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.

The counter-streaming instabilities arising in three-component electron plasmas are investigated analytically and numerically in the general non-symmetric case, i.e. when Here n1 n2 and na represent the electron particle density in the first and second beams and in the background (ambient) stationary plasma, respectively; U1 and U2 represent the streaming velocities of the two counter-streaming electron beams. No magnetic or temperature effects are considered; consequently the three components interact only through the electric collective fields and only longitudinal modes are present. The positive ions here represent a stationary neutralizing background. Combined analytical and numerical solutions of the dispersion equation indicate that the basic properties of the unstable plasma modes may change significantly, depending on the values of the dimensionless parameters e, a and g. Thus, the standing wave spectrum (Re ω = 0) which occurs in the symmetric case (ε = a = 1) without background (gr = 0) may be replaced by a mixed travellingstanding wave spectrum having a rather complex structure; the maximum growth rate could be also strongly affected. The transformation of the instability from ‘absolute’ into mixed ‘convective and absolute’ may have significant physical implications, especially for finite size plasma systems or finite length unstable interaction regions. The results are relevant for laboratory and (especially) astrophysical situations in which counter-streaming electron beams having unequal streaming velocities (and particle densities) penetrate plasma regions with significant relative particle concentration.

It is shown that both lower hybrid and modified electron acoustic instabilities can be excited in a hot anti-loss-cone plasma co-existing with a rarefied cold plasma, provided the anti-loss-cone factor, ρ, exceeds a value Tm/Tt, where Tm and Tt are the parallel temperatures of missing and trapped electrons respectively. These instabilities are excited in a bounded range of wavenumbers and the growth rates are enhanced with the increase of cold plasma density. For

Tm/Tt < ρ > (Tm/Tt)½

both the instabilities are of resonant type whereas for ρ > (Tm/Tt)½ both may be converted into non-resonant types. These instabilities are expected to give rise to the heating of protons as well as electrons in the magnetosphere beyond the plasmapause.

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 determination of electron temperature of a low density shock-heated argon plasma (3 Torr ≤ p1 ≤ 10 Torr, 5500 °K ≤ 9500 °K) by means of microwave diagnostics is improved with a test section which permits the simultaneous transmission of two microwave beams at different frequencies, and with two corrections applied to the measured attenuation of transmitted waves. The purpose of these corrections is to obtain the true attenuation due to wave power dissipation into the plasma, which is dependent on the electron temperature and density. The first correction takes into account the diffraction of waves by apertures of the test section and the wave defocusing by the plasma. The second correction considers the effect of wave beam bending due to the electron density gradient in the flow direction of the plasma. Both corrections diminish the measured wave attenuation. Consequently a lower ratio of attenuation to phase shift of transmitted waves is determined, which in turn yields lower values of electron collision frequency and electron temperature. This report describes the electron temperature evaluation technique in detail, and presents results. The electron temperature values obtained have a range of uncertainty of – 20 % and +10% only, with exceptions at the beginning of the test time. In most tests, the electron temperature is equal or lower by approximately 1000 °K in comparison with the heavy particle temperature.

A new approach to the problem of the radiation emitted from a localized external current source embedded in a magnetoplasma is described. It is argued that the calculation of the fields in the radiation zone can be substantially simplified by adopting at the outset a suitable parametrization of the dispersion surface. We illustrate the approach by calculating the far fields using the full expression for the dielectric tensor of a warm magnetized electron gas. In this case one can take the angle of rotation about the external magnetic field and the square of the refractive index as the curvilinear co-ordinates of the dispersion surface. The form of the surfaces of constant phase and the amplitudes of the emitted waves are described for each topologically different region of parameter space and their structures are related to the shapes of the refractive index surfaces. Attention is also drawn to the existence of locally cylindrical waves that can produce beams which are highly collimated in the direction of the external magnetic field.

A formalism is described which permits calculation of the low frequency response of a resistive plasma with non-circular cross-section in magnetohydrodynamic equilibrium to an externally imposed current field in the direction of the ignorable co-ordinate. This formalism is limited to slow variations on the resistive penetration or ‘skin’ time-scale and eliminates rapid motions at the hydrodynamic rate. It is useful for calculating the effectiveness of low frequency Ohmic heating and for the study of feedback stabilization. It also determines stability criteria and gives estimates of growth rates. The presence of a hyperbolic axis in the Doublet configuration makes the incorporation of a finite resistivity in the treatment important.

