The stability of straight field-aligned electron beams, immersed in an external magnetic field of finite magnitude, with respect to the excitation in them of circularly polarized (spiral) electromagnetic waves is a problem calling for detailed investigation, particularly in the context of the study and development of free-electron lasers. Traditionally the problem is treated using the theory of electromagnetic waves scattering off electron-beam density oscillations. This is done, however, without considering the inverse influence of the beam on the dispersion properties of the electromagnetic waves. On the other hand, it is well known that the presence of the beam introduces substantial changes in the characteristics of the electromagnetic waves interacting with the beam, and, moreover, this results in the appearance of radically new types of waves that are entirely absent in free space. The paper is dedicated to the study of the nonlinear dynamics of the interaction of such radically changed electromagnetic waves with the beam density oscillations.

An expression is obtained for the collision integral describing the simultaneous interaction of plasma particles with resonant and non-resonant waves. It is shown that this collision integral is determined by two processes: a ‘direct’ nonlinear interaction of particles and waves, and the influence of the non-stationarity of the system. The expression for the nonlinear collision integral is found to be quite different from the expression for a quasi-linear collision integral; in particular, the nonlinear integral contains higher-order derivatives of the distribution function with respect to momentum than the quasi-linear one.

The evolution of the distribution function due to the simultaneous nonlinear interaction of plasma particles with resonant and non-resonant waves is studied. A stationary particle distribution resulting from a balance of the quasi-linear interaction and the nonlinear one is found. The temporal evolution of an initial δ-function-shaped distribution (like a ‘beam’) is examined in the one-dimensional case. General formulae are obtained for stochastic particle acceleration (taking account of the nonlinear interaction studied here).

Starting from a three-wave interaction coefficient for a homogeneous Vlasov plasma, we show that the parametric decay to half-harmonics has zero growth rate if the wavenumber of the pump wave vanishes. Earlier proofs of this fact for electrostatic decay modes are thus extended for a general case. As a specific example, we study the decay of a fast magnetosonic wave to two slow waves.

During propagation of a relativistic electron beam in hydrogen gas at sub-torr pressures using a foil-less diode, low-frequency oscillations in the megahertz range are observed in the net current wave forms, and continue even after passage of the beam. The novel feature of the experiment is that both beam generation and propagation take place in the same low-pressure regime, and hence the beam parameters are functions of gas pressures. Analysis of the experimental results shows that the low-frequency oscillations result from the resistive-hose instability.

It is well known that ion-acoustic double layers occur in plasmas containing two-temperature electron species and positive ions. In a recent study Verheest suggested that such structures can occur when there is only one electron species but both negative and positive ion species. There a stationary modified Korteweg de Vries equation was derived to support his deduction. This prediction, however, contradicts our own arbitrary-amplitude studies, which also cover the Verheest parameter regime. Here we resolve the discrepancy by examining both approaches in the pseudo-potential formulation in more relevant detail. The implications of this study extend beyond the realm of the present subject.

The range of ▿ ∧ (u ∧ B) is determined for an axisymmetric poloidal incompressible B and incompressible u, by solving ▿ ∧ (u ∧ B) = ▿ ∧ v for u, assumed to be confined to within a surface of revolution. Two constraints on V are shown to be necessary for the existence of solutions, viz that the integral of rç/|B| must vanish on each flux surface, and that the integral of v1 around any dosed field line must vanish. The construction of the general solution proves that the constraints are sufficient conditions, providing also that the second derivative, with respect to the poloidal flux function, of the volume contained by flux surfaces does not vanish. The general solution is stated for the homogeneous case, v = 0. For the particular case of poloidal v1 an integral property of the solution u is established.

The steady currents driven in a spherical plasma by a rotating magnetic field via the Hall effect are studied analytically. The total field is shown to be symmetric across the origin. Integral relationships are obtained between Ohmic dissipation, angular momentum and the oscillating axial current density. The topology of the sum of a Hill's vortex field and a rotating field is documented. Analytical solutions for the driven current are obtained by expansion for the limits corresponding to small rotation frequency, to small number density, to large rotating-field magnitude, to small resistivity, and to small rotating-field magnitude combined with very small resistivity. The latter solution, relevant to the reactor limit, indicates that, with control of the vertical field magnitude, an MHD equilibrium can be generated with total current any fraction of the currentcorresponding to synchronous rotation of the electrons. Oscillating currents sufficient to drive the synchronous current are determined.

The parametric excitation of surface waves in a warm inhomogeneous plasma is investigated. It is demonstrated that the coupling between the surface wave and plasmons that can be excited in the transition layer must be taken into account. The growth rate and the threshold value for the instability process are calculated. It is also shown that thermal effects are of importance even for very low temperatures, since the plasmons can now propagate out of the resonance region.

The Kelvin-Helmholtz instability of a tangential velocity discontinuity in a plasma flow when cosmic-ray pressure is taken into account is studied. It is shown that a new unstable mode can exist. This appears when an effective Mach number exceeds some critical value. In the case of strong flow mediation by cosmic rays the wave vectors of the most-unstable waves are directed along the plasma velocity vector for both subsonic and supersonic flows.

Using first-order smoothing theory, Fourier analysis and perturbation methods, we obtain the evolution equation of the wave spectrum as well as the nonlinear forces generated by Alfvénic turbulence in a finite-β plasma with dispersion and phenomenological Landau-damping effects. The stability of Alfvénic turbulence is then analysed by solving the derived mean-field equations. It is shown that parallel-propagating turbulent Alfvén waves with dispersion can be modulationally unstable, leading to amplification of large-scale Alfvén waves and acoustic waves when Landau-damping effects are strong and weak respectively.

The emission of extraordinary mode radiation in a plasma with Langmuir turbulence driven by an electron beam is considered. The process of emission considered in this paper is the plasma maser effect, which is essentially an energy up-conversion process. The energy necessary for the growth of the extraordinary mode is derived from the Langmuir turbulence. The nonlinear dispersion relation of the extraordinary mode in the presence of Langmuir turbulence is obtained and its growth rate calculated. The scope of application of the results to space-plasma observation is then stressed.

The quasi-linear diffusion coefficients for the inherently space-dependent wave amplitudes in lower-hybrid heating and current-drive experiments are derived and compared with the usual space-independent approximation. The distribution function is derived and the dependence on the radio-frequency field amplitude gradient of the ‘plateau’, which is an essential quantity in thetheoretical description of LH experiments, is stressed.