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.

Fluctuations and scattering of transverse electromagnetic waves by density fluctuations in a magnetized plasma in the presence of parametric decay of the pump wave are investigated. The spectral density of electron-density fluctuations is calculated. It is shown that the differential scattering cross-section has sharp maxima at the ion-acoustic and lower-hybrid frequencies when parametric decay of the lower-hybrid pump wave occurs. We note that scattering at the ion-acoustic frequency is dominant. When the pump-wave amplitude tends to the threshold strength of the electric field the scattering cross-section increases anomalously, i.e. there is critical opalescence.

Inhomogeneity effects on the absorption of high-frequency electromagnetic waves by magnetized Maxwellian plasmas are considered, and in particular the propagation and absorption of the ordinary and extraordinary modes propagating perpendicularly to the magnetic field are analysed. We show that, for small values of the ratio of the electron plasma frequency to the electron-cyclotron frequency, the inhomogeneity effects are more important for the ordinary mode, and that for values of this ratio close to or greater than unity the effects become pronounced for the extraordinary mode. It is also shown that, for a given value of this ratio, and for a fixed value of the ratio of electron-cyclotron frequency to wave frequency, the inhomogeneity effects tend to increase as the ambient magnetic field decreases. The temperature dependence of the effect, the dependence on the direction of propagation l'elative to the inhomogeneity, the influence of temperature anisotropy, and the isolated contribution of the gradients of different plasma parameters are investigated. Several circumstances in which instabilities may occur are mentioned.

An approach to the evaluation of the collisional transfer rates of the components of the temperature tensor between drifting tri-Maxwellians for an arbitrary central interaction force between the particles is given. We describe an explicit calculation of the transfer rates of the parallel and perpendicular temperatures of test particles in an isotropie background gas. With a concise form for the transfer rates, we also find the time-independent solution of the transport equation for the anisotropic temperature of ions, as test particles in a drifting neutral background with an external magnetic field.

In this paper we consider force-free equilibrium solutions of the MHD equations in a spherical geometry for the case in which magnetic flux crosses the boundary of the containing vessel. The main motivation is to model more faithfully actual spheromak experiments in the laboratory, for which boundaries are unlikely to be magnetic surfaces. We show how a general inhomogeneous boundary field may be constructed from individual components. In particular, we consider the cases of a boundary field of dipolar form and one of quadrupolar form. We then go on to discuss solutions for fields embedded in point or ring electrodes using the ‘general solution’, some of which can be used to model experiments such as the PS-1- or CTX-type spheromaks.

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.

This paper develops a theoretical framework for the description and classification of small-amplitude waves with frequencies much less than the ion gyrofrequency, propagating in an ion-beam plasma system. In this respect, the results extend to the strongly magnetized regime the results obtained previously by Zank and McKenzie and applied by Greaves et al. to study wave propagation in such a system for frequencies in excess of the ion gyrofrequency but less than the electron plasma frequency. For completeness, the full wave equation governing an ion-beam plasma system for any strength of applied magnetic field is derived. In specializing to the strong-magnetic-field limit, we find that the class of refractive-index topologies (which characterize the kinematic properties of wave propagation) is less rich than in the un-magnetized case. After investigating the topology of the refractive-index surface and the phase-, ray- and group-velocity surfaces, we construct a CMA diagram appropriate to the strongly magnetized ion-beam plasma system. The temporal stability and spatial amplification of the slow ion-acoustic mode for frequencies less than the stationary ion plasma frequency is investigated. We show that a strong magnetic field normal to the drift direction of the ion beam stabilizes long-wavelength modes that would be unstable in the unmagnetized case.

A study is made of the transient development of two-dimensional linearized surface waves generated by a localized steady pressure distribution on the interface between a uniformly streaming, semi-infinite, infinitely conducting plasma subjected to a gravitational field and the confining vacuum magnetic field. The linearized equations associated with an initial-value problem are used to obtain the large-time asymptotic behaviour of the disturbance in the far field.

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.

The strongly nonlinear axisymmetric motion of a z–pinch in an external magnetic octupole field is investigated numerically. A surface-current ideal-MHD approximation of the pinch is used, which allows a ‘contour-dynamics’ formulation of the problem. It is found that the plasma motion in the strongly nonlinear regime results in a collision between the plasma and one (or several) of the X-points. Thereafter, the X-point splits into two magnetic nulls (Y-points), which remain on the plasma surface and between which current reversal occurs. This phenomenon results in a strong force exerted on the outer parts of the plasma and directed towards the centre of the configuration. The force is able to stop the outward plasma motion under certain parameter conditions, which are found to be similar to those observed in experiments on the straight Extrap configuration.

