Table of contents

An interpretation of non-standard, central MHD events in the TCV tokamak during localized ECRH is presented. It is shown that the non-standard behaviour is a consequence of specific features in the electron temperature profile produced when ECRH power is deposited close to the q = 1 surface and by the advection and mixing of electron thermal energy resulting from a resistive MHD instability.

The losses of fast ions (65 keV deuterons, 3 MeV protons and 1 MeV tritons) and their deposition patterns on the plasma facing components (PFCs) are studied for a high-nTτ scenario of the Helias type stellarator W7-X. For these computations a system of numerical codes is used which allows self-consistent computation of finite-β equilibria and the corresponding magnetic fields, tracing of guiding centres of fast particles taking into account slowing down and pitch angle scattering and determination of the deposition patterns of the lost fast ions on the PFCs. For this purpose the geometry of the first wall and the target plates has been implemented. These results will serve as a basis for heat load protection in the case of deuterons and for plasma diagnostics in the case of protons and tritons.

The problem of determining the orbits of energetic ions in the confining magnetic field of a tokamak plasma and their phase space characteristics is considered analytically. First, starting from the orbit invariants in the simplified magnetic field of a tokamak plasma, a quartic equation describing the trajectories in configuration space is derived. Then from an examination of the coefficients of the orbit equation, the orbit types and their classification are deduced. Analytic solutions of the orbit equation are given and the partition of phase space into regions of trapped (passing) particles and loss cones is determined. Finally, as a specific application, the trajectories and phase space characteristics of 3.5 MeV α particles in the magnetic field of the JET tokamak are calculated.

Impurity behaviour in the core of an ignited fusion reactor (ITER FDR) is investigated under the assumption that the impurity fluxes are dominated by neoclassical transport. Equilibrium impurity profiles are evaluated for two temperature profiles and compared with the results for purely anomalous diffusion with a core diffusion coefficient of D_an = 0.5 m²/s. The neoclassical fluxes are calculated taking collisions of all relevant plasma species into account. The diffusion coefficient in the core is below 0.1 m²/s and decreases with increasing Z of the impurity. The mean drift velocities are always outwardly directed and cause an effective screening for high-Z elements. Due to the low diffusion coefficient, the He concentration profile in the core is strongly rising. Helium concentrations on-axis are c_He ≈ 15-17%. In contrast to the calculation with purely anomalous transport and c_He ≈ 9% on-axis, the He density is not only determined by the recycling edge source but by the interplay of low core transport, increasing dilution and decreasing fusion source. The increased dilution causes a reduction of total fusion power by ≈ 8-11%. With an additional anomalous core diffusion for He of D_an^He = 0.2 m²/s the central He concentration decreases to c_He ≈ 10%.

The stability of the fishbone mode in the presence of trapped energetic ions in plasmas of spherical tokamaks is investigated. It has been shown that, when plasma β is sufficiently high to result in a magnetic valley in the equilibrium magnetic field, the fishbone mode is stable due to the inversion of direction of the toroidal precession. This result is valid for both high frequency and low frequency fishbone branches. It is based on general qualitative analysis and calculations involving a suggested analytical expression for the equilibrium magnetic field and calculated bounce and precessional frequencies of the energetic ions. Stability conditions are obtained which agree with experimental observations.

A new model for the H mode pedestal (edge) width is proposed based on turbulence suppression by the combined effects of magnetic and E × B shear. The resultant scaling of the pedestal width includes the toroidal Larmor radius and the magnetic shear. A plasma current dependence of the width appears indirectly through the magnetic shear, and thus the dependence becomes poloidal-Larmor-radius-like as observed on many machines. One of the features of this model is that an approximately linear machine size dependence of the width appears through the spatial profiles of the safety factor and magnetic shear. A comparison of this model with Alcator C-Mod and JET data shows that it can reproduce the data almost equally well or even better than a scaling based on the poloidal Larmor radius. The magnetic shear dependence of the pedestal width can explain the somewhat divergent characteristics observed in experiments. On the other hand, extrapolation between different machines or prediction to ITER by the model cannot be straightforward due to different magnetic shear profiles. The method for predicting the pedestal parameters in ITER is developed based on the primitive assumption that the ITER shear profile relative to the existing machine is identified, which predicts a pedestal temperature of 3-4 keV for the range of pedestal densities in the Q = 10 operation window. Experimental validation and the predictive capability of the model are still limited, and further data accumulation and examination, in particular, the profile data of the magnetic shear from each machine, are indispensable to further improve the model.

