F. Ryter

Chapter 2: Plasma confinement and transport

The understanding and predictive capability of transport physics and plasma confinement is reviewed from the perspective of achieving reactor-scale burning plasmas in the ITER tokamak, for both core and edge plasma regions. Very considerable progress has been made in understanding, controlling and predicting tokamak transport across a wide variety of plasma conditions and regimes since the publication of the ITER Physics Basis (IPB) document (1999 Nucl. Fusion 39 2137-2664). Major areas of progress considered here follow. (1) Substantial improvement in the physics content, capability and reliability of transport simulation and modelling codes, leading to much increased theory/experiment interaction as these codes are increasingly used to interpret and predict experiment. (2) Remarkable progress has been made in developing and understanding regimes of improved core confinement. Internal transport barriers and other forms of reduced core transport are now routinely obtained in all the leading tokamak devices worldwide. (3) The importance of controlling the H-mode edge pedestal is now generally recognized. Substantial progress has been made in extending high confinement H-mode operation to the Greenwald density, the demonstration of Type I ELM mitigation and control techniques and systematic explanation of Type I ELM stability. Theory-based predictive capability has also shown progress by integrating the plasma and neutral transport with MHD stability. (4) Transport projections to ITER are now made using three complementary approaches: empirical or global scaling, theory-based transport modelling and dimensionless parameter scaling (previously, empirical scaling was the dominant approach). For the ITER base case or the reference scenario of conventional ELMy H-mode operation, all three techniques predict that ITER will have sufficient confinement to meet its design target of Q = 10 operation, within similar uncertainties.

Identification of plasma-edge-related operational regime boundaries and the effect of edge instability on confinement in ASDEX Upgrade

Local edge parameters on the ASDEX Upgrade tokamak are investigated at the L-mode to H-mode transition, during phases with various types of edge-localized modes (ELMs), and at the density limit. A scaling law for the boundary electron temperature, , is found which describes the H-mode threshold for deuterium-puffed discharges with favourable ion -drift direction. The region of stable operation is bounded by type I ELMs near the ideal ballooning limit and by a minimum temperature necessary to avoid thermal instability of the plasma edge. Stationary operation with type III ELMs imposes an upper limit on the edge temperature. Within the entire range of boundary densities investigated , both L-mode and H-mode are found to be accessible. During type I ELMy H-mode, a relation of global confinement with the edge pressure gradient is found which is connected with a loss of the favourable density dependence predicted by the ITER-92P and ITER-93H ELMy H-mode scalings. At high density, better confinement is achieved in H-modes with an edge pressure gradient below the ideal ballooning limit, e.g. during type III ELMy H-mode with impurity-seeded radiation.

Physics of transport in tokamaks

This paper is an overview of recent results relating to turbulent particle and heat transport, and to the triggering of internal transport barriers (ITBs). The dependence of the turbulent particle pinch velocity on plasma parameters has been clarified and compared with experiment. Magnetic shear and collisionality are found to play a central role. Analysis of heat transport has made progress along two directions: dimensionless scaling laws, which are found to agree with the prediction for electrostatic turbulence, and analysis of modulation experiments, which provide a stringent test of transport models. Finally the formation of ITBs has been addressed by analysing electron transport barriers. It is confirmed that negative magnetic shear, combined with the Shafranov shift, is a robust stabilizing mechanism. However, some well established features of internal barriers are not explained by theory.

