Table of contents

A Hamiltonian formulation is constructed for a finite ion Larmor radius fluid model describing ion temperature-gradient driven and drift Kelvin–Helmholtz modes. The Hamiltonian formulation reveals the existence of three invariants obeying detailed conservation properties, corresponding roughly to generalized potential vorticity, internal energy and ion momentum parallel to the magnetic field. These three invariants are added to the energy to form a variational principle that describes coherent structures (CSs), such as monopolar and dipolar vortices or modons. It is suggested that the invariants are responsible for the coherence and longevity of CSs and for their robustness during binary collisions.

This paper analyses the properties of a critical gradient transport model based on a few assumptions: electrostatic gyroBohm scaling law, existence of an instability threshold and finite background transport below the threshold. A quantitative criterion of stiffness is proposed, which provides the means for a quantitative assessment and inter-machine comparison. It is also shown that this transport model is compatible with a two-term scaling law of global confinement, as proposed recently by the International Tokamak Physics Activity–Confinement Data Base and Modelling Topical Group. This model has also been applied to analyse a variety of experiments mostly using electron heat modulation on JET, ASDEX-Upgrade, TORE SUPRA and FTU. The thresholds are found to be in the expected domain for micro-instabilities in tokamaks. However, the stiffness factor is found to cover a broad range of variation.

In this paper, we present a model-based strike point sweeping technique applied to JET, based on a singular value decomposition of a suitable static matrix of the CREATE_L linearized model, linking gaps to active currents. By doing so, it is possible to find a combination of current perturbations in the active coils inside the vessel able to move the strike points without significantly affecting the overall plasma shape. This allows, in principle, a spread of the divertor heat load with almost no interference with other control systems.

The generality of the proposed approach is widely discussed, showing (via simulations) that the method is very effective for a rather large range of JET plasma configurations, and does not seem to be significantly influenced by currents induced in passive structures.

The proposed technique has also been successfully validated experimentally on two different configurations, showing the reliability and viability of the method.

As a result of the two-dimensional consideration, a general analytic approach to the non-linear regime of fluctuation reflectometry allowing determination of its spectral and correlation characteristics in explicit form is developed. The expressions for average signal and cross-correlation function of radial correlation reflectometry valid for arbitrary plasma density profile, turbulence spatial distribution and wave number spectra are derived. The analytical predictions are compared to the results of one- and two-dimensional numerical modelling.

Time intervals between edge localized modes (ELMs) from the ASDEX Upgrade tokamak have been analysed to determine whether the ELM dynamics is chaotic (deterministic) or random (noise dominated). Two different methods have been used to detect unstable periodic orbits or unstable fixed points, which are indicators of chaos, in the ELM time series. It has been found that these time series generally are noise dominated, with the notable exception of five individual discharges in which traces of chaos have been detected.

Polarimetry, a powerful diagnostic tool, can provide information on the density and magnetic field, utilizing the Faraday and the Cotton–Mouton effects in a magnetized plasma. Both effects contribute to the change of the polarization of an electromagnetic wave traversing a magnetized plasma such that, unless both effects are small, the measurable output polarization does not provide the 'pure' effects in terms of Faraday rotation angle and Cotton–Mouton phase shift angle, which are directly related to simple line-of-sight integrals of the electron density times certain components of the magnetic field. In view of the importance of the latter, a new formalism has been developed, which delivers narrow limits to these quantities in terms of analytic formulae that contain nothing but the input and output polarization parameters. The approach is valid for vertical lines of sight in toroidal devices whose toroidal field dominates over other field components perpendicular to the line of sight. Examples relating to measurements at JET demonstrate the capabilities of the method.

Several Ohmic discharges of the ADITYA tokamak are simulated using the Tokamak Simulation Code (TSC), similar to that done earlier for the TFTR tokamak. Unlike TFTR, the dominant radiation process in ADITYA is through impurity line radiation. TSC can follow the experimental plasma current and position to very good accuracy. The thermal transport model of TSC including impurity line radiation gives a good match of the simulated results with experimental data for the Ohmic flux consumption, electron temperature and Z_eff. Even the simulated magnetic probe signals are in reasonably good agreement with the experimental values.

