Table of contents

Electron Cyclotron Heating (ECH) discharges of the tokamak ASDEX Upgrade, exhibiting T_e profile resilience, are used to test the Weiland model in the case of dominant electron heating. Electron heat transport is investigated also transiently, with heat pulse propagation induced by ECH power modulation. The Weiland model, dominated by the Trapped Electron Mode physics in this parameter range, predicts the experimental T_e well, both the time averaged profile as well as the amplitude and phase of the T_e perturbation. Interestingly, in the confinement region the experimental ∇T_e/T_e is up to three times larger than the critical threshold predicted by the model.

Perturbative transport experiments have been performed at the stellarator TJ-II. Both the inward propagation of edge cooling pulses induced by the injection of nitrogen, and the outward propagation of heat pulses due to spontaneous spikes of the central temperature have been analysed. It has been found that the observed propagation is incompatible with diffusive transport models. Simultaneous inward and outward propagation eliminates an explanation in terms of a pinch. A numerical simulation with a resistive interchange turbulence model suggests that the observed propagation is related to the successive destabilizations of pressure gradient driven modes associated with rational surfaces.

Plasma generation has been achieved in the stellarator W7-AS using neutral beam injection only. Plasma evolution is analysed using a zero-dimensional model. The model gives guidelines for this method to be successful. Both a low neutral gas starting pressure and a small fraction of wall recycling are necessary to get `ignition' by beams. The predictions of the model are compared to experiments on W7-AS and LHD.

The two-dimensional multifluid code TECXY has been used to model the biasing (with respect to the first wall) of the toroidal belt limiter ALT-II on the tokamak TEXTOR-94 and of the new toroidal pump limiter being installed on Tore Supra tokamak in the framework of the CIEL project. It is well known that the edge flow pattern can be influenced by the poloidal electric drifts from imposing radial electric fields. The modelling with TECXY introduces imprinted bias currents in the scrape-off layer (SOL) for the case of negative (limiter) biasing, and imprinted bias potentials for the case of positive biasing. This allowed us to simulate sufficiently well the experimental I-V characteristics for either biasing of ALT-II and also reproduced the essential features and trends of the observed plasma profiles in the SOL of TEXTOR-94. For negative biasing a moderate improvement of the pumping exhaust efficiency can be achieved in the case of TEXTOR. For Tore Supra, however, only a negligible improvement of the limiter performance with biasing can be predicted, which is explained by the relatively weak drift flows in Tore Supra.

Neoclassical transport and α particle confinement are analysed for three 3-D reactor designs - the QAS3, the ST/sphellamak hybrid and the sphellamak - using the VENUS code. It is observed that neither the QAS3 nor the ST/sphellamak is truly a quasi-axisymmetric configuration. Thus the transport is governed by the helical deformation of the magnetic field strength, and these configurations do not effectively confine the trapped α particles. On the other hand, the sphellamak is a nearly isodynamic structure in the plasma core, which leads to almost perfect α confinement, and the neoclassical transport is very similar to that obtained in a 2-D equivalent tokamak.

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.

It is shown that (3,2) neoclassical tearing modes (NTMs) in ASDEX Upgrade can, under similar external control parameters, occur at significantly different values of β_N, with the NTMs occurring at higher β_N sometimes having a less detrimental impact on the energy confinement. This is found to be due to a coupling between the (3,2) NTM and a (4,3) mode, which can either occur continuously and clamp the (3,2) amplitude for the time of the existence of the (4,3) or occur in bursts on a timescale much shorter than the usual resistive timescale, where each burst leads to a rapid reduction of the (3,2) NTM called an amplitude drop. The amplitude drops may be due to stochastization in the presence of two islands of different helicity and sufficient amplitude, which can act as an anomalous increase in resistivity. These observations point towards the possible existence of a regime where the energy confinement deterioration due to NTMs is acceptable for reactor scale experiments.

