It is shown that an equilibrium of a magnetoplasma with a small separatrix angle at the magnetic neutral point possesses a greater magnetic energy than its corresponding equilibrium with a large separatrix angle. Hence, it is energetically possible for a configuration with two oppositely directed magnetic fields in contact to proceed to a potential field through the process of field line reconnexion. The excessive magnetic energy would be released into kinetic and thermal energies.

The spectra of low-frequency surface waves propagating along a warm magneto- plasma layer bounded by dielectric are investigated, using a two-fluid hydrodynamic plasma model. It is shown that such propagation is possible only for some definite directions of the external magnetic field B0, with respect to the plasma-dielectric interfaces. The spectra obtained for a thick plasma layer correspond to the well-known results for a magneto-active plasma, bounded on one side by a vacuum, derived in the limit of one-fluid hydrodynamics.

A study is made of a parametric instability in a magnetized plasma in which an electromagnetic pump wave of either right- or left-hand circular polarization decays into a Langmuir wave and another circularly polarized wave, all with wave vectors colinear with the external magnetic field. The analysis is based on a multiple-time-scale perturbation expansion of the fluid equations, incorporating the effects of temperature, collisions, and the spatial variation of the pump wave. The threshold values of the pump field intensity required for instability and the growth rates above threshold are calculated.

Equilibrium solutions, which represent configurations of a magnetoplasma with the geometry of double-inverse-pinch, are presented.

The theory of scattering by charged particle density fluctuations of a plasma is developed for the case of zero magnetic field. The source current is derived on the basis of, first, a three-wave interaction between the incident and scattered electromagnetic waves and one electrostatic plasma wave (either Langmuir or ion-acoustic), and secondly, a synchronous interaction between the same two electromagnetic waves and the discrete components of the charged particle fluctuations. Previous work is generalized by no longer making the assumption that the frequency of the electromagnetic waves is large compared to the plasma frequency. The general result is then applied to incoherent scatter, and to scatter by strongly driven plasma waves. An expansion is carried out for each of these cases to determine the lower order corrections to the usual high-frequency scattering formulae.

The most common approach to the study of plasma nonlinearities is by a form of perturbation theory which first studies the linearized equations, then evaluates effects of nonlinearities in terms of these linear solutions. Such an approach is probably justifiable for the effect of weak nonlinearities, but will almost certainly miss features that are exclusively nonlinear in nature (i.e. effects which cannot be described by modifying linear theory, or effects which are present only when e.g. a source of disturbances in a plasma reaches a certain threshold amplitude). It is the object of this paper to investigate one possible such nonlinear effect.

The formalism for the calculation of the absorption of radiation by a hydrogen plasma at common laboratory conditions is summarized. The hydrogen plasma absorption coefficient for laser radiation has been computed for a wide range of electron densities (1015- 1018 cm-3) and temperatures (10 000–40 000 °K). The results of this computation are presented in a graphical form that permits a determination of the absorption coefficient for the following laser wavelengths: 0.176, 0.325, 0.337, 0.442, 0.488, 0.51, 0.633, 0.694, 1.06, 1.15, 2.36, 3.39, 5.40 and 10.6 Μm. The application of these results and laser radiation absorption measurements to plasma diagnostics is discussed briefly.

Most of this paper is concerned with the construction of suitable Lagrangian functions for the dynamics of a cold plasma, in such a way as to retain the relativistically covariant formalism. In one method, this is achieved by the introduction of a set of three variables which label the world lines of the particles. A second method results in a Clebsch type of representation. Sturrock's relativistic Lagrangian and Low's hot plasma Lagrangian are also briefly discussed in the context of the present work. The behaviour of the canonical stress tensor is considered. The applicability of many of the general results of part 1 is ensured by establishing the existence of the Lagrangian function.

The reciprocity theorem for monopole antennas, a gridded parallel plate, parallel-plane grids and a plane plate, which radiate and receive an electron plasma wave in an unbounded plasma, is introduced theoretically, based on the electron fluid model. The theorem holds experimentally if the d.c. bias potential of antennas is lower than about the floating potential. The measured reception pattern of an antenna is equal to its radiation pattern. The wave amplitude and the impedance between the antenna and the plasma are measured experimentally.

