Table of contents

The power exhaust from a burning plasma is a key problem in the design of future fusion reactors. Presently employed divertor materials restrict the stationary heat flux to 10 MW m⁻². This paper deals with the power load onto the divertor target of W7-AS. The divertor experiments of W7-AS serve as a testbed for W7-X, since this is also equipped with a modular island divertor and its edge structure is similar to that of the W7-AS. The heat flux onto the divertor target is determined by means of infrared thermography. In W7-AS divertor discharges, bunches of edge localized modes (ELMs) with an overall duration of a few milliseconds expel plasma, mostly at the transition from high to low confinement regimes or during density ramps. The heat flux and energy loss they produce is comparable to strong ELMs (type I ELMs) in a tokamak. These bunches of ELMs induce further asymmetries of the heat flux deposition onto the divertor targets.

This paper presents the results of JET experiments aimed at studying the operational space of plasmas with a Type III ELMy edge, in terms of both local and global plasma parameters. In JET, the Type III ELMy regime has a wide operational space in the pedestal n_e – T_e diagram, and Type III ELMs are observed in standard ELMy H-modes as well as in plasmas with an internal transport barrier (ITB). The transition from an H-mode with Type III ELMs to a steady state Type I ELMy H-mode requires a minimum loss power, P_TypeI. P_TypeI decreases with increasing plasma triangularity. In the pedestal n_e – T_e diagram, the critical pedestal temperature for the transition to Type I ELMs is found to be inversely proportional to the pedestal density (T_crit ∝ 1/n) at a low density. In contrast, at a high density, T_crit, does not depend strongly on density. In the density range where T_crit ∝ 1/n, the critical power required for the transition to Type I ELMs decreases with increasing density. Experimental results are presented suggesting a common mechanism for Type III ELMs at low and high collisionality. A single model for the critical temperature for the transition from Type III to Type I ELMs, based on the resistive interchange instability with magnetic flutter, fits well the density and toroidal field dependence of the JET experimental data. On the other hand, this model fails to describe the variation of the Type III n_e – T_e operational space with isotopic mass and q₉₅. Other results are instead suggestive of a different physics for Type III ELMs. At low collisionality, plasma current ramp experiments indicate a role of the edge current in determining the transition from Type III to Type I ELMs, while at high collisionality, a model based on resistive ballooning instability well reproduces, in term of a critical density, the experimentally observed q₉₅ dependence of the transition from Type I to Type III ELMs. Experimental evidence common to Type III ELMs in standard ELMy H-modes and in plasmas with ITBs indicates that they are driven by the same instability.

The peakedness of the density profile in source-free MHD-quiescent L-mode plasmas with lower hybrid current drive is observed to decrease with decreasing peaking of the current profile. For the discharges investigated, which include normal and reversed magnetic shear plasmas, the relationship can be summarized as n_e0/⟨n_e⟩ ≅ 1.2l_i, where l_i is the normalized internal inductance. Density profiles are monotonically peaked at negative shear. Since density profiles remain peaked at zero loop voltage and negligible core particle source, the effect is attributed to an anomalous process of inward convection. No significant evidence was found for a correlation of density peaking with collisionality, nor of a dependence on temperature peaking within the parameter range investigated. The peaking of the temperature profiles and of the current profiles is uncorrelated in this dataset, allowing, for the first time, an experimental distinction between their effects on the density profile. The results are supportive of theories explaining particle convection by the anomalous curvature pinch or turbulent equipartition by trapped electrons, rather than by anomalous thermodiffusion.

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 Lönnroth et al 2003 Plasma Phys. Control. Fusion45 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.

Charge exchange recombination spectroscopy, utilizing a fast lithium beam as the recombination source, has been successfully applied to measuring edge ion temperature profiles of fully stripped carbon and helium ions in Ohmic, L-mode and H-mode plasmas with a radial resolution of about 6 mm. The temperatures of the carbon and helium ions agree within their respective experimental error bars in discharges where both could be measured. Depending on the plasma scenario, impurity content, beam penetration, etc, either helium or carbon can be the better choice for accurate edge measurements. The impact of edge localized modes (ELMs) on this diagnostic method has been noted. Temperature profiles in between ELMs can be determined as long as the ELM frequency is less than half the frame rate of the detector, i.e. less than about 60 Hz. In a first application, accurate measurements in L-mode plasmas with dominant electron heating and low density show much higher ion temperatures than electron temperatures across the separatrix.

Toroidicity-induced Alfvén 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 P_ICRH > 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.

The ability to recognize the transition from the L-mode to the H-mode or from the H-mode to the improved H-mode reliably from a conveniently small number of measurements in real time is of increasing importance for machine control.