A simplified analysis is given of the problem of estimating the `epistemic probability' for ITER to attain a power amplification factor Q larger than a certain lower bound. Attention is restricted to the parameters of ITER-FEAT and the 1998 ITER design. The probabilistic framework is briefly discussed and the distributional interval estimates for Q following from the interval estimates of the confinement time are derived (a) for ITER operation at constant fusion output power P_fus, and (b) for operation at a temperature that maximizes Q = P_fus/P_aux. The second situation requires a radial integration of the flux surface averaged energy balance. Instead of a local transport model, a simple class of temperature profiles is used. The results are represented graphically. A generalization of the widely used fusion triple product plot against temperature is suggested. The analysis presupposes that at the reference operating point in situation (a), and in the range of operating temperatures projected to be achievable in situation (b), the conditions for reaching standard ELMy H mode in ITER are met. The practical conclusion of the article is that under this premise ITER-FEAT has a fairly large epistemic probability of obtaining plasma conditions with prevalent alpha particle heating.

Large coherent MHD modes are observed to reduce the neutral beam current drive efficiency and 2.5 ,MeV neutron emission in DIII-D by as much as ~65%. These modes result in large (width w≲20 cm for minor radius a≈60 cm), stationary, single helicity magnetic islands, which might cause anomalous deuterium beam ion losses through orbit stochasticity. An analytic estimate predicts that co-going, passing deuterons with E≳40 keV become stochastic at island widths comparable to those in the experiment. A Hamiltonian guiding centre code is used to follow energetic particle trajectories with the tearing mode modelled as a radially extended, single helicity perturbation. In the simulations, the lost neutral beam current drive and neutron emission are 35% and 40%, respectively, which is consistent with the measured reductions of 40±14% and 40±10%. Several features of the lost particle distribution indicate that orbit stochasticity is the loss mechanism in the simulations and strongly suggest that the same mechanism is responsible for the losses observed in the experiment.

A Monte Carlo code is employed to study the interaction of neutral beams with a field reversed configuration (FRC). The code follows the exact particle trajectories in the self-consistent equilibrium calculated including the beam and plasma currents. For high enough beam currents, a self-consistent confining effect is observed which prevents expansion of the beam along the FRC axis. The beam current drive and the power and momentum transferred are calculated for a variety of beam parameters. The results are slightly affected by the details of the injection geometry. The dependence on the neutral current I_N and beam energy E_N is influenced by several factors, such as particle losses through the ends, the density increase around the injection region and the finite Larmor radius effect.

Hydrocarbon pellets were injected into NBI and ECH plasmas of the Compact Helical System (CHS) heliotron/torsatron. The ablation of the pellet was observed from horizontal and vertical directions using two CCD cameras, and the velocities of the pellet during ablation were measured with an 11 channel fan array. It was observed that the pellet trajectory was strongly curved in NBI cases, whereas in ECH cases it was straight. When the toroidal direction of the tangential NBI was changed from clockwise to counter-clockwise, the direction of the curved trajectory completely changed. For the first time, it was also found that the pellet was accelerated during the ablation, for example from 270 to 600 m/s. The ablation of the pellet is simulated for the case with fast ions from NBI (40 keV). The results strongly support the idea that the pellet can be mainly ablated by collisions with fast ions. As a result, it is found that the pellet is accelerated by a jet of the ablation cloud resulting from one-side heating due to the toroidally circulating fast ions.

The results of a series of experiments done in RTP which had the purpose to avoid or ameliorate radiative density-limit disruptions, will be reported. Avoidance of disruptions was achieved by stabilizing the m = 2 radiation induced tearing mode (RTM) with electron cyclotron resonance heating (ECRH). Both continuous and modulated power deposition was studied. It was found that stabilization with modulated ECRH in phase with the O-point was less efficient than continuous ECRH, contrary to theoretical expectations. Detailed scans of the EC power deposition and of the power intensity were in agreement with the assumption that radiative heat loss is the driving mechanism of this m = 2 mode. Amelioration of disruptions was achieved, in a pilot experiment, by applying ECRH at the end of the energy quench. In this way, the current decay that follows a major density-limit disruption could be reversed.

