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.

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.

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.

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 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 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.

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.

The theory of the slow reaction of a charged particle in the combined presence of a strong quasi-static magnetic field and a high-frequency electromagnetic field (generalized oscillation-centre motion) is constructed by using a Hamiltonian formalism with non-canonical variables and pseudo-canonical transformations. The theory combines the features studied in our previous works for the case in which only one of the previously mentioned fields is present. The new averaging transformation is based on the fact that the Larmor frequency of the quasi-static field is of the same order as the external frequency of the high-frequency field. Our theory is manifestly gauge-invariant and involves only physical quantities (particle velocity and electromagnetic fields). Explicit expressions for the drift velocity of the oscillation centre and for the ponderomotive force are derived.

It is shown that a plasma in which the background magnetic field varies in a direction perpendicular to its line of action can support ‘Rossby-type’ electrostatic waves at frequencies very much less than the ion gyrofrequency. The intrinsic wave propagation mechanism at work is structurally similar to that in the atmospheric Rossby wave, which comes about from fluid perturbations being in quasi-geostrophic equilibrium (i.e. the Coriolis force nearly balances the pressure gradient) and the latitudinal variation of the vertical component of rotational frequency vector (the β-effect) so that the time rate of change of the vertical component of the fluid vorticity is equal to the northward transport of the planetary vorticity. In a plasma this ‘geostrophic balance’ arises from the near-vanishing of the Lorentz force on the ion motion while the β-effect is provided by the transverse spatial variation of the ambient magnetic field. Unlike the atmosphere, however, such a magnetized plasma is capable of supporting two distinct types of Rossby wave. The interesting dispersive and anisotropic features of these waves are revealed by the properties of their wave operators and described in terms of the geometry of their wavenumber surfaces. Since these surfaces intersect, inhomogeneity or nonlinearity will give rise to strong mode-mode coupling in regions where the phases of both modes nearly match.

Grad's 13-moment theory is used to model thermal transport in laser-produced plasmas where conditions are such that one may not assume that the plasma is collision-dominated. The equations are presented for a multi-fluid model in slab geometry and are solved numerically for various cases. Comparisons are made with classical theory and with simulations of collisionless plasmas. Results show that, although there are differences between 13-moment and classical predictions, the two theories agree on the general behaviour of the plasma. In particular, 13-moment theory fails to explain the heat-flux inhibition implied by some experimental observations. The theory has also been applied to model thermal transport in plasmas with a population of suprathermal electrons.

Using first-order smoothing theory, Fourier analysis and perturbation methods, a new equation is derived governing the evolution of the spectrum tensor (including the energy and helicity spectrum functions) of the random velocity field as well as the ponderomotive and mean electromotive forces generated by random Alfvén waves in a plasma with weak magnetic diffusion. The ponderomotive and mean electromotive forces are expressed as series involving spatial derivatives of mean magnetic and velocity fields whose coefficients are associated with the helicity spectrum function of the random velocity field. The effect of microscale random Alfvén waves, through ponderomotive and mean electromotive forces generated by them, on the propagation of large-scale Alfvén waves is also investigated by solving the mean-field equations, including the transport equation of the helicity spectrum function.

Drift-Alfvén vortices are investigated, taking into account the nonlinear ion dynamics parallel to the external magnetic field. It is found that the parallel ion motion restricts the vortex speed.

The influence of nonlinearities and plasma resistivity on the so-called trivial marginal modes of ideal MHD is investigated. It turns out that to lowest significant order of a reductive perturbation analysis nonlinearities have no influence, while in toroidal confinement configurations resistivity induces a local plasma diffusion across the magnetic surfaces. This is demonstrated for tokamaks with zero poloidal current density. In addition, the appearance of singularities in the plasma motion parallel to the magnetic field lines suggests a profile condition at the edge of the plasma. Heat conduction would directly tend to keep these effects at lower level, while indirectly it creates a reinforcement mechanism through the coupling to usual cross diffusion.

A nonlinear drift mode equation for finite ion temperature plasma is derived. Possibilities of explosive instabilities for the drift wave are obtained. To discuss the modulational instability of drift wave, a nonlinear evolution equation for the drift mode is deduced from a third-order secularity elimination condition using the multiple time and space scales technique. The effect of low-frequency localized structure on particle transport has been investigated and the diffusion tensor is calculated using Ficks law.