Stationary flows with an ignorable coordinate are analysed and the differential equation for the only independent current function of the problem is obtained for the polytropic, incompressible and adiabatic cases. The possibility of confinement for the stationary symmetric plasma fluxes is then investigated and the confinement conditions are given. Some examples are solved for the particular case of helical symmetry; for general flows it is possible to construct magnetically confined plasma columns only with cylindrical shape; whereas if the plasma velocity has the direction of the ignorable coordinate, we show that it is possible to construct magnetically confined plasma columns with helical shape and plasma flux along the helices.

Plasma-wave instability caused entirely by an external large-scale electric field E0 is considered for the pure electron Bernstein mode. It is assumed for the angle α between the wave vector k and the normal n to the direction of the external magnetic field B0 that the relation α≈tanα[Lt ]1 is fulfilled. The quasistatic time variation of the field E0, which is parallel to B0, provides the possibility of realizing the direct initiation (by the large-scale field E0) mechanism for the development of instability. An expression for the growth rate is obtained for the case when the external electric field E0 together with Landau damping and pair Coulomb collisions are taken into account in a modified dispersion relation (MDR). This expression is correct in the framework of linear theory for the frequency ranges typical of electron cyclotron waves and Bernstein modes. The influence of the electric field in the MDR is taken into account through the method of Brinca and Dysthe. A numerical analysis of obtained instability is performed for specific values of the plasma parameters.

The nonlinear mechanism for kinetic-Alfvén-wave (KAW) excitation by upper-hybrid waves (UHWs) is discussed. Taking into account perpendicular dispersion of KAWs, caused by effects of finite ion Larmor radius and electron inertia, we examine a new channel for UHW decay, in which a pump UHW decays into another UHW and an ultralow-frequency wave, KAW: UHW→KAW+UHW. A nonlinear dispersion relation is derived, and the growth rate of the parametric decay instability is calculated for a pump UHW propagating at an arbitrary angle to the background magnetic field. We find that the resulting KAWs often have a two-peaked spectrum with different perpendicular dispersions. Using satellite observations, the analytical results are applied to show that the considered process represents an effective mechanism for KAW generation and the consequent spreading of the UHW spectrum in the Earth's magnetosphere and solar corona.

The dynamic equation and coupling coefficient of the three-wave interaction among kinetic Alfvén waves (KAWs) are derived by use of plasma kinetic theory. Linear and nonlinear effects of finite ion Larmor radius are kept for arbitrary value of the ‘kinetic variable’ κ=k⊥ρi. The parametric decay KAW→KAW+KAWis investigated and the threshold amplitude for decay instability in a Maxwellian plasma is calculated. The growth rate of decay instability varies as k2⊥ in both limits κ2[Lt ]1 and κ2[Gt ]1. The main tendency of KAWs is towards nonlinear destabilization at very low wave amplitudes Bk/B0[lsim ]10−3. Two applications concerning KAW dynamics in the magnetosphere and in the solar corona show that three-wave resonant interaction among KAWs may be responsible for the turbulent character of their behaviour, often observed in space plasmas.

The nonlinear dynamics of kinetic-Alfvén–wave (KAW) turbulence is studied. Weak KAW turbulence induced by three-wave interaction among parallel-propagating KAWs has a direct energy cascade in the wavenumber domain ks⊥>ρ−1i and an inverse cascade in the domain ks⊥<ρ−1i, resulting in Kolmogorov-type spectra, Wk∼(kz) −1/2(k⊥)−p, with exponents p=4 and p=3.5 respectively. The interaction including antiparallel-propagating KAWs, usually most effective, results in an inverse energy cascade over the whole k⊥ range and p=2 (at k⊥<ρ−1i) and p=3.5 (for k⊥>ρ−1i) spectra. Three applications concerning KAW turbulence in flaring loops, in the Earth's magnetosphere and in tokamaks are considered. It is suggested that turbulent KAW spectra are common in space plasmas.

A nonlinear thermal instability in a layer of electrically conducting fluid in the presence of a magnetic field is discussed. Steady-state bifurcation results in the formation of patterns: rolls, squares and hexagons. The stability of various patterns is also investigated. It is found that in the absence of a magnetic field only rolls are stable, but when the magnetic field strength exceeds a certain finite value, squares and hexagons also become stable.

We study the effect of charge fluctuations on the propagation of adiabatic linear and nonlinear dust-acoustic waves by considering the electrons and ions to be in Boltzmann equilibria, and the dust grains to satisfy the fluid equations with full adiabatic equation of state. Linear dust-acoustic waves are damped owing to the dust-charge fluctuations, and the damping rate decreases with increasing adiabatic dust pressure. Nonlinear dust-acoustic waves are governed by the set of coupled Boussinesq-like and dust-charge perturbation equations. It is shown that for unidirectional propagation, the Boussinesq-like equation reduces to usual Korteweg–de Vries (KdV) equation. At early times, the localized solutions of the KdV equation are damped owing to the dust-charge perturbations. The soliton amplitude decreases with increasing adiabatic dust plasma pressure and increases with Mach number. Soliton solutions are found only in the supersonic regime.

The nonlinear propagation of coupled Langmuir and dust-acoustic waves in a multi-component dusty plasma is considered. The coupled mode propagation is described by a Schrödinger–Boussinesq system, which reduces to the Schrödinger–KdV system for unidirectional wave propagation. For stationary propagation, the coupled waves are governed by a generic Hamiltonian that is integrable in both sub- and the supersonic regimes of Mach number. Depending on the parameter regimes, exact analytical solutions for the coupled waves having single-, double- and triple-hump structures for the Langmuir field intensity are obtained. The exact governing equations for large-amplitude waves are also derived, and are solved approximately. The existence conditions for large-amplitude localized solutions in the quasineutral limit are discussed.

