Table of contents

Plasma fluctuations in the scrape-off layer (SOL) of the TCV tokamak exhibit statistical properties which are universal across a broad range of discharge conditions. Electron density fluctuations, from just inside the magnetic separatrix to the plasma–wall interface, are described well by a gamma distributed random variable. The density fluctuations exhibit clear evidence of self-similarity in the far SOL, such that the corresponding probability density functions collapse upon renormalization solely by the mean particle density. This constitutes a demonstration that the amplitude of the density fluctuations is simply proportional to the mean density and is consistent with the further observation that the radial particle flux fluctuations scale solely with the mean density over two orders of magnitude. Such findings indicate that it may be possible to improve the prediction of transport in the critical plasma–wall interaction region of future large scale tokamaks.

Real-time control of many plasma parameters will be an essential aspect in the development of reliable high performance operation of next step tokamaks. The main prerequisites for any feedback scheme are the precise real-time determination of the quantities to be controlled, requiring top quality and highly reliable diagnostics, and the availability of robust control algorithms.

A new set of real-time diagnostics was recently implemented on JET to prove the feasibility of determining, with high accuracy and time resolution, the most important plasma quantities. Some of the signals now routinely provided in real time at JET are: (i) the internal inductance and the main confinement quantities obtained by calculating the Shafranov integrals from the pick-up coils with 2 ms time resolution; (ii) the electron temperature profile, from electron cylotron emission every 10 ms; (iii) the ion temperature and plasma toroidal velocity profiles, from charge exchange recombination spectroscopy, provided every 50 ms; and (iv) the safety factor profile, derived from the inversion of the polarimetric line integrals every 2 ms. With regard to feedback algorithms, new model-based controllers were developed to allow a more robust control of several plasma parameters.

With these new tools, several real-time schemes were implemented, among which the most significant is the simultaneous control of the safety factor and the plasma pressure profiles using the additional heating systems (LH, NBI, ICRH) as actuators. The control strategy adopted in this case consists of a multi-variable model-based technique, which was implemented as a truncated singular value decomposition of an integral operator. This approach is considered essential for systems like tokamak machines, characterized by a strong mutual dependence of the various parameters and the distributed nature of the quantities, the plasma profiles, to be controlled. First encouraging results were also obtained using non-algorithmic methods like neural networks, which have been successfully applied to non-linear and ill-posed problems, for example the determination of the divertor radiated power.

The real-time hardware and software architectures adopted are also described with particular attention to their relevance to ITER.

Determination of both the radial and poloidal components of electron density fluctuation parameters in a tokamak edge plasma was achieved by operation of two narrow Li-beams (FWHM ≈10 mm at a distance of 100 mm from the source), which were separated by 50 mm. Beams of thermal lithium atoms were generated using a newly developed oven, which provides a long operation time and a high reliability. The lithium atoms, with a mean velocity of ≈1.7 km s⁻¹, were injected radially into the plasma edge, where they were excited and ionized by the plasma. The line radiation (resonance transition 2s–2p, λ = 670.8 nm) of the excited atoms was observed, which enables determination of the electron density profiles. The measurements are performed with high temporal (Δt ≃ 2 µs) and spatial (Δ_r ≃ 1 mm in the radial and Δ_p ≃ 10 mm in the poloidal direction) resolution, thus also allowing determination of the fluctuations. This new diagnostic permits studies of both radial and poloidal fluctuation parameters like the correlation length, wavenumber, frequency spectrum, propagation velocity and lifetime. The method can be applied continuously over long discharges without disturbing the plasma.

Two series of JET shots, one on hot ion shots and one on hot electron shots, have been analysed in order to improve the understanding of how the temperature ratio T_e/T_i influences the performance. Comparisons are also made with ITER simulations which are in the hot electron regime. The temperature ratio has been varied between different shots, in partly interpretative simulations of one shot and locally. The effect of the variation of the temperature ratio depends strongly on how it is done but can also be different in different types of shots. In general, however, an increased electron heating deteriorates confinement rather strongly. This is the situation for increasing the alpha power in ITER. ITER simulations show, however, that the effect is not dramatic.

The instability of the geodesic acoustic mode (GAM) in tokamak turbulence is analysed. It can be caused by dynamic shearing of the ambient turbulence by GAMs combined with the poloidal inhomogeneity of the turbulent flux. The dispersion relation is derived. The competition between the drive mechanism and the damping by turbulence viscosity is discussed. GAMs are more unstable for high safety factors.

A semi-analytical method is proposed to evaluate the dielectric response of a plasma to electromagnetic waves in the ion cyclotron domain of frequencies in a D-shaped but axisymmetric toroidal geometry. The actual drift orbit of the particles is accounted for. The method hinges on subdividing the orbit into elementary segments in which the integrations can be performed analytically or by tabulation, and it relies on the local book-keeping of the relation between the toroidal angular momentum and the poloidal flux function. Depending on which variables are chosen, the method allows computation of elementary building blocks for either the wave or the Fokker–Planck equation, but the accent is mainly on the latter. Two types of tangent resonance are distinguished.

