Nonlinear structures in the developed stage of the two-dimensional modulational instability of a whistler wave are investigated. On the basis of the results obtained, some suggestions are made regarding the nonlinear dynamics of three-dimensional modulational instability and three-dimensional whistler solitons.

The interaction of high-frequency and low-frequency waves in magnetized plasmas is considered. The narrowness of high-frequency wave packets makes possible a concise Hamiltonian description of the problem. Some concrete problems are studied with the help of the derived equations. The competitive role of scattering in self-consistent density and magnetic-field fluctuation are considered. The self-focusing and solitons of potential plasma waves and magnetohydrodynamic waves are studied.

Using the ballooning-mode transport model proposed by Connor, Taylor & Turner (1984), we derive the thermal conductivity induced by ideal ballooning instability and compare it to experimental observations from auxiliary-heated tokamaks. We show how this model can be improved by means of a finite-beta equilibrium and also apply it to obtain a confinement scaling law for high-beta, purely Ohmically heated tokamaks. Finally, we employ this transport mode to find that tokamaks with supplemental stabilization, for example due to gyroradius, energetic particle or shaping effects, can self-consistently access the second stability regime at rather high heating power.

It is shown that the conservation law for total momentum of an ion-beam plasma system can be cast in the form of a classical energy integral of a particle in a potential well. By using boundary conditions appropriate to a solitary pulse, we derive conditions for the existence of finite-amplitude solitons propagating in the system. Under suitable conditions, as many as three forward-propagating solitary waves can exist. It is interesting to note that the criterion for their existence is intimately related to the absence of convective instabilities in an ion-beam plasma. Exact ‘sech2’ type solutions are available in the weakly nonlinear regime. Solitary-wave profiles for the general case are obtained numerically.

A systematic analysis of envelope upper-hybrid wave propagation near the magnetosonic speed has been presented. Using the full set of fluid equations for the low-frequency dynamics, we obtain various model nonlinear equations describing the magnetosonic response to the envelope waves. In particular, we derive driven KdV as well as driven Boussinesq equations that are valid for near-magnetosonic propagation. These equations are coupled to the usual Schrödinger-like equation for the envelope wave. Exact stationary solutions of the coupled equations are explicitly obtained. It is shown that a, new class of upper-hybrid solitons with antisymmetric wave envelope exist for nearmagnetosonic propagation. Integral invariants for the driven KdV case have been obtained and evaluated for localized solutions. A set of stationary governing equations is derived that takes account of the full nonlinearity in the low-frequency response as well as departures from the frozen-in-field approximation. A detailed comparison of the various model equations as well as their validity has been made.

Some new aspects of an analogy between plasma in a magnetic field and a rotating shallow liquid are considered. Effects of gyroscopic screening and resonant wave excitation are studied. The results of numerical simulations of the nonlinear evolution of sheared flows in rotating shallow water are presented.

In this paper a multi-fluid approach is used to describe electrostatic interactions in an ion-beam plasma system. The structure of the wave equation governing the system exhibits the anisotropic and dispersive nature of the waves, whose properties are analysed in terms of the dispersion relation. The main purpose of this paper is to classify the different waves that can arise in an ion-beam plasma system in a systematic fashion. The classification is facilitated by introducing a three-parameter CMA diagram that illustrates the topological changes in not only the wavenumber, or refractive-index, surface but also the ray-velocity surface. Furthermore, an analytic expression governing wave amplification in an ion-beam plasma is incorporated within the framework of a generalized CMA diagram. Such a description provides a simple interpretation for the onset of wave amplification in terms of a topological change in the refractive-index surface. It is hoped that by collating the wave properties in a unified form, many of the complicated wave features observed in an experiment may be interpreted more easily.

A non-local theory of whistler and quasi-static mode excitation by an annular electron beam in a plasma cylinder is presented. Čerenkov and slow-cyclotron interaction are considered in the weak-beam approximation. The growth rate is found to be quite sensitive to the beam radius except in the case of slow-cyclotron interaction of quasi-static modes. The growth rate varies significantly with beam velocity in the case of Čerenkov interaction of quasi-static modes, but in other cases it is rather insensitive to the beam velocity.

Two different families of explicit stationary solutions of the Hasegawa–Mima equation are obtained. In the first case the well-known modon (dipole vortex) is used as the zeroth-order solution, and new solutions that are close to but distinctly different from it are found by perturbation analysis. In the second case the dispersive term of the equation is treated as a small parameter, and a radially symmetric solution (a monopole vortex) is used as the zeroth-order approximation. Both families of solutions are found to be infinite and to contain an arbitrary function. A recent general proof of the existence of infinitely many stationary solutions containing an arbitrary function is examined and found to be invalid.

Nonlinear interactions of two azimuthally symmetric compressional hydromagnetic waves propagating in a cylindrical waveguide filled with cold magnetized plasma are investigated. Two cases are considered: the nonlinear interaction of two identical oppositely propagating compressional waves and the nonlinear interaction of two compressional waves propagating with equal group velocities. In the first case the second-order perturbation fields generated through self- and mutual interactions of the waves are calculated and their effect on the otherwise-formed simple linear standing-wave pattern is studied. The possibility of observing a resonant nonlinear interaction is shown. In the second case, in order to describe the nonlinear evolution of the wave amplitudes, two coupled nonlinear Schrödinger (NLS) equations are presented. When excited individually, both the waves are seen to be modulationally stable; but when excited simultaneously, a strong nonlinear wave-wave coupling comes into play, which makes the waves modulationally unstable. The corresponding growth rate of the instability is also calculated.

