General expressions have been derived relating the attenuation, A, to the group and phase refractive indices μ′ and μ. This has been done by considering a perturbation about the case in which the collision frequency is zero. It is found that the expressions forμ′ –μ and the imaginary part of the refractive index are closely related in form so that the attenuation can be related to the difference in the group and phase paths, P′–P. Approximations of this form have been obtained in the past but only for situations in which the Q.L. and Q.T. approximations are valid. The expressions derived in this paper are not restricted in this way and numerical calculations show that the ranges of these Q.L. and Q.T. approximations are rather limited. Numerical calculations have enabled new approximations with much greater ranges of validity to be established for these cases.

Laser-created plasmas are characterized by high photon occupation numbers. Analysis of the induced Compton scattering of an auxiliary laser beam, tunable in frequency and incident angle, is used as a fine diagnostic mechanism for measuring the subcritical plasma distribution function.

The threshold of a parametric instability in which the frequency of the excited Langmuir waves is exactly the arithmetic mean of two pump frequencies, is calculated. The kinetic equation is used to describe the ion dynamics. The threshold is infinitely high when the difference between the two pump frequencies is exactly double the frequency of ion-acoustic waves if pump waves of equal intensity are assumed. For very large values of Te/Ti the threshold reaches its lowest values when the difference frequency is slightly more or slightly less than twice the resonant frequency of the ion-acoustic waves.

Finite amplitude effects in the propagation of axisymmetric hydromagnetic waves in a cylindrical, magnetized plasma are considered. The influence of the Hall term and the presence of neutral atoms on the resulting second-order fields is treated. For the specific case of torsional wave propagation, the combined effect of these two factors is to produce a substantial second-order azimuthal field, in addition to the axial field predicted by earlier work which neglected these factors. In some circumstances this azimuthal field is much larger than the axial field.

This paper reports on the observation of nonlinear effects in the propagation of axisymmetric (m = 0) torsional hydromagnetic waves in a partially ionized helium afterglow plasma. In accordance with the predictions of a weakly nonlinear theory, magnetic field perturbations oscillating at twice the frequency of the primary wave have been observed. Good quantitative agreement between the experimental data and theoretical calculations is obtained for moderate primary wave amplitudes.

Profile modification by the ponderomotive force of the mode-converted Langmuir waves at critical density of a laser-irradiated plasma is investigated. A nonlinear Schrödinger equation governing the interaction of Langmuir waves with slow plasma motion is obtained taking into account the plasma inhomogeneity, dissipation, and a driver. The initial value problem is solved by means of the inverse scattering method. The soliton formation and self-consistent density steepemng at the critical layer are investigated.

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.

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.

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.

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.

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.