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.

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.

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.

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.

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.

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.

This paper studies the nonlinear coupling between a large amplitude propagating lower-hybrid wave and two electromagnetic waves in a plasma. Using a two-fluid model and Vlasov and Maxwell's equations, we derive a dispersion relation governing this three-wave interaction process. It is shown that a finite wavenumber lower-hybrid pump can decay into a whistler and a kinetic Alfvén wave. Calculations of the threshold condition suggest that this decay process may occur both in the laboratory and in the ionosphere.

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.

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.

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 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.

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.