The nonlinear behaviour of surface waves propagating along a plasma column is investigated. The experiments include (i) measurements of the nonlinear dispersion of the waves and (ii) observation of the evolution of the shape of the wave envelope and of the wave spectrum when the waves are excited with an amplitude-modulated signal. Comparison with theory shows that (i) the measured nonlinear wavelength shift corresponds to increasing wave phase velocity with increasing wave amplitude, (ii) the observed narrowing of the wave envelope can be associated with the formation of periodic nonlinear waves described by dn Jacobi elliptic function solutions of the nonlinear Schrödinger equation and (iii) the observed strong changes of the wave spectrum are mainly related to a nonlinear effect of phase modulation.

This paper presents a theoretical model of a plasma column sustained by an electromagnetic surface wave in the dipolar (m =1) mode for two different gas-discharge regimes: free-fall/diffusion and recombination respectively. The dispersion characteristics of the wave and the axial profiles of the plasma density, wave power, wavenumber and wave-field components for a given regime are specified by one numerical parameter σ = ωR/C, where ω is the angular wave frequency, R the plasma radius and c the speed of light, irrespective of the gas nature and pressure. It is established that there exists a ‘critical’ value of this parameter, σcr = 0·3726, below which a plasma is not likely to be sustained. A comparison between the axial structures of plasma columns sustained by electromagnetic waves in the dipolar and azimuthally symmetric modes is made. The model is in agreement with the available experimental results.

Motivated by plasma and wave measurements in the cusp auroral region, we have investigated electron-acoustic solitons in a plasma consisting of fluid ions, a cool fluid electron and a hot Boltzmann electron component. A recently described method of integrating the full nonlinear fluid equations as an initial-value problem is used to construct electron-acoustic solitons of arbitrary amplitude. Using the reductive perturbation technique, a Korteweg-de Vries equation, which includes the effects of finite cool-electron and ion temperatures, is derived, and results are compared with the full theory. Both theories admit rarefactive soliton solutions only. The solitons are found to propagate at speeds greater than the electron sound speed (ε0c/ε0ε)½υε, and their profiles are independent of ion parameters. It is found that the KdV theory is not a good approximation for intermediate-strength solitons. Nor does it exhibit the fact that the cool- to hot-electron temperature ratio restricts the parameter range over which electron-acoustic solitons may exist, as found in the arbitrary-amplitude calculations.

A simplified analytic description is used to understand recent results of large-scale numerical simulations of resonant absorption and to disentangle the basic physics. It is shown that very efficient absorption takes place at frequencies where a discrete external kink and an Alfvén continuum mode merge into a modified external kink mode. The relation between this ‘hybrid’ mode and ‘pure’ continuum or discrete spectrum modes is discussed.

An investigation is made of wave generation and the radiation of third harmonics by an electrostatic wave in a narrow inhomogeneous layer of a warm plasma. The amplitudes of the third-harmonic wave are calculated. It is found that they depend both on the nonlinear interaction of the initial waves and on the interaction of second harmonics with the initial wave. The generation of third harmonics by interaction of the initial waves is a four-wave process, i.e. a higher-order nonlinearity.

Plasma heating at the electron-cyclotron frequency by an ordinary wave propagating at right-angles to a unidirectional magnetic field is considered. The injected microwave power is assumed to be sufficiently large that the relativistic change in electron gyrofrequency during one flight through the wave beam is much greater than inverse time of flight. The electron motion in the wave field is described using the Hamiltonian formalism in the adiabatic approximation. It is shown that energy coupling from the wave to electrons is due to a bifurcation of the electron trajectory, which results in a jump in the adiabatic invariant. The probability of a bifurcational transition from one trajectory to another is calculated analytically and used for the estimation of the beam power absorbed in the plasma.

The coupling of hydromagnetic Alfvén waves is studied numerically in a dipolc-field model of the magnetosphere. The two coupled hydromagnetic equations derived by Radoski are solved as an implicit boundary-value problem, namely the boundary conditions at the magnetopause are determined self-consistently. Thus the calculated wave-field distribution inside the magnetosphere can match all known linear characteristic features of the stormtime Pc5 waves observed on 14/15 November 1979 from satellites. A set of proper boundary conditions is found, excellent agreement between the numerical results and observations is demonstrated. Based on the very limited spatial coverage (L ≈ 6·6 and within a latitudinal region ( −10°, 10°)), of the data provided by the satellites, the theoretical model can successfully reconstruct the global micropulsations in the magnetosphere and identify the source regions of hydromagnetic waves.

A theoretical and numerical analysis is performed on the conditions under which electron stochastic detrapping due to small misalignments between the laser wave vector and the global symmetry of the system occurs in magnetically guided free-electron lasers. In particular, it is shown that the threshold for stochasticity is only weakly dependent on the transverse momentum of trapped particles, which allows some simple general conclusions to be drawn regarding the maximum values allowed for this misalignment.

The properties of electromagnetic wave propagation in a uniformly densitymodulated plasma are studied, starting from a unidimensional scalar wave (Hill) equation for the wave electric field. Introduction of the formalism of the spatial propagator Q(z2, z1), from the point z1 to the point z2 allows reduction of the problem to determination of the propagator relevant to a single plasma layer that constitutes the entire periodic structure. The transmission coefficient of a single layer can be computed for any kind of density profile by means of the Magnus approximation, satisfying energy flux conservation at each order in the relevant expansion. The appearance of ‘forbidden zones’ in parameter space leads to the possibility that the incident electromagnetic wave can be partially or completely reflected if a sufficient number of periods are present. The explicit computation of the transmission coefficient for a series of n successive layers confirms this effect as the result of a ‘resonant’ interaction of the incident wave and the ‘periodicity’ of the medium.