An important operational range for TEXTOR-DED is the case of a high ergodization at the plasma edge. Under these conditions, the edge magnetic field forms a proper ergodic layer and a laminar zone. The laminar zone is established by magnetic field lines which intersect wall elements after only a few toroidal turns (open ergodic system). For this, both the heat and particle transport in the plasma edge are dominated by the laminar zone which shows a well defined structure compared with that of the ergodic layer. For the present analysis the regions containing field lines with connection lengths corresponding to one or to two poloidal turns are of particular interest; the radial width of these regions is of the same order as the width of the unperturbed SOL of a `classical' limiter or divertor configuration. Field lines running poloidally twice around the torus introduce a particular new feature, they impose a connection between radially separated areas and thus enhance the radial temperature and particle transport. A new 2-D modelling approach code for the laminar zone of an ergodic divertor has been developed which is strongly oriented on the topology of the magnetic field lines in the plasma edge. A 2-D finite element method is used in order to model the perpendicular transport of particles and energy. For obtaining a solution of the parallel transport, an analytical model is discussed providing expressions for averaged particle and energy sources. By considering the topological properties of the magnetic field and corresponding assumptions in the code, the transport calculation in the perturbed plasma edge gives a first insight into the generic transport properties of the TEXTOR-DED laminar zone. As an important application for later experiments the power fluxes to the wall elements are estimated. They show a strong variation perpendicular to the perturbation coils and a medium variation over the helical divertor footprints.

In discharges with internal transport barriers produced by combined NBI and ICRF heating using the hydrogen minority scheme in JET, confinement and fusion performance are strongly affected by the direction of propagation of the ICRF waves. When the waves propagate along the plasma current, the formation of an internal transport barrier is prompter and the neutron yield is up to a factor of two higher than that for propagation against the current. An ICRF induced pinch of resonating trapped ions is put forward as a candidate for explaining the observations. Simulation results are presented which show that this effect is strong enough to provide a credible explanation for the experimental results.

Observations of a performance limiting feedback phase instability in the HBT-EP tokamak are reported. The phase instability consists of a rapid growth of the phase difference between an m/n = 2/1 tearing mode and an external resonant magnetic perturbation. Observations of mode angular dynamics during phase instability test discharges show good agreement with theoretical estimates of the phase instability timescale. The phase instability limits feedback performance in HBT-EP by decreasing the feedback loop's phase accuracy as gain increases.

Measurements of profiles of soft X ray emissivity with 1.5 mm radial resolution are combined with high resolution electron density and temperature measurements in the edge region of the Alcator C-Mod tokamak to facilitate transport analysis of medium-Z impurities during H modes. Results from detailed modelling of the radiation and transport of fluorine are compared with experimental measurements, yielding information about the transport coefficients in the H mode transport barrier region. Evidence is found for a strong inward impurity pinch just inside the separatrix. The region of strong inward pinch agrees very well with the region of strong electron density gradient, suggesting that the inward pinch could be driven by the ion density gradient, as predicted by neoclassical theory. Simulations using the neoclassical impurity convection profile agree very well with experiments. Transport modelling shows that the X ray pedestal width is largely determined by the diffusion coefficient in the transport barrier. This allows diagnosis of changes in the edge diffusion coefficient on the basis of observations of X ray pedestal width changes. Significant differences in the edge diffusion coefficient are seen between different types of H mode. Several scalings for the edge diffusion coefficient in the enhanced D_α H mode are also identified. This may help elucidate the physical processes responsible for this attractive confinement mode.

In JET, during some vertical displacement events (VDEs), the plasma current and position are toroidally asymmetric. These events are referred to as asymmetric VDEs (AVDEs). Analysis of the interactions among the current carrying systems reveals that the repelling force between the plasma and the vessel is of little significance in asymmetric events, even if it is the main symmetric repelling force. The sideways force acting on the vessel is shown to be due mainly to the interaction with the toroidal field of the asymmetric circulation of currents in the wall. The asymmetric current path in the vessel is then calculated analytically for a simplified geometry and used together with experimental data to estimate the sideways force on the vessel.