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This work is aimed at the analysis of pellet injection experiments by means of a magnetohydrodynamic code that computes the processes of pellet ablation, expansion, ionization, and magnetic confinement of the ablated substance. In particular, experimental pellet injection scenarios stemming from the tokamak ASDEX-Upgrade (D2 pellets) and the stellarator W7-AS (carbon pellets) are analyzed by means of this time-dependent quasithree-dimensional MHD pellet code. Pellet penetration depths measured in ASDEX-Upgrade at LFS (low-field-side) and HFS (high-field-side) pellet injection, are compared with computational results. It was found that the penetration depths of deuterium pellets observed in about twenty randomly selected LFS and HFS injection scenarios could accurately be reproduced by a single code in which drift effects were intentionally ignored. This may be understood as an indication of the negligible effect drift exerts on the ablation process. At the same time, the distribution of the ablated and partially ionized substance may very well be affected by the drift of the ionized particles in the direction of the decreasing magnetic field. With the help of the Dα radiation patterns observed, the magnitudes of the heat fluxes affecting the pellet and the ablation cloud were estimated. The calculations show that the thermal heat fluxes (electron and ion) acting along the magnetic field lines are not sufficient to explain the size of the radiating filaments observed. The effect of extra-thermal electrons on the ablation history of pellets injected in W7-AS is demonstrated: the particle end energy fluxes causing measured pellet ablation profiles are determined. Based on a statistically well-designed computational data set, an empirical scaling of the penetration depths in terms of the background plasma parameters was attempted. It is shown that the form of the temperature profile of the background plasma cannot be ignored while deriving scaling laws; the specification of the central or the bulk temperature alone is insufficient. Quantitative data are provided for the magnitudes of various additional processes such as the anomalous thermal conduction across the field lines or the grad(B)-induced drift of the shielding cloud surrounding the pellet. The modelling of supersonic gas jets, a fuelling method that appears to be an alternative to pellet injection, is also considered. Since the massive stream of a cold gas represents a disturbance for the recipient plasma similar to that of a pellet, its dynamics can be described by the same means as the evolution of pellet clouds. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Significant progress has been made on ASDEX Upgrade during the last two years in the basic understanding of transport, in the extension of the improved H-mode in parameter space and towards an integrated operating scenario and in the development of control methods for major performance limiting instabilities. The important features were the understanding of particle transport and the control of impurity accumulation based on it, the satisfactory operation with predominantly tungsten-clad walls, the improved H-mode operation over density ranges and for temperature ratios covering (non-simultaneously) the ITER requirements on ν*, n/nGW and Te/Ti, the ELM frequency control by pellet injection and the optimization of NTM suppression by DC-ECCD through variation of the launching angle. From these experiments an integrated scenario has emerged which extrapolates to a 50% improvement in n T τ or a 30% reduction of the required current when compared with the ITER base-line assumptions, with moderately peaked electron and controllable high-Z density profiles.

The MFBE_2001 code computes the magnetic field in a form suitable for field line tracing inside and outside the plasma boundary of two- and three-dimensional finite-β equilibria. It is a modified version of the Magnetic Field Solver for Finite-β Equilibria (MFBE) code which was developed for the investigation of stellarator equilibria without net toroidal current. The numerical method used in MFBE_2001 is based on the `virtual casing' principle which also allows the computation of magnetic fields of equilibria with net toroidal current, such as quasi-axisymmetric and tokamak equilibria. The numerical accuracy of the code is tested for an axisymmetric tokamak equilibrium and the corresponding three-dimensional one including the toroidal field ripple. For this purpose, the results obtained with the code system VMEC/NEMEC+MFBE_2001+GOURDON are compared with those computed with the axisymmetric equilibrium code DIVA.

Scrape-off layer (SOL) currents are measured by means of Langmuir probes and shunts in the divertor of ASDEX Upgrade. They consist of the overlayed contributions of thermoelectric and Pfirsch–Schluter (PS) currents. The SOL currents exhibit a drastic decrease when the line-averaged density approaches the Greenwald density in the H-mode. An analytical model is presented which reproduces the measured thermoelectric current quantitatively. Matching of the analytical model with the measured current scaling yields information about divertor temperatures and SOL e-folding lengths.

