Quantum field theory is used to investigate the resonant nonlinear interaction between three longitudinal waves propagating at any arbitrary angle to a uniform magnetic field in a plasma. The coupled mode equations, coupling coefficient and a formula for the growth rates are derived.

The dispersion relations for the quasi-static lower hybrid surface waves are derived. Conditions for their existence and their linear excitation by a small density electron beam are discussed. Instabilities appearing in low-frequency surface waves are also discussed.

An enhancement of evolution rates in two-dimensional plasma models by a large factor containing the square root of the coupling parameter is known to occur. It is shown here to persist even when all collective effects are removed from weak-coupling calculations, under a simplified boundary condition preserving the isotropy of the system. Long-range vorticity is shown to develop. A careful treatment of time integrals allows irreversibility to be discussed with fewer ambiguities than usual with respect to limit ordering. Applications to three- dimensional laboratory plasmas are tentatively suggested. Future computer simulations should determine the usefulness of the comparatively simple relationships found among moments of the pair correlation. The new effects are shown to be qualitatively similar to some found in other approaches to plasma interactions in uniform magnetic fields.

This article treats some aspects of the propagation of a highly energetic heavy ion beam through a fusion target chamber. The stability of this beam to various perturbations is especially emphasized, first for vacuum propagation, and then for propagation through a background plasma. The results are illustrated by detailed calculations for a beam carrying 3 kA of current and consisting of 70GeV, singly ionized uranium ions. We find that such a beam will propagate stably through the target chamber. As a second example we have applied some of our results to the recently proposed I53+ concept in which up to a hundred beams of 40GeV iodine ions each carrying 4.2 kA of current are directed to the target. Our conclusions for this case are less optimistic, as such beams are likely to be subject to space-charge problems due to the increased value of v/γ and are prone to instabilities of the two-stream type.

Following Akhmanov's approach, self-focusing of a laser pulse in a transient plasma has been studied. The beamwidth parameter and hence the laser intensity and the frequency shift (time derivative of the phase) have been evaluated as a function of time and the distance of propagation. It is seen that the time dependence of the axial intensity changes appreciably as the pulse propagates. The present investigation is restricted to a pulse whose incident intensity has Gaussian radial dependence.

An amplitude dependent criterion for modulational stability of long Alfvén waves parallel to the magnetic field is interpreted in terms of a recently obtained inverse scattering solution to the modified nonlinear Schrödinger equation. It is found that the solitons formed are of two types. In the strongly unstable case, normal solitons are formed. In the transition region of weakly unstable and stable cases, the anomalous type, which in a limiting case becomes the algebraic soliton, dominates. In the strongly stable case, no solitons are formed.

A kinetic equation for a two-dimensional inviscid hydrodynamic fluid is derived in two ways. First, the equations of motion for the modes of the fluid are interpreted as stochastic equations resembling the Langevin equation. To lowest order a Fokker–Planck equation can be derived which is the kinetic equation for one mode. Secondly, a suitable iteration scheme is applied to the Hopf equation which results in the same kinetic equation. A parameter describing the time scale is arbitrary and cannot be determined by the applied methods alone. It is shown that the kinetic equation satisfies the conservation requirements and relaxes to an equilibrium which is a rigorous solution of the Hopf equation.

The parametric decay of an intense electromagnetic (pump) wave into a back-scattered electromagnetic wave and an electron plasma wave is considered. The dispersion relation for a homogeneous magnetized plasma in the presence of the pump wave is developed in the cold-plasma approximation with the pump frequency large compared to the cyclotron and plasma frequencies. Formulae are derived for the growth rate γ and threshold power PT associated with the instability. The effects of the magnitude and direction of the static magnetic field on γ and PT are studied numerically.

Using finite group theory, self-similar solutions for the one-dimensional Vlasov– Poisson system are considered, both for electron plasmas, with a fixed ion background, and for a single species beam. Difficulties arising from the Poisson equation are pointed out and handled by using an exponential group of transformations. Introducing, for the beam, a water-bag model, we find that the boundary condition problem, imposed by self-similarity, can be solved through the introduction of a ‘virtual particle’ concept. In order to test the analytical solution obtained, we perform a numerical simulation using a particle code. Complete agreement is found.

