It is shown how existence domains for arbitrary-amplitude ion-acoustic solitons and double layers are determined numerically by cut-off conditions on the corresponding Sagdeev potential. A two-electron-temperature model is considered, and in positive-ion plasmas the cut-off conditions are given in terms of the electron parameters, while for negative-ion plasmas such conditions are described in terms of parameters characterizing the role of the negative ion species.

Exact wave solutions of the nonlinear jnagnetohydrodynamic equations for a highly conducting incompressible fluid are obtained for the cases where the physical quantities are independent of one Cartesian co-ordina.te and for where they vary three-dimensionally but both the streamlines and magnetic field lines lie in parallel planes. It is shown that there is a class of exact wave solutions with large amplitude propagating in a straight but non-uniform magnetic field with constant or non-uniform velocity.

The filamentation of electromagnetic waves in a free-electron laser with deeply trapped electrons is analysed. This instability is the result of particle bunching along transverse directions (with respect to the fast wave vector), as opposed to the untrapped-electron case, where it is a result of longitudinal bunching. Two cases are considered: (i) the non-resonant or reactive one, with purely imaginary growth rates; and (ii) the resonant one, with large (small) values of the real (imaginary) part of the perturbing frequency. In particular, we find that the reactive instability occurs only when the wiggler amplitude is unusually large. On the other hand, we show that the resonant process (with frequencies close to the synchrotron frequency) may be relevant for conventional free-electron lasers and that the growth rate for quasi-trans verse perturbations may be larger than that corresponding to longitudinal perturbations. Owing to the inhomogeneity and anisotropy of our system, low-frequency magnetic fields are generated. These fields, as well as the transverse electric fields, are analysed, and their role in the low-frequency dynamics is clarified.

Previous work on non-relativistic electrons isotropically scattered by neutral atoms is extended to the relativistic case, and an equation is derived for the electron drift velocity. In the non-relativistic case the drift-velocity equation contains a corrected momentum-transfer term arising from the fact that the collision phenomenon is characterized by the mean free path rather than by the mean collision time. In the present work it is found that the time variation of the electron mass has a very complicated effect on the relativistic equation for the drift velocity. In addition, an unexpected theoretical result is obtained: a negative magneto-resistance effect in which the magneto-resistance decreases as the magnitude of a magnetic field imposed on the plasma increases. However, this effect is not a relativistic one but is rather due to the correction in the momentum-transfer term.

Using kinetic theory, low-frequency electrostatic instabilities driven by an anisotropic ion beam are investigated: In our model both the ions and electrons are magnetized, while the beam drift is across the external magnetic field. Both the ion-acoustic and ion–ion two-stream instabilities are excited. Regions of parameter space for the existence of either instability are distinguished. Detailed comparisons are made with the isotropie case.

In a plasma in which both the ions and electrons are magnetized we investigate low-frequency electrostatic instabilities driven by an anisotropic ion beam drifting parallel to the external magnetic field. The instability spectrum is found to be dominated by the ion-acoustic and ion-ion two-stream instabilities. Detailed comparisons are made with the isotropie case.

The multi-dimensional structure of weak, energetic-particle-modified shocks is investigated by means of appropriate perturbation techniques. The time-dependent shock-structure equation is found to be a generalized form of the well-known one-dimensional Burgers equation, whose steady state, in the absence of cosmic rays, is shown to be related to an equation modelling steady transonic flow in several dimensions. The time-dependent (1 + 2)- and (1 + 3)-dimensional Burgers equations are integrated exactly by means of Hirota's technique for one-shock solutions. On the basis of the exact solutions, a discussion relating the various length scales associated with the shock is presented.

On the basis of the dynamic equations governing the evolution of magneto-hydrodynamic fluctuations expressed in terms of Elsässer variables and of their correlation functions derived by Marsch and Tu, a new set of equations is presented here describing the evolutions of the energy spectrum e± and of the residual energy spectra eR and es of MHD turbulence in an inhomogeneous magnetofluid. The nonlinearities associated with triple correlations in these equations are analysed in detail and evaluated approximately. The resulting energy-transfer functions across wavenumber space are discussed. For e± they are shown to be approximately energy-conserving if the gradients of the flow speed and density are weak. New cascading functions are heuristically determined by an appropriate dimensional analysis and plausible physical arguments, following the standard phenomenology of fluid turbulence. However, for eR the triple correlations do not correspond to an ‘energy’ conserving process, but also represent a nonlinear source term for eR. If this source term can be neglected, the spectrum equations are found to be closed. The problem of dealing with the nonlinear source terms remains to be solved in future investigations.

The energy gain of a non-relativistic charged particle in a quasi-perpendicular shock is studied. This is done by the usual procedure of transforming the shock structure to a perpendicular one. The difference with earlie'r studies is that we are able to derive a new, exact expression for this energy gain in closed form. Two successive approximations of this expression are presented and discussed. Finally, the average energy gain of an isotropie particle distribution in the original shock system is derived.

From the Vlasov-fluid model a set of approximate stability equations describing the stability of the pure z–pinch is derived. The equations are valid for equilibria with small gyroradius compared with the pinch radius, but the perturbation wavenumber k may be of the order of the gyroradius ρi, δ = kρi = 0(1) - so-called gyrokinetic ordering. The equations are used to study the stability of the m = 0 and m = 1 internal modes of the z–pinch. In the limit of zero gyroradius δ → 0 we recover previously obtained results. For δ ≠ 0 we find that increasing δ at first gives a rapidly decreasing growth rate, and for δ ≈ l the growth rate compared with perpendicular MHD is γ/γMHD ≈ 0·09. For larger δ however, the growth rate increases to a quite large value. For the m = O mode we find, provided that drift resonances can be neglected, a stability criterion for δ ≥ 1, which is fulfilled both for the Bennett equilibrium and the constant-current-density equilibrium.

In this paper the exact solution in a function-series form is given of the multi-fluid ion-beam plasma model proposed by Zank & McKenzie. The general condition necessary for the existence of finite-amplitude solitons propagating in the system is obtained and the upper bound on the velocity of solitary wave is found.

Collisions in a cylindrically symmetric non-neutral (electron) plasma, where the Larmor radius is much smaller than the Debye length, and the consequent particle transport, are studied. The plasma is confined radially by a strong axial magnetic field and axially by electric potentials. Hence two particles may interact repeatedly. Eventually they drift too far away from each other poloidally to interact any more, owing to shear in the E × B drift. The consequent build-up of correlation is limited by correlational disintegration due to collisions with ‘third particles’ between the repeated interactions. A kinetic equation including these effects is derived, and the cross-field particle transport along the density gradient is found. An associated equilibration time is shown to scale as B and to be in good agreement with the experimentally obtained values of Briscoli, Malmberg and Fine.