An inhomogeneous plasma column surrounded by a glass wall is described through full first order in temperatures Te and Ti using a complete electromagnetic treatment. We study the response of this system to a purely TE wave with K perpendicular to the axis. Comparison with existing theories and experimental results is made in the electron–wave domain (ions play no role) with zero steady magnetic field, i.e. in the case of temperature (Tonks-Dattner) resonances. Perhaps surprising at first sight, there is poor agreement with experiment at low density, the classic T½e theory (scalar perturbed pressure approximation) giving far better results. Simple arguments concerning the different levels of approximation in the description of the longitudinal k2 enable us to distinguish the crucial difference existing between a scalar pressure and a complete T description and to understand this result. We generalize these findings, demoastrating that a description is always more realistic than a one in the range ωpe<ω.

A model for nonlinear Landau stabilization of a linear instability is treated analytically. The model may apply to any dissipative system described by: (i) a linear dissipation function γ(k), of one degree of freedom k, which presents a limited unstable domain δK and a damped region for lower values of k, and (ii) a transition probability for the nonlinear Landau damping (nonlinear wave–particle interaction) proportional to k – K'. For a sharply pointed γ(k), the model leads to a kinetic regime presenting periodic relaxation oscillations of large and constant amplitude. Starting from weak turbulence, the system organizes itself into a periodic regime, which may be of interest in connexion with research in morphogenesis. For a smoothed γ(k), the relaxation oscillations damp, slowing down towards a turbulent energy level.

Electromagnetic waves propagating transverse to an external magnetic field in a high-β (β being the ratio of the kinetic pressure to the magnetic pressure) plasma become unstable through purely growing modes when β∥e, (electron β parallel to the magnetic field) exceeds a certain minimum value β∥*. For J ≦ 2 (J being the distribution index), the region of instability consists of a single band of unstable wavenumbers k, whereas for J ≥ 3 more than one unstable wave number band may exist. The growth rates are largest for J = 0, and tend to decrease as J increases. The presence of hot ions increases the instability region by exciting a low-frequency instability. This instability gets excited at considerably lowered values of β‖e, and has growth rates of the order of ion cyclotron frequency. The effect of T‖i/T‖e and T‖e/T⊥e is destabilizing, whereas that of T⊥i/T⊥e is stabilizing.

Equilibrium and non-equilibrium properties of the three-dimensional guiding-centre plasma (in which the particles move with the guiding-centre drift across constant magnetic field lines, and according to Newton's laws along the field lines) are investigated. In equilibrium, the transverse spatial diffusion and conductivity coefficients are calculated, and are shown to be related via a generalized Einstein relation. The diffusion coefficient consists of a Bohm-like 1/B contribution which tends to zero as the plasma volume tends to infinity, as well as a classical 1/B2 contribution, which is independent of the size of the system. The Gibbs ensemble is constructed, and it is seen that thermal equilibrium results for the pair correlation, fluctuation spectra etc. are exactly the same as for the three-dimensional unmagnetized plasma. In the non-equilibrium case the appropriate Liouville equation and BBGKY hierarchy are considered. It is shown that to first order there is no tendency for the system (assumed spatially uniform) to relax towards thermal equilibrium.

The problem is considered of the analytical calculation of the fluctuation level of the collective electric field in the case of a collisionless non-dissipative plasma subject to a reactive marginal instability. The existence of this instability only depends on the negative sign of the real part of the dielectric constant e and is not related to the dispersive or dissipative effects described by the frequency dependence or the imaginary part of c. A typical example is given by the non- resonance two streams instability with a symmetric distribution function. In this situation the methods of the thermodynamics of Vlasov systems can be applied to calculate the fluctuation level connected with the instability, provided the Vlasov system is near enough to the marginally stable state and the effect of mode coupling can be neglected (at least for a certain time). In the linear limit, the unstable equilibrium is associated with a minimum of the entropy. When the instability develops new nonlinear terms appear in the dielectric coefficient c, related to the inhomogeneization of the system associated with the growing collective field. These nonlinear terms counterbalance the negative sign of the linear part of c, leading to a saturation of the instability. A neighbouring inhomogeneous equilibrium with long wavelength is then realized, which corresponds to a maximum of the entropy and is stable (under the assumed approximations). The corresponding electrostatic potential is proportional to u−uc, where u is the velocity corresponding to the maxima of the two-stream distribution and uc is the critical value of u for the onset of the instability. The results of the thermodynamic method for the neighbouring equilibria are compared with those obtained by solving the stationary Vlasov equation with conventional analytical methods or with computer calculations.