The results of the nonlinear computer investigationof the whistler mode instability with the aid of particle-in-cell simulation methods are presented. The electron plasma considered is hot (kT‖ = 20 keV), anisothermal (T⊥/T‖ ≃ 2) and embedded in a static magnetic field such that β‖ = 0.8. A detailed Fourier analysis of the electromagnetic activity developed under the above stated conditions is carried out: the waves are shown to be electron-like and excellent agreement with the linear stability analysis for the first stages of evolution is found. The feed-back effect of the waves on the particles is shown to result in a continuous decrease of the thermal anisotropy ratio T⊥/T‖ corresponding changes in the Fourier spectra of the electromagnetic activity are observed; additional changes in the wave spectrum are introduced by the interaction between various instability modes. At the end of the run (ωpt ⋍600), the state of the system resembles a quasi-stable equilibrium, in which the electromagnetic energy achieves its maximum value: in this state, unlike the equilibrium one usually considered in the linear stability analysis, a thermally anisotropic plasma with T⊥/T‖⋍1·35 appears to be quasi-stable against the whistler mode instability. This last result is relevant for the geostationary magnetospheric conditions (in the equatorial region) where quasi-stationary states with T⊥/T‖ about 1·3 are observed.

Shielding of test charges in warm, isotropic electron and electron–ion (Te ≫ Ti) plasmas is studied analytically and numerically. For a plasma with hot Maxwellian electrons and cold mobile ions, the potential due to a charge moving faster than the ion acoustic velocity has an ion acoustic Cerenkov cone. Ahead of the particle, the shielding is the usual electron Debye type with a modified longer shielding length. Potential wells with γ−1 dependence exists inside the cone. The potential falls off as along the cone surface. Outside the cone, the potential decays exponentially. A charge moving slower than the ion acoustic velocity also creates a cone, with potential decay as γ−3 outside the cone, potential wells decaying as γ−1 inside the cone, and potential wells falling off as along the cone surface. In both cases a radial logarithmic singularity exists along the trailing axis. Using a mono-energetic ion distribution, the singularity is removed and an ion thermal Cerenkov cone appears. For a monoenergetic electron plasma, assuming immobile ions, a test charge moving faster than the electron thermal velocity excites a thermal Cerenkov cone. Outside the cone, the far-field potential falls off in quadrupole form as γ−3. Inside the cone, potential wells decay as γ−1.

The shock conditions for a perfect gas in aligned-fields magnetogasdynamics are solved to give all variables downstream as rational functions of the density ratio. The thermodynamically admissible, evolutionary shock solutions are exhaustively classified into seven shock polar types, including a new type of supersonic, sub -Alfvénic polar. Example polars of each type are presented in the magnetograph (dimensionless magnetic induction vector plane) and in the Taniuti–Resler diagram (M, A plane) in order to display, respectively, the shock geometry and the state of the gas. A short discussion of the relation of the shock properties to flow over bodies is presented.

Multi-fluid equations derived in a previous paper are used to study small- amplitude wave motion in a partially ionized chemically-reacting plasma. The plasma is assumed to be infinite and without external fields. The dispersion equations are derived and solved both numerically and analytically for several limiting cases. The effects of chemical reactions have been explicitly obtained. It is found that at the long-wavelength limit, the ionization and recombination terms play the dominant role for the damping of certain longitudinal waves even for a nearly frozen plasma.

Uncommonly large electron density fluctuations, accompanied by large skewness and flatness factors, have been observed in the transitional zone of a plasma jet. This paper investigates these further by a digital analysis of Langmuir probe signals from this zone. The electron aggregate is found split into a decaying laminar-fluid remnant and a growing population of turbulent fluid. The uncommon statistics are caused by the double-humped histogram, while those of each population separately are normal. The mean electron density of the aggregate displays no simple chemical decay trend, but that of the laminar population fits known argon recombination schemes.

The dependence of the asymptotic behaviour of small ion-acoustic waves on the number of resonant electrons is investigated by assuming an electron equation of state corresponding to the observed flat-topped electron distribution functions. The result is a modified Korteweg-de Vries equation with a stronger nonlinearity.

The drift magnetosonic waves in a finite-pressure plasma are considered. Instabilities arising from the magnetic drift resonance of particles with waves are investigated for two cases: quasi-perpendicular and oblique propagations. It is shown that, in a wide range of both the density and temperature gradients, these waves can be excited even in a high-β (β≥1) plasma.

The magnetic field and flow with an X-type neutral point or stagnation point are studied numerically for the steady state of incompressible, finitely conducting, viscous fluid in two dimensions. There appear two transition layers connecting smoothly the regions on either side, each of which contains almost uniform magnetic field and flow. The electric currents are concentrated in the vicinity of the neutral point and along the transition layers. The magnetic field is regarded as almost frozen in the fluid in other current-free regions, even in the case of moderate conductivities. The current-core over the neutral point is accompanied by a remarkable shear of currents, which may contribute to reducing the local electrical conductivity effectively. Thus the re-connexion of magnetic lines of force may be possible even in very highly conducting fluids. It is shown that the re-connexion is not essentially influenced by dissipations due to finite electrical conductivity or viscosity, but definitely by external conditions such as the applied electric field in the magnetic field and flow.

Propagation characteristics of two magnetosonic waves, the fast and slow modes, in layered plasmas with different β values are studied, where β is the ratio of plasma pressure to magnetic pressure. In the first part we consider the efficiency of wave penetration from one region to another with different β ratios, β1 and β2. In particular, the condition for the total reflexion, amplitude and phase of the reflexion and transmission coefficients at the interface are obtained for both modes. The results indicate that the range of deviation of the ratio β2/β1 from unity is very small for penetration of the slow mode, while the ratio for the fast mode covers a wide range. In the second part, the fast and slow normal modes of magnetosonic waves in layered plasmas are discussed and their phase and group velocities, and the spatial damping rate due to partial leakage of wave energy are compared between two modes. From these, it is concluded that the presence of the slow magnetosonic waves is restricted to within the high-β plasma region. Finally, application of these to the earth's magnetosphere is given qualitatively.

The problem of propagation of finite-amplitude electromagnetic waves in a plasma containing random irregularities is studied. Using a recently developed perturbation technique, a general equation for finite amplitude coherent waves is derived. Included in this equation are both the effects of quasi-harmonic nonlinear heating of electrons and random scattering by irregularities. The equation is solved in general by the equivalent linearization procedure. The amplitude of the coherent wave is found to be attenuated by collision and scattering. Both attenuation are affected by the nonlinear heating of the electrons. Curves showing the results for a specific example will be presented.