The applicability of the quasilinear (QL) theory in the modelling of radio-frequency (RF) heating and current drive (CD) in nearly collisionless plasmas is investigated. In these experiments the wave spectrum excited by the generator and the antenna is normally coherent so that the standard justification of the QL theory, namely that particles interact with a random phase ensemble of waves, cannot be applied. The QL theory is, nevertheless, valid provided that the wave phase seen by nearly resonant particles is effectively randomized before the nonlinearity of the particle motion in the wave starts to become important. In the case of Landau resonances at frequencies in the ion cyclotron range or below, when electrons normally resonate with only one wave at a time, the main randomization mechanism is due to Coulomb collisions. A numerical technique to evaluate the diffusion coefficient of the standard map, due to Rechester et al (1981 Phys. Rev. A 23 2264), has been extended to take into account weak collisions. It allows an efficient and accurate evaluation of the velocity diffusion coefficient as a function of collisionality and wave amplitude, and, in particular, leads to an explicit quantitative criterion for the transition from the nonlinear to the QL regime.

When this criterion is satisfied the heating rate predicted by the QL kinetic equation becomes independent of the collision frequency, and exactly balances the linear Landau damping rate of the wave. With a simplified but quantitatively correct model of the collision operator, it is shown that the same criterion justifies the linearization of the Vlasov equation to describe wave propagation. In the linear regime the two equations form a closed and internally consistent system for the description of RF heating and CD in fusion plasmas, with a well-defined validity criterion, which is satisfied by a large margin in most experimental situations.

The close correlation between the edge electrostatic fluctuations around the last closed flux surface and the magnetohydrodynamic (MHD) activity in the case of lower hybrid current drive (LHCD) is observed and analysed in the HT-7 tokamak. The turbulent transport is primarily driven by a coherent MHD mode, indicating that the electrostatic fluctuations are strongly correlated with MHD activity. The results supply direct evidence that the edge electrostatic fluctuations in tokamak plasmas can be decreased by suppressing internal tearing mode activity and thus reduce the radial plasma transport. The coherent electrostatic fluctuations may be possibly attributable to the radial plasma transport accompanied by the internal tearing mode activity. Studies show that the smaller electrostatic fluctuations at a frequency of 10 kHz may be mainly ascribed to the suppressed MHD activity, possibly due to the formation of an internal transport barrier and flow shear in the edge region. It is speculated that the change of mode region resulting from the mode coupling/transform, excited by the modified current profile by LHCD, could also provide some contribution to the MHD reduction.

High power density, phased antenna operation can often be limited by antenna voltage handling and/or impurity and density production. Using a pair of two-strap antennas for comparison, the performance of a four-strap, fast wave antenna is assessed for a variety of configurations and antenna phases in Alcator C-Mod. To obtain robust voltage handling, the antenna was reconfigured to eliminate regions where the RF E-field is parallel to B or to reduce the RF E-field to <1.0 MV m⁻¹. To limit impurity generation, BN tiles were used to replace the original Mo tiles, a BN clad septum was inserted to limit field line connection length, and BN–metal interfaces were shielded from the plasma. With these modifications, the antenna heating efficiency and impurity generation are nearly identical to those of the two-strap antennas and independent of antenna phase in L-mode discharges. This antenna has achieved 11 MW m⁻² in both heating and current drive phases in both L-mode and H-mode discharges.

Dynamic plasma screening effects on the electron capture process in kappa-Maxwellian plasmas are investigated using the semiclassical version of the Bohr–Lindhard model. The interaction potential and screened electron capture radius are obtained by considering the longitudinal component of the plasma dielectric function. The semiclassical electron capture probability is also obtained as a function of the impact parameter, Debye length, projectile velocity, and spectral index. It is found that the dynamic screening effects on the electron capture probability are more significant for low projectile energies. The maximum position of the scaled electron capture probability approaches the target nucleus with increasing projectile energy. The dynamic screening effect is also found to decrease with increasing spectral index.