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.

Lie group point transformations applied to the one-dimensional Vlasov– Maxwell equations yield general similarity forms for the dependent and independent variables. One class of such solutions is seemingly like Bern-stein-Greene-Kruskal solutions in allowing a relatively free choice of electric field, but with a more complex time dependence. The phase trajectories of the particles are found here for both temporally damped and (possibly unphysical) growing electric fields in this class by numerical integration in the original and in transformed co-ordinates. The analysis, which includes an analytic consideration of phase-plane fixed (critical) points, shows the advantages of the new co-ordinates, and reveals qualitative features of the distribution function.

A model of linear wave conversion problems is formulated, which forms a natural generalization of the Budden resonance tunnelling model. The structure of the model is such as to conserve energy flux, and also is such as to allow explicit solution in terms of contour integrais. An arbitrary number of wave modes may participate. Explicit expressions for the conversion coefficients in terms of quantities derivable from the dispersion relations are obtained. A standard way of extending the model, by which resonant absorption is retrieved as conversion into an additional short wave mode, is included. The formulae obtained, are shown to include a complete solution to the problem of linear conversion in a magnetized plasma when the waves are nearly parallel to the magnetic field.

From the BBGKY equations for a pure electron plasma a derivation is made of a collision integral that includes the combined effects of particle gyration in a strong magnetic field and non-uniformities of both the distribution function and the self-consistent electric field on the collisional scale. A series expansion of the collision integral through the distribution function and the electric field on the collisional scale is carried out to third order in derivatives of the distribution function and to second order in derivatives of the electric field. For the strong-magnetic-field case when collision-term contributions to only first order in 1/B are included, a particle flux transverse to the magnetic field proportional to l/B2 is derived. The importance of long-range collective collisions in this process is shown. The result is in contrast with the classical l/B4 proportionality, and is in accordance with earlier studies.

The effect of toroidicity during lower-hybrid mode conversion is examined by treating the wave propagation in an inhomogeneous medium as an eigenvalue problem for ω2 (m, n), m, n poloidal and toroidal wavenumbers. Since the fre-quency regime near ω = ω2LH is an accumulation point for the eigenvalue spectrum, the degenerate perturbation technique must be applied. The toroidal eigenmodes are constructed by a zeroth-order superposition of monochromatic solutions with different poloidal dependence m; thus they generically exhibit a wide spectrum in k‖ for given fixed ω2 even for small inverse aspect ratio є. When the average 〈k‖〉 is in the neighbourhood of kmin, the minimum wave-number for accessibility of the mode conversion regime, it is possible that excitation of toroidal modes rather than geometrie optics may determine the wave coupling to the plasma. Our results are not changed significantly by a small amount of dissipation. The level of density fluctuations in modem tokamaks, on the other hand, may cause enough k‖ scattering to mask the toroidicity effects. Nevertheless, it is shown that a wide k‖ spectrum excited by a monochromatic pump will persist even with vanishing fluctuation level.

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.

Nonlinear regular structures in a magnetized plasma connected with drift magneto-acoustic waves (DMA) are investigated theoretically. Three-dimensional nonlinear equations of weakly dispersive DMA waves are obtained. These equations contain both the scalar nonlinearity and the vector one, and generalize the two-dimensional Kadomtsev–Petviashvili (KP) equation. The existence is shown of regular stationary structures due to the scalar nonlinearity: one-dimensional solitons, two-dimensional rational solitons, chains of solitons and so-called ‘crosses’. The stability of one-dimensional DMA solitons is investigated. It is shown that soliton stability depends on the sign of the wave dispersion as in the case of systems described by the KP-type equation.

The ponderomotive force in a magnetized plasma is derived by carrying out the renormalization of wave–particle interactions based on the Vlasov equation. A significant feature of the resuit is non-singular behaviour at resonance even in the case of perpendicular propagation. This is shown to be related to the onset of the diffusive motion of particles due to the orbit instability near resonance, where the ponderomotive force is eventually small.

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 set of hydrodynamic equations for the ion component of a magnetized low-pressure plasma, including the nonlinear ion drift and waves related to it, taking into account dispersion effects of order k2⊥ρ2i (k⊥is the characteristic transverse wavenumber and ρi is the ion Larmor radius), is obtained. The reduction of these equations using the standard assumptions of vortex theory is given. The problem of the integrals of motion of the simplified equations is discussed. Account is taken of the gravitational force (which models curvature of the magnetic field lines), the three-dimensionality of the perturbations (drift-Alfvén effects) and plasma rotation. It is suggested that the ion-drift hydrodynamics discussed here should be the basis for the analysis of the ion drift and the vortices related to it, as well as for the theory of decay processes with participation of the ion-drift waves.

