A study is made of the stability of ion-acoustic solitons in a magnetized non-thermal plasma with warm ions. A Zakharov–Kuznetsov equation (KdV–ZK, or Korteweg–de Vries equation in three dimensions) is derived. This equation admits solutions representing compressive and rarefactive solitons propagating in any direction oblique to the external magnetic field. When the coefficient of the nonlinear term of this equation vanishes, the nonlinear behaviour of ion acoustic waves is described by a modified KdV–ZK (MKdV–ZK) equation, which is also derived. This equation also has solitary-wave solutions. Finally, the three-dimensional stability of these solitons is investigated by the small-k perturbation expansion method of Rowlands and Infeld.

Transport equations are investigated for a cylindrical plasma in the presence of electrostatic fluctuations. In a weakly turbulent regime, the transport matrices that relate the anomalous particle and heat fluxes and the parallel current to the thermodynamical forces are determined by employing drift-kinetic and gyrokinetic orderings for the electrons and ions. The calculation is based on the kinetic equations for the ensemble-averaged and fluctuating distribution functions. The crucial difference with previous works is the inclusion of an extra term in the drift-kinetic equation for the fluctuating electron distribution function. This extra term, which arises from the ensemble-averaged first-order (in a Larmor radius expansion) electron distribution function, leads to the Ware pinch components of the particle and heat fluxes and a correction to the Ohmic current. Furthermore, Shaing's ansatz, which was introduced in the synthetic theory of anomalous and neoclassical transport, is shown to be connected with this extra term in the context of a turbulent plasma, and the physical meaning and the validity of this ansatz are revealed. In drift-wave turbulence, the transport matrices, expressed in an implicit form by considering the frequency of fluctuations as a parameter, are rewritten in an explicit form by determining its frequency through the dispersion relation. The Onsager symmetry is shown to be broken for this explicit form of anomalous transport matrix.

A synthetic theory of neoclassical and anomalous transport in a weakly turbulent tokamak plasma is presented. The neoclassical effect on the anomalous particle and heat fluxes and the parallel current in the presence of electrostatic fluctuations is investigated using the kinetic equations for the ensemble-averaged and fluctuating distribution functions. It is found in the drift-kinetic and gyro-kinetic orderings for electrons and ions that the Ware pinch components of the anomalous particle and heat fluxes and the parallel current are sensitive to the toroidal effect, although the other components of particle and heat fluxes are little influenced. In the banana regime, these Ware pinch components and the anomalous parallel current are shown to be significantly reduced when the condition [mid ](ω − ωE)/ k∥ve[mid ] < (2ε)1/2 is satisfied, where ω and k∥ are the frequency and the parallel wavenumber of fluctuations, ωE is the drift frequency due to the radial electric field, ve is the thermal velocity for electrons and ε is the inverse aspect ratio. Interpolated formulae that can be used throughout all collisonality regimes are also obtained for the Ware pinch components and the anomalous parallel current.

The Zakharov-Kuznetsov equation governs the behaviour of weakly non-linear ion-acoustic waves in a plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic field. We consider the more realistic situation in which the electrons are non-isothermal. With an appropriate modified form of the electron number density proposed by Schamel, we show that the reductive perturbation procedure leads to a modified Zakharov–Kuznetsov (mZK) equation. The stability of plane-periodic and solitary travelling-wave solutions of the mZK equation to two-dimensional long-wavelength perturbations is investigated using the method of Rowlands and Infeld.

The concept of magnetic entropy, the entropy pertaining to a magnetic configuration, is introduced and illustrated through its application to the description of the magnetic states assumed preferentially by a tokamak and of the transition between them. The magnetic equilibria associated with stationary magnetic entropy admit a bifurcation, and a new state can arise that can be attained spontaneously with an increase in the magnetic entropy. The thermodynamic relations between entropy production, heat transport and plasma energy allow one to express quantitatively the modifications of these quantities generated by the magnetic transition to the new state and to identify it with the L–H transition. The power and temperature thresholds of the transition are expressed in terms of the confinement time of the L state, and definite scalings are derived that compare favourably with observations. The theory implies the hysteresis and the upper density limit of the H state.

The correspondence between the forced magnetic reconnection induced by perturbing the boundary of the simple Taylor model and the surface-wave-induced magnetic reconnection given by Alfvén resonance theory is pointed out explicitly by showing that the theory of forced magnetic reconnection is actually embedded in the Alfvén resonance theory. The advantages of viewing the forced reconnection as surface-wave-induced reconnection are briefly discussed in the context of the formation of small-scale structures at the magnetospheric boundary and solar coronal heating.

Streaming instabilities are studied for an inhomogeneous distribution of dust particles. Such situations are characteristic of stellar neighbourhoods, where the star's plasma wind ploughs through a surrounding dust shell. This should result in the acceleration of dust particles at the expense of the plasma momentum, which may throw light on certain dynamical features of the dust cloud vis-à-vis the plasma dynamical features. Streaming instabilities are a first step towards such a study. Various cases of the relative magnitudes of the plasma and dust velocities are analysed, and the role of inhomogeneities is highlighted.