A stability analysis is presented of the electrothermal modes of perturbation of a spatially homogeneous, two-temperature and fully ionized plasma with wave-vector K perpendicular to the magmetic field. It is found that the wavelength of the fastest growing unstable, non-convective mode is of the order of (mi/ me)½ ae, with maximum growth rate of the order of (me/ mi) vei, where ae and vei are the electron Larmor radius and electorn-ion collision frequency respectively. Depending on the values of ωτ and β, this analysis also shows the presence of a convective mode which persists in the limit of long wavelengths. This theory has been consistently examined with homogeneous equilibrium plasma models constructed under the assumption of either a scalar or a tensor electric conductivity. A comparison of these results with the previous steady-state profiles obtained in parts 1 and 2 of this series indicates that current filamentation can take place as a result of electrothermal instabilities in the plasma.

A method has been developed for the derivation of Chew–Goldberger–Low (CGL) theory for a collisionless plasma in the presence of a strong magnetic field. The pressure tensor in the pressure tensor equation is expanded in the inverse power of Larmor frequency. In the zeroth order, CGL equations are obtained and, the higher order, finite Larmor radius corrections to CGL equations are derived.

The stability problem of the boundary regions of cold blanket systems with induced currents parallel to the lines of force is formulated. Particular interest is focused on two types of mode: first electrostatic modes driven by the combined effects of a transverse resistivity gradient due to a spatially non-uniform electron temperature and a longitudinal current, second electromagnetic kink-like modes driven by the torque arising from a transverse current density gradient and magnetic field perturbations. It is found that the combination of various dissipative and neutral gas effects introduces strong stabilizing effects within specific parameter ranges. For particular steady-state models investigated it is shown that these effects become of importance in laboratory plasmas at relatively high densities, low temperatures and moderate magnetic field strengths. Stability diagrams based on specific steady-state cold plasma blanket models will be presented.

The quasi-linear equations describing the resonant evolution of a weakly inhomogeneous plasma slab under the action of Bernstein modes resulting from linear conversion of an externally injected extraordinary wave are obtained, together with a tractable form of the pertinent dispersion relation. The coefficients of electron diffusion in velocity space are computed, and their effect is compared to the effect of Coulomb collisions.

The Schrödinger equation describes the motion of a particle in a statistical sense. It consequently possesses the two main properties of the Vlasov equation (dynamic and statistic) and can replace this last equation provided we take sophisticated initial conditions. The scheme must be considered as a new attempt to discretize intelligently the amount of information contained in the phase space distribution and to stop, without destroying it, the flow of information which usually goes to high wavenumbers in velocity space. The method is applied to the breaking of highly nonlinear waves in a cold plasma (usually treated by the Lagrangian method) and to double beam instability. It is shown that such an Eulerian scheme works quite well with a much smaller number of discretized functions than are required in the regular Fourier—Fourier or Fourier-Hermite methods. The central point is the introduction of the phase space Wigner distribution function which is a useful mathematical tool in spite of its poor physical properties.

The ½ subharmonic excitation is studied for the ionization wave in a positive column glow discharge. When an oscillation with about twice the frequency (and twice the wavenumber) of the resonant one is applied by modulating the discharge current, the ½ subharmonic is excited if the applied voltage exceeds a certain critical value. However, the excitation phenomenon differs from that of the ion-acoustic wave, since the ionization wave has a backward wave property in contrast to the forward one. Such an excitation mechanism is theoretically explained by the Van der Pol equation.

A model equation for nonlinear drift Alfvén waves in the region where they do not couple to the electrostatic drift wave branch is derived. Two conservation relations are derived and the results are compared to that of the Hasegawa—Mima equation. The spectrum is found to cascade to both smaller and larger k. The convective cell formation is studied for two different orderings of the parameters. The relation between characteristic scale lengths parallel and perpendicular to the drift flow for the onset of cell formation has been found.

The stopping power of a plasma for a relativistic electron beam (REB) is derived by taking a Weibel-type electromagnetic instability into account in a collisionless plasma. A quasi-linear theory is developed to derive the stopping power of the plasma due to the electromagnetic instability. The wave–particle interaction by use of the renormalization theory leads to a saturation level of instability. Thus the purely growing electromagnetic instability, including the effect of the beam temperature, decides an effective stopping length of the REB in the plasma.

This paper describes the space-charge double-layer that forms between two plasmas with different densities and thermal energies. Three progressively more realistic models are treated by fluid theory, taking into account four species of particles: electrons and ions reflected by the double-layer, and electrons and ions transmitted through it. First, the two plasmas are assumed to be cold, and the self-consistent potential, electric field and space-charge distributions within the double-layer are determined. Second, the effects of thermal velocities are taken into account for the reflected particles, and the modifications to the cold plasma solutions are established. Third, the further modifications due to thermal velocities of the transmitted particles are examined. The applicability of a one-dimensional fluid description, rather than plasma kinetic theory, is discussed. One valuable product of this description is the potential difference across the double- layer in terms of the parameters of the two plasmas which it separates. A useful length parameter is defined characterizing the distance over which most of this potential is dropped. Comparisons are then made between theoretical predictions, and double-layer potentials and lengths deduced from laboratory and space plasma experiments.