Electromagnetic modes with the electric vector of the wave lying in the plane defined by the wave vector and the external d.c. electric field are studied theoretically in weakly ionized plasmas with several sorts of ions. The corresponding instability criteria are also given. The analysis is based on kinetic equations with BGK model collision integrais for the one-particle distribution functions of the charged constituents (electrons and all sorts of ions). The linear theory of perturbation is applied. Special attention is given to the long-wave domain (modal wavelengths much larger than the electron mean free path): it is in this domain that the instabilities are found to set in first as the electron drift is gradually increased. The increments of these instabilities are, however, smaller than in the short-wave domain which was mainly studied before. Apart from the modes which exist in weakly ionized plasmas with only one ion species, and which re-appear in the case studied here with somewhat altered characteristics, a new slow mode, specifie for multi-species weakly ionized plasmas, is found. Its phase velocity is below the electron thermal velocity, and its existence, as well as the conditions of excitation of the corresponding instability, depend on the plasma composition and non-isothermality (viz. the ratio Te/Ti). In some situations, two such modes are possible. The analysis of the instabilities is completed by a brief description of two (sometimes three) branches of ion acoustic instability, specific for the multi-species plasmas and propagating strictly along the direction of the external electric field.

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 problem of vortices of ion-drift and related flute-drift, balloon-drift and drift-Alfvén waves is analysed, taking into account the finiteness of the Larmor radius of the ions. It is shown that the structure of the stationary ion-drift vortices is similar to that of the Alfvén waves. It is found that the stationary ion-drift vortices in a plasma confined in a curvilinear magnetic field are characterized, generally speaking, by two different spatial scales. The role of plasma rotation in the vortex problem is investigated.

One technique to extend microwave scattering as a probe of long-wavelength density fluctuations in magnetically confined plasmas is to consider the launching and scattering of extraordinary (X-mode) waves nearly perpendicular to the field. When the incident frequency is less than the electron cyclotron frequency, this mode can penetrate beyond the ordinary mode cut-off at the plasma frequency and avoid significant distortions from density gradients typical of tokamak plasmas. In the more familiar case, where the incident and scattered waves are ordinary, the scattering is isotropic perpendicular to the field. However, because the X-mode polarization depends on the frequency ratios and the ray angle to the magnetic field, the coupling between the incident and scattered waves is complicated. This geometrical form factor must be unfolded from the observed scattering in order to interpret the scattering due to density fluctuations alone. The geometrical factor is calculated here for the special case of scattering perpendicular to the magnetic field. For frequencies above the ordinary-mode cut-off the scattering is relatively isotropic, while below cut-off there are minima in the forward and backward directions which go to zero at approximately half the ordinary-mode cut-off density.

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).

A ‘particle’ model of plasma behaviour, suitable for application to the study of plasma-optical Systems, has been developed. A plasma-optical System which removes macroscopic droplets from a neutralized beam of ions and electrons, produced by an arc, has been modelled and its performance has been analysed. The particle model employs an extremely efficient treatment of the electron motion through a background gas, which in this case consists of neutral particles. The distribution of distances travelled by electrons in the course of many collisions with the neutral background is generated using a Monte Carlo method and samples from the distribution are used to determine the electron motion at each integration step. In sheath regions, for instance, direct integration is still necessary, but for most electrons the simulation is very fast, largely removing the numerical ‘stiffness’ of the particle method. This method will be equally effective for time-dependent fields such as occur in RF discharges used in ‘plasma processing’. The variation in ion current to a substrate, where the ions deposit as a thin film, has been studied. The objective is to maximize the deposition rate whilst preventing macroscopic particles which arise at the are from striking the film. An alternative System whose calculated transmittal rate from source to target is higher, for long mean-free-paths, is also examined.

The problem of envelope solitons of surface waves is considered on the basis of results for the nonlinear dispersion relation of the waves in a plasma column. The soliton solutions are derived as particular cases of the general solutions obtained by a universal procedure and expressed in terms of Jacobi elliptic functions. Since the two types of interactions, namely the (ω + ω) – ω and the (ω – ω) + ω interactions (where ω is the frequency of the carrier wave) included in the nonlinear dispersion relation act in opposite ways, existence both of bright and dark solitons is shown to be possible. The effect of the ponderomotive force that in our case is expressed through the contribution of the (ω – ω) + ω interaction leads to the formation of dark solitons. The effect of the losses is also considered.

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.

A new collisional relaxation model, applicable to small deviations from equilibrium, is established. In distinction from previous models, the new model involves three different collision frequencies for momentum transfer, energy transfer and randomization, extends the relaxation function to include the full pressure tensor rather than only its trace, and describes relaxation to individual rather than composite Maxwellian distributions. The new model is deduced in §2, and the final result is represented by equations (28) to (31). Simplified versions of the model are given in §3, and all relevant collision frequencies are quantitatively specified there. In §4, the model is applied to the kinetic theory of waves in a magnetized two-component plasma. As a particular example, magnetosonic waves are discussed for the sake of demonstrating a wave damping mechanism due to incomplete collisional activation of translatorial degrees of freedom.

The two-dimensional Korteweg-de Vries equation is first derived for a weakly relativistic ion acoustic wave propagating in a collisionless plasma. We show that the relativistic effect greatly influences the phase velocity, the amplitude and the width of a solitary wave solution, and that the presence of streaming ions gives rise to the formation of a precursor. We also discuss three limiting cases of the present results.