We have measured the level of density fluctuations 〈δne2(K)〉 for ‖K‖ ∼ 1/λD as a function of the angle between k and the current within a collisionless shock. The cut-off angle is in good agreement with that predicted for current-driven ion wave turbulence and one-dimensional heating of the ions. This agreement provides further evidence that ion-wave instability is responsible for the observed turbulence within the shock.

In the neo-classical theory of transport process in a toroidal plasma with long mean free path, the value of the poloidal rotation is determined by ambipolarity. This paper investigates the time-dependent phase during which this rotation develops. Diffusion arises from resonant particles, for which v∥ ≃ Er /Bφ. The time a particle spends in resonance, and hence its radial displacement, is now determined by the rate of change of Er, rather than collisional scattering. The time for Er to approach its quasi-stationary value is comparable to the mean time for an ion to travel the connexion length. This is short compared with typical experimental durations. The mass flow also builds up parallel to the magnetic field, but its contribution to the poloidal flow is small compared with the Er /B electric drift.

The probability that a fast charged particle slowing down in a plasma will react with an ambient ion prior to thermalization is calculated, as is the probability that an ambient ion scattered by the incident particle will similarly react. Results are given for an α particle from the DT reaction in a DT plasma.

In part 1 (Infeld 1972), it was shown that a nonlinear stationary wave in a cold plasma is marginally stable to all perturbations that are functions of the spatial direction parallel to the direction of propagation only. The stability analysis is extended here in part 2 to include general spatial variations. Within the limitations of the treatment, it is found that, for wave amplitudes up to maximal value (onset of trapping), the wave is marginally stable. Hence one would expect these large-amplitude cold plasma waves to exist in practice.

The one-dimensional analysis of part 1 is also extended to include waves with relativistic velocities, and such waves are again found to be marginally stable.

The stability of normal isothermal magnetohydrodynamic shock waves is studied with respect to isothermal as well as adiabatic perturbations. The problem is solved by the normal-mode analysis. The isothermal normal MHD shock appears to be stable.

A similarity technique is used to solve the problem of the ion rarefaction wave associated with a sheath growing at constant speed from a cylindrical or spherical probe into an infinite plasma.

A new treatment of soliton and laminar shock-like structures in single ion species and counter-streaming plasmas in perpendicular magnetic fields is presented. Charge separation effects are treated exactly, and may become important for high Alfvén Mach number flows. The theory contains the familiar quasi-neutrality theory in the limit B20 ≪ Μ0nmec2 and the Longmire theory in the limit B20 ≫ Μ0nmec2. The introduction of the potential ψ as the primary dependent variable, instead of the magnetic field B, clarifies the role of ion dynamics. New pseudo-potential functions are defined which generate classes of solutions for single ion species, rigid piston problems, and multispecies problems. They also provide information about the evolution of particle piston solutions. Results include the fact that a small amount of resistivity allows shock solutions for very large Mach numbers, and for zero dissipation the parameter

does not affect the solutions except in the scale length.

The effect of a magnetic field on the diffusion of a cylindrical column of ionization, having an initial electron density much greater than that of the ambient weakly ionized plasma in which it is embedded, is examined for the case in which the electron gyro-frequency is much greater than the electron neutral collision frequency Ve. The nonlinear diffusion equations are solved by means of a perturbation expansion based on their exact solution for the case Ve = 0. This approach leads to a singular perturbation problem, and shows that, when the column is not closely aligned with the field the distribution of plasma differs appreciably from that obtained from an ordinary anisotropic diffusion equation.

The interaction between three modes in a non-homogeneous plasma is analyzed in a very simple situation. It is shown that, unlike the homogeneous case, and on account of the regular character of the perturbation procedure used, the problem does not call for a nonlinear algorithm. A strong interaction takes place when both pump and idler modes exist inside the plasma and all modes have wavelengths (much) smaller than the plasma non-homogeneities.

The stability of a magneto-sonic wave of small (but finite) amplitude, propagating in a low- β plasma across a magnetic field, is investigated. It is shown that such a wave is unstable with respect to parametric splitting into many satellite waves. Wavenumbers of the satellite waves differ from that of the original magneto-sonic wave. Thus, the sateffite waves leave an interaction space, and form oscillating ‘tails ’ in front of and behind the initial pulse.

The structure of a steady plane shock in a fully ionized gas has been investigated using the Boltzmann equation with the Gross–Krook type model as the governing equation and the discrete-ordinate method as a tool. The present results agree well with the results obtained by the continuum approach for weak shocks. For strong shocks the present approach gives results that are considerably different from those yielded by the continuum approach, particularly in the high pressure region. Also, the present method gives smooth and continuous shock profiles for high Mach numbers. On the other hand, the results from the continuum approach contain discontinuities in slope. The ion and electron distribution functions across the shock are found to be singly peaked for all cases considered and the effects of the induced electric field is small.

In a plasma at rest, the electrostatic potential around a point charge obeys the well-known Debye shielding law. Modifications, for the ease of a flowing plasma, have been studied in the limiting cases of either long or short distances for subsonic and hypersonic velocities. Only recently this was extended to include all distances, restricted to a two-dimensional case. However, neither of these modifications includes the ionic motions. In this paper, we derive general expressions for the electrostatic potential which are valid for all distances and flow velocities in one-, two- and three-dimensional cases. This is done first with unperturbed ions, and then for the case where ionic motions, which are seen to be important for mesothermic flow velocities, are included. In both cases, the results are discussed and illustrated.