A model is developed for use in integrated modelling codes to predict the height, width and shape of the H-mode pedestal as well as the frequency and width of edge localized modes (ELMs). The model for the H-mode pedestal in tokamak plasmas is based on flow shear reduction of anomalous transport, while the periodic ELM crashes are triggered by MHD instabilities. The formation of the pedestal and the L–H transition in this model are the direct result of flow shear suppression of transport. Suppression of the anomalous transport enhances the role of neoclassical transport in the pedestal region. The ratio of suppression of anomalous thermal transport in electron and ion channels controls the ratio of electron to ion temperature at the top of the pedestal. Two mechanisms for triggering ELMs are considered. ELMs are triggered by ballooning modes if the pressure gradient exceeds the ballooning limit or by peeling modes if the edge current density exceeds the peeling mode criterion. The models for the pedestal and ELMs are used in a predictive integrated modelling code to follow the time evolution of tokamak discharges from L-mode through the transition from L-mode to H-mode, with the formation of the H-mode pedestal, and, subsequently, the triggering of ELMs. The objective is to produce self-consistent predictions of the width, height and shape of the H-mode pedestal and the frequency of ELMs. The dependences of pedestal temperature, pedestal width and ELM frequency as a function of plasma heating power, magnetic field and density are discussed.

A series of hot-electron plasmas were produced at JET with the aim of clarifying the dependence of the energy confinement time on the electron to ion temperature ratio, T_e/T_i. Although these plasmas showed a clear increase in the ion heat diffusivity with higher T_e/T_i, their energy confinement time remained constant. In this paper we propose that these observations are consistent with the predictions of the Weiland model of energy transport. A feedback loop amplifying the ion diffusivity simultaneously flattens the ion temperature profile, and keeps the ion heat flux constant. The electron transport shows no dependence on T_e/T_i, and hence there is no scaling of the confinement time with the temperature ratio. To support these claims we show a series of numerical simulations using the Weiland model. For scaling law purposes it is also interesting to note that the energy confinement time does not show any dependence on the effective input power ratio, P_e/P_i, either.

The expansion dynamics of a finite-size plasma is examined from an analytical perspective. Results regarding the charge distribution as well as the electrostatic potential are presented. The acceleration of the ions and the associated cooling of the electrons that takes place during the plasma expansion is described. An extensive analysis of the transition between the semi-infinite and the finite-size plasma behaviour is carried out. Finally, a test of the analytical results, performed through numerical simulations, is presented.

This paper reports on the results of an experimental investigation into electron cyclotron resonance heating (ECRH) using the fundamental O-mode in the large helical device (LHD). The aim of the experiment is to understand the mechanism of the selective excitation of the O-mode EC wave and, thereby, optimize the performance of the ECRH. The polarization angle and the ellipticity of the electric field of the incident high power millimetre waves were varied in the experiment using a pair of grating polarizers. The responses of the plasma stored energy and electron temperature were measured to evaluate the effects. The optimum values of the polarization angle and the ellipticity for the ECRH were identified experimentally. A simple model of power branching between the O- and X-modes is introduced in order to interpret the observed experimental results. Specific to the ECRH in the LHD configuration, the effect of magnetic shear in the plasma peripheral region is considered.

Neoclassical transport theory describes local diffusive transport. For those magnetic configurations where this approach is valid it has the benefit of being independent of the plasma profiles. In contrast for configurations where many particle orbits have large deviations from their birth surface, non-local contributions to the particle flux have to be considered. In this work a newly developed Monte Carlo code has been used to compute global ion fluxes for the same plasma parameters for two devices with very different magnetic configurations, namely the Wendelstein 7-X helias, which is under construction at Greifswald (Germany), and the TJ-II heliac, in operation at Madrid (Spain). Whereas the results indicate that the local diffusive approach is valid for W7-X under the considered plasma conditions, a non-local treatment is mandatory for TJ-II. These global flux simulations show the appearance of fluxes in regions where there are no gradients; larger fluxes than those expected from local estimations in the gradient regions; and fluxes which are increasing towards the edge.

Fixed boundary three-dimensional anisotropic pressure equilibria are computed that are consistent with a family of distribution functions that load particles preferentially towards v_∥ ≃ v and model the effects of balanced tangential neutral beam injection. The total pressure surfaces remain coupled with the magnetic surfaces even when the parallel beam pressure greatly exceeds its perpendicular counterpart. The anisotropy factors and the Shafranov shift, which increases with the anisotropy, are calculated in a currentless two-field period quasiaxisymmetric stellarator device.