The ionization equilibrium between the constituents of a multi-temperature plasma is investigated within the thermodynamics of fluid mixtures. As a result, a law of mass action is derived that, in the approximation of ideal gases for the constituents, leads to a direct generalization of Saha's equation. The main properties of this generalization are discussed, and contrasted with those of other equations which have appeared in the literature.

The amplification of an electromagnetic wave by net stimulated bremsstrahlung (the emission by stimulated bremsstrahlung minus the absorption by inverse bremsstrahlung) injected into a non-relativistic dilute electron beam travelling in a uniform magnetic field is considered. The d.c. ponderomotive force by net stimulated emission is calculated by using quantum kinetics. From the calculated ponderomotive force, the amplification of the intensity of the electromagnetic wave by the net stimulated bremsstrahlung is derived as a function of the relevant parameters of the electromagnetic wave and the electron beam. It is found that masing is possible when the perpendicular temperature of the electron beam is greater than its parallel temperature. It is shown that the efficiency of a practical gyrotron cannot be explained by the phase-bunching concept, and that simulated bremsstrahlung has nothing to do with any phase bunching.

The components of the dielectric tensor for a plasma described by a relativistic loss-cone electron distribution are written in a simple way, which takes full account of relativistic effects, harmonics and Larmor radius, for perpendicular and oblique propagation. For sufficiently oblique propagation and temperatures in the thermonuclear range, a still simpler form of the dielectric tensor is derived. The role of the wave parameters in the absorption is discussed, and some comments are made about the weakly relativistic and non-relativistic approaches. A numerical example is given for both the extraordinary and ordinary modes.

The steady-state migration of ions, driven by a uniform electric field against full-stop collisions, is investigated in some detail. The required phase-space distribution is obtained very easily from Boltzmann's equation together with explicit recognition of energy conservation and population balance for the stagnant ion pool. We go on to decompose this aggregate solution into ion tiers classified by the number of background impacts previously endured. Such a decomposition permits us to detect the presence of Poisson statistics (as to collision number) lurking within the composite, thermalized Maxwellian, and likewise also a multiple-scattering hierarchy having the maiden, first-flight distribution for its natural kernel. Scattering-sequence accounting, in particular, allows a quantitative (even though unwieldy) distinction to be made between ions of varying residence times. A model of this sort is motivated by the technique of ion implantation through sample immersion within a plasma at higher electric potential. Numerical consequences of the solution obtained here reveal that both ion density and average kinetic energy relax to their terminal values within just a few mean free-path lengths. Such modest scaling of plasma-sheath extent evidently carries a beneficial implication for the technological ease with which surface properties (such as metal corrosion resistance and hardness) remain open to improvement via ion bombardment.

The theory of plasma ablation by laser irradiation from cylindrical and spherical solid targets is considered when thermal conduction is dominant and absorption is local at the critical density. Analytic solutions for both inhibited and uninhibited heat fluxes are developed, but only investigated in detail when flux limiting does not introduce a step discontinuity. In most cases it is found that only a restricted region of flow is steady, and must be terminated by a rarefaction wave. The transition from quasi-planar to strongly divergent flow is shown to depend on a characteristic parameter, which represents the ratio of the thermal conduction length to the target radius.

The weakly relativistic theory of absorption and emission of electron cyclotron waves in hot magnetized plasmas is developed for a large class of anisotropic electron distribution functions. The results are expressed in terms of the weakly relativistic plasma dispersion functions, and therefore of the well-known plasma Z-function. The particular case of a loss-cone electron distribution function is presented as a simple example.

The microscopic and macroscopic behaviours of a linear reflex discharge in the presence of low-frequency turbulence are investigated under the action of moderate lower-hybrid wave power. The frequency and wavenumber spectra of both the low-frequency fluctuations and the high-frequency waves are measured using a correlation-analysis technique with two probes. The low-frequency fluctuations may be attributed to drift-wave turbulence. The fluctuation level is raised when RF power is coupled to the plasma, thus leading to considerably enhanced radial transport. The coupling between low-frequency fluctuations and high-frequency waves can be seen clearly from the spectra. The high-frequency wavenumber spectra measured inside the antenna are in reasonable agreement with the lower-hybrid wave dispersion. However, the wavenumbers observed in the lower-hybrid resonance region outside the antenna are – in contrast with expectation – not larger than in the plasma edge region. From the electric-field energy-density spectra and from measurements of the density and the temperatures, a detailed energy balance can be performed. The calculated heating rates are anomalously large for both the electrons and the ions. The absorption processes, relevant for the present experiment, are discussed.

A low-temperature plasma containing polar molecules with constant electric dipole moment as the neutral component is considered. The thermodynamic functions and the dispersion properties of such a plasma are investigated.

Ion-acoustic solitons in a plasma with different adiabatic ion constituents and isothermal electrons are studied via a reductive perturbation method. The basic fluid equations then give rise to KdV or modified KdV equations, depending upon the relative ion densities. At critical densities, rarefactive and compressive fast ion-acoustic solitons are possible. Explicit stationary solutions are discussed in the special case of cold ions, in a plasma containing two species of negative ions and one of positive ions. The inclusion of heavier ions, even at low densities, increases the amplitudes of the critical solitons.