The propagation and dispersion relation of a TM mode in a plasma duct in a slab geometry has recently been studied by Parashar and Lalita [J. Plasma Phys.55, 387 (1996)]. It is the purpose of the present note to show that their dispersion relation is incorrect.

A synthesized formulation of classical, neoclassical and anomalous transport in toroidal confinement systems with electromagnetic fluctuations and large mean flows is presented. The positive-definite entropy production rate and the conjugate flux–force pairs are rigorously defined for each transport process. The Onsager symmetries of the classical and neoclassical transport matrices are derived from the self-adjointness of the linearized collision operator. The linear gyrokinetic equation with given electromagnetic fluctuations determines the anomalous fluxes with the quasilinear anomalous transport matrix, which satisfies the Onsager symmetry.

We investigate the existence of MHD leaky waves in compressible and layered plasmas. We consider perturbations of complex frequency in a slab model with three layers. We develop a general method that includes the ‘cubic modes’ as well as other kinds of leaky waves, and allows us to derive many results in closed form. There are several physical mechanisms that can produce leakage. We give two numerical examples to exhibit the different behaviours that can arise. Finally we comment on the connection of the present results with those obtained by other authors, and correct some errors.

It is shown that particle trapping plays an important role in the appearance of anomalous or strange diffusion in turbulent fields, mainly by inducing a non-Gaussian statistics of the stochastic displacements. Trapping processes are responsible for the important deviation observed between the traditional prediction of Bohm scaling for diffusion in low-frequency turbulence and the numerically checked prediction by Isichenko. Also, several theoretical models are proposed or reviewed.

The problem of direct excitation of the shear Alfvén wave by antennas in the boundary of a fusion plasma is considered. In the plasma scrape-off layer the physics of this wave is determined by finite electron inertia. Expressions for the wave electric and magnetic field are derived without any assumption on the smallness of the ratio of frequency to ion cyclotron frequency. It is shown that the shear Alfvén wave propagates as a guided beam along the steady magnetic field over a wide range of frequencies below the ion cyclotron frequency, and is predominantly excited by current elements parallel to the steady magnetic field. A simple transmission-line analogy suggests that guidance of the Alfvén wave is also expected in the presence of strong plasma inhomogeneity.

The symmetry group of the Vlasov–Fokker–Planck equation (VFPE) is constructed. The effects of the Poisson equation on this group is studied, and different types of similarity solutions of the whole system of equations (VFPE+Poisson equation) are obtained.

The Hamiltonian dynamics of a two-degree-of-freedom system is shown to mimic the structure of an incompressible fluid if the fluid streamlines are considered instead of the pathlines used by many authors. This approach is formally equivalent to the determination of magnetic field lines, which satisfy the same mathematical equations. Turbulence in this case is seen as Hamiltonian chaotic dynamics perturbed by time, which plays the role of the codimension parameter of such chaos. Any spatial Lie symmetry leads to a laminar flow, whereas stationary flow could be considered chaotic but not turbulent. The transition from laminar to turbulent flow is associated with the destruction of KAM trajectories produced by time evolution.

Hamiltonian vortices and reconnection in magnetized plasmas are investigated analytically and numerically using a two-fluid model. The equations are written in the Lagrangian form of three fields that are advected with different velocities. This system can be considered as a generalization and extension of the two-dimensional Euler equation for an ordinary fluid. It is pointed out that these equations allow solutions in the form of singular current-vortex filaments, drift-Alfvén vortices and magnetic islands, and admit collisionless magnetic reconnection where magnetic flux is converted into electron momentum and ion vorticity.

An explosive instability of the ion-temperature-gradient (ITG)-driven modes (ηi modes) near the boundary of marginal stability is considered as a driving mechanism for subcritical turbulence. It is shown that boundedness of the wave interaction region leads to saturation of the instability. The possibility of coherent soliton-like structure formation in both slab and toroidal geometries is demonstrated by numerical simulation. An analytical soliton solution is found in some special cases.

Two-field models for Rayleigh–Taylor modes are investigated. The changes due to external velocity shear (without flow curvature) are reviewed, and the influences of the various terms in the models are discussed. It is shown that, in principle, velocity shear in combination with dissipation leads to the suppression of linear Rayleigh–Taylor modes in the long-time limit. The long-wavelength modes first seem to be damped; however, later they show an algebraic growth in time, before ultimately the exponential viscous damping wins. In general, the amplitudes become very large, and therefore the often-quoted stability of Rayleigh–Taylor modes in the presence of velocity shear is more a mathematical artefact than a real physical process. Vortices, on the other hand, can lead (together with velocity shear) to a quite different dynamical behaviour. Because of a locking of the wave vectors, pronounced oscillations appear. This effect is demonstrated by a simple model calculation. When vortices and velocity shear are generated from linear instability, the resulting oscillatory state finally becomes unstable with respect to Rayleigh–Taylor modes on a long time scale (‘secondary instability’).

Transmission, reflection and absorption of a transverse electromagnetic wave by a thermal plasma slab of finite width are investigated theoretically. By solving the Maxwell–Boltzmann equations using a mode-analysis method under appropriate boundary conditions, the coefficients of transmission and reflection of the electromagnetic wave and the absorption rate by plasma electrons are obtained as Fourier series. We discuss the relevant physics of the results.

E×B guiding-centre (GC) motion in a special configuration of three low-frequency electrostatic waves can be considered as a paradigmatic Hamiltonian system for studying adiabatic motion and separatrix crossings. A peculiarity of this system is that a single initial condition gives rise to two stroboscopic phase-space trajectories. According to the classical Hamiltonian theory, the proportion of points on the stroboscopic trajectories is a function of the time evolution of the surfaces enclosed by the separatrices in the phase space. This behaviour is qualitatively observed in test-particle numerical experiments. The ability of numerical integration methods like the ‘classical’ fourth-order Runge–Kutta integration scheme or a third-order symplectic integrator to reproduce the statistics is analysed.