The effects of the background plasma as well as of the non-resonant plasma-cyclotron and cyclotron–cyclotron interactions on the oblique unstable electrostatic waves generated by resonant plasma–cyclotron (P–C) and cyclotron–cyclotron (C–C) interactions in magnetized non-symmetric two-stream plus background plasma systems are theoretically investigated. Two main effects are reported: (a) preferential increase or decrease of the maximum growth rates of certain m−modes for appropriate plasma parameters and (b) an additional contribution to the frequency shift from the integer multiple values of half the cyclotron frequency. Closed analytical expressions for the maximum growth rates and frequency shifts of both plasma-cyclotron and cyclotron–cyclotron unstable interactions are presented and discussed. The theoretical results obtained in this paper are supported by recent experimental results on electron counter-streaming instabilities in the presence of significant background plasma concentrations in which dominant electric field emissions at 3Ωe/2 have been observed to occur.

The two-particle correlations in a turbulent plasma are analyzed on a quite general basis by using the modern methods of non-equilibrium statistical mechanics. It is shown that the binary correlations can be split (in a time in- variant way) into a part which decays quickly by ballistic motion, and a long- living part: ‘the natural correlations’. The latter are continuously regenerated from the one-particle distribution function by the internal interactions, even in the absence of true collisions. The general theory can be made operational by using approximation schemes, among which the ‘RQL2’ method, which generalizes the renormalized quasi-linear approximation, leads to results comparable to, but more general than, those developed by previous authors. The explicit relation of the long-living enhanced correlations to the concept of ‘clumps’ will be developed in a forthcoming paper.

Temperature effects on the electrostatic instability of non-symmetric electron plasma systems consisting of two warm counter-streaming beams and of warm background particles are investigated linearly (analytically and numerically) and nonlinearly (by computer simulation experiments) for the case of Heaviside and moderately warm Maxwellian particle distribution functions. The non-symmetry is due to unequal temperatures, streaming velocities and particle densities in the beams. Other variable parameters investigated are the relative thermal velocities of the beams and background as well as the relative background particle concentration. When the beam temperatures are unequal, unstable waves with Re ω > 0 and propagating in the direction of the beam with lower temperature occur; this is in contrast to the equal temperature symmetric two-stream case, in which the unstable waves have Re ω = 0 (standing waves) and the temperature effect is only to decrease the growth rate. When three warm components are present in the system, the following results hold: (i) the beam temperatures have the effect of decreasing the importance of the unstable standing waves with Re ω > 0 (and growth rate yB) relative to the waves with Re w = 0 (growth rate yA) which occur in cold three-component symmetric systems; in addition to this, both γA, max and γB, max decrease with increasing temperature; (ii) the background temperature has the general effect of reducing the absolute maximum growth rate. For relative background temperatures above a certain critical value, a separation (in k and ω spaces) of regions B and A occurs; γA, max increases and γB, max decreases with increasing relative background temperature.

The collisional absorption of two laser beams is considered by solving the kinetic equation for the plasma electron. Results show that the simultaneous effects of two laser beams on the heating rate is greater as compared with the individual contribution of each laser beam when the two laser beams have a difference of frequencies equal to the plasma frequency.

The dynamic stability of a stratified layer of partially ionized compressible plasma is discussed to investigate the effects of finite electrical conductivity and ion viscosity. The prevailing magnetic field is assumed to be uniform and vertical. For a semi-infinite plasma having a one-dimensional exponential density gradient along the vertical, the dispersion relation has been obtained by variational methods. It is found that the ion viscosity and ion–neutral collisions, whether included jointly or separately, do not change the stability criterion of the perfectly conducting system. Their inclusion, however, has a tendency to reduce the growth rate of the unstable perturbations showing that they have a stabilizing influence. On the other hand the inclusion of the effects of finite resistivity and compressibility of the medium is found to be destabilizing as the wavenumber range over which the plasma would otherwise be stable, becomes unstable.