent error field observations in JET imply an error field size scaling that leads to a projection that the ITER/FDR facility will be somewhat more tolerant to error fields than thought previously. ICRF experiments on JET and Alcator C-Mod indicate that plasmas heated by central energetic particles have benign ELMs compared with the usual type 1 ELM of NBI heated discharges.

The main limitation to the performance of JET optimized shear (OS) discharges is due to MHD instabilities, mostly in the form of a disruptive limit. The structure of the MHD mode observed as a precursor to the disruption, as measured from SXR and ECE diagnostics, shows a global ideal MHD mode. The measured mode structure is in good agreement with the calculated mode structure of the pressure driven kink mode. The disruptions occur at relatively low normalized beta (1 < βN < 2), in good agreement with calculated ideal MHD stability limits for the n = 1 pressure driven kink mode. These low limits are mainly due to the extreme peaking factor of the pressure profiles. Other MHD instabilities observed in JET OS discharges include, usually benign, chirping modes. These modes, which occur in bursts during which the frequency changes, have the same mode structure as the disruption precursor but are driven unstable by fast particles.

Discharge optimization for improving MHD stability of both core and edge was essential for the achievement of record fusion power discharges, in the ELM-free hot ion H mode regime, in the recent JET DT operation. The techniques used to increase edge stability are described. In particular the successful technique of current rampdown used to suppress the outer mode is reported. The increased stability of the outer mode by decreasing the edge current density confirms its identification as an n = 1 external kink. Decreasing the plasma current, however, decreases the ELM-free period, which is consistent with stability calculations that show an earlier onset of the ballooning limit. In order to increase external kink stability without causing a deterioration in the ELM-free period, a compromise was achieved by using plasma current rampdown, while working at the highest plasma current values possible. Results from a plasma current scan show that at the time of occurrence of the first giant ELM, the plasma stored energy, as well as the pressure measured at the top of the edge pedestal increase linearly with plasma current, for a given plasma configuration and power. This is consistent with models of the edge transport barrier, where the transport barrier width is proportional to the ion (or fast ion) poloidal Larmor radius. The MHD observations in DT and deuterium only discharges were found to be similar. Thus the experience gained on the control of MHD modes in deuterium plasmas could be fully exploited in the DT campaign.

High fusion performance has been achieved in optimized shear discharges in JET with the early appearance of internal transport barriers (ITBs) in the high power phase in both DD and DT plasmas. An ITB has been produced in a large variety of conditions, including LHCD only, ICRH only, NBI only and NBI + ICRH with LHCD preheat. An ITB may coexist with the edge barrier. The high pressure gradient produced by ICRH combined with high power NBI heating starting in a low density plasma with q(0) ≈ 1.5-2 is the main prerequisite for an efficient ITB in high performance discharges. Strong coupling between q profiles, MHD activity, energy confinement and fusion yield has been observed. The transition from L to H mode can be triggered by MHD events. The transition is accompanied by significant momentary changes in the density fluctuation spectrum in the peripheral plasma. The ITB may persist for some time in both ELM-free and ELMy H mode.

The ideal MHD β limit of reversed shear equilibria, due to n = 1, n = 2 and ballooning modes, is investigated for peaked pressure profiles, consistent with those occurring when the internal transport barrier is established in JET optimized shear discharges. Higher βN can be reached with the control of the minimum q value, and a conducting wall can further improve the stable domain. The n = 2 mode plays an insignificant role, unless the conducting wall improves the n = 1 stability when the shear reversal is large. Increasing the amount of shear reversal generally improves MHD stability, and the effect is stronger for the n = 2 mode. β* ( = 2μ0 P2 1/2/B02) increases with normalized current (Ip/aB0) but βN is only weakly affected.