Table of contents

In this paper the transverse and longitudinal dielectric tensor elements are evaluated for radio-frequency waves in an axisymmetric tokamak with circular magnetic surfaces, without the smallness assumption of the inverse aspect ratio and poloidal magnetic field. A collisionless plasma model is considered. The Vlasov equation is solved separately for untrapped and trapped particles as a boundary-value problem. The cyclotron and bounce resonances are accounted. The coordinate system with the `straight' magnetic field lines was used. The separate contributions of untrapped and trapped particles to the dielectric tensor components are expressed by the summation of bounce resonant terms, which include the double integration in velocity space, the resonant denominators, the phase coefficients, the standard elementary and elliptic functions. The permittivity elements presented in the paper are suitable to analyse the spatial structure of the electromagnetic fields and their interaction with charged particles (e.g. during the plasma heating and current drive generation) in the frequency range of Alfvén, fast magnetosonic, ion-cyclotron and lower hybrid waves, for both the low and large aspect ratio tokamaks.

The edge parameters of electron cyclotron resonance heated plasmas in the TJ-II stellarator are reported. Data from atomic beam diagnostics and electrical probes have been used for edge and scrape-off layer characterization. Scans in heating power and plasma density for H and He plasmas have been performed, for a given magnetic configuration. A linear increase of the diffusion coefficient at the last-closed magnetic surface with the ratio of injected power to plasma density and a similar value of that parameter for the two atomic species investigated were obtained. Global particle confinement times between 3 and 15 ms have been deduced, and transition to an enhanced confinement mode in H plasmas has been observed under some conditions. The role of high-energy particle losses, due to trapping into the relatively high magnetic ripple, in the global energy balance of TJ-II plasmas is addressed.

Significant features, consisting of flats and humps, have been observed in impurity-ion ultraviolet line-emission profiles measured on the TJ-II flexible heliac, thereby providing evidence for the existence of topological structures in the plasma interior. The data for this study were collected using a fast spectroscopic scanning system with good spatial resolution capabilities; they were analysed using an in-house developed pattern recognition algorithm. This algorithm is capable of separating effects due to plasma fluctuations and noise from those caused by two-dimensional structures. In the paper we describe the data collection system and the pattern recognition algorithm and we analyse plasma radiation profiles from standard TJ-II configurations to demonstrate that this pattern recognition algorithm can identify real features in these. Next, we analyse profile data from a configuration scan made on the TJ-II and finally we report on the features found, their typical widths and symmetry, as well as on the time evolution and correlation with the electron density.

The statistical theory of strong turbulence in inhomogeneous plasmas is developed for the cases where fluctuations with different scale lengths coexist. Nonlinear interactions in the same kind of fluctuations as well as nonlinear interplay between different classes of fluctuations are kept in the analysis. Nonlinear interactions are modelled as turbulent drag, nonlinear noise and nonlinear drive, and a set of Langevin equations is formulated. With the help of an Ansatz of a large number of degrees of freedom with positive Lyapunov number, Langevin equations are solved and the fluctuation dissipation theorem in the presence of strong plasma turbulence has been derived. A case where two driving mechanisms (one for the micro mode and the other for semi-micro mode) coexist is investigated. It is found that there are several states of fluctuations: in one state, the micro mode is excited and the semi-micro mode is quenched; in the other state, the semi-micro mode is excited, and the micro mode remains at finite but at a suppressed level. A new type of turbulence transition is obtained, and a cusp-type catastrophe is revealed. A phase diagram is drawn for turbulence which is composed of multiple classes of fluctuations. The influence of the inhomogeneous global radial electric field is discussed. A new insight is given for the physics of the internal transport barrier. Finally, the non-local heat transport due to the long-wavelength fluctuations, which are noise-pumped by shorter-wavelength fluctuations, is analysed and its impact on transient transport problems is discussed.

E_r×B flow shear is simulated with a fully kinetic five-dimensional neoclassical Monte Carlo simulation both for JET and ASDEX Upgrade. Here, E_r is the radial electric field and B is the magnetic field. It is shown that high enough shear for turbulence suppression can be driven at low (L) to high (H) transition conditions without taking into account anomalous processes in E_r shear formation. For typical plasma parameters, at a certain edge temperature, shear is weaker in JET than in ASDEX Upgrade, thus requiring a higher edge temperature for L-H transition as observed also in experiments. However, although the simulation is carried out at experimentally observed L-H transition temperatures of each device, shear is still weaker in JET, which proposes that the critical shear in JET should be lower than in ASDEX Upgrade. The parametric dependence of the shear on temperature, density and magnetic field is investigated and the effects of density and temperature gradients, plasma current and the direction of the ∇B drift on the shear are discussed.

Two parametric relations are proposed for calculating the level energies of an electron bound in a screened Coulomb potential in a plasma. The first relation is between the energies of levels which have the same ℓ quantum number. The second relation is able to represent the bound-state energies for 1s, 2p, 3d...levels as a function of the screening parameter to a good degree of accuracy. These two relations taken together can give the energies of any level up to and including n = 8, and estimated energies for n = 9 and 10 for any value of n_e and T_e. These are relevant for at least three topics in plasma physics. The application of these relations for the calculation of the partition function of plasmas is discussed.

The ripple-averaged kinetic theory of neoclassical transport in multiple-helicity stellarators is presented anew, using a formulation which ameliorates several shortcomings of the conventional approach. In particular, during the averaging procedure the usual simplifying assumptions of symmetric local ripples and `small' rotational transform per field period are avoided through an appropriate choice of coordinate system and local model for the magnetic field strength; averages are truly performed along a field line and not along the toroidal-angle coordinate, as is common. Phase space divides naturally into three portions in which particles are (1) locally trapped, (2) locally reflected but not trapped, and (3) locally passing; the second of these is lacking in the conventional description. As an example of the theory's many possible applications, the monoenergetic radial transport coefficient in the asymptotic 1/ν regime is derived and radial profiles of this quantity are determined for the Large Helical Device and Wendelstein 7-X. The results are compared with those obtained using the conventional approach; significant differences are found in the case of Wendelstein 7-X and verified numerically using the Drift Kinetic Equation Solver (DKES).

A model of neoclassical tearing modes (NTMs) allowing for a finite width of the transition layer near the island separatrix, where perturbed plasma parameters vary significantly, is proposed. In contrast to traditional models of NTMs, this model includes the parameter ρ_i/w properly, where ρ_i is the ion Larmor radius, and w is the magnetic island width. It is shown that both the polarization current and bootstrap current effects on these modes prove to be weakened compared with those predicted by traditional theories of NTMs. The competition of these effects results in a critical beta for NTM onset which is lower than that usually used for interpretation of experimental observations and predictions for reactor-grade tokamaks.

The up-down potential asymmetry in the toroidal magnetic plasma is caused by the separation of ions and electrons due to the toroidicity of the confining magnetic field and/or due to the effect of flow along the vertical magnetic field. In the SINP tokamak an interesting phenomenon of inversion of up-down asymmetry during a discharge has been observed experimentally. The origin of this up-down potential asymmetry and its inversion is attributed to two oppositely directed vertical velocities, causing the separation of charged species.