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.

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.

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.

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.

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.

An alternative representation of the dielectric tensor εij(k, ω) for a relativistic magnetized plasma in thermal equilibrium is presented. This representation involves an infinite series expansion in powers of , as well as an asymptotic expansion for large Here ωc = eB0/mc is the nonrelativistic cyclotron frequency, k⊥ is the wavenumber perpendicular to the magnetic field B0êz, and α is the dimensionless parameter defined by α = mc2/KBT. The present work generalizes Shkarofsky's (1966) representation. Moreover, unlike Trubnikov's (1958) formal result, in which the k⊥ and kz dependences of εij(k, ω) are inexorably coupled, the present representation naturally separates the k⊥ and kz dependences of εij(k, ω). As an application, the general expression is simplified for the case of a weakly relativistic plasma, and the dispersion relation is obtained for electromagnetic waves, including first-order relativistic effects. The method developed in this paper can be used for other non-thermal distributions.

Tokamak equilibria are considered as extremum magnetic-energy states. Two quadratic invariants ∫Ψd3x, and ∫A.Bd3x are found to yield finite-beta equilibria in toroidal geometry. The theory predicts ‘bell’-shaped current profiles for relaxed discharges at finite beta. A ‘main-sequence’ curve of ql/q0 versus βp is presented for circular discharges with low ql and is found to form a limiting curve for experimental data.

The Bineau reduction to scalar form of the equation governing ideal zero-frequency linearized displacements from a hydromagnetic equilibrium possessing a continuous symmetry is performed in ‘universal co-ordinates’, applicable to both the toroidal and helical cases. The resulting generalized Newcomb equation (GNE) has in general a more complicated form than the corresponding one-dimensional equation obtained by Newcomb in the case of circular cylindrical symmetry, but in this cylindrical case we show that the equation can be transformed to that of Newcomb. In the two-dimensional case there is a transformation that leaves the form of the GNE invariant and simplifies the Frobenius expansion about a rational surface, especially in the limit of zero pressure gradient. The Frobenius expansion about a mode rational surface is developed and the connection with Hamiltonian transformation theory is shown. The derivations of the ideal interchange and ballooning criteria from the formalism are discussed.

We derive a Fokker–Planck equation for relativistic and degenerate electrons interacting with ions. The ions may be degenerate and relativistic. Applications to a supernova plasma and laser–plasma interaction motivate this work.