The interaction of high-frequency and low-frequency waves in magnetized plasmas is considered. The narrowness of high-frequency wave packets makes possible a concise Hamiltonian description of the problem. Some concrete problems are studied with the help of the derived equations. The competitive role of scattering in self-consistent density and magnetic-field fluctuation are considered. The self-focusing and solitons of potential plasma waves and magnetohydrodynamic waves are studied.

A systematic analysis of envelope upper-hybrid wave propagation near the magnetosonic speed has been presented. Using the full set of fluid equations for the low-frequency dynamics, we obtain various model nonlinear equations describing the magnetosonic response to the envelope waves. In particular, we derive driven KdV as well as driven Boussinesq equations that are valid for near-magnetosonic propagation. These equations are coupled to the usual Schrödinger-like equation for the envelope wave. Exact stationary solutions of the coupled equations are explicitly obtained. It is shown that a, new class of upper-hybrid solitons with antisymmetric wave envelope exist for nearmagnetosonic propagation. Integral invariants for the driven KdV case have been obtained and evaluated for localized solutions. A set of stationary governing equations is derived that takes account of the full nonlinearity in the low-frequency response as well as departures from the frozen-in-field approximation. A detailed comparison of the various model equations as well as their validity has been made.

A non-local theory of whistler and quasi-static mode excitation by an annular electron beam in a plasma cylinder is presented. Čerenkov and slow-cyclotron interaction are considered in the weak-beam approximation. The growth rate is found to be quite sensitive to the beam radius except in the case of slow-cyclotron interaction of quasi-static modes. The growth rate varies significantly with beam velocity in the case of Čerenkov interaction of quasi-static modes, but in other cases it is rather insensitive to the beam velocity.

Two different families of explicit stationary solutions of the Hasegawa–Mima equation are obtained. In the first case the well-known modon (dipole vortex) is used as the zeroth-order solution, and new solutions that are close to but distinctly different from it are found by perturbation analysis. In the second case the dispersive term of the equation is treated as a small parameter, and a radially symmetric solution (a monopole vortex) is used as the zeroth-order approximation. Both families of solutions are found to be infinite and to contain an arbitrary function. A recent general proof of the existence of infinitely many stationary solutions containing an arbitrary function is examined and found to be invalid.

The components of the dielectric tensor for a plasma described by a relativistic loss-cone electron distribution are written in a simple way, which takes full account of relativistic effects, harmonics and Larmor radius, for perpendicular and oblique propagation. For sufficiently oblique propagation and temperatures in the thermonuclear range, a still simpler form of the dielectric tensor is derived. The role of the wave parameters in the absorption is discussed, and some comments are made about the weakly relativistic and non-relativistic approaches. A numerical example is given for both the extraordinary and ordinary modes.

The microscopic and macroscopic behaviours of a linear reflex discharge in the presence of low-frequency turbulence are investigated under the action of moderate lower-hybrid wave power. The frequency and wavenumber spectra of both the low-frequency fluctuations and the high-frequency waves are measured using a correlation-analysis technique with two probes. The low-frequency fluctuations may be attributed to drift-wave turbulence. The fluctuation level is raised when RF power is coupled to the plasma, thus leading to considerably enhanced radial transport. The coupling between low-frequency fluctuations and high-frequency waves can be seen clearly from the spectra. The high-frequency wavenumber spectra measured inside the antenna are in reasonable agreement with the lower-hybrid wave dispersion. However, the wavenumbers observed in the lower-hybrid resonance region outside the antenna are – in contrast with expectation – not larger than in the plasma edge region. From the electric-field energy-density spectra and from measurements of the density and the temperatures, a detailed energy balance can be performed. The calculated heating rates are anomalously large for both the electrons and the ions. The absorption processes, relevant for the present experiment, are discussed.

A low-temperature plasma containing polar molecules with constant electric dipole moment as the neutral component is considered. The thermodynamic functions and the dispersion properties of such a plasma are investigated.

Analytical solutions are presented for the linear growth rate of oblique plasma waves in a magnetized plasma due to resonant interactions with a model ringbeam distribution. Explicit closed-form solutions for the angular dependence are obtained in terms of modified Bessel functions of the first kind. In the limits of either quasi-longitudinal or quasi-transverse propagation the analytical solutions take the form of simple algebraic expansions, which allow an immediate comparison of the relative contributions from different harmonic resonances, and which also determine the conditions for marginal stability for any specific resonance. The results can be applied, for instance, to the growth of waves following ionization of neutrals originating from cometary, planetary, or interstellar material in the solar wind. In a weakly unstable plasma the analytical results also provide an important check on the complex numerical codes that hitherto constituted the only method available for evaluating the growth of oblique plasma waves.

An eigenvalue equation is derived for electrostatic waves with frequencies below the ion bounce frequency in a plasma confined by a magnetic quadrupole. This integral equation for the electrostatic potential is developed to second order in the curvature and contains the effects of electron and ion temperature gradients. A dispersion equation for flute modes is derived from it. The present theory applied to the private flux region of the UMIST quadrupole predicts that low-frequency flute modes will propagate in the electron and ion diamagnetic drift directions.

є-Expansion renormalization-group theory is applied to a model Alfvén-wave turbulence equation. In particular, the effect of small ‘unresolvable’ subgrid scales on the large scales is computed. It is found that the removal of the subgrid scales leads to a renormalized response function v. The Lorenzian wavenumber spectrum of Chen & Mahajan can be recovered for finite є, but the nonlinear coupling constant still remains small, fully justifying the neglect of higher-order nonlinearities introduced by the renormalization-group procedure.

A study of the ideal magnetohydrodynamic linear eigenvalue spectrum for free-boundary modes in the Z-pinch is presented. The application of a variational method to estimate eigenvalues is described and limitations imposed by the nature of the spectrum are discussed. An analytic expression for the long-wavelength m = 0 growth rate is derived

The nonlinear behaviour of short-wavelength perturbations in the two-fluid cosmic-ray hydrodynamical model is examined. We show that such a perturbation leads to shock formation and derive the appropriate wave equation. We show that a discontinuous perturbation incident on a weak cosmic-ray shock destabilizes, in a time-asymptotic sense, the shock.