A study is presented for electrostatic waves propagating at large angles with respect to the background magnetic field in collisional, fully ionized plasmas carrying a field-aligned current. In addition to a mode at the usual lower-hybrid frequency, it is found that the presence of electron drift velocity introduces two more modes of oscillation at several times the lower-hybrid frequency. Under appropriate conditions, a resistive instabifity, with frequency very close to the lower-hybrid frequency and growth rate proportional to the electron–ion collisional frequency, can occur. A necessary condition is that the parallel phase velocity of the wave be smaller than the electron drift velocity. A numerical example is given to illustrate the essential features of the instability.

The one-dimensional plasma double layer is modelled by numerically integrating the time-dependent Vlasov and Poisson equations. A constant magnetic field at an arbitrary angle with respect to the layer is included. The model shows that such a plasma region can generate as well as reflect Langmuir waves and shows how RF emission may arise. An axial magnetic field does not inhibit the formation of a double layer, although a non-axial field may do so.

The unified structure of steady, one-dimensional shock waves in argon, in the absence of an external electric or magnetic field, is investigated. The analysis is based on a two-temperature, three-fluid continuum approach, using the Navier—Stokes equations as a model and including non-equilibrium collisional as well as radiative ionization phenomena. Quasi charge neutrality and zero velocity slip are assumed. The integral nature of the radiative terms is reduced to analytical forms through suitable spectral and directional approximations. The analysis is based on the method of matched asymptotic expansions. With respect to a suitably chosen small parameter, which is the ratio of atom-atom elastic collisional mean free-path to photon mean free-path, the following shock morphology emerges: within the radiation and electron thermal conduction dominated outer layer occurs an optically transparent discontinuity which consists of a chemically frozen heavy particle (atoms and ions) shock and a collisional ionization relaxation layer. Solutions are obtained for the first order with respect to the small parameter of the problem for two cases: (i) including electron thermal conduction and (ii) neglecting it in the analysis of the outer layer. It has been found that the influence of electron thermal conduction on the shock structure is substantial. Results for various free-stream conditions are presented in the form of tables and figures.

The definition of the ‘combined field’ and the ‘combined field potentials’ allows one to formulate a constrained minimum energy problem. The constraints can be put in a relativistically covariant form. The equations of stable equilibrium, for a non-rotating charged fluid, are obtained. If the physical conditions are suitably chosen, a special kind of Alfvén-like velocity may exist.

A calculation with respect to momentum transfer by the electron–neutral collisions is carried out, based on an idea that collision phenomena should be characterized by mean free path rather than by the collision time, and correction terms are derived for the previous equation of momentum conservation and the previous approach to the Boltzmann collision integral.

The propagation of a superluminous plane wave of fixed profile through a cold electron plasma, in a direction perpendicular to the ambient magnetostatic field, is considered. The polarization is such that the electric vector has no component parallel to the magnetostatic field. The analysis is referred to the frame of reference in which all the field quantities are uniform in space, and the exact governing equations are cast into the form of an autonomous system of four nonlinear, first-order, coupled differential equations. The equations contain the parameter n that specifies the wave speed, c/n, in the laboratory frame, and inspection reveals that the limiting case n = 0 admits two exact solutions, which are monochromatic, of arbitrary amplitude, and recover the standard solutions of linear theory in the small-amplitude limit. The possibility of the existence of corresponding period solutions for the case n ≫ 1 is then investigated by a perturbation treatment. I t is found that the analysis can be carried through explicitly, and, to the first order in n, the outcome confirms the existence of periodic solutions, and yields the dependence of the period'on an amplitude parameter. The results are checked against a direct numerical integration procedure that incorporates a method of searching for periodic solutions, and close quantitative agreement is found for sufficiently small values of n.

We make some investigations regarding the anomalous energy absorption in a turbulent plasma through high-frequency parametric instabilities. We establish the optimum threshold conditions with respect to the pump frequency. The influence of the turbulence spectrum on the parametric phenomena is investigated.

A stability analysis which directly uses particle distribution functions determined from experiments or transport theory, rather than model distributions, is carried out. The features of distribution functions relevant to whistlers, ion cyclotron waves, including their low-frequency extensions for propagation along the magnetic field, and to ion-acoustic waves are analyzed in detail. The dependence of wave growth on the precise shape of the distributions and the numerical feasibility of the method is demonstrated by the use of measured solar wind distributions.

Herein is described a calculation of the effective coffision frequency νeff of a low- density, shock-heated argon plasma under the influence of a weak electric field which oscillates harmonically with angular frequency ω. It is shown that, for the high frequency case ω > where is the collision frequency in a Maxwellian gas plasma, one has νeff ⋍ 2, provided that the imaginary part of the argon plasma conductivity is negligibly small in comparison to the real part. The influence of the theoretical model used to calculate νeff on the values of the electron temperature Te derived from measurements is compared with the results obtained in a data reduction for which the hard-sphere model for particle encounters was utilized.

A statistical theory of one- and two-dimensional temperature anisotropy driven Weibel instabilities is proposed. The theory is based on a two-temperature canonical distribution and the mean field approximation. It applies to a nonlinear, periodic, charge-neutralized, and collisionless system. Using a partition function formalism, equations of state are derived which predict upper bounds on the magnetic field energy produced by a quasi-static evolution of these instabilities. Theoretical predictions are in good agreement with results from numerical simulations.

The interaction of nonlinear Langmuir wave packets corresponding to periodic solutions of the nonlinear Schrödinger equation with thermal plasma particles is considered. The mechanism of interaction is nonlinear Landau damping. The wave packets are slowed down owing to interaction but their amplitudes remain essentially unchanged. The characteristic scale lengths of the slowing down are determined.