Results of stability analysis are presented for two types of plasma with good confinement: internal transport barriers (ITBs) on Tore Supra and the radiative improved (RI) mode on TEXTOR. The stability analysis has been performed with an electrostatic linear gyrokinetic code, evaluating the growth rates of microinstabilities. The code developed, KINEZERO, is aimed at systematic microstability analysis. Therefore the trade-off between having perfect quantitative agreement and minimizing computation time is made in favour of the latter. In the plasmas analysed, it is found that the onset of the confinement improvement involves a trigger. For the ITB discharges, negative magnetic shear is involved, whereas for the RI discharges, the triggering role is played by the increase of the impurity concentration. Once the improved confinement is triggered, the simultaneous increases of temperature and density gradients imply an increase in both the growth rate and the rotation shearing rate. The rotation shear is found to be high enough to maintain an improved confinement through the stabilization of the large scale modes.

Electron energy transport in the Wendelstein 7-AS stellarator exhibits a strong sensitivity to the boundary value of the rotational transform when the magnetic shear is low. Pronounced confinement maxima close to the low order rational values correlate with a low density of other rational numbers in these favourable ranges. The dependence is lost if magnetic shear is increased by large plasma currents. The hypothesis is proposed that, at rational flux surfaces, electron energy transport is increased above the already anomalous level and that magnetic shear reduces the additional enhancement. An empirical model that incorporates these features into a simple expression for the electron heat conductivity can reproduce the experimental dependences over a wide range of external control parameters, e.g. the rotational transform and the net plasma current. Except for the explicit shear dependence, this model bears a remarkable similarity to the RTP model, which successfully describes the electron transport barriers near low order rational q surfaces in RTP and other tokamaks.

We present a preliminary investigation of the plasma column displacement in the RFX reversed field pinch (RFP) experiment, carried out with different diagnostics. Determinations of the plasma position have been obtained by a set of external pick-up coils, a multichannel far infrared (FIR) polarimeter and a soft x-ray (SXR) tomographic camera. These diagnostics provide complementary information about the plasma position. In particular, the location of the polarimetric chords allows a direct estimate of the horizontal magnetic axis shift. The analysis of the isoemissivity SXR surfaces also allow investigations of the differential shift of the various magnetic surfaces. A comparison of the results of these three diagnostics is reported, and their agreement is found to be satisfactory and consistent with our expectations.

Results from an array of theoretical and computational tools developed to treat the instabilities of most interest for high performance tokamak discharges are described. The theory and experimental diagnostic capabilities have now been developed to the point where detailed predictions can be productively tested so that competing effects can be isolated and either eliminated or confirmed. The linear MHD stability predictions using high quality discharge equilibrium reconstructions are tested against the observations for the principal limiting phenomena in DIII-D: L mode negative central shear (NCS) disruptions, H mode NCS edge instabilities, and tearing and resistive wall modes (RWMs) in long pulse discharges. In the case of predominantly ideal plasma MHD instabilities, agreement between the code predictions and experimentally observed stability limits and thresholds can now be obtained to within several per cent, and the predicted fluctuations and growth rates to within the estimated experimental errors. Edge instabilities can be explained by a new model for edge localized modes as predominantly ideal instabilities with low to intermediate toroidal mode number. Accurate ideal calculations are critical to demonstrating RWM stabilization by plasma rotation, and the ideal eigenfunctions provide a good representation of the RWM structure when the plasma rotation slows. Ideal eigenfunctions can then be used to predict stabilization using active feedback. For non-ideal modes, the agreement in some cases is promising. Δ' calculations, for example, indicate that some discharges are linearly unstable to classical tearing modes, consistent with the observed growth of islands in those discharges. Nevertheless, there is still a great deal of improvement required before the non-ideal predictive capability can routinely approach levels similar to those for the ideal comparisons.