Equations are presented for the coupling between high- and low-frequency waves in a collisional plasma that models the ionospheric E region. New collapsing solutions can be found from these equations, even for frequencies smaller than the electron–neutral and ion–neutral collision frequencies.

The time evolution to a steady state of the interaction of an obliquely incident P-polarized wave with an inhomogeneous collisional cold plasma is investigated. The two-dimensional numerical solutions presented show that the rate of energy absorption and the amplitude of the magnetic field do not depend on time during this evolution (after a short transient period). Using this important result, a simple analytical two-dimensional model solution for this evolution has been constructed. It is shown that this solution fuliils the energy conservation law and thus describes the transformation of wave energy into oscillatory and thermal energy during this process. An interesting analogy between this process and that of Landau damping follows from the analytic solution.

A self-consistent stability analysis of relativistic non-neutral cylindrical electron flows propagating along applied magnetic fields is considered within the framework of the macroscopic cold-fluid-Maxwell equations. The full influence of the equilibrium self-electric and self-magnetic fields is retained. Then the E x B drift (E being the radial electric field created by the uncompensated charge) generates a radial shear, vz(r) and v0(r). The effect of the shear in the axial velocity component, as reflected in the relative axial motion of adjacent concentric layers of beam particles, is investigated. The self-consistent treatment of the problem thus shows that the equilibrium state considered in this paper is unstable.

The full relativistic dielectric tensor for a Maxwellian plasma in the electron-cyclotron range of frequencies is investigated. A new representation for arbitrary values of the wave frequency and direction of propagation of the anti-Hermitian part is presented that avoids the standard expansions of the Bessel functions. A compact form of the wave damping for ω ≽ 2ωc is obtained that is useful for the investigation of synchrotron radiation in hot plasmas.

We investigate the effect of a weak ambipolar field on non-local heat transport by solving the reduced Fokker-Planck equation in the non-diffusive approximation for the electron distribution function. It turns out that for a moderately high-Z plasma with steep gradients the maximum-heat-flow expression is modified and the ensuing results compare favourably with the experimental values. However, in the gentle-gradient limit the classical Spitzer-Härm heat flux expression is unaltered.

Nonlinear modulational instability and the evolution of a pulse that is initially non-solitonic for Langmuir waves described by the Zakharov equations are considered. The average Lagrangian method has been used to derive the nonlinear dispersion relation for Stokes waves. It is found that the region of instability increases with the amplitude of the perturbed Langmuir field. The propagation of the pulse is studied with the help of the Rayleigh-Ritz optimization method. It is noted that the width of the pulse oscillates rapidly for high initial pulse velocity.

The purpose of this paper is to derive the asymptotic solutions to a class of inhomogeneous integral equations that reduce to algebraic equations when a parameter ε goes to zero (the kernel becoming proportional to a Dirac δ function). This class includes the integral equations obtained from the system of Vlasov and Poisson equations for the Fourier transform in space and the Laplace transform in time of the electrostatic potential, when the equilibrium magnetic field is uniform and the equilibrium plasma density depends on εx, with the co-ordinate z being the direction of the magnetic field. In this case the inhomogeneous term is given by the initial conditions and possibly by sources, and the Laplace-transform variable ω is the eigenvalue parameter.

A driven dissipative magnetohydrodynamic state is calculated that is consistent with a non-ideal boundary condition relevant to magnetically and mechanically active boundaries of laboratory or astrophysical plasmas. The solution is based on the results from previous analytical and computational investigations of electrically driven states, and is characterized by finite helical distortions and a small flow velocity. It is shown that such a configuration may persist even in the absence of previously assumed rigid perfectly conducting boundaries. It is proposed as a model for an astrophysical ‘flux rope’, and suggests an additional in situ diagnostic for such flux ropes.

Equations are derived for the kinetic-theory analysis of small-amplitude Alfvén waves in cylindrical plasmas carrying force-free currents. The equations, which include ion Larmor-radius effects to second order, are applicable to reversed-field pinches as well as to tokamaks. Fourier mode amplitudes are derived for model antennas with radial current feeds, and a quantitative analysis is made of the antenna resistance and the wave density fields in a small tokamak during Alfvén-wave heating. The effect of the plasma current on the wave thermal energy flux is discussed.

The dispersion relation for low-frequency surface waves at a current sheet between two magnetized plasmas is derived using the cold-plasma dielectric tensor with finite ion-cyclotron frequency. The magnetic field direction is allowed to change discontinuously across the sheet, but the plasma density remains constant. The cyclotron frequency causes a splitting of the dispersion relation into a number of mode branches with frequencies both less than and greater than the ion-cyclotron frequency. The existence of these modes depends in particular upon the degree of magnetic field discontinuity and the direction of wave propagation in the sheet relative to the magnetic field directions. Sometimes two modes can exist for the same direction of propagation. The existence of modes undamped by Alfvén resonance absorption is predicted. Analytical solutions are obtained in the low-frequency and magnetic-field-reversal limits. The solutions are obtained numerically in the general case.