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.

Stochastic fields perturb the evolution of coherent wave–particle resonances. Knowledge of the probabifity distribution obeyed by the trapping parameter places upper limits on the time interval where the noiseless description of the resonance is acceptable. Alternatively, given the interaction time, estimates of the relative intensity of the coherent mode and turbulent fields required for a typical resonance effect to occur are obtained.

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.

On a time-scale of the order of the energy relaxation time, a high power laser beam, propagating in a strongly ionized magnetoplasma is shown to be unstable for small scale fluctuations. In the domain r0 < [mi/m]½ λm. v2/[ω2c + v2] (r0, λm, v, ωc, and m being respectively the spatial scale of the perturbation, electron mean free path, collision frequency, cyclotron frequency and mass and mi being the ion mass) the main loss of excess electron energy is due to thermal conduction; in the other limit collisional loss dominates. It is shown that for small scale fluctuations the growth rate increases with (i) increasing magnetic field and (ii) increasing r0. For large scale fluctuations the magnetic field does not show any effect; the growth rate, however, diminishes with increasing spatial scale. A maximum growth rate is obtained both for some optimum value of scale length and for intensity of the main beam.

Ion-cyclotron waves are excited by cesium and potassium ion beams in cesium and potassium Q-machine plasmas. The ion beams are injected along the magnetic field with care to avoid beam transverse velocities. The observed ion-cyclotron mode frequencies are below those driven by electron currents. These resonant instabilities are convective in character with small spatial growth rates ki/kr ≃ 0.05. Plasma ion heating is observed and is consistent with a model in which mode amplitudes are saturated by diffusion effects.

Relativistic electron beam heating of a dense plasma through the two-stream instability is studied. A large amplitude beam-plasma wave excited by the instability induces waves of wide wavenumber spectrum at low phase velocities through secondary parametric instability processes. In some cases such a complicated mode coupling of the beam-plasma wave into low phase velocity waves and their saturation may be described in terms of soliton formation. A beam stopping length associated with this process is obtained.

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.

Ion-cyclotron waves are excited by a cesium ion beam in a cesium Q-machine plasma with drifting plasma electrons. These interactions differ significantly from those in the case of drifting ions in that the drifting electrons play an active role in the instability mechanism. The observed mode frequencies are slightly below those of the electron current driven modes. These waves can be convectively or absolutely unstable, depending on the ion beam velocity. For low beam velocities the instabifities are convective in character with large spatial growth rates ki/kr ∼ 0.2. For larger beam velocities the instabilities are absolute in character with temporal growth rates 0.04. The absolute instabilities are similar to two-stream instabilities. Plasma ion heating is observed and is consistent with a model in which mode amplitudes are saturated by diffusion effects.

Thomson scattering was used to determine space- and time-resolved electron velocity distribution components parallel and transverse to the magnetic field direction in a Penning-type reflex discharge in hydrogen. Electron densities were of the order 1013 cm-3, and temperatures about 3eV. For magnetic field strengths less than about 200 G, Maxwellian distributions were obtained over an energy range six times the thermal energy. Temperatures were in excellent agreement with Langmuir probe data. However, for fields of about 4500 G chaotic plasma potentials were observed with the Langmuir probe. In this regime, in which the plasma was unstable, Thomson scattering showed electron velocity distributions having central temperatures of about 2eV and wing temperatures of 15–20 eV. The experiment design employed led to extremely low stray light levels permitting clean measurements at the laser wavelength and detection of scattered signals as faint as two photons.

Using the stationary equilibrium energy principle a sufficient condition is obtained for the stability of a compressible stratified fluid with a non-uniform horizontal magnetic field, with an aligned shear flow. The condition is used to provide a simple generalization of a known result for a specific atmospheric model.

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.

The quasi-static lower hybrid eigenmodes of a plasma column in a cylindrical waveguide are determined, and their linear excitation by a small density electron beam is discussed for the cases of a hot electron beam as well as for a cold electron beam. It is shown that under certain conditions, finite geometry effects introduce important quantitative and qualitative differences with respect to the results obtained in an infinite geometry.

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.