Impurity behaviour in the ASDEX Upgrade divertor tokamak with large area tungsten walls

At the central column of ASDEX Upgrade, an area of 5.5 m2 of graphite tiles was replaced by tungsten-coated tiles representing about two-thirds of the total area of the central column. No negative influence on the plasma performance was found, except for internal transport barrier limiter discharges. The tungsten influx ΓW stayed below the detection limit only during direct plasma wall contact or for reduced clearance in divertor discharges spectroscopic evidence for ΓW could be found. From these observations a penetration factor of the order of 1% and effective sputtering yields of about 10-3 could be derived, pointing to a strong contribution by light intrinsic impurities to the total \mbox{W-sputtering}. The tungsten concentrations ranged from below 10-6 up to a few times 10-5. Generally, in discharges with increased density peaking, a tendency for increased central tungsten concentrations or even accumulation was observed. Central heating (mostly) by ECRH led to a strong reduction of the central impurity content, accompanied by a very benign reduction of the energy confinement. The observations suggest that the W-source strength plays only an inferior role for the central W-content compared to the transport, since in the discharges with increased W-concentration neither an increase in the W-influx nor a change in the edge parameters was observed. In contrast, there is strong experimental evidence, that the central impurity concentration can be controlled externally by central heating.

H mode discharges with feedback controlled radiative boundary in the ASDEX Upgrade tokamak

Puffing of impurities (neon, argon) and deuterium gas in the main chamber is used to feedback control the total radiated power fraction and the divertor neutral particle density simultaneously in the ASDEX Upgrade tokamak. The variation of Psep=Pheat-Prad(core) by impurity radiation during H mode shows a similar effect on the ELM behaviour as that obtained by a change of the heating power. For radiated power fractions above 90%, the ELM amplitude becomes very small and detachment from the divertor plates occurs, whilst no degradation of the global energy confinement is observed (completely detached high confinement mode). Additional deuterium gas puffing is found to increase the radiated power per impurity ion in the plasma core owing to the combined effect of a higher particle recycling rate and a lower core penetration probability. The outer divertor chamber, which is closed for deuterium neutrals, builds up a high neutral pressure, the magnitude of which is determined by the balance of particle sources and pumping. For this particular situation, the effective pumping time of neon and argon is considerably reduced, to less than 0.3 s, mainly owing to an improved divertor retention capability. The radiation characteristics of discharges with a neon driven radiative mantle are modelled using a 1-D radial impurity transport code that has been coupled to a simple divertor model describing particle recycling and pumping. The results of simulations are in good agreement with experiment

Density response to central electron heating: theoretical investigations and experimental observations in ASDEX Upgrade

Theory of ion temperature gradient (ITG) and trapped electron modes (TEMs) is applied to the study of particle transport in experimental conditions with central electron heating. It is shown that in the unstable domain of TEMs, the electron thermodiffusive flux is directed outwards. By means of such a flux, a mechanism is identified likely to account for density flattening with central electron heating. Theoretical predictions are compared with experimental observations in ASDEX Upgrade. A parameter domain (including L- and H-mode plasmas) is identified, in which flattening with central electron heating is observed in the experiments. In general, this domain turns out to be the same domain in which the dominant plasma instability is a TEM. On the contrary, the dominant instability is an ITG in plasmas whose density profile is not affected significantly by central electron heating. The flattening predicted by quasi-linear theory for low density L-mode plasmas is too small compared to the experimental observations. At very high density, even when the dominant instability is an ITG, electron heating can provide density flattening, via the coupling with the ion heat channel. In these conditions the anomalous diffusivity increases in response to the increased ion heat flux, while the large collisionality makes the anomalous pinch small and the Ware pinch important.

