The propagation of fast magnetosonic waves in an inhomogeneous medium with planar flow in investigated. The equations describing the rays along which the waves propagate are derived, as well as the equations for the variations of the wave amplitude along the rays. These equations are solved for the case of steady flow that depends only on the radius. In addition, it is shown that a spectrum of eigenmodes may exist if the steady flow contains a shock. For that purpose, the reflection coefficient of a fast magnetosonic wave form a shock is derived, and it is shown that the waves can be localized in a region bounded by a shock and a critical surface. A criterion for stability of the spectrum is derived.

The propagation of magnetovortex waves in an inhomogeneous medium with planar flow and perpendicular magnetic field is investigated. The linearized MHD equations are studied with the aid of the WKB approximation. Within the latter, a set of ordinary differential equations along the streamlines of the basic flow is derived. These equations govern the variations of the transverse as well as the parallel magnetovortex waves along its rays. The amplitude equations are solved explicitly for a particular geometry of the basic flow, and the solutions are investigated for subsonic as well as for supersonic basic flows.

We study the Vlasov–Poisson system of equations in Fourier-transformed velocity space. First we reformulate some results of the linear theory: in the new representation the van Kampen–Case eigenmodes are found to be ordinary functions with convenient continuity properties. We give a transparent derivation of the free-streaming temporal echo in terms of the kinematics of wave packets in Fourier-transformed velocity space. We further extend this analysis to include Coulomb interactions, which allows us to establish a connection between the echo theory, the second-order oscillations of Best and the phenomenon of linear side bands. The calculation of the time evolution of the global second-order electric field is performed in detail in the case of a Maxwellian equilibrium distribution function. We conclude that the phenomenon of linear side bands may be properly explained in terms of the intrinsic features of the equilibrium distribution function.

The generation of nonlinear plasma waves with arbitrary phase velocities by an intense laser pulse is considered in order to determine the dependence of the maximum amplitude of driven waves on the group velocity of the laser pulse (or the phase velocity of excited wakefields). Analytical as well as numerical studies of the problem are carried out within the so-called quasi-static approximation. In the case of square-shaped laser pulses the analytical expression for the maximum amplitude as a function of the pump amplitude and the phase velocity is derived. The numerical analysis in the case of Gaussian pulses confirms the result that follows from the analytical formula: the lower the phase velocity of the wakefleld, the greater is its maximum amplitude for a given amplitude of the driving pulse.

We study nonlinear self-interactions including modulational instability in the case of a plane electromagnetic pulse propagating through a magnetized cold plasma at an arbitrary oblique angle to the external magnetic field. For intended applications to pulsar magnetospheres, the magnetic field is so large that both the electron- and ion-cyclotron frequencies are enormous compared with the plasma frequency or the frequency ω of the wave itself. The plasma is assumed to contain two singly charged species, either electrons and positrons or electrons and ions. (No approximation is made with respect to the mass ratio.) We restrict ourselves to the case eE0/mω ≪ 1 (i.e. the wave amplitude E0 excites the electrons to weakly, but not fully, relativistic velocities). We consider a pulse whose linear polarization is in the plane of the wave vector and the magnetic field. (The orthogonal polarization is purely electromagnetic, and induces no motion along magnetic field lines.) The pulse is assumed to be modulated along the direction of the group velocity vector. We show, using a self-consistent multiple-scales solution, that the envelope obeys the nonlinear Schrödinger equation, and from the coefficients of this equation we derive the conditions for modulational instability. Computation of the nonlinear coefficients requires detailed consideration of ponderomotive, relativistic and harmonic effects, all of which, in the ‘weakly relativistic’ case considered here, enter at the same order in the approximation scheme. Unlike the case of propagation parallel to a strong magnetic field, in oblique propagation we find a wide parameter range for modulational instability and soliton formation on time scales appropriate for pulsar micropulses.

