The theory for fundamental plasma emission by the three-wave processes L ± S→T (where L, S and T denote Langmuir, ion sound and transverse waves, respectively) is developed. Kinematic constraints on the characteristics and growth lengths of waves participating in the wave processes are identified. In addition the rates, path-integrated wave temperatures, and limits on the brightness temperature of the radiation are derived.

The theory for second harmonic plasma emission by the weak turbulence (or random phase) processes L + L ± S→T, proceeding in two three-wave steps, L ± S→L′ and L + L′→T, where L, S and T denote Langmuir. ion sound and electromagnetic waves, respectively, is developed. Kinematic constraints on the characteristics and growth lengths of waves participating in the wave processes, and constraints on the characteristics of the source plasma, are derived. Limits on the brightness temperature of the radiation and the levels of the L′ and S waves are determined. Expressions for the growth rates and path-integrated wave temperatures are derived for simple models of the wave spectra and source plasma.

The theory for third and higher harmonic plasma emission by the weak turbulence (or random phase) process L + T′→T (where L denotes a Langmuir wave, and T and T′ denote transverse waves) is developed. Kinematic constraints on the characteristics and growth lengths of waves participating in the wave processes are identified. The cases of L waves produced either directly by a streaming instability, or by the decay L→L′+S (S is an ion sound wave) of L waves generated by a streaming instability, are considered. Limits on the brightness temperature of the radiation are determined, and expressions for the growth rate and path-integrated wave temperatures are derived.

The relation between various surface quantities required in hydrodynamic calculations, and the relation between the parallel and perpendicular currents in an arbitrary magnetic toroidal plasma configuration with scalar pressure, are generalized to the case of anisotropic pressure. Magnetic co-ordinates for hydrodynamic equilibria in this configuration are defined. A general expression for the mean velocity of diffusion through a magnetic surface, on the basis of the one-fluid magnetohydrodynamic equation with anisotropic pressure, is derived.

The spectral characteristics of the high-frequency part of the slow electromagnetic mode, specific for plasmas placed in an external d.c. electric field, as well as the features of the corresponding instability, are analysed for weakly ionized argon gas-discharge plasmas with E/n ranging from 25 to 150 Td, and with electron temperatures between 60000 and 70000 K. The analysis is based on the linear theory of perturbation, and the dynamics of the electrons is described by appropriately modified kinetic equations for the one-particle distribution function. Attention is focused on the collisional processes between electrons and neutrals, and both elastic and excitational collisions are taken into account. Apart from the ‘indirect’ collision effects (modifications of the form of the electron steady-state distribution function, evaluated here analytically, with the thermal motion of the neutrals included), their ‘direct’ influence (arising from perturbations of the collision integrals) is also significant in the electron temperature range considered. As a consequence of the ‘direct’ influence of inelastic collisions, in particular, the mode studied was found to exist in two distinctly separate wavelength ranges. The instability was found to develop only in the one corresponding to shorter wavelengths (below some 30 cm).

This work is intended to explain why the resonant response of the magnetosphere prefers to have discrete frequencies. Using a cylindrical model for the outer magnetosphere with a plasma density profile proportional to 1/r, we show that the eigenequation characterizing the eigenmodes of the hydromagnetic waves in this model has two turning points along the radial axis. The locations of the turning points depend upon the values of the eigenperiod and the associated east-west wavenumber of the eigenmode. The energy spectrum of the excited cavity modes is seen to have sharp peaks at discrete frequencies when the surface perturbations have a uniform spectrum in the frequency range of interest. We, therefore, have also shown that only the discrete set of the magnetospheric cavity eigenmodes can efficiently couple the perturbations excited on the boundary of the magnetosphere to the field-line resonant mode excited inside the inner turning point of the cavity eigenmode. The most likely values of east-west wavenumbers and wave period range are determined.

Starting from classical transport theory, equations for particle density, particle momentum and electron and ion temperatures are derived for steady-state, toroidal plasma configurations in a parameter regime like that of ACT-I. A set of simplified equations for particle density and electron and ion temperatures are solved numerically. Radial density and temperature profiles are shown and compared with experiments.

The application of Hamilton's principle to the problem of the determination of the structure of low free energy state plasmoids is discussed. It is shown that Clebsch representations of the vector fields and representations involving side conditions on the functional result in the same sets of Euler–Lagrange equations. The relationship of these representations to the problem of containment forces in vortex structures (plasmoids) is considered. It is demonstrated that the lowest free energy state of an incompressible plasma is always Lorentz force and Magnus force free. For a compressible plasma obeying the adiabatic gas laws, the Magnus force is finite. Introduction of conservation of angular momentum as an additional side condition also results in finite containment forces.

An asymptotic expression for the dielectric tensor e of a hot magnetized plasma is obtained employing the steepest descents method, via the transformation of the components of ε into their integral representation. The electrostatic Bernstein dispersion relation for oblique and perpendicular propagation is discussed under this treatment. It is shown that with this procedure the computation of the dispersion relation is up to 20 times faster when it is compared with the original expression, and the relative accuracy is usually as good as O·l% for a typical case.

A general solution condition for collisionless sheaths is developed. Previous work has assumed that the Bohm criterion or the generalized Bohm criterion ensures a self-consistent sheath solution. This paper shows that for nonmonotonic collisionless sheath structures, such as double sheaths containing trapped ions, the generalized Bohm criterion is a necessary but not a sufficient condition. The general solution condition developed is always sufficient and the generalized Bohm criterion is shown to be special case of it. The general solution condition is applied to a double emitter sheath containing trapped ions. First, it is shown that the low-energy part of the plasma ion distribution coming into the sheath cannot be neglected as claimed in some analyses, because the shift in mean ion velocity through the pre-sheath (generalized Bohm speed) depends strongly on low-energy ions. Second, it is shown that the presence of trapped ions moves the point of critical self-consistency away from the collisionless sheath-neutral plasma asymptotic match and into the collisionless sheath. Consequently, both the sheath structure and the generalized Bohm speed depend on the amount of trapped ions. Thus collisional effects may dominate the structure of a presumably collisionless sheath through the trapping mechanism and the collisional pre-sheath which determines the low-energy ion component entering the collisionless sheath.

The process of parallel whistler-mode propagation in a weakly relativistic plasma is interpreted in terms of the periodic energy exchange between wave field and perturbed electron currents. The physical meaning of the thermal and relativistic corrections to the value of the refractive index of these waves in a cold plasma is considered in detail.

Accounting for an external electron current gradient, a set of nonlinear fluid equations governing the dynamics of kink instability in an inhomogeneous magnetized plasma has been derived. In the linear regime, the dispersion relation is analysed and the variation of the growth rate is graphically shown. In the nonlinear regime, it is shown that a quasi-stationary solution of the mode coupling equations can be represented as a dipolar vortex. Conditions under which the latter arises are given.

This paper deals with the application of a Fokker–Planck code to the problem of heat conduction down steep thermal gradients. The results are compared with those obtained with other codes based on the Fokker–Planck equation in which various simplifying assumptions are made in the calculation of the Rosenbluth potentials. The particular problem considered is that of heat flow between spherical shells at different temperatures. The difference between the heat flows resulting from isotropic and anisotropic distributions is specially emphasized. The results show that, for calculating temperature, the usual Legendre polynomial expansion for the angular dependence of the distribution function gives reasonable results even when it is limited to two terms. However, the heat fluxes can differ by a factor of two when the Rosenbluth potentials are calculated from angular averages of the distribution function even when in the rest of the calculation the Legendre expansion is retained to all orders.