The effect of a metal wall on confinement in JET and ASDEX Upgrade

In both JET and ASDEX Upgrade (AUG) the plasma energy confinement has been affected by the presence of a metal wall by the requirement of increased gas fuelling to avoid tungsten pollution of the plasma. In JET with a beryllium/tungsten wall the high triangularity baseline H-mode scenario (i.e. similar to the ITER reference scenario) has been the strongest affected and the benefit of high shaping to give good normalized confinement of H98???1 at high Greenwald density fraction of fGW???0.8 has not been recovered to date. In AUG with a full tungsten wall, a good normalized confinement H98???1 could be achieved in the high triangularity baseline plasmas, albeit at elevated normalized pressure ?N?>?2. The confinement lost with respect to the carbon devices can be largely recovered by the seeding of nitrogen in both JET and AUG. This suggests that the absence of carbon in JET and AUG with a metal wall may have affected the achievable confinement. Three mechanisms have been tested that could explain the effect of carbon or nitrogen (and the absence thereof) on the plasma confinement. First it has been seen in experiments and by means of nonlinear gyrokinetic simulations (with the GENE code), that nitrogen seeding does not significantly change the core temperature profile peaking and does not affect the critical ion temperature gradient. Secondly, the dilution of the edge ion density by the injection of nitrogen is not sufficient to explain the plasma temperature and pressure rise. For this latter mechanism to explain the confinement improvement with nitrogen seeding, strongly hollow Zeff profiles would be required which is not supported by experimental observations. The confinement improvement with nitrogen seeding cannot be explained with these two mechanisms. Thirdly, detailed pedestal structure analysis in JET high triangularity baseline plasmas have shown that the fuelling of either deuterium or nitrogen widens the pressure pedestal. However, in JET-ILW this only leads to a confinement benefit in the case of nitrogen seeding where, as the pedestal widens, the obtained pedestal pressure gradient is conserved. In the case of deuterium fuelling in JET-ILW the pressure gradient is strongly degraded in the fuelling scan leading to no net confinement gain due to the pedestal widening. The pedestal code EPED correctly predicts the pedestal pressure of the unseeded plasmas in JET-ILW within ?5%, however it does not capture the complex variation of pedestal width and gradient with fuelling and impurity seeding. Also it does not predict the observed increase of pedestal pressure by nitrogen seeding in JET-ILW. Ideal peeling ballooning MHD stability analysis shows that the widening of the pedestal leads to a down shift of the marginal stability boundary by only 10?20%. However, the variations in the pressure gradient observed in the JET-ILW fuelling experiment is much larger and spans a factor of more than two. As a result the experimental points move from deeply unstable to deeply stable on the stability diagram in a deuterium fuelling scan. In AUG-W nitrogen seeded plasmas, a widening of the pedestal has also been observed, consistent with the JET observations. The absence of carbon can thus affect the pedestal structure, and mainly the achieved pedestal gradient, which can be recovered by seeding nitrogen. The underlying physics mechanism is still under investigation and requires further understanding of the role of impurities on the pedestal stability and pedestal structure formation.

Global energy confinement H-mode database for ITER

Describes the content of an H-mode confinement database that has been assembled for the ITER project. Data were collected from six machines of different sizes and shapes: ASDEX, DIII-D, JET, JFT-2M, PBX-M and PDX. A detailed description of the criteria used in the selection of the data and the definition of each of the variables is given. The authors also present an analysis of the conditions of the database, the scalings (power law and offset linear) of the data with both dimensional and dimensionless variables, and predictions of the expected confinement time for ITER

Experimental studies of electron transport

Electron transport in tokamaks has many different features which are briefly reviewed. The paper is focused on electron heat transport in conventional tokamak plasmas. An inter-machine comparison indicates that the non-dimensional gradient length of the electron temperature profiles R/L Te is almost independent of the devices and varies little with plasma parameters. This strongly suggests that electron heat transport is governed by turbulence with a threshold in R/L Te . This is confirmed by modulation experiments using electron cyclotron heating. Simulations with empirical and physics-based transport models confirm this assumption.

ITER H mode confinement database update

This paper describes an update of the H mode confinement database that has been assembled for the ITER project. Data were collected from six machines of different sizes and shapes: ASDEX, DIII-D, JET, JFT-2M, PBX-M and PDX. The updated database contains better estimates of fast ion energy content and thermal energy confinement times, discharges with RF heating, data using boronization, beryllium and pellets, more systematic parameter scans, and other features. The list of variables in the database has been expanded, and the selection criteria for the standard dataset have been modified. We also present simple scalings of the total and thermal energy confinement time to the new dataset