Taking the Langevin approach to the evaluation of kinetic fluctuations with respect to a Maxwellian distribution characterized by different constant temperatures and mean velocities per species, the form factors and electrostatic field fluctuations of a multi-component plasma are derived. It is shown that the generalization of the Callen-Welton theorem for non-equilibrium systems, derived using thermodynamical arguments, has to be revised. Explicit values of the intensities of the electrostatic-field fluctuations are calculated, in the high-and low-frequency regimes. The former do not require any modelling of the collision integral. The latter have been calculated with a model that is more correct and simpler, than the Bhatnagar-Gross-Krook model.

It is shown, using kinetic equations with BGK model collision integrals, that in a multi-species weakly ionized plasma the quasi-perpendicular ion-cyclotron instability (waves of growing amplitude) excited by the electron drift parallel to the background magnetic field first sets in for long waves (modal wavelengths much larger than the electron mean free path) as the drift is gradually increased, much as in plasmas with only one ion species. Only waves with modal frequencies close to some cyclotron harmonics of some of the ion species present are taken into account in the present work. Owing to the mutual commensurability of all the ion-cyclotron frequencies, more than one species of ions may be ‘resonant’ with any mode of the type considered. The role of ‘resonant’ and ‘non-resonant’ ion species is investigated, both in general and for some particular plasmas. Some numerical details are also given. It is shown that although in most instances the threshold drifts vary monotonically (but not linearly) as the plasma composition is varied, there are cases in which maxima or minima (often depending on the degree of non-isothermality) of the threshold drift magnitude are predicted for some specific plasma compositions. These are usually encountered in plasmas containing ions with different charge numbers.

A detailed analysis of wave dispersion in a plasma-filled waveguide in a finite external magnetic field is presented. The mutual influence of modes on their dispersion curves is treated. A new phenomenon is demonstrated: the coupling of the waveguide EH and HE modes and the parallel appearance of a backward wave. The values of Ω and ωp (the cyclotron and plasma frequencies) and R (the waveguide radius) at which coupling between arbitrary EH and HE modes becomes possible are found. The dispersion relations and field distributions of two new mode families that arise owing to the presence of the anisotropic plasma are analysed.

Using first-order smoothing theory, Fourier analysis and perturbation methods, we obtain the evolution equation of the wave spectrum as well as the nonlinear forces generated by random Alfvén waves in a finite-β plasma with phenomenological Landau-damping effects. The effect of microscale random Alfvén waves on the propagation of large-scale hydromagnetic waves is also investigated by solving the mean-field equations. It is shown that parallel-propagating random Alfvén waves are modulationally stable and that obliquely propagating random Alfvén waves can be modulationally unstable when the energy of random waves is converted to slow magneto-acoustic waves that can be Landau-damped, providing a dissipation mechanism for the Alfvén waves.

In a cold plasma with no compressional field perturbation the equations governing the two perpendicular components of magnetic-field perturbation decouple. These two equations depend only upon spatial derivatives along the background magnetic field, and give the impression of independent field-line motion in the two transverse directions. However, the perturbation magnetic field b must be divergence-free. It is not meaningful to ask if the field perturbation on an individual background line of force satisfies ∇. b = 0. To decide whether b is divergence-free, we need to know about its spatial variation, i.e. what the state of the neighbouring field lines is. In this paper we investigate two classes of solutions: first we allow the perturbation magnetic flux to satisfy ∇. b = 0 by threading across the background lines of force; the second solution closes b by allowing the perturbation flux to encircle the background field lines (torsional Alfvén waves). For both of these solutions we study the relationship between neighbouring field lines, and are able to derive a set of criteria that the background medium must satisfy. For both classes we find restrictions upon the background magnetic-field geometry - the first class also has a constraint upon the plasma density. The introduction of perfectly conducting massive boundaries is also considered, and a relation given that they must satisfy if the field perturbation is to remain transverse. The criteria are presented in such a manner that it is easy to test if a given medium will be able to support the solutions described above. For example, a three-dimensional dipolo geometry is able to carry oscillatory toroidal fields; but not purely poloidal ones or a torsional Alfvén wave.

We rederive the dispersion relation for a plasma containing a spatially cyclic equilibrium magnetic field, and discuss the polarization of the resulting waves.

In a cold plasma, the 0 and X modes are determined by the orientation of the first-order electromagnetic fields with respect to the equilibrium magnetic field B0. In the particular case where the direction of B0 is a function of position the distinction between these types of waves is lost. In this paper, two semi-infinite regions of homogeneous cold plasma are connected by a finite zone in which the equilibrium magnetic field has a spatially periodic shear. This system is studied self-consistently to reveal the mode-con version and transmission characteristics of plasmas containing field structures of this kind, and preliminary calculations of the full coefficients are presented. The results thus obtained are directly relevant to situations where magnetic shear is important.

The general Hamiltonian-averaging transformation developed to study the motion of a charged particle in a strong magnetic field and various electromagnetic perturbations permits a clear definition of the dynamics of the guiding centre. In the case of a high-frequency electromagnetic perturbation, the equations of evolution of the phase-space co-ordinates are sums of guiding-centre terms, resonant terms at any of the cyclotron resonance frequencies n(r‖k‖–ω)+lΩ≈0(l and n are integers) and ponderomotive terms. In this paper we consider the n = 1 resonances giving a contribution one order stronger than the ponderomotive terms to the equations of motion. The guiding-centre transformation therefore suffices to derive the leading terms of the averaged dynamics. A simple case of isolated resonance is then considered for which, depending on the value of the external parameters (initial particle energy, amplitude of the perturbation), the phase space may possess one or two trapping regions. Even in the latter situation, the particle trajectories can be described analytically by the set of 12 Jacobian elliptic functions.

An understanding of the energy transfer that takes place during magnetic reconnection is crucial to the study of this fundamental process. It depends on two factors: the type of reconnection regime (which is determined by the boundary conditions) and the degree of compressibility. Here we examine the role of compressibility in the energetics of a family of reconnection models. When the inflow Mach number (or reconnection rate) Me is small the effects of compressibility may be more important than the differences between regimes. We find that for a slow-compression regime with Me = 0·005 compressibility decreases by 39% the efficiency of the shocks in converting magnetic energy and increases by 14% the ratio of thermal to kinetic energy in the outflow jet. This compares with a 13% decrease in the shock efficiency and a 7% decrease in the jet ratio obtained by choosing instead a flux-pile-up regime. As Me is increased, however, the differences between regimes become larger and may be comparable to or greater than the effects of compressibility. Thus when the above Mach number is doubled we find that a change of regime now has 1–6 times the effect on the jet energy ratio as the introduction of compressibility. For those regimes, therefore, which only exist at low inflow Mach numbers, compressibility will always be important. At higher values of Me the type of regime may be the dominant factor governing the energetics.

The wave differential operator is obtained directly from the perturbed Vlasov equation for an inhomogeneous equilibrium magnetic field including consistently the effects of strong wave damping and linear mode conversion. In the process, conditions on the parallel wavenumber and the magnetic-field gradient for which such a method is valid are obtained. From these equations it is shown that the inclusion of parameter-gradient terms arising from the spatial dependence of the equilibrium magnetic field is important for accurate calculation of mode conversion from fast to ion-Bernstein wave, although the dispersion-relation-based operator can be sufficient to describe transmission and reflection of the fast wave. Finally, the coupled second-order equations used by Fuchs & Bers (1988) are obtained, allowing direct identification of the ‘modes’ referred to in that paper in terms of components of the electric field. By reconciling these two different approaches, some insight is gained into the mode-conversion process.