This paper considers Alfvén waves in a radially stratified medium where all background quantities, namely mass density, magnetic field strength and mean flow velocity, depend only on the distance from the centre, the latter two being assumed to lie in the radial direction. It is shown that the radial dependence of Alfvén waves is the same for two cases: (i) when the velocity and magnetic field perturbations are along parallels, in the one-dimensional case of only radial and time dependence; (ii) in the three-dimensional case with dependence on all three spherical coordinates and time, for velocity and magnetic field perturbations with components along parallels and meridians, represented by the radial components of the vorticity and electric current respectively. Elimination between these equations leads to the convected Alfvén-wave equation in the case of uniform flow, and an equation with an additional term in the case of non-uniform flow with mean flow velocity a linear function of distance. The latter case, namely that of non-uniform flow with flow velocity increasing linearly with distance, is analysed in detail; conservation of mass flux requires the mass density to decay as the inverse cube of the distance. The Alfvén-wave equation has a critical layer where the flow velocity equals the Alfvén speed, leading to three sets of two solutions, namely below, above and across the critical layer. The latter is used to specify the wave behaviour in the vicinity of the critical layer, where local partial transmission occurs. The problem has two dimensionless parameters: the frequency and the initial Alfvén number. It is shown, by plotting the wave fields relative to the critical layer, that these two dimensionless parameters appear in a single combination. This simplifies the plotting of the wave fields for several combinations of physical conditions. It is shown in the Appendix that the formulation of the equations of MHD in the original Elsässer (1956) form, often used in the recent literature, does not apply if the background mass density is non-uniform on the scale of a wavelength. The present theory, based on exact solutions of the Alfvén-wave equation for a inhomogeneous moving medium, is unrestricted as to the relative magnitude of the local wavelength and scale of change of properties of the background medium. The present theory shows that the rate-of-decay of wave amplitude is strongly dependent on wave frequency beyond the critical layer, i.e. the process of change with distance of the spectrum of Alfvén waves in the solar wind starts at the critical layer.

We investigate a three-wave decay interaction involving a surface wave in which a bulk electromagnetic plasma wave decays into another bulk electromagnetic plasma wave and a surface polariton. It is shown that a p-polarized light wave transmitted from vacuum into a plasma at a particular angle of incidence can propagate as a bulk electromagnetic plasma wave without attenuation. The nonlinear boundary conditions for the surface wave are formulated in terms of the surface charge and the volume current, taking full account of the rippling of the free boundary. The coupled-mode equations are derived and solved in the parametric approximation to obtain the threshold and the growth rate. We assess the relative strength of the kinematic and the dynamic nonlinearities in the parametric interaction.

The parametric interaction of an upper-hybrid pump wave with kinetic Alfvén and electromagnetic waves that propagate in parallel and perpendicular directions to the ambient magnetic field is investigated on the basis of two-fluid magnetohydrodynamics. A nonlinear dispersion relation describing three-wave interaction and instability growth rates are found. The theoretical results are used for the interpretation of satellite observations in the magnetospheric plasma. It is shown that as a result of the decay of an upper-hybrid wave, electromagnetic waves propagating in both parallel and perpendicular directions to the ambient magnetic field are generated. The instability growth rate is much higher in the case of left-polarized electromagnetic wave generation than in the case of ordinary electromagnetic wave generation. The nonlinear parametric processes studied here could also take place during powerful bursts on the Sun, and in the magnetosphere of Jupiter.

Beam instabilities in the strongly magnetized electron–positron plasma of a pulsar magnetosphere are considered. We analyse the resonance conditions and estimate the growth rates of the Cherenkov and cyclotron instabilities of the ordinary (O), extraordinary (X) and Alfvén modes in two limiting regimes: kinetic and hydrodynamic. The importance of the different instabilities as a source of coherent pulsar radiation generation is then estimated, taking into account the angular dependence of the growth rates and the limitations on the length of the coherent wave–particle interaction imposed by the curvature of the magnetic field lines. We conclude that in the pulsar magnetosphere, Cherenkov-type instabilities occur in the hydrodynamic regime, while cyclotron-type instabilities occur in the kinetic regime. We argue that electromagnetic cyclotron-type instabilities on the X, O and probably Alfvén waves are more likely to develop in the pulsar magnetosphere.

A dispersion equation is derived for a cylindrical waveguide of circular cross-section partially filled with chiroplasma. The propagation characteristics of electromagnetic waves in the family of waveguide modes are studied. The dispersion curves are given. It is found that the propagation constant changes almost linearly with the chirality admittance for the parameters that we choose, and increases with increasing filled area.

Beam instabilities that arise in the compression zone of a gyrotron oscillator can degrade the beam quality and hence adversely affect the operating characteristics of the device. This paper investigates a class of space-charge instabilities that are related to unstable Bernstein modes. These are investigated both by simulations with a 2½-dimensional fully electromagnetic particle-in-cell code and by solving the linear dispersion equation (obtained with kinetic theory). Use of the code makes it possible to study effects that cannot be taken into account in the linear dispersion relation, such as the effect of static self-fields. The simulation strongly suggests that the instability is convective. The dependence of growth rate and frequency spectrum on beam parameters is calculated both with simulation and the analytical method, and the results show good agreement. A detailed analysis of the electromagnetic fields calculated in the simulation shows that the unstable waves are not (as has frequently been assumed in the past) purely electrostatic.

A new mechanism for the formation of pinching plasma instability related to a tangential discontinuity is discussed. With this in mind we use a simple model of the Davydov–Zakharov class. It appears that there is a strong dependence of the instability increment on current density, resulting from the corresponding dispersion relation. Modulation of a current pulse is shown to be a possible way of stabilizing powerful discharges.