An ELMy ASDEX Upgrade plasma equilibrium is reconstructed taking into account the bootstrap current. The peeling mode stability of the equilibrium is numerically analysed using the GATO [1] code, and it is found that the bootstrap current can drive the plasma peeling mode unstable. A high-n ballooning mode stability analysis of the equilibria revealed that, while destabilizing the peeling modes, the bootstrap current has a stabilizing effect on the ballooning modes. A combination of these two instabilities is a possible explanation for the type I ELM phenomenon. A triangularity scan showed that increasing triangularity stabilizes the peeling modes and can produce ELM-free periods observed in the experiments.

ASDEX Upgrade is a poloidal divertor experiment very similar to ITER with respect to magnetic field properties and especially to the plasma boundary geometry. A large part of the programme on ASDEX Upgrade is therefore dedicated to investigating and optimizing reactor-relevant plasma boundary issues. This contribution is concerned with H-mode studies and edge physics in general. The L/H-power threshold, H-mode confinement, details of ELM dynamic and 'dithering' L/H-transitions will be discussed. The edge physics investigations are concerned with model calculations and validations, the characteristic 'approach' to the density limit (DL), target plate sputtering and the influence of hydrocarbons, asymmetries and drifts depending on the direction of the toroidal magnetic field, and finally first results of high-Z material experiments.

The Mirnov oscillations observed in the ASDEX tokamak are analysed with regard to the generally accepted interpretation scheme according to which (1) Mirnov oscillations are caused by currents flowing parallel to the magnetic field on rational magnetic surfaces and (2) the field perturbation is frozen within the plasma. If the second statement holds, the frequency is obtained from the profiles of the electron density, the ion temperature and, if applicable, the toroidal or poloidal rotation velocity. It is shown that there are modes which are consistent with the above interpretation. On the other hand, mode coupling is observed. Mode coupling is also invoked to reconcile the experimental findings with the predictions of a theory based on statement (1); according to this theory, there is a poloidal variation of both the phase velocity and the amplitude of the Mirnov oscillations. While the observed phase velocity fits well into this picture, the poloidal variation of the amplitude cannot be ascribed to only one mode in the majority of cases. In addition, the possibility of coherent MHD activity due to currents in the scrape-off layer is discussed.

Recent results from ASDEX Upgrade are presented. An improved understanding of energy and particle transport emerges in terms of a 'critical gradient' model for the temperature gradients. Coupling this to particle diffusion explains most of the observed behaviour of the density profiles, in particular the finding that strong central heating reduces the tendency for density profile peaking. Internal transport barriers with Te and Ti in excess of 20 keV (but not simultaneously) have been achieved. By shaping the plasma, a regime with small type II ELMs has been established. Here, the maximum power deposited on the target plates was greatly reduced at constant average power. Also, an increase of the ELM frequency by injection of shallow pellets was demonstrated. ELMfree operation is possible in the QH-mode regime previously found in DIII-D which has also been established on ASDEX Upgrade. Regarding stability, a regime with benign NTMs was found. During ECCD stabilisation of NTMs, bN could be increased well above the usual onset level without a reappearance of the NTM. ECRH and ECCD have also been used to control the sawtooth repetition frequency at a moderate fraction of the total heating power. The inner wall of the ASDEX Upgrade vessel has increasingly been covered with tungsten without detrimental effects on plasma performance. Regarding scenario integration, a scenario with a large fraction of noninductively driven current ( 50%), but without internal tranport barrier has been established. It combines improved confinement (tE=tITER98 1:2) and stability (bN 3:5) at high Greenwald fraction (ne=nGW 0:85) in steady state and with type II ELMy edge

Feedback-controlled puffing of neon and deuterium has been applied to control the edge-localized-mode behavior and the target plate power deposition during high-power H -mode discharges in ASDEX Upgrade. A regime has been found in which more than 90% of the heating power is lost through radiation and divertor detachment occurs, without deterioration of the energy confinement. The plasma remains in the H mode, exhibiting small-amplitude, high-frequency ELM's, which do not penetrate to the target plates in the strike zone region.

