The dispersion relation for a collisionless moving electron plasma when the directions of motion and wave propagation are normal to the magnetic field is analyzed. It is shown that the ordinary wave remains unaffected, but the extraordinary wave shows a different behaviour, especially at small phase velocities. It has different cut-off frequencies, propagates for all frequencies from zero to infinity, changes the sense of polarization accompanied by anomalous dispersion and does not show any resonance.

The electromagnetic streaming instability yields substantial growth for propagation at large angles to the beam. Transverse Landau damping suppression of the mode is calculated for a variety of beam parameters. The saturated stage of the instability (bunching in position space) can produce large electric fields oscillating at the plasma frequency in the vicinity of the beam. These fields can cause further ionization, and define the final channel radius. Comparison with experiment is satisfactory.

A theory of the amplitude modulation of plasma waves is developed by applying the Karpman-Krushkal theory of quasi-monochromatic wave propagation analysis of the nonlinear wave-particle resonant effect leads to the modified nonlinear Schrüdinger equation with a non-local nonlinear term, which has been independently derived by Ichikawa & Taniuti on the basis of a reductive perturbation approach. The effect of the non-local nonlinear term is described explicity by investigating the modulation instability of an ion plasma wave.

We describe a family of exact nonlinear solutions of Vlasov's equations; the linear counterpart being circularly waves. An exact solution for a sub-group of initial conditions is given. The plasmas treated are multi-species, infinite and homogeneous, embedded in a uniform magnetic field.

Equilibria of magnetoplasma with planar symmetry are presneted. Among the equilibria illustrated are configurations of plasmas confined inside a cylindrical wall and plasma in a double-inverse-pinch device.

Electromagnetic waves propagating perpendicular to an external magnetic field in a non-uniform anisotropic plasma can become unstable due to the excitation of either resonant ion instability or resonant electron instability. The former instability can exist in the absence of both the temperture anisotropy and the temperature gradients, whereas for the excitation of resonant electron instability the presence of at least one of them is necessary. An off-resonance drift cyclotron instability can also get excited if the temperature gradients are much stronger than the magnetic field gradients.

The multiple water-bag model can be used to describe a uniform warm plasma as accurately as one wishes. Moreover, it makes boundary-value problems in such a plasma tractable. As a special case, the problems of the influence of a point charge on a spherical grid and of the mutual influence between two spherical grids are solved. From these results, the self-impedance of a double-sphere dipole antenna is deduced. If the spheres are widely separated it exhibits a resonance at the plasma frequency, whereas if the spheres are close there is an anti-resonance at this frequency. The mutual impedance of a quadrupole probe comprising two double-sphere antennae is also studied, and is found, usually, to be not very sensitive to the finite radius of the spheres. For determining the electron temperature of the plasma, this last device seems better than a double-sphere antenna alone.

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.

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.