A numerical investigation of the evolution of localized disturbances in the form of solitary waves is performed for the full system of equations describing planar waves in a cold collisionless quasineutral plasma. It is shown that, for a wide range of angles of inclination of the magnetic field vector to the direction of wave propagation, such a kind of initial disturbance never results in a wave propagating steadily, but leads to decay due to radiation of periodic waves. These results confirm the recent theoretical conclusion of Il'ichev [J. Plasma Phys.55, 181–194 (1996)] about the non-existence of solitary waves in a cold plasma for the range of angles of inclination in question.

The dissipative drift-wave instability is considered in a non-uniform weakly ionized magnetoplasma when additional ionization is caused by electrons moving in the field of the wave. It is demonstrated that the instability can be considerably enhanced due to the wave-induced perturbations of the ionization/recombination balance and may therefore strongly affect transport properties of the plasma.

The classical transport coefficients provide an accurate description of transport processes in collision-dominated plasmas. These transport coefficients are used in a cylindrically symmetric, electrically driven, steady-state magnetohydrodynamic (MHD) model with flow and an energy equation to study the effects of transport processes on MHD equilibria. The transport coefficients, which are functions of number density, temperature and magnetic field strength, are computed self-consistently as functions of radius R. The model has plasma-confining solutions characterized by the existence of an inner region of plasma with values of temperature, pressure and current density that are orders of magnitude larger than in the surrounding, outer region of plasma that extends outward to the boundary of the cylinder at R=a. The inner and outer regions are separated by a boundary layer that is an electric-dipole layer in which the relative charge separation is localized, and in which the radial electric field, temperature, pressure and axial current density vary rapidly. By analogy with laboratory fusion plasmas in confinement devices, the plasma in the inner region is confined plasma, and the plasma in the outer region is unconfined plasma. The solutions studied demonstrate that the thermoelectric current density, driven by the temperature gradient, can make the main contribution to the current density, and that the thermoelectric component of the electron heat flux, driven by an effective electric field, can make a large contribution to the total heat flux. These solutions also demonstrate that the electron pressure gradient and Hall terms in Ohm's law can make dominant contributions to the radial electric field. These results indicate that the common practice of neglecting thermoelectric effects and the Hall and electron pressure-gradient terms in Ohm's law is not always justified, and can lead to large errors. The model has three, intrinsic, universal values of β at which qualitative changes in the solutions occur. These values are universal in that they only depend on the ion charge number and the electron-to-ion mass ratio. The first such value of β (about 3.2% for a hydrogen plasma), when crossed, signals a change in sign of the radial gradient of the number density, and must be exceeded in order that a plasma-confining solution exist for a plasma with no flow. The second such value of β (about 10.4% for a hydrogen plasma), when crossed, signals a change in sign of the poloidal current density. Some of the solutions presented exhibit this current reversal. The third such value of β is about 2.67 for a hydrogen plasma. When β is greater than or equal to this value, the thermoelectric, effective electric-field-driven component of the electron heat flux cancels 50% or more of the temperature-gradient-driven ion heat flux. If appropriate boundary conditions are given on the axis R=0 of the cylinder, the equilibrium is uniquely determined. Analytical evidence is presented that, together with earlier work, strongly suggests that if appropriate boundary conditions are enforced at the outer boundary R=a then the equilibrium exhibits a bifurcation into two states, one of which exhibits plasma confinement and carries a larger axial current than the other state, which is close to global thermodynamic equilibrium, and so is not plasma-confining. Exact expressions for the two values of the axial current in the bifurcation are presented. Whether or not a bifurcation can occur is determined by the values of a critical electric field determined by the boundary conditions at R=a, and the constant driving electric field, which is specified. An exact expression for the critical electric field is presented. Although the ranges of the physical quantities computed by the model are a subset of those describing fusion plasmas in tokamaks, the model may be applied to any two-component, electron–ion, collision-dominated plasma for which the ion cyclotron frequency is much larger than the ion–ion Coulomb collision frequency, such as the plasma in magnetic flux tubes in the solar interior, photosphere, lower transition region, and possibly the upper transition region and lower corona.

Starting from a more general formalism due to Lamalle [Plasma Phys. Contr. Fusion32, 1409 (1997)], the dielectric response of a tokamak plasma to a radiofrequency (RF) perturbation is evaluated using a simple decorrelation model, assuming the poloidal cross-section of the magnetic surfaces to be circular and retaining leading-order terms in the drift parameter. Toroidicity, poloidal magnetic field and particle trapping are included in the model. Constants of the motion are used as independent variables. A semi-analytical method is adopted to evaluate the bounce spectrum of the dielectric response (needed to solve the wave equation) and the associated RF diffusion operator (required for solving the Fokker–Planck equation). The accent is on a study of this bounce spectrum. In particular, the link between the discrete bounce spectrum and the continuous bounce integral is highlighted. The critical parameter for the global justification of the replacement of the sum on the bounce spectrum by a bounce average is the relative magnitude of the decorrelation and bounce times. That for the local justification is the second derivative of the periodic part of the relative wave–particle phase. Numerical examples are provided to give a qualitative feeling for the justification of this substitution. The relation between the results presented here and those based on Hamiltonian models or on a simplified geometry is discussed.