This paper uses incompressible visco-resistive MHD to study the propagation of linear resonant waves in an inhomogeneous plasma. The background density and magnetic field are assumed to depend only on one spartial Cartesian coordinate, and the magnetic field is taken to be unidirectional and perpendicular to the direction of inhomogeneity. The equation that governs the component of the velocity normal to the plane formed by the direction of the inhomogeneity and the magnetic field is derived under the assumption that the coefficients of viscosity and resistivity are sufficiently small that dissipation of energy is confined to a narrow dissipative layer. The solutions to this equation are obtained in the form of decaying normal surface modes with wavelengths much larger than the characteristic scale of the inhomogeneity. The effect of non-stationarity inside the dissipative layer is taken into account, and valid solutions are found even when the ratio of the thickness of the dissipative layer to the inhomogeneity length scale is of the order of or smaller than the ratio of the inhoinogeneity length scale to the wavelength. These solutions are the generalization of the solutions obtained by Mok and Einaudi, which are only valid when the first ratio is much larger than the second. The rate of wave damping is shown to be independent of the values of the viscosity and the resistivity. However, the behaviour of the solutions in the dissipative layer depends strongly on the viscosity and the resistivity. In the case that the effect of dissipation dominates the effect of non-stationarity, the solutions behave in the dissipative layer as found by Mok and Einaudi. When the effect of dissipation is steadily decreased in comparison with the effect of nonstationarity, the solutions become more and more oscillatory, and their amplitudes grow very rapidly in the dissipative layer. Eventually, when nonstationarity dominates dissipation, the amplitudes of the solutions become so large in the dissipative layer in comparison with those outside the dissipative layer that practically all the energy of the perturbations is concentrated in the dissipative layer.

The stability of an MHD tangential discontinuity is studied in an incompressible plasma where viscosity is taken into account at one side of the discontinuity. When the shear velocity is smaller than the threshold value for the onset of the Kelvin-Helmholtz (KH) instability, two surface waves can propagate along the discontinuity. There is a critical value for the shear velocity, which is smaller than the threshold value for the onset of the KH instability. When the shear velocity is smaller than the critical value, the two surface waves propagate in Opposite directions. When the shear velocity is larger than the critical velocity, the two waves propagate in the same direction, and the wave with smaller phase velocity is a negative-energy wave. Viscosity causes this negative-energy wave to be unstable, and the instability increment is proportional to the viscosity coefficient.

A composite interstellar model consisting of stars and optically thin radiating plasma is considered in order to investigate the thermal instability arising from possible radiation and other heat-loss mechanisms. The stellar dynamics is governed by the Vlasov equation, while the gas is supposed to be a hydromagnetic plasma, described by the MHD equations, with a density- and temperature-dependent heat-loss function. It is shown that while with cold stars the system is in general unstable irrespective of thermal effects of the plasma, with warm stars having a Maxwellian distribution the thermal plasma considerably influences the stability of the composite system. It is also shown that the otherwise stable composite (with warm stars) configuration may become unstable in the presence of a radiating plasma because of coupling between the heat-loss mechanisms and stellar populations.

A general treatment of ion resonance instability for a non-neutral plasma column is performed using a macroscopic cold-fluid-Maxwell model. The azimuthal motion of the plasma components has an important influence on the behaviour of the instability. When the electrons are in slow rotational equilibrium, the instability occurs in both slow and fast ion rotational equilibrium. However, there is stability when the electrons are in fast rotational equilibrium except that the l = 1 mode becomes unstable and independent of plasma rotation. The kink (l = 1) mode only occurs when the plasma column boundary exceeds a certain threshold value that depends on the ratio of the plasma frequency to the cyclotron frequency.

The study of the diffusion of magnetic field lines is based on a stochastic model with a Hamiltonian structure. A Liouville equation can then be associated with Hamilton's equations representing the magnetic line. This allows a statistical description of all observable quantities. In particular, the mean-square displacements (MSD) of a field line and the mean-square relative distance (MSRD) of two lines are considered. Equations for these quantities are obtained by applying the direct-interaction approximation (DIA) to the stochastic Liouville equation. The running diffusion coefficient is derived from the MSD equation. The status of the temporal and spatial Markovian approximations in the DIA is discussed. The MSRD's evolution establishes the existence of a clumping effect between two lines, which eventually leads to gyrotropization of the system. A clump life length is defined. In both cases the equations of motion are shown to be identical to the equations obtained within the Langevin treatment of magnetic fluctuations. This shows the equivalence between the DIA and the Corrsin approximation performed in the Langevin approach.

Lie symmetries, conservation laws, and Lagrangian and Hamiltonian formulations of the triple degenerate, derivative nonlinear Schrödinger (TDNLS) equations for weakly nonlinear dispersive, magnetohydrodynamic (MHD) waves are derived. The equations describe how Alfvén waves propagating parallel to the background magnetic field B interact with the magneto-acoustic modes near the triple umbilic point where the fast, slow and Alfvén mode phase speeds coincide. The Lie point symmetries are used to derive classical similarity solutions of the equations. In particular, the similarity solutions corresponding to time translation, space translation and rotational invariance symmetries are reduced to quadrature. The dispersionless TDNLS system is of hydrodynamic type, and has three families of characteristics analogous to the slow, intermediate and fast modes of MilD. The Riemann invariants corresponding to each of these families are obtained in closed analytic form. Examples of solitary wave and periodic travelling wave solutions are investigated by plotting the contours of the Hamiltonian H(v, w) in the (v, w) phase plane, where the canonical variables v and w correspond to the normalized transverse magnetic field perturbations. An analysis of the prolongation Lie algebra is carried out in order to investigate the integrability of the equations.

A numerical code that computes stationary radial electric fields E0r induced by ponderomotive forces of radio-frequency waves is developed. The computed value of E0r is typically several hundred volts per centimetre when the wave frequency is 1 % lower or higher than the ion-cyclotron frequency. This value of E0r suggests that the ponderomotively induced electric field would be an effective bias in tokamaks. Numerical data are presented to illustrate the properties of this bias field.