We derive the Alfvén-wave equation for an atmosphere in the presence of a non-uniform vertical magnetic field and the Hall effect, allowing for Alfvén speed and ion gyrofrequency that may vary with altitude; the pair of coupled second-order differential equations for the horizontal wave variables, namely magnetic field or velocity perturbations, is reduced to a single complex, second-order differential equation. The latter is applied to spinning Alfvén waves in a magnetic flux tube, in magnetohydrostatic equilibrium, in an isothermal atmosphere. The exact solution is found in terms of hypergeometric functions, from which it is shown that at ‘high altitude’the magnetic field perturbation tends to grow to a non-small fraction of the background magnetic field. By ‘high-altitude’ is meant far above the critical level, which acts as a reflecting layer for left-polarized waves incident from below, i.e. from the ‘low-altitude’ range. We also obtain the exact solution near the critical level, where the left-polarized wave has a logarithmic singularity, and the right-polarized wave is finite. The latter is plotted in this region of wave frequency comparable to ion gyrofrequency, and it is shown that the Hall effect can cause oscillations of wave amplitude and non-monotonic phases with slope of alternating sign. The latter corresponds to ‘tunnelling’, i.e. waves propagating in opposite directions or trapped in adjoining atmospheric layers; this could explain the appearance of inward- and outward-propagating waves, with almost random phases, in the solar wind beyond the earth, for which the Hall effect on Alfvén waves should be significant.

Phase-sensitive probe diagnostics as well as two-point-correlation analysis of radio-frequency probe signals are applied to investigate small-amplitude lower-hybrid (LH) waves launched into a linear nonuniform plasma column by a slow-wave antenna. The LH wave propagation in the inhomogeneous plasma is described by a model taking into account the wavenumber spectrum of the antenna. Special attention is focused on the interaction of the LH waves with the low-frequency density fluctuations. The LH frequency and wavenumber spectra observed can be explained by scattering of the LH waves from the (incoherent) low-frequency density fluctuations. Moreover, the enhanced damping, which is found to be much higher than expected from collisional and electron Landau dampings, is correlated with the level of low-frequency fluctuations.

Using the exact solution methods developed and illustrated previously, we systematically explore (ω, k) space in order to determine all the unstable modes of velocity-shear-produced electromagnetic waves in magnetized, relativistic electron beams (here ω and k are the complex frequency and real wavenumber). This is done for various physical parameters of the problem, namely shear factor and ratio of pipe to beam radii. The solution of the dispersion relation is supplemented by a marginal stability analysis based on the behaviour of the turning points of the purely real-frequency solution ωr, (k): these are bifurcation points where complex solutions originate or terminate.

When Bernstein waves (B waves) are excited in a magnetized plasma, their self-interaction by nonlinear Landau damping (NLD) becomes the dominant mechanism for the electron heating of the bulk plasma. We examine this behaviour numerically. This occurs only for B waves with relatively small k∥ because the damping of the B waves becomes very small. This occurs in the relatively broad B-wave frequency range betweenω/ωc = 1.45 and 1.78. For B waves with large k∥ (k∥R > 0.15), virtual waves are not generated via self-interaction due to NLD because the quasi-linear cyclotron damping of the B waves becomes the dominant mechanism. The numerical results agree well with experimental ones.

The influence of ion streaming and weak relativistic effects on the modulational instability of ion-acoustic waves in a collisionless unmagnetized plasma is investigated. An averaging method is used to derive a weakly nonlinear dispersion relation, from which the instability criterion is deduced. Conflicting results in the literature are resolved.

The characteristics of Alfvén surface waves along a cylindrical annular streaming column with a solid core and surrounded by a tenuous medium, and pervaded by a longitudinal magnetic field are studied analytically and numerically. Both axisymmetric (m = 0) and non-axisymmetric (m ≠ 0) modes are found to be dispersive. The Alfvén-wave velocity decreases with increasing magnetic field. Under an infinitesimal perturbation, the motion of the system is laminar and stable for all values of m for all short and long wavelengths if the unperturbed state is non-streaming. If the system is streaming, there will be unstable domains not only for m = 0 but also for m ≠ = 0 owing to the strong destabilizing influence of the streaming. However, this instability can be suppressed completely if the magnetic field is sufficiently high that the Alfvén-wave velocity is greater than the streaming velocity. The thicker the solid core the greater is its stabilizing influence for m = ±1, and vice versa for m = 0. A longitudinal field imparts a degree of rigidity to the conducting fluid, so it always has a strong stabilizing influence.