Discriminant analysis has been applied to regime identification of plasma discharges in the ASDEX Upgrade tokamak. An observation consists of a set of plasma parameters averaged over a time slice in a discharge. The data set consists of all observations over different discharges and time slices. Discriminant analysis yields coefficients allowing the classification of a new observation. The results of a frequentist and a formal Bayesian approach to discriminant analysis are compared. With five plasma variables, a failure rate of 1.3% for predicting the L-mode and the H-mode confinement regime was achieved. With five plasma variables, a failure rate of 5.3% for predicting the H-mode and the improved H-mode confinement regime was achieved.

The coefficients derived by discriminant analysis have been applied subsequently to discharges to illustrate the operation of regime identification in a real time control system.

Evidence from injection into the TCV device of laser ablated, non-recycling silicon impurities shows that the transport of impurities confinement can be remarkably different from that of energy. The ratio of impurity to energy confinement times ranges from near unity in Ohmic discharges to 5 in the presence of high power ECCD. In Ohmic discharges in deuterium, above a threshold of density and of safety factor near q₉₅ = 4.5, the impurity confinement time increases abruptly by a factor of 2 and is sometimes accompanied by indefinite retention of non-recycling impurities within the sawtooth mixing radius.

By varying the pressure-gradient and average shear at a selected surface in a given arbitrary stellarator equilibrium and by inducing a coordinate variation such that the perturbed state remains in equilibrium, a family of magnetohydrodynamic equilibria local to the surface is constructed. The equilibria are parameterized by the pressure-gradient and averaged magnetic shear. The geometry of the surface is not changed. The perturbed equilibria are analysed for infinite-n ballooning stability and marginal stability diagrams are constructed that are analogous to the (s, α) diagrams constructed for axisymmetric configurations.

The method describes how pressure and rotational-transform gradients influence the local shear, which in turn influences the ballooning stability. Stability diagrams for the quasi-axially symmetric NCSX, a quasi-poloidally symmetric configuration and the quasi-helically symmetric HSX are compared. Regions of second-stability are observed in both NCSX and the quasi-poloidal configuration, whereas no second-stable region is observed for the quasi-helically symmetric device.

To explain the different regions of stability, the curvature and local shear of the quasi-poloidal configuration are analysed. The results are seemingly consistent with the following simple explanation: ballooning instability results when the local shear is small in regions of bad curvature with sufficient pressure-gradient. Examples will be given that show that the structure and stability of the ballooning mode is determined by the structure of the potential function arising in the Schrödinger form of the ballooning equation.

A theory of spontaneous generation of zonal flows by kinetic drift-Alfvén turbulence in the finite-pressure plasma (β > m_e/m_i) is generalized to include the ion diamagnetic effects and the finite ion Larmour radius effects. In the framework of the corresponding set of generalized two-fluid magnetohydrodynamic equations and on the assumption of a distinct time- and space-scale separation between the turbulent oscillations and the zonal flow, a set of coupled equations is derived to describe the interaction between the turbulence and the flow, consisting of the evolution equation for the spectral function of turbulence and the mean-field equations for zonal flow. The possibility of spontaneous zonal flow generation by the kinetic drift-Alfvén turbulence is investigated in details in several cases. In the case of kinetic drift-Alfvén turbulence with the space scale of the order of the ion Larmour radius or below, the instability caused by the resonant interaction of the wave packet with the slow modulations of zonal flow has been analysed, and the criterion for the onset of the zonal flow instability has been derived. In the case of short-wavelength turbulence, two regimes are considered. It is shown, that, when the frequency of short-wavelength oscillations is close to the electron-drift frequency and the zonal perturbation of plasma density can be described by the Boltzmann Law, the instability criterion is a generalization of the previously obtained result to the case of non-equal temperatures of the ions and electrons. The new regime is found, in which the zonal perturbation of plasma density is negligible. The condition for the onset of resonant instability is obtained.

Lower hybrid current drive experiments in the ergodic divertor (ED) configuration have been carried out on Tore Supra for 9 years (1991–1999). This paper gives an overview of the results regarding both the current drive and the divertor efficiencies: waves coupling, current drive efficiency and fast particle confinement, energy confinement, thermal load on the ED plasma facing components, impurity screening. It is shown that the coupling remains good enough for high power transmission up to 26 MW m⁻². The current drive efficiency, measured on not fully non-inductive discharges, is only marginally affected by the loss of fast electrons due to the perturbed magnetic structure which is documented from hard x-ray measurements. Electron confinement follows, as in the limiter case, the Rebut–Lallia–Watkins scaling without any losses related to the width of the ergodic layer extending to 15% of the minor radius. The heat flux on the divertor neutralizers from both thermal particles and fast electrons accelerated near the antennae is detailed. Plasma contamination due to carbon and oxygen is analysed from a large database: it is shown that, for a large enough gap between the ED modules and the antennae, the contamination by these species is reduced by a factor of ∼3 with respect to the limiter case.