The instability of the ordinary electromagnetic mode propagating perpendicular to an external magnetic field is studied for two counter-streaming plasmas with anisotropic temperatures. A necessary and sufficient condition for this instability is derived and the growth rate is calculated. Although instability can occur in a plasma with low β‖e, provided the streaming velocity is comparable to the parallel electron thermal velocity, β‖e of the order of unity and large electron temperature anisotropy (T‖e≫ T⊥e) are required for large growth rates. These large growth rates are typically of the order of the electron cyclotron frequency. Comparison with the electrostatic two-stream instability is made.

Using the water-bag model of an electron plasma the nonlinear interaction of two plasma wave pulses (each of sufficiently narrow wave-number spectrum) is discussed. It is shown that, for the special case of a resonant (zero group velocity) pulse interacting with a non-resonant pulse, the interaction produces an effective slowing down of the group velocity of the non-resonant pulse. An application of this theory to the explanation of the apparent resonances at fractions of the plasma frequency observed in the ionosphere is discussed.

In this paper we consider the interaction between waves and particles in a weakly turbulent, collision-free plasma for the case of pure Coulomb interaction and zero magnetic field. Starting with the Vlasov equation we suggest a solution by means of a perturbation expansion and a diagram technique, which classifies the various interaction processes and leads to the derivation of kinetic equations.

A model kinetic equation for the internal fluid of diatomic molecules which interacts with thermal radiation is proposed. The cross-collision term developed for the molecule-photon interaction has the property that molecules and the sum of internal and photon energies are conserved. An alternative approach to this term based on the product of two BGKW collision operators yields the same result. It is also shown that the proposed model leads to an H-theorem.

The influence of the cathodes of a double-ended Q-machine on a flute instability of the Rayleigh–Taylor type is investigated for a low β plasma column. It is shown that flute modes are strongly affected by the end plate conditions and by the machine length. The occurrence of ion-rich sheaths is a necessary condition for the validity of the dispersion relation of the unbounded case. The range of values of the column length for the existence of a given flute mode is determined.

We study the effects of circularly polarized plasma waves in anisotropic homogeneous plasmas. The waves propagate in the direction of an external uniform magnetic field. It is shown that in many cases only one mode, with wavenumber k, is present in the plasma. We present a computer model suitable for the study of such cases. The model is used to simulate linearly stable and unstable phenomena. A good agreement with previous predictions of linear theory is obtained. Nonlinear effects are studied and mechanisms that stop instabilities are described.

A Lagrangian, for the slowly varying complex amplitude of an almost monochromatic electrostatic plasma wave in an unmagnetized plasma, is derived. The method is a variant of the averaged Lagrangian technique of Whitham, adapted for use in plasma physics by employing Low's Lagrangian, together with certain elimination procedures to simplify the Lagrangian to usable form. The expansion in powers of the wave amplitude is carried out to quartic terms, and non-adiabatic terms are also retained. Variations with respect to the amplitude lead to a nonlinear Schrödinger equation for the amplitude, while variations of the particle trajectories lead to a modified Vlasov equation, which includes the nonlinear reaction of the wave on the average trajectories. It is assumed that there are no resonant particles. These equations are coupled through the nonlinear frequency shift. It is found that the particle aspect of the plasma has a profound effect on the stability of the system, due to resonance of the wave envelope with particles moving at the group velocity. This effect, nonlinear Landau damping, is always destabilizing, leading to growth of modulations. In terms of the nonlinear Schrodinger equation, the effect changes the equation from a Hartree-Fock equation with a delta-function interaction to one with a non-momentum-conserving, non-local interaction. In the limit of fairly small wavelength, of the modulations, it is shown that the growth rate approaches that expected from plasma kinetic theory.

The effects of dynamic shielding of charged-particle interactions on the predicted values of hte transport properties of partially ionized argon are considered. It is found that, at low degreesof ionization, dynamic shielding effects are of little importance, because charged-particle encounters are infrequent, so that the perturbed Lorentzian method may be used to obtain a rapidly convergent solution. At higher degrees of ionization, where the Chapman–Enskog solution converges rapidly, dynamic shielding effects can be taken into account using the expressions presented in the appendix to this paper. It is also found that the static shielding model, assuming complete shielding by electrons only, yields results that are quite close to those obtained when dynamic shielding is considered.

The behaviour of a plasma permeated by a magnetic field, where the field possessess a hyperbolic neutural point, is considered. Results from numerical solutions of the magnetohydrodynamic formulation for such flows are reported. Problems are posed with the solar flare models of Dungey, Sweet & Petschek in mind. No evidence is found to support the idea that compression of the field lines near a hyperbolic null, in the presence of electrical resistance, can radically alter the geometry of those field lines (e.g. the formation of switch-off shocks). These computations do show that, for large values of the magnetic Reynolds number, a rate of annihilation, more rapid than that derived from order-of-magnitude estimates, is possible.

A derivation of the quasilinear equations is given, which is sufficiently general to include damped waves. The cause of some difficulties in previous derivations, momentum and energy conservation, and the origin of irreversibility are discussed.

It is shown that some recent solutions representing a dipole field immersed in an infinite plasma, which is perfectly conducting, belong to the vorticity equation in steady inviscid hydrodynamics. Further solutions of this equation, referring to the same problem, are constructed and discussed.

An asymptotic solution is given of hte particle motion in an arbitrary quasimonochromatic wave. Zero stationary magnetic field and untrapped particles are considered. The number of adiabatically trapped particles, the total momentum conservation and the space-averaged distribution function of non-resonant particles are derived for the case of an electrostatic wave with time-dependent amplitude.

The kinetic equations for infinite homogeneous turbulent plasma in a magnetic field are analyzed using a projection operator which allows the time dependence to be maintained in a more exact and consistent manner than has been possible heretofore. By introducing approximations on the multi-time correlation function rather than the fluctuations, as is conventionally done, a hierarchy of equations is obtained which predicts different behaviour for the system especially in connexion with wave-wave interations. These effects are further highlighted by showing how the present results reduce to those obtained by various authors.

The resonant three-wave interactions in an infinite homogeneous magnetized plasma are re-examined using the improved hierarchy presented in part 1. An equation for the wave energy is obtained which, for a spectrum made up entirely of marginally stable waves, is shown to be a second-order Markoffian differential equation, rather than a first-order equation as obtained by others. The conditions under which a first-order equation is derived are examined and discussed. For a spectrum composed of waves with small growth, rates, it is shown that the equation for the plasmon density always has a stationary solution, thus eliminating the occurrence of an ‘explosive instability’ in such systems.

One correction to column 2, table 2, page 455, has already been given (J. Plasma Physics, vol. 4, 1970, p. 643). In addition, the computed downstream convective velocities in columns 2, 3 and 4 of table 2 are given in a co-ordinate system moving at 29·8 km s-1 in the direction opposite planetary motion (-T direction), not in a heliocentric system as stated. The measured T-component and magnitude of downstream velocity in column 1 of table 2 only must be read as -59 ± 14 and 169 ± 20 km s-1, respectively, for a valid comparison with these computed results. However, the calculations have also assumed that the shock is moving at 29·8 km s-1 in the -T direction with respect to Earth (i.e. shock velocity is zero in the heliocentric system). This describes a non-physical situation, which could only apply to one of a series of crossings of a bow shock with an oscillating location. The conclusions of the paper are unchanged if the shock is assumed stationary, and if measured, computed and biased results are all expressed in a heliocentric system.