From the BBGKY equations for a multi-component plasma a derivation of generalized kinetic equations valid for non-uniform, neutral as well as non-neutral plasmas in strong electric and magnetic fields is made. Explicit effects of particle gyration and non-uniformities on the collisional scale are included in the collision terms. For each particle species the collision terms describing interaction between the same or other particle species consist of two parts. The first part is a generalization of the corresponding classical term, to which it reduces when fields and non-uniformities are negligible on the collisional scales. The second part is non-vanishing when non-uniformities are taken account of on the collisional scale. For the case of a neutral plasma, particle transport transverse to the magnetic field and along the density gradient is found. The result shows an increase of particle transport as compared with the classical formula when the Larmor radii are smaller than the Debye length. The underlying mechanism for this increase is pointed out.

We consider the following problem: how far, in what sense and with what practical applications might the analysis of the quasi-static evolution of a (strictly) dissipative plasma column in vacuum be carried out independently of computational means (however necessary at a later stage) in the framework of a conveniently simplified, yet significant, mathematical model. We show that the the (two-region) evolution problem of concern can be reduced to the (numerical) solution of just three nonlinear non-autonomous evolution equations in three unknowns, say Ẋ = Ẋ(X, t), with X ≡ (X1, X2, X3), where the corresponding mapping (X, t)↣ Ẋ can be made effective at the cost of inverting a non-canonical Fredholm operator of the second kind that is completely defined for the given X = X(t) and t. The assumption of sufficiently slow evolution allows us to work with the static-equilibrium momentum equation. Under axial (or cylindrical) symmetry, we know that the ‘radial’ equilibrium condition leads to a semi-linear elliptic equation in the meridional (or (x, y)) plane. The Fredholm operator arises from the inversion of the Laplacian appearing in that equation.

A 0·50 m long compact-toroid transport experiment (CTTX) has been studied with a number of diagnostics, including Thomson scattering, to determine local plasma properties and gradients indicative of transport processes. The CTTX bias and main field strengths were –0·09 and 0·35 T. Compact toroid formation and lifetime were studied at static fill pressures of 20, 100 and 150 mTorr deuterium, between 3 and 30μs after firing of the main bank. Thomson-scattering diagnosis was carried out using a Q-switched Nd: glass laser operated at both fundamental (1053 nm) and second-harmonic wavelengths (527 nm). For each pressure, scattering tests were conducted at radii r of 0·1, 1·0, 1·85 and 2·60 cm and axial positions z of 6·7, 13·0 and 19·0 cm (1054 nm); supplementary data were obtained at r = 0·1, 1·35 and 2·10 cm at z = 6·7 cm (527 nm). Electron densities and temperatures were in the ranges 1021–1022 m-3 and 2–20 eV. Thomson-scattering results are compared with diamagnetic loop, inter-ferometry, luminosity and piezoelectric pressure-probe data. Axial behaviour of the formation CT plasma varies significantly with initial fill pressure: continuous axial contraction occurs at ISOmTorr; whereas the 20 mTorr plasma appears first to contract then expand. Particle loss times are found to decrease from 70 μs at 20 mTorr to 24 μs at 100 mTorr and 12 μs at 150 mTorr. Energy decay times are 6, 7 and 5 μs for 20, 100 and 150 mTorr respectively. Flux-decay times are approximately 20 μs for 20 mTorr, 12 μs for 100 mTorr and 20 μs for 150 mTorr fill pressure. These values are two to four times longer than would be expected from theory using classical transport. In order to explain the sustained magnetic flux, the role of electric fields within the compact toroid is considered.

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.

Nonlinear decay of an ordinary electromagnetic pump wave into an electro-acoustic wave and an upper-hybrid wave in a two-electron-temperature plasma has been investigated analytically. In contrast with the work of Sharma, Ramamurthy & Yu (1984), it is found that the decay can take place in the absence of the restrictive condition Ti ≫ Te and the plasma be magnetized. Using a hydrodynamical model of the plasma, the nonlinear dispersion relation and growth rate are obtained. A comparison of the present investigation is made with earlier work, and its possible application to the ELMO bumpy torus is discussed.

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

We discuss critical curves that allow us to predict, qualitatively, the topological behaviour of higher-order modes in a two-electron-temperature plasma as wavenumber and hot electron fraction are varied. The relationship of these higher-order modes to the electron-acoustic wave is elucidated.

The stability of finite-amplitude weakly dispersive circularly polarized MHD wave trains with respect to oblique modulations is investigated. The mathematical model is a multi-dimensional extension of the DNLS equation. We have found that the right-hand-polarized wave, which is stable with respect to parallel modulations, is unstable with respect to certain oblique modulations for most primary wavenumbers.

The parametric decay of an electrostatic ion-cyclotron wave into a low-frequency mixed-mode (EM-ES) kinetic Alvén wave and an electrostatic ion-cyclotron side-band has been investigated in a homogeneous low-β plasma. A nonlinear dispersion relation describing this parameteric interaction is derived. The partially electrostatic nature of the kinetic Alfvén wave and the component of the low-frequency ponderomotive force along the direction of the external magnetic field lead to the dominant coupling. Possible applications in the ionosphere, in the earth's magnetosphere and in laboratory plasmas are discussed.