ASDEX Upgrade is equipped with an ICRH system consisting of 4 generators of 2 MW power each and 4 double loop antennas. The generators, tuneable in frequency from 30 to 120 MHz, cover several heating scenarios over a wide range of magnetic fields (1 T

Experiments on the maximum attainable beta values of ASDEX discharges show that the limits for this parameter lie in the range of theoretical predictions. In a previous publication a theoretical identification of the corresponding instabilities has been attempted. No significant correlation with global plasma instabilities could be found, but the two-dimensional MHD equilibria calculated on the basis of ASDEX experimental parameters turned out to be close to the marginal ideal ballooning limit. In the work presented here, the previous investigation on resistive ballooning modes is extended. Separatrix bounded as well as limiter controlled plasma equilibria are considered. Because of the small aspect ratio of ASDEX (A 4) all equilibrium as well as stability calculations are performed in full toroidal geometry. After the formulation of a system of four equations describing the resistive evolution of velocity and magnetic fields in the high-m stability limit in co-ordinate invariant form and its Fourier approximation in the neighbourhood of a localization field line, the resulting quasimode equations are solved, applying methods of finite-element discretization. Complex growth rates γ are found, with a positive real part for values of the toroidal mode number n below 100. Calculated values of Re {γ} ≤ 10−3/τA S−1 (with τA being the Alfven time) are small and therefore in agreement with the experimentally observed non-disruptive behaviour at the βp limit. Thus we believe that the characteristic signatures which govern ASDEX high βp discharges can be explained by resistive ballooning modes.

The resistive ballooning mode is studied in a separatrix geometry for parameters consistent with the H-mode. Besides the 'usual' ideal and resistive ballooning modes accessing a second stable regime at large plasma pressure gradients (α), there is another class of resistive ballooning modes, which do not stabilize as a increases. The properties of these modes are discussed in detail. Large pressure gradients associated with the H-mode, near the separatrix, can destabilize this class of rapidly growing resistive ballooning modes. It is found that since these modes are stabilized by increasing plasma pressure, the possibility of a second stable window also exists for these resistive ballooning modes.

Tokamak discharges with repetitive pellet fuelling were investigated in the ASDEX divertor device. The importance of sufficiently high divertor recycling for a high density at the separatrix and for successful density buildup in the bulk plasma was demonstrated. In contrast to low recycling discharges where no permanent improvement of the energy confinement time was achieved, in OH-heated discharges with high recycling an energy confinement time of 160 ms was reached, the normal value being 80 ms in the rollover region. The peaked density profiles in this case were accompanied by reduced or suppressed sawtooth activity and finally ended in a phase of strong central impurity accumulation. The particle transport was characterized by strong, non-classical inward drift, while the improved energy transport can be explained by the following alternatives: (la) a local model which assumes neo-Alcator χe for the electrons and χi= 3χneocl for the ions in the gas puff cases, reducing to χi= χneocl for the optimum pellet cases; (1b) the assumption χi= χneocl under all conditions and an electron energy confinement worse than neo-Alcator in the rollover region in gas-puff-discharges; (2) a profile consistency picture where Te(a) determines the energy confinement. Low power, NI heated discharges with pellet fuelling behave like Ohmic discharges, while for high power in the L-mode no successful density buildup was possible, and τE was not improved. The H-regime was extended from a density maximum e = 0.8 × 1020 m-3 without pellets to e = 1.2 × 1020 m-3 by the injection of pellets. In this case a density buildup takes place, but further density profile peaking could not be observed.

Recently, the conditions for stability of an arbitrarily shaped, finite-pressure toroidal plasma against localized ideal and resistive modes were presented. The characteristic time scale for local instability with respect to ideal modes is small compared with that for resistive modes so that an investigation of ideal local stability is a prerequisite for an assessment of non-ideal local stability. Here we consider the stability of a particular class of non-circular cross-section tokamak equilibria with respect to such modes. The equilibria are described analytically so that no ordering or expansion procedure is necessary, and both ideal and resistive stability are investigated over the whole plasma region. The effects of plasma shape (vertical elongation and triangularity), as well as aspect ratio are investigated and particular reference is made to next-generation tokamak designs (e.g. JET).

We investigate the effects of plasma flow on axisymmetric, self-consistent equilibria in toroidal geometry. The investigation is of considerable interest in relation to hot plasmas confined in toroidal systems with longitudinal current. On the basis of the one-fluid MHD plasma model, we use a concise formulation to elucidate important features of the equilibrium. In contrast to previous flow calculations which were treated almost exclusively in the low-beta approximation, we retain, together with flow, all beta effects.As in the treatment of the full flow problem at low beta, we find conditions for equilibrium. The form of our description allows a quite general discussion of its nature and existence for finite beta. This shows that there is a close relationship between the solvability conditions for equations arising from integrals of the system, and the nature of the characteristics of the partial differential equation describing the radial force balance. In the case of large aspect-ratio, these considerations lead to a generalized Bennett relation and to an expression for plasma displacement exhibiting beta and flow effects.

