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 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 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.

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.

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.

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.

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.

Acceleration of an electron by the electrostatic field of ion wave fluctuations is considered including the external magnetic field. It is found that an accelerated electron can emit unstable electromagnetic waves which propagate along the guide magnetic field. As an example, we discuss the generation of right-handed circularly polarized whistler waves. Application of our result to laboratory and space plasmas is examined.

An exact solution of the MHD flow of an incompressible, electrically conducting, viscous fluid past a uniformly accelerated infinite plate has been presented. The velocity profiles are shown graphically and the numerical values of axial and transverse components of skin friction are tabulated. At high values of the Hall parameter, wt, the velocity is found to be oscillatory near the plate.

Finite ion Larmor radius effects (ε ≡ γLi/LΙ< 1 but finite) are found to cause a branching of the Alfvén ion cyclotron mode, whereas the growth rate of the mirror mode is found to be of the order of for ωci for ε≥ 0.1 and rather moderate values of plasma beta and temperature anisotropy. For this regime its growth rate considerably exceeds that of the Alfvén ion cyclotron mode.

In the vicinity of a turning point, a high-power laser radiation (in the upper- hybrid mode) is unstable for short wavelength, purely growing perturbations, viz, oscillating two-stream instability. The nonlinearity in the low-frequency response arises through the parallel pondermotive force whereas in the high- frequency response it arises through the equation of continuity. In the limits of long and short perpendicular wavelengths, κ┴ρe< 1 and κ┴ρe > 1, the growth rates are found to be γ∞ │κ┴.V0┴│2, where ρe and V0┴ are the electron Larmor radius and oscillatory drift velocity.

The linear stability of a uniformly imploding shell, modelled as an ideal polytropic fluid, is investigated. Two types of unstable modes are found: incompressible irrotational perturbations localized at the outer surface, ascribable to Rayleigh—Taylor instability, and compressible modes, associated with convective instabiiity. Kidder's result for the Rayleigh—Taylor modes is shown to hold independently of the form of the shell density profile. By means of a variational principle it is shown that the criterion for convective instability is the existence of a region within which d(pp-γ)/dr> 0. Analytic solutions for both spatial and temporal dependence of the perturbations are presented, and the results applied to pellets imploded by the action of a laser or charged-particle beam.

This paper presents an investigation of the excitation of an electrostatic pulse in a hot collisionless plasma by two Gaussian EM pulses at the difference frequency w1–w2, w1 and w2being the angular frequencies of two EM pulses. When the EM pulses have intensity distributions which are uniform in space and Gaussian in time, the generated electrostatic pulse is Gaussian in time with pulse width [t210 t220/ (t210+ t220)]½, where t10 and t20 are the EM pulse widths. When. the two EM pulses have Gaussian distributions in a plane transverse to the direction of propagation, the generation phenomena are considerably modified as a result of the cross-focusing of the two EM pulses.

The equilibrium statistical mechanics of electrostatic ion wave turbulence is studied within the framework of a continuum ion flow with adiabatic electrons. Attention is drawn to the fact that the wave field consists in general of two components, namely ion-acoustic and ion vortex modes. It is shown that the latter can significantly affect the equilibria on accoant of their ability both to emit and to scatter ion sound. Exact equilibria for the vortex—acoustic wave field are given in terms of a canonical distribution and the correlation functions are expressed in terms of a generating functional. A nonlinear transformation of the wave field, which removes the vortex-acoustic interaction energy to lowest order in the strength of the coupling, while preserving the phase space volume element, is then introduced. This enables the Feynman-Hibbs variational principle to be used to obtain an approximate generating functional based on a ‘trial’ energy functional, which is a quadratic in the new variables. Detailed calculations are carried out for the case in which the dominant coupling is an indirect interaction of the vortex modes mediated by the sound field. An equation for the spectrum of the vortex modes is obtained for this case, which is shown to possess a simple exact solution. This solution shows that the spectrum of fluctuations changes considerably as the total energy increases. At low levels of excitation the solution reduces to equipartition of energy. At higher levels the indirect interaction becomes significant and the formation of a condensed vortex state is possible when the mean energy exceeds the electron thermal energy. It is suggested that condensed vortex states could occur in the plasma sheet of the earth's magnetosphere and it is shown that the predicted ratio of the mean ion energy to the mean electron energy is consistent with the trend of observed values.