The signatures of resistive ballooning modes in ASDEX high beta discharges are investigated. It is shown that the growth rates of these modes increase significantly when βp reaches its maximum value during the discharge and therefore they can be used to explain the 'hard βp saturation' behaviour. A simple estimate of the corresponding electron heat conductivity gives values of χe > 1 m2s−1 in agreement with expectations from the observed confinement deterioration at maximum beta.

We investigate theoreticall y the MHD equilibrium of a resistive, low-density plasma in a model stellarator field. Th e effect of inertia on plasma motion is treated exactly and its influence on plasma loss determined. The results are valid for arbitrary aspect ratio. For the existence of a stationary equilibrium we show that there are two unconnected regions of solution, described in terms of the mass fluxes the long and the short way within a magnetic surface. For the region containing the case of the well-known classical resistive diffusion we argue that the increase in plasma loss due to inertia is strongly limited and does not appreciably exceed the classical diffusion rate.

Densities achievable in ASDEX Upgrade discharges are restricted by a disruptive limit in the L-mode caused by an edge-power imbalance which is linking divertor detachment, Marfe formation and the separatrix density. The attainable average densities depend then on the internal particle sources and the core transport and can exceed the empirical Greenwald density. In H-mode an upper density limit is found which represents a non-disruptive H - L back transition, which is preceded by the occurrence of type-III ELMs. Close to the Greenwald limit this H - L transition cannot be avoided at any power flux across the separatrix and - at high external neutral gas fluxes - confinement compared with ITER H-92P scaling degrades even before the back transition. The H-mode operational window is determined by local edge-barrier parameters and their gradients, respectively. The boundaries are represented by the L - H transition-temperature threshold, the ideal ballooning edge-pressure gradient limit, the upper temperature limit for type-III ELMs and an upper H-mode barrier density limitation. The cause for the last limitation is not yet identified; it may be due to resistive ballooning modes or the separatrix density limit. Despite the limited edge densities the Greenwald density could be surpassed by a factor of three with pellet refuelling from the low magnetic-field side. Pellet injection from the high-field side gains from the strong increase of fuelling efficiency due to the assisting toroidal outward drift of the formed high- ablatant. Higher densities are achievable in H-mode compared with low-field side injection and diminished convective losses avoid confinement degradation up to the Greenwald density. In gas-puffed type-I ELMy H-modes the plasma thermal energy and the edge-pressure gradients, which are limited by ballooning stability, are linked via a robust temperature-profile stiffness and the flat density profiles resulting from dominant edge refuelling at high densities. Their confinement does not improve with increasing density (and neutral gas fluxes) and may even slightly degrade. Therefore, the superior confinement of type-I ELMy H-modes compared with type-III ELMy ones at medium densities is actually offset at densities close to the Greenwald density. In contrast to the temperature-profile resilience density profiles can be changed both by deep refuelling (with pellets) and intrinsic transport improvements connected with density peaking (observed in CDH-modes), which offers the combination of high confinement and high density operation. The possible alliance with radiation cooling, divertor detachment and divertor compatible type-III ELMs could solve the power exhaust problem.

Recent experiments at ASDEX Upgrade have achieved advanced scenarios with high β N (>3) and confinement enhancement over ITER98(y, 2) scaling, H H98y2 = 1.1-1.5, in steady state. These discharges have been obtained in a modified divertor configuration for ASDEX Upgrade, allowing operation at higher triangularity, and with a changed neutral beam injection (NBI) system, for a more tangential, off-axis beam deposition. The figure of merit, β N H ITER89-P , reaches up to 7.5 for several seconds in plasmas approaching stationary conditions. These advanced tokamak discharges have low magnetic shear in the centre, with q on-axis near 1, and edge safety factor, q 95 in the range 3.3-4.5. This q-profile is sustained by the bootstrap current, NBI-driven current and fishbone activity in the core. The off-axis heating leads to a strong peaking of the density profile and impurity accumulation in the core. This can be avoided by adding some central heating from ion cyclotron resonance heating or electron cyclotron resonance heating, since the temperature profiles are stiff in this advanced scenario (no internal transport barrier). Using a combination of NBI and gas fuelling line, average densities up to 80-90% of the Greenwald density are achieved, maintaining good confinement. The best integrated results in terms of confinement, stability and ability to operate at high density are obtained in highly shaped configurations, near double null, with δ = 0.43. At the highest densities, a strong reduction of the edge localized mode activity similar to type II activity is observed, providing a steady power load on the divertor, in the range of 6 MW m -2 , despite the high input power used (> 10 MW).